%------------------------------------------------------------------------------
% 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 : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 06:58:51 PM UTC 2026
% Result : Theorem 15.02s 3.53s
% Output : Refutation 15.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 216
% Syntax : Number of formulae : 341 ( 18 unt; 0 typ; 12 def)
% Number of atoms : 12553 (5884 equ; 0 cnn)
% Maximal formula atoms : 530 ( 36 avg)
% Number of connectives : 29193 (3288 ~;2993 |;2536 &;19469 @)
% ( 575 <=>; 309 =>; 0 <=; 3 <~>)
% Maximal formula depth : 188 ( 12 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 2456 (2456 >; 0 *; 0 +; 0 <<)
% Number of symbols : 797 ( 793 usr; 311 con; 0-4 aty)
% ( 20 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 6113 ( 156 ^;4532 !;1425 ?;6113 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
term: $tType ).
thf(type_def_7,type,
subst: $tType ).
thf(type_def_8,type,
d_term: $tType ).
thf(type_def_9,type,
d_subst: $tType ).
thf(func_def_0,type,
term: $tType ).
thf(func_def_1,type,
subst: $tType ).
thf(func_def_2,type,
one: term ).
thf(func_def_3,type,
ap: term > term > term ).
thf(func_def_4,type,
lam: term > term ).
thf(func_def_5,type,
sub: term > subst > term ).
thf(func_def_6,type,
id: subst ).
thf(func_def_7,type,
sh: subst ).
thf(func_def_8,type,
push: term > subst > subst ).
thf(func_def_9,type,
comp: subst > subst > subst ).
thf(func_def_10,type,
var: term > $o ).
thf(func_def_18,type,
hoasap: subst > term > subst > term > term ).
thf(func_def_73,type,
hoaslam: subst > ( subst > term > term ) > term ).
thf(func_def_86,type,
hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
thf(func_def_107,type,
hoasvar: subst > term > subst > $o ).
thf(func_def_121,type,
pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
thf(func_def_124,type,
d_term: $tType ).
thf(func_def_125,type,
d_subst: $tType ).
thf(func_def_126,type,
d2term: d_term > term ).
thf(func_def_127,type,
d2subst: d_subst > subst ).
thf(func_def_128,type,
d_one: d_term ).
thf(func_def_129,type,
d_id: d_subst ).
thf(func_def_141,type,
sP0: ( subst > term > subst > $o ) > $o ).
thf(func_def_143,type,
sP2: ( subst > term > subst > $o ) > $o ).
thf(func_def_144,type,
sP3: ( subst > term > subst > $o ) > $o ).
thf(func_def_145,type,
sP4: ( subst > term > subst > $o ) > $o ).
thf(func_def_146,type,
sP5: ( subst > term > subst > $o ) > $o ).
thf(func_def_147,type,
sP6: ( subst > term > subst > $o ) > $o ).
thf(func_def_148,type,
sP7: ( term > $o ) > $o ).
thf(func_def_149,type,
sP8: ( term > $o ) > $o ).
thf(func_def_153,type,
sP12: ( subst > term > subst > $o ) > $o ).
thf(func_def_154,type,
sP13: ( subst > term > subst > $o ) > $o ).
thf(func_def_155,type,
sP14: ( subst > term > subst > $o ) > term > $o ).
thf(func_def_157,type,
sP16: ( subst > term > subst > $o ) > $o ).
thf(func_def_158,type,
sP17: ( subst > term > subst > $o ) > $o ).
thf(func_def_159,type,
sP18: ( subst > term > subst > $o ) > $o ).
thf(func_def_160,type,
sP19: ( subst > term > subst > $o ) > $o ).
thf(func_def_161,type,
sP20: ( subst > term > subst > $o ) > $o ).
thf(func_def_162,type,
sP21: ( subst > term > subst > $o ) > $o ).
thf(func_def_164,type,
sP23: ( subst > term > subst > $o ) > $o ).
thf(func_def_166,type,
sP25: ( subst > term > subst > $o ) > $o ).
thf(func_def_167,type,
sP26: ( subst > term > subst > $o ) > $o ).
thf(func_def_170,type,
sP29: ( subst > term > subst > $o ) > $o ).
thf(func_def_177,type,
sP36: ( subst > term > subst > $o ) > $o ).
thf(func_def_178,type,
sP37: ( subst > term > subst > $o ) > $o ).
thf(func_def_179,type,
sP38: term > ( term > $o ) > $o ).
thf(func_def_183,type,
sP42: ( subst > term > subst > $o ) > $o ).
thf(func_def_185,type,
sP44: ( subst > term > subst > $o ) > $o ).
thf(func_def_187,type,
sP46: ( subst > term > subst > $o ) > $o ).
thf(func_def_188,type,
sP47: ( subst > term > subst > $o ) > $o ).
thf(func_def_190,type,
sP49: ( subst > term > subst > $o ) > $o ).
thf(func_def_191,type,
sP50: term > ( subst > term > subst > $o ) > $o ).
thf(func_def_192,type,
sP51: ( subst > term > subst > $o ) > $o ).
thf(func_def_193,type,
sP52: ( subst > term > subst > $o ) > $o ).
thf(func_def_196,type,
sP55: ( term > $o ) > $o ).
thf(func_def_197,type,
sP56: ( term > $o ) > $o ).
thf(func_def_198,type,
sP57: ( term > $o ) > $o ).
thf(func_def_199,type,
sP58: ( term > $o ) > $o ).
thf(func_def_202,type,
sP61: ( term > $o ) > $o ).
thf(func_def_203,type,
sP62: ( term > $o ) > $o ).
thf(func_def_204,type,
sP63: ( subst > term > subst > $o ) > $o ).
thf(func_def_205,type,
sP64: ( subst > term > subst > $o ) > $o ).
thf(func_def_206,type,
sP65: ( subst > term > subst > $o ) > $o ).
thf(func_def_207,type,
sP66: ( subst > term > subst > $o ) > $o ).
thf(func_def_208,type,
sP67: ( subst > term > subst > $o ) > $o ).
thf(func_def_209,type,
sP68: ( subst > term > subst > $o ) > $o ).
thf(func_def_210,type,
sP69: ( subst > term > subst > $o ) > $o ).
thf(func_def_211,type,
sP70: ( subst > term > subst > $o ) > $o ).
thf(func_def_212,type,
sP71: ( subst > term > subst > $o ) > $o ).
thf(func_def_217,type,
sP76: ( term > $o ) > $o ).
thf(func_def_218,type,
sP77: ( term > $o ) > subst > $o ).
thf(func_def_219,type,
sP78: ( term > $o ) > $o ).
thf(func_def_220,type,
sP79: ( term > $o ) > $o ).
thf(func_def_221,type,
sP80: ( term > $o ) > $o ).
thf(func_def_224,type,
sP83: ( term > $o ) > $o ).
thf(func_def_225,type,
sP84: ( term > $o ) > $o ).
thf(func_def_227,type,
sP86: ( term > $o ) > $o ).
thf(func_def_228,type,
sP87: ( term > $o ) > $o ).
thf(func_def_230,type,
sP89: ( subst > term > subst > $o ) > $o ).
thf(func_def_231,type,
sP90: ( subst > term > subst > $o ) > $o ).
thf(func_def_233,type,
sP92: ( subst > term > subst > $o ) > $o ).
thf(func_def_234,type,
sP93: ( subst > term > subst > $o ) > $o ).
thf(func_def_235,type,
sP94: ( subst > term > subst > $o ) > $o ).
thf(func_def_237,type,
sP96: ( term > $o ) > $o ).
thf(func_def_238,type,
sP97: ( term > $o ) > $o ).
thf(func_def_240,type,
sP99: ( subst > term > subst > $o ) > $o ).
thf(func_def_242,type,
sP101: ( subst > term > subst > $o ) > $o ).
thf(func_def_243,type,
sP102: ( subst > term > subst > $o ) > $o ).
thf(func_def_244,type,
sP103: ( term > $o ) > $o ).
thf(func_def_245,type,
sP104: ( term > $o ) > $o ).
thf(func_def_246,type,
sP105: ( term > $o ) > $o ).
thf(func_def_247,type,
sP106: ( subst > term > subst > $o ) > $o ).
thf(func_def_251,type,
sP110: ( subst > term > term ) > $o ).
thf(func_def_252,type,
sP111: ( subst > term > subst > $o ) > $o ).
thf(func_def_253,type,
sP112: ( subst > term > subst > $o ) > $o ).
thf(func_def_254,type,
sK113: term ).
thf(func_def_255,type,
sK114: term > $o ).
thf(func_def_256,type,
sK115: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_257,type,
sK116: ( term > $o ) > term > term ).
thf(func_def_258,type,
sK117: term ).
thf(func_def_259,type,
sK118: subst > term > subst > $o ).
thf(func_def_260,type,
sK119: term > $o ).
thf(func_def_261,type,
sK120: subst > term > subst > $o ).
thf(func_def_262,type,
sK121: term ).
thf(func_def_263,type,
sK122: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_264,type,
sK123: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_265,type,
sK124: ( subst > term > term ) > term ).
thf(func_def_266,type,
sK125: ( subst > term > term ) > subst ).
thf(func_def_267,type,
sK126: ( subst > term > term ) > subst ).
thf(func_def_268,type,
sK127: ( term > $o ) > term ).
thf(func_def_269,type,
sK128: term > ( term > $o ) > term ).
thf(func_def_270,type,
sK129: ( term > $o ) > term ).
thf(func_def_271,type,
sK130: ( term > $o ) > term ).
thf(func_def_272,type,
sK131: ( term > $o ) > term ).
thf(func_def_273,type,
sK132: ( subst > term > subst > $o ) > term ).
thf(func_def_274,type,
sK133: ( subst > term > subst > $o ) > term ).
thf(func_def_275,type,
sK134: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_276,type,
sK135: ( subst > term > term ) > term ).
thf(func_def_277,type,
sK136: ( subst > term > term ) > subst ).
thf(func_def_278,type,
sK137: ( subst > term > term ) > subst ).
thf(func_def_279,type,
sK138: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_280,type,
sK139: term ).
thf(func_def_281,type,
sK140: subst > term > subst > $o ).
thf(func_def_282,type,
sK141: ( subst > term > subst > $o ) > term > term ).
thf(func_def_283,type,
sK142: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_284,type,
sK143: ( subst > term > term ) > subst ).
thf(func_def_285,type,
sK144: ( subst > term > term ) > term ).
thf(func_def_286,type,
sK145: ( subst > term > term ) > subst ).
thf(func_def_287,type,
sK146: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_288,type,
sK147: term ).
thf(func_def_289,type,
sK148: term > $o ).
thf(func_def_290,type,
sK149: ( term > $o ) > term ).
thf(func_def_291,type,
sK150: ( term > $o ) > term ).
thf(func_def_292,type,
sK151: ( term > $o ) > term ).
thf(func_def_293,type,
sK152: ( term > $o ) > term ).
thf(func_def_294,type,
sK153: term > $o ).
thf(func_def_295,type,
sK154: subst > term > subst > $o ).
thf(func_def_296,type,
sK155: term ).
thf(func_def_297,type,
sK156: term > ( term > $o ) > term ).
thf(func_def_298,type,
sK157: ( subst > term > subst > $o ) > ( term > $o ) > term ).
thf(func_def_299,type,
sK158: ( subst > term > subst > $o ) > subst ).
thf(func_def_300,type,
sK159: ( subst > term > subst > $o ) > subst ).
thf(func_def_301,type,
sK160: ( subst > term > subst > $o ) > term ).
thf(func_def_302,type,
sK161: ( subst > term > subst > $o ) > subst ).
thf(func_def_303,type,
sK162: ( subst > term > subst > $o ) > subst ).
thf(func_def_304,type,
sK163: ( subst > term > subst > $o ) > term ).
thf(func_def_305,type,
sK164: ( subst > term > subst > $o ) > subst ).
thf(func_def_306,type,
sK165: ( subst > term > subst > $o ) > subst ).
thf(func_def_307,type,
sK166: ( subst > term > term ) > subst ).
thf(func_def_308,type,
sK167: ( subst > term > term ) > subst ).
thf(func_def_309,type,
sK168: ( subst > term > term ) > term ).
thf(func_def_310,type,
sK169: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_311,type,
sK170: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_312,type,
sK171: term ).
thf(func_def_313,type,
sK172: term ).
thf(func_def_314,type,
sK173: subst > term > subst > $o ).
thf(func_def_315,type,
sK174: ( subst > term > subst > $o ) > subst ).
thf(func_def_316,type,
sK175: ( subst > term > subst > $o ) > subst ).
thf(func_def_317,type,
sK176: ( subst > term > subst > $o ) > term ).
thf(func_def_318,type,
sK177: ( subst > term > subst > $o ) > subst ).
thf(func_def_319,type,
sK178: ( subst > term > subst > $o ) > subst ).
thf(func_def_320,type,
sK179: ( subst > term > subst > $o ) > term ).
thf(func_def_321,type,
sK180: ( subst > term > subst > $o ) > subst ).
thf(func_def_322,type,
sK181: ( subst > term > subst > $o ) > subst ).
thf(func_def_323,type,
sK182: ( subst > term > subst > $o ) > term ).
thf(func_def_324,type,
sK183: ( subst > term > subst > $o ) > term ).
thf(func_def_325,type,
sK184: term > $o ).
thf(func_def_326,type,
sK185: term ).
thf(func_def_327,type,
sK186: ( term > $o ) > term ).
thf(func_def_328,type,
sK187: ( term > $o ) > term ).
thf(func_def_329,type,
sK188: ( term > $o ) > term ).
thf(func_def_330,type,
sK189: term > ( term > $o ) > term ).
thf(func_def_331,type,
sK190: ( term > $o ) > term ).
thf(func_def_332,type,
sK191: term ).
thf(func_def_333,type,
sK192: subst ).
thf(func_def_334,type,
sK193: term > $o ).
thf(func_def_335,type,
sK194: ( term > $o ) > subst > term ).
thf(func_def_336,type,
sK195: ( term > $o ) > term ).
thf(func_def_337,type,
sK196: ( term > $o ) > term ).
thf(func_def_338,type,
sK197: term > ( term > $o ) > term ).
thf(func_def_339,type,
sK198: ( term > $o ) > term ).
thf(func_def_340,type,
sK199: subst ).
thf(func_def_341,type,
sK200: term > $o ).
thf(func_def_342,type,
sK201: term ).
thf(func_def_343,type,
sK202: term ).
thf(func_def_344,type,
sK203: term > $o ).
thf(func_def_345,type,
sK204: ( term > $o ) > term ).
thf(func_def_346,type,
sK205: ( term > $o ) > term ).
thf(func_def_347,type,
sK206: ( term > $o ) > term ).
thf(func_def_348,type,
sK207: term > ( term > $o ) > term ).
thf(func_def_349,type,
sK208: ( term > $o ) > term ).
thf(func_def_350,type,
sK209: ( term > $o ) > term ).
thf(func_def_351,type,
sK210: term > ( term > $o ) > term ).
thf(func_def_352,type,
sK211: ( term > $o ) > subst > term ).
thf(func_def_353,type,
sK212: ( term > $o ) > term ).
thf(func_def_354,type,
sK213: ( term > $o ) > term ).
thf(func_def_355,type,
sK214: ( subst > term > subst > $o ) > term > term ).
thf(func_def_356,type,
sK215: term ).
thf(func_def_357,type,
sK216: subst > term > subst > $o ).
thf(func_def_358,type,
sK217: ( subst > term > subst > $o ) > subst ).
thf(func_def_359,type,
sK218: ( subst > term > subst > $o ) > subst ).
thf(func_def_360,type,
sK219: ( subst > term > subst > $o ) > term ).
thf(func_def_361,type,
sK220: ( subst > term > subst > $o ) > subst ).
thf(func_def_362,type,
sK221: term ).
thf(func_def_363,type,
sK222: term ).
thf(func_def_364,type,
sK223: subst > term > subst > $o ).
thf(func_def_365,type,
sK224: ( term > $o ) > term ).
thf(func_def_366,type,
sK225: term > $o ).
thf(func_def_367,type,
sK226: term ).
thf(func_def_368,type,
sK227: subst > term > subst > $o ).
thf(func_def_369,type,
sK228: term ).
thf(func_def_370,type,
sK229: ( subst > term > subst > $o ) > term ).
thf(func_def_371,type,
sK230: ( subst > term > subst > $o ) > subst ).
thf(func_def_372,type,
sK231: ( subst > term > subst > $o ) > subst ).
thf(func_def_373,type,
sK232: ( subst > term > subst > $o ) > subst ).
thf(func_def_374,type,
sK233: ( subst > term > subst > $o ) > term ).
thf(func_def_375,type,
sK234: ( subst > term > subst > $o ) > subst ).
thf(func_def_376,type,
sK235: ( subst > term > subst > $o ) > subst ).
thf(func_def_377,type,
sK236: ( subst > term > subst > $o ) > term ).
thf(func_def_378,type,
sK237: ( subst > term > subst > $o ) > subst ).
thf(func_def_379,type,
sK238: ( subst > term > subst > $o ) > term ).
thf(func_def_380,type,
sK239: ( subst > term > subst > $o ) > term ).
thf(func_def_381,type,
sK240: ( subst > term > term ) > subst ).
thf(func_def_382,type,
sK241: ( subst > term > term ) > term ).
thf(func_def_383,type,
sK242: ( subst > term > term ) > subst ).
thf(func_def_384,type,
sK243: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_385,type,
sK244: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_386,type,
sK245: ( subst > term > subst > $o ) > subst ).
thf(func_def_387,type,
sK246: ( subst > term > subst > $o ) > term ).
thf(func_def_388,type,
sK247: ( subst > term > subst > $o ) > subst ).
thf(func_def_389,type,
sK248: ( subst > term > subst > $o ) > subst ).
thf(func_def_390,type,
sK249: ( subst > term > subst > $o ) > subst ).
thf(func_def_391,type,
sK250: ( subst > term > subst > $o ) > subst ).
thf(func_def_392,type,
sK251: ( subst > term > subst > $o ) > term ).
thf(func_def_393,type,
sK252: ( subst > term > subst > $o ) > subst ).
thf(func_def_394,type,
sK253: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_395,type,
sK254: ( subst > term > term ) > term ).
thf(func_def_396,type,
sK255: ( subst > term > term ) > subst ).
thf(func_def_397,type,
sK256: ( subst > term > term ) > subst ).
thf(func_def_398,type,
sK257: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_399,type,
sK258: ( subst > term > subst > $o ) > subst ).
thf(func_def_400,type,
sK259: ( subst > term > subst > $o ) > subst ).
thf(func_def_401,type,
sK260: ( subst > term > subst > $o ) > term ).
thf(func_def_402,type,
sK261: ( subst > term > subst > $o ) > subst ).
thf(func_def_403,type,
sK262: ( subst > term > subst > $o ) > term ).
thf(func_def_404,type,
sK263: ( subst > term > subst > $o ) > term ).
thf(func_def_405,type,
sK264: ( term > $o ) > term ).
thf(func_def_406,type,
sK265: term > ( term > $o ) > term ).
thf(func_def_407,type,
sK266: ( term > $o ) > term ).
thf(func_def_408,type,
sK267: ( term > $o ) > term ).
thf(func_def_409,type,
sK268: ( term > $o ) > term ).
thf(func_def_410,type,
sK269: term ).
thf(func_def_411,type,
sK270: term > $o ).
thf(func_def_412,type,
sK271: subst ).
thf(func_def_413,type,
sK272: term > $o ).
thf(func_def_414,type,
sK273: term ).
thf(func_def_415,type,
sK274: ( term > $o ) > subst > term ).
thf(func_def_416,type,
sK275: ( term > $o ) > term ).
thf(func_def_417,type,
sK276: ( term > $o ) > term ).
thf(func_def_418,type,
sK277: ( term > $o ) > term ).
thf(func_def_419,type,
sK278: ( term > $o ) > term ).
thf(func_def_420,type,
sK279: ( term > $o ) > term ).
thf(func_def_421,type,
sK280: term > ( term > $o ) > term ).
thf(func_def_422,type,
sK281: ( term > $o ) > term ).
thf(func_def_423,type,
sK282: term > ( subst > term > subst > $o ) > term ).
thf(func_def_424,type,
sK283: subst > term > subst > $o ).
thf(func_def_425,type,
sK284: term ).
thf(func_def_426,type,
sK285: term ).
thf(func_def_427,type,
sK286: subst > term > subst > $o ).
thf(func_def_428,type,
sK287: ( subst > term > subst > $o ) > subst ).
thf(func_def_429,type,
sK288: ( subst > term > subst > $o ) > term ).
thf(func_def_430,type,
sK289: ( subst > term > subst > $o ) > subst ).
thf(func_def_431,type,
sK290: ( subst > term > subst > $o ) > subst ).
thf(func_def_432,type,
sK291: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_433,type,
sK292: ( subst > term > term ) > subst ).
thf(func_def_434,type,
sK293: ( subst > term > term ) > term ).
thf(func_def_435,type,
sK294: ( subst > term > term ) > subst ).
thf(func_def_436,type,
sK295: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_437,type,
sK296: ( subst > term > subst > $o ) > subst ).
thf(func_def_438,type,
sK297: ( subst > term > subst > $o ) > term ).
thf(func_def_439,type,
sK298: ( subst > term > subst > $o ) > subst ).
thf(func_def_440,type,
sK299: ( subst > term > subst > $o ) > subst ).
thf(func_def_441,type,
sK300: term > ( subst > term > subst > $o ) > term ).
thf(func_def_442,type,
sK301: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_443,type,
sK302: ( subst > term > term ) > subst ).
thf(func_def_444,type,
sK303: ( subst > term > term ) > term ).
thf(func_def_445,type,
sK304: ( subst > term > term ) > subst ).
thf(func_def_446,type,
sK305: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_447,type,
sK306: term ).
thf(func_def_448,type,
sK307: term > $o ).
thf(func_def_449,type,
sK308: subst > term > subst > $o ).
thf(func_def_450,type,
sK309: term ).
thf(func_def_451,type,
sK310: ( subst > term > subst > $o ) > subst ).
thf(func_def_452,type,
sK311: ( subst > term > subst > $o ) > term ).
thf(func_def_453,type,
sK312: ( subst > term > subst > $o ) > subst ).
thf(func_def_454,type,
sK313: ( subst > term > subst > $o ) > subst ).
thf(func_def_455,type,
sK314: ( subst > term > subst > $o ) > ( term > $o ) > term ).
thf(func_def_456,type,
sK315: ( subst > term > subst > $o ) > subst ).
thf(func_def_457,type,
sK316: ( subst > term > subst > $o ) > term ).
thf(func_def_458,type,
sK317: ( subst > term > subst > $o ) > subst ).
thf(func_def_459,type,
sK318: ( subst > term > subst > $o ) > subst ).
thf(func_def_460,type,
sK319: ( subst > term > subst > $o ) > term ).
thf(func_def_461,type,
sK320: ( subst > term > subst > $o ) > term ).
thf(func_def_462,type,
sK321: term ).
thf(func_def_463,type,
sK322: subst > term > subst > $o ).
thf(func_def_464,type,
sK323: ( subst > term > subst > $o ) > term > term ).
thf(func_def_465,type,
sK324: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_466,type,
sK325: ( subst > term > term ) > term > subst ).
thf(func_def_467,type,
sK326: ( subst > term > term ) > term > term ).
thf(func_def_468,type,
sK327: ( subst > term > term ) > term > subst ).
thf(func_def_469,type,
sK328: ( subst > term > term ) > term > subst ).
thf(func_def_470,type,
sK329: ( subst > term > term ) > term > term ).
thf(func_def_471,type,
sK330: ( subst > term > term ) > term > subst ).
thf(func_def_472,type,
sK331: ( subst > term > subst > $o ) > term ).
thf(func_def_473,type,
sK332: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_474,type,
sK333: term ).
thf(func_def_475,type,
sK334: subst > term > subst > $o ).
thf(func_def_476,type,
sK335: ( subst > term > subst > $o ) > term > term ).
thf(func_def_477,type,
sK336: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_478,type,
sK337: ( subst > term > term ) > subst ).
thf(func_def_479,type,
sK338: ( subst > term > term ) > subst ).
thf(func_def_480,type,
sK339: ( subst > term > term ) > term ).
thf(func_def_481,type,
sK340: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_482,type,
sK341: term ).
thf(func_def_483,type,
sK342: term ).
thf(func_def_484,type,
sK343: term ).
thf(func_def_485,type,
sK344: term ).
thf(func_def_486,type,
sK345: term ).
thf(func_def_487,type,
sK346: term ).
thf(func_def_488,type,
sK347: term ).
thf(func_def_489,type,
sK348: term ).
thf(func_def_490,type,
sK349: term ).
thf(func_def_491,type,
sK350: subst > term > subst > $o ).
thf(func_def_492,type,
sK351: term > $o ).
thf(func_def_493,type,
sK352: ( subst > term > subst > $o ) > subst ).
thf(func_def_494,type,
sK353: ( subst > term > subst > $o ) > subst ).
thf(func_def_495,type,
sK354: ( subst > term > subst > $o ) > subst ).
thf(func_def_496,type,
sK355: ( subst > term > subst > $o ) > term ).
thf(func_def_497,type,
sK356: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_498,type,
sK357: term > ( term > $o ) > term ).
thf(func_def_499,type,
sK358: ( subst > term > subst > $o ) > subst ).
thf(func_def_500,type,
sK359: ( subst > term > subst > $o ) > subst ).
thf(func_def_501,type,
sK360: ( subst > term > subst > $o ) > term ).
thf(func_def_502,type,
sK361: ( subst > term > subst > $o ) > subst ).
thf(func_def_503,type,
sK362: ( subst > term > term ) > term ).
thf(func_def_504,type,
sK363: ( subst > term > term ) > subst ).
thf(func_def_505,type,
sK364: ( subst > term > term ) > subst ).
thf(func_def_506,type,
sK365: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_507,type,
sK366: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_508,type,
sK367: subst ).
thf(func_def_509,type,
sK368: term ).
thf(func_def_510,type,
sK369: term ).
thf(func_def_511,type,
sK370: subst ).
thf(func_def_512,type,
sK371: term ).
thf(func_def_513,type,
sK372: term ).
thf(func_def_514,type,
sK373: subst ).
thf(func_def_515,type,
sK374: term ).
thf(func_def_516,type,
sK375: subst > term > term ).
thf(func_def_517,type,
sK376: subst > term > term ).
thf(func_def_518,type,
sK377: ( subst > term > term ) > subst ).
thf(func_def_519,type,
sK378: ( subst > term > term ) > term ).
thf(func_def_520,type,
sK379: ( subst > term > term ) > subst ).
thf(func_def_521,type,
sK380: ( subst > term > term ) > term ).
thf(func_def_522,type,
sK381: ( subst > term > term ) > subst ).
thf(func_def_523,type,
sK382: ( subst > term > term ) > subst ).
thf(func_def_524,type,
sK383: subst ).
thf(func_def_525,type,
sK384: subst ).
thf(func_def_526,type,
sK385: subst ).
thf(func_def_527,type,
sK386: subst ).
thf(func_def_528,type,
sK387: term ).
thf(func_def_529,type,
sK388: term ).
thf(func_def_530,type,
sK389: term ).
thf(func_def_531,type,
sK390: term ).
thf(func_def_532,type,
sK391: term ).
thf(func_def_533,type,
sK392: term ).
thf(func_def_534,type,
sK393: term ).
thf(func_def_535,type,
sK394: term ).
thf(func_def_536,type,
sK395: term ).
thf(func_def_537,type,
sK396: subst > term > subst > $o ).
thf(func_def_538,type,
sK397: term ).
thf(func_def_539,type,
sK398: term > $o ).
thf(func_def_540,type,
sK399: ( term > $o ) > term > term ).
thf(func_def_541,type,
sK400: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_542,type,
sK401: ( subst > term > term ) > subst ).
thf(func_def_543,type,
sK402: ( subst > term > term ) > subst ).
thf(func_def_544,type,
sK403: ( subst > term > term ) > term ).
thf(func_def_545,type,
sK404: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_546,type,
sK405: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_547,type,
sK406: term > ( subst > term > subst > $o ) > term ).
thf(func_def_548,type,
sK407: subst > term > subst > $o ).
thf(func_def_549,type,
sK408: term ).
thf(func_def_550,type,
sK409: subst > term > subst > $o ).
thf(func_def_551,type,
sK410: term ).
thf(func_def_552,type,
sK411: term > ( subst > term > subst > $o ) > term ).
thf(func_def_553,type,
sK412: ( subst > term > term ) > term ).
thf(func_def_554,type,
sK413: ( subst > term > term ) > subst ).
thf(func_def_555,type,
sK414: ( subst > term > term ) > subst ).
thf(func_def_556,type,
sK415: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_557,type,
sK416: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_558,type,
sK417: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_559,type,
sK418: ( subst > term > term ) > term ).
thf(func_def_560,type,
sK419: ( subst > term > term ) > subst ).
thf(func_def_561,type,
sK420: ( subst > term > term ) > subst ).
thf(func_def_562,type,
sK421: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_563,type,
sK422: term > $o ).
thf(func_def_564,type,
sK423: subst > term > subst > $o ).
thf(func_def_565,type,
sK424: term ).
thf(func_def_566,type,
sK425: term > ( term > $o ) > term ).
thf(func_def_567,type,
sK426: ( subst > term > subst > $o ) > ( term > $o ) > term ).
thf(func_def_568,type,
sK427: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_569,type,
sK428: ( subst > term > term ) > subst ).
thf(func_def_570,type,
sK429: ( subst > term > term ) > term ).
thf(func_def_571,type,
sK430: ( subst > term > term ) > subst ).
thf(func_def_572,type,
sK431: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_573,type,
sK432: term ).
thf(func_def_574,type,
sK433: subst > term > subst > $o ).
thf(func_def_575,type,
sK434: ( subst > term > subst > $o ) > term ).
thf(func_def_576,type,
sK435: ( subst > term > subst > $o ) > subst ).
thf(func_def_577,type,
sK436: ( subst > term > subst > $o ) > subst ).
thf(func_def_578,type,
sK437: ( subst > term > subst > $o ) > subst ).
thf(func_def_579,type,
sK438: ( subst > term > subst > $o ) > term ).
thf(func_def_580,type,
sK439: ( subst > term > subst > $o ) > subst ).
thf(func_def_581,type,
sK440: ( subst > term > subst > $o ) > subst ).
thf(func_def_582,type,
sK441: ( subst > term > subst > $o ) > term ).
thf(func_def_583,type,
sK442: ( subst > term > subst > $o ) > subst ).
thf(func_def_584,type,
sK443: ( subst > term > subst > $o ) > term ).
thf(func_def_585,type,
sK444: ( subst > term > subst > $o ) > term ).
thf(func_def_586,type,
sK445: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_587,type,
sK446: ( subst > term > term ) > subst ).
thf(func_def_588,type,
sK447: ( subst > term > term ) > term ).
thf(func_def_589,type,
sK448: ( subst > term > term ) > subst ).
thf(func_def_590,type,
sK449: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_591,type,
sK450: ( subst > term > subst > $o ) > term ).
thf(func_def_592,type,
sK451: ( subst > term > subst > $o ) > term ).
thf(func_def_593,type,
sK452: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_594,type,
sK453: ( subst > term > term ) > subst ).
thf(func_def_595,type,
sK454: ( subst > term > term ) > subst ).
thf(func_def_596,type,
sK455: ( subst > term > term ) > term ).
thf(func_def_597,type,
sK456: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_598,type,
sK457: term ).
thf(func_def_599,type,
sK458: subst > term > subst > $o ).
thf(func_def_600,type,
sK459: ( subst > term > subst > $o ) > subst ).
thf(func_def_601,type,
sK460: ( subst > term > subst > $o ) > subst ).
thf(func_def_602,type,
sK461: ( subst > term > subst > $o ) > subst ).
thf(func_def_603,type,
sK462: ( subst > term > subst > $o ) > term ).
thf(func_def_604,type,
sK463: ( subst > term > subst > $o ) > term > term ).
thf(func_def_605,type,
sK464: ( subst > term > subst > $o ) > term ).
thf(func_def_606,type,
sK465: ( subst > term > subst > $o ) > subst ).
thf(func_def_607,type,
sK466: ( subst > term > subst > $o ) > subst ).
thf(func_def_608,type,
sK467: ( subst > term > subst > $o ) > subst ).
thf(func_def_609,type,
sK468: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_610,type,
sK469: ( subst > term > term ) > term ).
thf(func_def_611,type,
sK470: ( subst > term > term ) > subst ).
thf(func_def_612,type,
sK471: ( subst > term > term ) > subst ).
thf(func_def_613,type,
sK472: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_614,type,
sK473: ( term > $o ) > term ).
thf(func_def_615,type,
sK474: term ).
thf(func_def_616,type,
sK475: term > $o ).
thf(func_def_617,type,
sK476: ( term > $o ) > ( subst > term > subst > $o ) > term ).
thf(func_def_618,type,
sK477: ( term > $o ) > term > term ).
thf(func_def_619,type,
sK478: subst > term > subst > $o ).
thf(func_def_620,type,
sK479: term ).
thf(func_def_621,type,
sK480: term > $o ).
thf(func_def_622,type,
sK481: term ).
thf(func_def_623,type,
sK482: subst > term > subst > $o ).
thf(func_def_624,type,
sK483: ( subst > term > subst > $o ) > subst ).
thf(func_def_625,type,
sK484: ( subst > term > subst > $o ) > subst ).
thf(func_def_626,type,
sK485: ( subst > term > subst > $o ) > subst ).
thf(func_def_627,type,
sK486: ( subst > term > subst > $o ) > term ).
thf(func_def_628,type,
sK487: ( term > $o ) > term ).
thf(func_def_629,type,
sK488: term > ( term > $o ) > term ).
thf(func_def_630,type,
sK489: ( term > $o ) > term ).
thf(func_def_631,type,
sK490: ( term > $o ) > term ).
thf(func_def_632,type,
sK491: ( subst > term > subst > $o ) > term ).
thf(func_def_633,type,
sK492: ( subst > term > subst > $o ) > subst ).
thf(func_def_634,type,
sK493: ( subst > term > subst > $o ) > subst ).
thf(func_def_635,type,
sK494: ( subst > term > subst > $o ) > subst ).
thf(func_def_636,type,
sK495: ( subst > term > subst > $o ) > term ).
thf(func_def_637,type,
sK496: ( subst > term > subst > $o ) > term ).
thf(func_def_638,type,
sK497: ( subst > term > subst > $o ) > term ).
thf(func_def_639,type,
sK498: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_640,type,
sK499: ( subst > term > term ) > subst ).
thf(func_def_641,type,
sK500: ( subst > term > term ) > term ).
thf(func_def_642,type,
sK501: ( subst > term > term ) > subst ).
thf(func_def_643,type,
sK502: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_644,type,
sK503: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_645,type,
sK504: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_646,type,
sK505: ( subst > term > term ) > subst ).
thf(func_def_647,type,
sK506: ( subst > term > term ) > subst ).
thf(func_def_648,type,
sK507: ( subst > term > term ) > term ).
thf(func_def_649,type,
sK508: subst > term > subst > $o ).
thf(func_def_650,type,
sK509: term ).
thf(func_def_651,type,
sK510: term > ( subst > term > subst > $o ) > term ).
thf(func_def_652,type,
sK511: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_653,type,
sK512: ( subst > term > term ) > subst ).
thf(func_def_654,type,
sK513: ( subst > term > term ) > subst ).
thf(func_def_655,type,
sK514: ( subst > term > term ) > term ).
thf(func_def_656,type,
sK515: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_657,type,
sK516: term ).
thf(func_def_658,type,
sK517: term ).
thf(func_def_659,type,
sK518: term ).
thf(func_def_660,type,
sK519: term ).
thf(func_def_661,type,
sK520: subst ).
thf(func_def_662,type,
sK521: term ).
thf(func_def_663,type,
sK522: subst > term > subst > $o ).
thf(func_def_664,type,
sK523: ( term > $o ) > term ).
thf(func_def_665,type,
sK524: ( subst > term > subst > $o ) > term > $o ).
thf(func_def_666,type,
sK525: subst ).
thf(func_def_667,type,
sK526: subst ).
thf(func_def_668,type,
sK527: term ).
thf(func_def_669,type,
sK528: term ).
thf(func_def_670,type,
sK529: term ).
thf(func_def_671,type,
sK530: term ).
thf(func_def_672,type,
sK531: term ).
thf(func_def_673,type,
sK532: term ).
thf(func_def_674,type,
sK533: term ).
thf(func_def_675,type,
sK534: ( subst > term > term ) > term ).
thf(func_def_676,type,
sK535: ( subst > term > term ) > subst ).
thf(func_def_677,type,
sK536: term > subst > term > term ).
thf(func_def_678,type,
sK537: term ).
thf(func_def_679,type,
sK538: term ).
thf(func_def_680,type,
sK539: term ).
thf(func_def_681,type,
sK540: term > subst > term > term ).
thf(func_def_682,type,
sK541: subst ).
thf(func_def_683,type,
sK542: subst ).
thf(func_def_684,type,
sK543: term ).
thf(func_def_685,type,
sK544: term ).
thf(func_def_686,type,
sK545: subst ).
thf(func_def_687,type,
sK546: term > ( term > $o ) > subst > term > $o ).
thf(func_def_688,type,
sK547: subst ).
thf(func_def_689,type,
sK548: term > $o ).
thf(func_def_690,type,
sK549: term ).
thf(func_def_691,type,
sK550: ( term > $o ) > term ).
thf(func_def_692,type,
sK551: term ).
thf(func_def_693,type,
sK552: term > $o ).
thf(func_def_694,type,
sK553: subst ).
thf(func_def_695,type,
sK554: term ).
thf(func_def_696,type,
sK555: ( term > $o ) > term ).
thf(func_def_697,type,
sK556: term > subst > ( term > $o ) > term > $o ).
thf(func_def_698,type,
sK557: ( subst > term > term ) > subst ).
thf(func_def_699,type,
sK558: ( subst > term > term ) > term ).
thf(func_def_700,type,
sK559: ( subst > term > term ) > subst ).
thf(func_def_701,type,
sK560: subst > term > term ).
thf(func_def_702,type,
sK561: term ).
thf(func_def_703,type,
sK562: term ).
thf(func_def_704,type,
sK563: term > d_term ).
thf(func_def_705,type,
sK564: term ).
thf(func_def_706,type,
sK565: term ).
thf(func_def_707,type,
sK566: term ).
thf(func_def_708,type,
sK567: subst ).
thf(func_def_709,type,
sK568: term ).
thf(func_def_710,type,
sK569: ( subst > term > term ) > term ).
thf(func_def_711,type,
sK570: ( subst > term > term ) > subst ).
thf(func_def_712,type,
sK571: term > subst > term > term ).
thf(func_def_713,type,
sK572: term > subst > term > term ).
thf(func_def_714,type,
sK573: term ).
thf(func_def_715,type,
sK574: ( subst > term > term ) > subst ).
thf(func_def_716,type,
sK575: ( subst > term > term ) > subst ).
thf(func_def_717,type,
sK576: ( subst > term > term ) > term ).
thf(func_def_718,type,
sK577: ( subst > term > term ) > term ).
thf(func_def_719,type,
sK578: ( subst > term > term ) > subst ).
thf(func_def_720,type,
sK579: ( subst > term > term ) > subst ).
thf(func_def_721,type,
sK580: subst ).
thf(func_def_722,type,
sK581: subst > term > term ).
thf(func_def_723,type,
sK582: term ).
thf(func_def_724,type,
sK583: subst > term > term ).
thf(func_def_725,type,
sK584: term ).
thf(func_def_726,type,
sK585: term ).
thf(func_def_727,type,
sK586: term ).
thf(func_def_728,type,
sK587: term ).
thf(func_def_729,type,
sK588: term ).
thf(func_def_730,type,
sK589: term ).
thf(func_def_731,type,
sK590: ( subst > term > term ) > subst ).
thf(func_def_732,type,
sK591: ( subst > term > term ) > term ).
thf(func_def_733,type,
sK592: term > subst > term > term ).
thf(func_def_734,type,
sK593: subst ).
thf(func_def_735,type,
sK594: term ).
thf(func_def_736,type,
sK595: term ).
thf(func_def_737,type,
sK596: subst ).
thf(func_def_738,type,
sK597: term ).
thf(func_def_739,type,
sK598: term > $o ).
thf(func_def_740,type,
sK599: subst ).
thf(func_def_741,type,
sK600: term ).
thf(func_def_742,type,
sK601: term > $o ).
thf(func_def_743,type,
sK602: term ).
thf(func_def_744,type,
sK603: term > ( term > $o ) > ( term > $o ) > subst > term ).
thf(func_def_745,type,
sK604: subst ).
thf(func_def_746,type,
sK605: term > $o ).
thf(func_def_747,type,
sK606: term > $o ).
thf(func_def_748,type,
sK607: term ).
thf(func_def_749,type,
sK608: ( subst > term > subst > $o ) > term > $o ).
thf(func_def_750,type,
sK609: subst > term > subst > $o ).
thf(func_def_751,type,
sK610: ( term > $o ) > term ).
thf(func_def_752,type,
sK611: term ).
thf(func_def_753,type,
sK612: subst ).
thf(func_def_754,type,
sK613: term > $o ).
thf(func_def_755,type,
sK614: term > $o ).
thf(func_def_756,type,
sK615: ( term > $o ) > ( term > $o ) > subst > term > term ).
thf(func_def_757,type,
sK616: term ).
thf(func_def_758,type,
sK617: subst ).
thf(func_def_759,type,
sK618: term ).
thf(func_def_760,type,
sK619: term ).
thf(func_def_761,type,
sK620: term ).
thf(func_def_762,type,
sK621: term ).
thf(func_def_763,type,
sK622: term ).
thf(func_def_764,type,
sK623: subst ).
thf(func_def_765,type,
sK624: term ).
thf(func_def_766,type,
sK625: subst > term > subst > $o ).
thf(func_def_767,type,
sK626: term ).
thf(func_def_768,type,
sK627: term ).
thf(func_def_769,type,
sK628: term ).
thf(func_def_770,type,
sK629: term ).
thf(func_def_771,type,
sK630: term ).
thf(func_def_772,type,
sK631: term > $o ).
thf(func_def_773,type,
sK632: subst ).
thf(func_def_774,type,
sK633: term > $o ).
thf(func_def_775,type,
sK634: subst ).
thf(func_def_776,type,
sK635: term ).
thf(func_def_777,type,
sK636: ( subst > term > subst > $o ) > term > $o ).
thf(func_def_778,type,
sK637: term ).
thf(func_def_779,type,
sK638: subst > term > subst > $o ).
thf(func_def_780,type,
sK639: ( term > $o ) > term ).
thf(func_def_781,type,
sK640: subst ).
thf(func_def_782,type,
sK641: subst > term > subst > $o ).
thf(func_def_783,type,
sK642: ( term > $o ) > term ).
thf(func_def_784,type,
sK643: ( subst > term > subst > $o ) > term > $o ).
thf(func_def_785,type,
sK644: subst > d_subst ).
thf(func_def_786,type,
sK645: ( subst > term > term ) > ( subst > term > subst > $o ) > term ).
thf(func_def_787,type,
sK646: ( subst > term > subst > $o ) > subst > term > term ).
thf(func_def_788,type,
sK647: ( subst > term > subst > $o ) > term ).
thf(func_def_789,type,
sK648: term > ( subst > term > subst > $o ) > term ).
thf(func_def_790,type,
sK649: term > ( subst > term > term ) > subst ).
thf(func_def_791,type,
sK650: term > ( subst > term > term ) > term ).
thf(func_def_792,type,
sK651: term > ( subst > term > term ) > subst ).
thf(func_def_793,type,
sK652: ( subst > term > term ) > term ).
thf(func_def_794,type,
sK653: subst > term > subst > $o ).
thf(func_def_797,type,
ph655:
!>[X0: $tType] : X0 ).
thf(f15089,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f2202,f2903,f2934,f3128,f3268,f3464,f8837,f8846,f11474,f14373,f14490,f14981,f15088]) ).
thf(f15088,plain,
( spl654_371
| ~ spl654_487 ),
inference(avatar_contradiction_clause,[status(thm)],[f15087]) ).
thf(f15087,plain,
( $false
| spl654_371
| ~ spl654_487 ),
inference(subsumption_resolution,[status(thm)],[f14495,f8833]) ).
thf(f8833,plain,
( ( $true
= ( sK322 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| ~ spl654_487 ),
inference(avatar_component_clause,[status(thm)],[f8832]) ).
thf(f8832,definition,
( spl654_487
<=> ( $true
= ( sK322 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ),
introduced(definition,[new_symbols(naming,[spl654_487])],[avatar_definition]) ).
thf(f14495,plain,
( ( $true
!= ( sK322 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
| spl654_371 ),
inference(forward_demodulation,[status(thm)],[f3463,f3865]) ).
thf(f3865,plain,
! [X97: term] :
( ( d2term @ d_one )
= X97 ),
inference(forward_demodulation,[status(thm)],[f1412,f1314]) ).
thf(f1314,plain,
! [X227: d_term] : ( d_one = X227 ),
inference(cnf_transformation,[status(thm)],[f749]) ).
thf(f749,plain,
( ( hoasapnotvar = $true )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( apinj1 = $true )
| ( ( sK517 != sK519 )
& ( ( ap @ sK519 @ sK518 )
= ( ap @ sK517 @ sK516 ) ) ) )
& ( ! [X4: term,X5: term,X6: term,X7: term] :
( ( X5 = X7 )
| ( ( ap @ X5 @ X4 )
!= ( ap @ X7 @ X6 ) ) )
| ( apinj1 != $true ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( hoaslamnotvar_gthm = $true )
& ( ! [X8: subst] :
( ( comp @ X8 @ id )
= X8 )
| ( axidr != $true ) )
& ( ( axidr = $true )
| ( ( comp @ sK520 @ id )
!= sK520 ) )
& ( termmset_gthm = $true )
& ( ( sP108 = $true )
| ( ( sub @ sK521 @ id )
!= sK521 )
| ! [X12: term > $o] :
( ( X12 @ ( sK523 @ X12 ) )
!= ( sK522 @ id @ ( sK523 @ X12 ) @ id ) )
| ( sP109 = $true )
| ( sP107 = $true )
| ( hoasinduction_no_psi_cond_lthm != $true ) )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
| ( ( sP108 != $true )
& ! [X14: term] :
( ( sub @ X14 @ id )
= X14 )
& ! [X15: subst > term > subst > $o,X17: term] :
( ( X15 @ id @ X17 @ id )
= ( sK524 @ X15 @ X17 ) )
& ( sP109 != $true )
& ( sP107 != $true ) ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ! [X18: d_subst] : ( d_id = X18 )
& ( ( ! [X19: subst] :
( ( comp @ id @ X19 )
= X19 )
& ! [X20: subst] :
( ( comp @ X20 @ id )
= X20 ) )
| ( substmonoid != $true ) )
& ( ( substmonoid = $true )
| ( ( comp @ id @ sK525 )
!= sK525 )
| ( ( comp @ sK526 @ id )
!= sK526 ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( one
= ( d2term @ d_one ) )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ( sP100 = $true )
| ( hoasinduction_lem3aa_lthm != $true ) )
& ( ( hoasinduction_lem3aa_lthm = $true )
| ( sP100 != $true ) )
& ( ( induction = $true )
| ( sP98 != $true ) )
& ( ( sP98 = $true )
| ( induction != $true ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
| ( ! [X23: term] :
( ( sub @ X23 @ id )
= X23 )
& ( $true != sP95 ) ) )
& ( ( sK527
!= ( sub @ sK527 @ id ) )
| ( $true = sP95 )
| ( hoasinduction_lem3v2_lthm != $true ) )
& ( pushprop_lthm_orig = $true )
& ( hoaslamnotvar_lthm = $true )
& ( hoaslamnotap_lthm = $true )
& ! [X25: d_term,X26: d_term] :
( ( ( d2term @ X25 )
!= ( d2term @ X26 ) )
| ( X25 = X26 ) )
& ( hoaslamnotvar = $true )
& ( ( hoasinduction_lem2 = $true )
| ( $true != sP91 ) )
& ( ( $true = sP91 )
| ( hoasinduction_lem2 != $true ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( axabs = $true )
& ( ! [X27: term,X28: term,X29: term,X30: term] :
( ( ( ap @ ( sub @ X27 @ id ) @ X30 )
!= ( ap @ ( sub @ X29 @ id ) @ X28 ) )
| ( X28 = X30 ) )
| ( hoasapinj2 != $true ) )
& ( ( hoasapinj2 = $true )
| ( ( ( ap @ ( sub @ sK528 @ id ) @ sK531 )
= ( ap @ ( sub @ sK530 @ id ) @ sK529 ) )
& ( sK529 != sK531 ) ) )
& ( ( induction2 = $true )
| ( sP88 != $true ) )
& ( ( sP88 = $true )
| ( induction2 != $true ) )
& ( induction2_gthm = $true )
& ( ( $true = sP85 )
| ( induction2lem != $true ) )
& ( ( induction2lem = $true )
| ( $true != sP85 ) )
& ( hoasinduction_lem1v2_gthm = $true )
& ( ( sP81 = $true )
| ( sK532
!= ( sub @ sK532 @ id ) )
| ( $true = sP82 )
| ( induction2_lthm != $true ) )
& ( ( induction2_lthm = $true )
| ( ( sP81 != $true )
& ! [X36: term] :
( ( sub @ X36 @ id )
= X36 )
& ( $true != sP82 ) ) )
& ( hoasapnotvar_lthm = $true )
& ( ( hoasinduction_lem3v2_f = $true )
| ! [X38: subst > term > term] :
( ( sub @ sK533 @ ( push @ ( sK534 @ X38 ) @ ( sK535 @ X38 ) ) )
!= ( X38 @ ( sK535 @ X38 ) @ ( sK534 @ X38 ) ) ) )
& ( ! [X41: term,X43: term,X44: subst] :
( ( sK536 @ X41 @ X44 @ X43 )
= ( sub @ X41 @ ( push @ X43 @ X44 ) ) )
| ( hoasinduction_lem3v2_f != $true ) )
& ( axclos = $true )
& ( ! [X45: term,X46: term] :
( ( X45 = X46 )
| ( ( lam @ X46 )
!= ( lam @ X45 ) ) )
| ( laminj != $true ) )
& ( ( laminj = $true )
| ( ( sK537 != sK538 )
& ( ( lam @ sK538 )
= ( lam @ sK537 ) ) ) )
& ( pushprop_lem3v2_lthm = $true )
& ( axassoc = $true )
& ( ulamvar1 != $true )
& ( ( hoasinduction_lem3b_lthm = $true )
| ! [X50: subst > term > term] :
( ( sub @ sK539 @ ( push @ one @ sh ) )
!= ( X50 @ sh @ one ) ) )
& ( ! [X51: term] :
( ( sK540 @ X51 @ sh @ one )
= ( sub @ X51 @ ( push @ one @ sh ) ) )
| ( hoasinduction_lem3b_lthm != $true ) )
& ( ( sP72 = $true )
| ( $true = sP75 )
| ( sP74 = $true )
| ( $true = sP73 )
| ( hoasinduction_lthm != $true ) )
& ( ( hoasinduction_lthm = $true )
| ( ( sP72 != $true )
& ( $true != sP75 )
& ( sP74 != $true )
& ( $true != sP73 ) ) )
& ( ( induction2lem_lthm = $true )
| ( ( sP60 != $true )
& ( sP59 != $true )
& ! [X53: subst] :
( ( comp @ X53 @ id )
= X53 )
& ! [X54: subst,X55: term] :
( ( comp @ sh @ ( push @ X55 @ X54 ) )
= X54 )
& ! [X56: term,X57: subst] :
( ( sub @ one @ ( push @ X56 @ X57 ) )
= X56 ) ) )
& ( ( sP60 = $true )
| ( sP59 = $true )
| ( sK541
!= ( comp @ sK541 @ id ) )
| ( sK542
!= ( comp @ sh @ ( push @ sK543 @ sK542 ) ) )
| ( sK544
!= ( sub @ one @ ( push @ sK544 @ sK545 ) ) )
| ( induction2lem_lthm != $true ) )
& ( ! [X63: subst,X64: term > $o,X65: term,X67: term] :
( ( sK546 @ X65 @ X64 @ X63 @ X67 )
= ( X64 @ ( sub @ X67 @ ( push @ X65 @ X63 ) ) ) )
| ( pushprop_lem0_lthm != $true ) )
& ( ( pushprop_lem0_lthm = $true )
| ! [X71: term > $o] :
( ( X71 @ ( sK550 @ X71 ) )
!= ( sK548 @ ( sub @ ( sK550 @ X71 ) @ ( push @ sK549 @ sK547 ) ) ) ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) )
= ( Y3 @ Y4 ) ) ) ) )
& ( apnotvar = $true )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( hoasinduction_gthm = $true )
& ( axapp = $true )
& ( ( hoasinduction_lem3_lthm = $true )
| ( ( sP54 != $true )
& ! [X73: term] :
( ( sub @ X73 @ id )
= X73 )
& ( $true != sP53 ) ) )
& ( ( sP54 = $true )
| ( ( sub @ sK551 @ id )
!= sK551 )
| ( $true = sP53 )
| ( hoasinduction_lem3_lthm != $true ) )
& ( ( pushprop_lem0 = $true )
| ! [X78: term > $o] :
( ( X78 @ ( sK555 @ X78 ) )
!= ( sK552 @ ( sub @ ( sK555 @ X78 ) @ ( push @ sK554 @ sK553 ) ) ) ) )
& ( ! [X80: term > $o,X81: subst,X82: term,X84: term] :
( ( sK556 @ X82 @ X81 @ X80 @ X84 )
= ( X80 @ ( sub @ X84 @ ( push @ X82 @ X81 ) ) ) )
| ( pushprop_lem0 != $true ) )
& ( induction2lem_gthm = $true )
& ( ( $true = sP48 )
| ( hoasinduction_lem2v2 != $true ) )
& ( ( hoasinduction_lem2v2 = $true )
| ( $true != sP48 ) )
& ( ( hoasinduction_lem3aaa = $true )
| ( $true != sP45 ) )
& ( ( $true = sP45 )
| ( hoasinduction_lem3aaa != $true ) )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ( hoasinduction_lem3a = $true )
| ( $true != sP43 ) )
& ( ( $true = sP43 )
| ( hoasinduction_lem3a != $true ) )
& ( ! [X85: subst > term > term,X86: term,X87: term] :
( ( ( ap @ ( sub @ X86 @ id ) @ X87 )
!= ( lam @ ( X85 @ sh @ one ) ) )
| ( ( sub @ ( X85 @ ( sK559 @ X85 ) @ ( sK558 @ X85 ) ) @ ( sK557 @ X85 ) )
!= ( X85 @ ( comp @ ( sK559 @ X85 ) @ ( sK557 @ X85 ) ) @ ( sub @ ( sK558 @ X85 ) @ ( sK557 @ X85 ) ) ) ) )
| ( hoaslamnotap != $true ) )
& ( ( hoaslamnotap = $true )
| ( ( ( lam @ ( sK560 @ sh @ one ) )
= ( ap @ ( sub @ sK561 @ id ) @ sK562 ) )
& ! [X94: subst,X95: term,X96: subst] :
( ( sub @ ( sK560 @ X96 @ X95 ) @ X94 )
= ( sK560 @ ( comp @ X96 @ X94 ) @ ( sub @ X95 @ X94 ) ) ) ) )
& ( hoasinduction_lem1 = $true )
& ( pushprop_lem2v2_gthm = $true )
& ! [X97: term] :
( ( d2term @ ( sK563 @ X97 ) )
= X97 )
& ( ( sP41 = $true )
| ( hoasapinj2_lthm != $true ) )
& ( ( hoasapinj2_lthm = $true )
| ( sP41 != $true ) )
& ( lamnotvar = $true )
& ( axvarshift = $true )
& ( hoasinduction_lem3b_gthm = $true )
& ( pushprop = $true )
& ! [X99: d_subst,X100: d_subst] :
( ( X99 = X100 )
| ( ( d2subst @ X100 )
!= ( d2subst @ X99 ) ) )
& ( ulamvarind = $true )
& ( substmonoid_gthm = $true )
& ( hoasinduction_lem2_lthm = $true )
& ( pushprop_lem2v2_lthm = $true )
& ( ( shinj = $true )
| ( ( sK564 != sK565 )
& ( ( sub @ sK564 @ sh )
= ( sub @ sK565 @ sh ) ) ) )
& ( ! [X103: term,X104: term] :
( ( X103 = X104 )
| ( ( sub @ X104 @ sh )
!= ( sub @ X103 @ sh ) ) )
| ( shinj != $true ) )
& ( ( axshiftcons = $true )
| ( ( comp @ sh @ ( push @ sK566 @ sK567 ) )
!= sK567 ) )
& ( ! [X107: term,X108: subst] :
( ( comp @ sh @ ( push @ X107 @ X108 ) )
= X108 )
| ( axshiftcons != $true ) )
& ( hoasapinj1_gthm = $true )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( hoasinduction_lem1_lthm = $true )
& ( ( sP39 = $true )
| ( hoasinduction_lem3v2 != $true ) )
& ( ( hoasinduction_lem3v2 = $true )
| ( sP39 != $true ) )
& ( ( hoasinduction_lem3v2_f_lthm = $true )
| ! [X110: subst > term > term] :
( ( sub @ sK568 @ ( push @ ( sK569 @ X110 ) @ ( sK570 @ X110 ) ) )
!= ( X110 @ ( sK570 @ X110 ) @ ( sK569 @ X110 ) ) ) )
& ( ! [X113: term,X115: term,X116: subst] :
( ( sK571 @ X113 @ X116 @ X115 )
= ( sub @ X113 @ ( push @ X115 @ X116 ) ) )
| ( hoasinduction_lem3v2_f_lthm != $true ) )
& ( ( d2subst @ d_id )
= id )
& ( pushprop_lem1v2_gthm = $true )
& ( ! [X117: term] :
( ( sK572 @ X117 @ sh @ one )
= ( sub @ X117 @ ( push @ one @ sh ) ) )
| ( hoasinduction_lem3b != $true ) )
& ( ( hoasinduction_lem3b = $true )
| ! [X120: subst > term > term] :
( ( X120 @ sh @ one )
!= ( sub @ sK573 @ ( push @ one @ sh ) ) ) )
& ( ( sP35 = $true )
| ( hoaslaminj_lthm != $true ) )
& ( ( hoaslaminj_lthm = $true )
| ( sP35 != $true ) )
& ( ! [X121: subst,X122: subst > term > term,X123: term,X124: subst > term > term] :
( ( ( X122 @ ( comp @ ( sK575 @ X122 ) @ ( sK574 @ X122 ) ) @ ( sub @ ( sK576 @ X122 ) @ ( sK574 @ X122 ) ) )
!= ( sub @ ( X122 @ ( sK575 @ X122 ) @ ( sK576 @ X122 ) ) @ ( sK574 @ X122 ) ) )
| ( ( lam @ ( X124 @ sh @ one ) )
!= ( lam @ ( X122 @ sh @ one ) ) )
| ( ( sub @ ( X124 @ ( sK578 @ X124 ) @ ( sK577 @ X124 ) ) @ ( sK579 @ X124 ) )
!= ( X124 @ ( comp @ ( sK578 @ X124 ) @ ( sK579 @ X124 ) ) @ ( sub @ ( sK577 @ X124 ) @ ( sK579 @ X124 ) ) ) )
| ( ( X124 @ X121 @ X123 )
= ( X122 @ X121 @ X123 ) ) )
| ( hoaslaminj != $true ) )
& ( ( hoaslaminj = $true )
| ( ! [X135: subst,X136: subst,X137: term] :
( ( sK581 @ ( comp @ X136 @ X135 ) @ ( sub @ X137 @ X135 ) )
= ( sub @ ( sK581 @ X136 @ X137 ) @ X135 ) )
& ( ( lam @ ( sK583 @ sh @ one ) )
= ( lam @ ( sK581 @ sh @ one ) ) )
& ! [X138: term,X139: subst,X140: subst] :
( ( sub @ ( sK583 @ X139 @ X138 ) @ X140 )
= ( sK583 @ ( comp @ X139 @ X140 ) @ ( sub @ X138 @ X140 ) ) )
& ( ( sK583 @ sK580 @ sK582 )
!= ( sK581 @ sK580 @ sK582 ) ) ) )
& ( hoaslamnotap_gthm = $true )
& ( ( substmonoid_lthm = $true )
| ( $true != sP33 ) )
& ( ( $true = sP33 )
| ( substmonoid_lthm != $true ) )
& ( ! [X141: term,X142: term,X143: term,X144: term] :
( ( ( ap @ X142 @ X141 )
!= ( ap @ X143 @ X144 ) )
| ( X141 = X144 ) )
| ( apinj2 != $true ) )
& ( ( apinj2 = $true )
| ( ( ( ap @ sK586 @ sK587 )
= ( ap @ sK585 @ sK584 ) )
& ( sK587 != sK584 ) ) )
& ( hoasinduction_lem2_gthm = $true )
& ( pushprop_lem3v2 = $true )
& ( pushprop_lem1_gthm = $true )
& ( ( hoasapinj1_lthm = $true )
| ( $true != sP32 ) )
& ( ( $true = sP32 )
| ( hoasapinj1_lthm != $true ) )
& ( ( $true = sP30 )
| ( ( sub @ sK588 @ id )
!= sK588 )
| ! [X151: subst > term > term] :
( ( sub @ sK589 @ ( push @ ( sK591 @ X151 ) @ ( sK590 @ X151 ) ) )
!= ( X151 @ ( sK590 @ X151 ) @ ( sK591 @ X151 ) ) )
| ( hoasinduction_lem3v2a_lthm != $true ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
| ( ( $true != sP30 )
& ! [X154: term] :
( ( sub @ X154 @ id )
= X154 )
& ! [X155: term,X157: subst,X158: term] :
( ( sK592 @ X155 @ X157 @ X158 )
= ( sub @ X155 @ ( push @ X158 @ X157 ) ) ) ) )
& ( ( ( comp @ sh @ ( push @ sK594 @ sK593 ) )
!= sK593 )
| ( ( sub @ one @ ( push @ sK595 @ sK596 ) )
!= sK595 )
| ! [X163: term,X164: term > $o,X165: subst,X166: term,X167: term > $o] :
( ( ( X167 @ ( sub @ X163 @ ( push @ X166 @ X165 ) ) )
= $true )
| ( $true
!= ( X164 @ X163 ) ) )
| ( pushprop_lem1_lthm != $true ) )
& ( ( pushprop_lem1_lthm = $true )
| ( ! [X168: subst,X169: term] :
( ( comp @ sh @ ( push @ X169 @ X168 ) )
= X168 )
& ! [X170: term,X171: subst] :
( ( sub @ one @ ( push @ X170 @ X171 ) )
= X170 )
& ( ( sK601 @ ( sub @ sK597 @ ( push @ sK600 @ sK599 ) ) )
!= $true )
& ( $true
= ( sK598 @ sK597 ) ) ) )
& ( ( $true = sP27 )
| ( $true = sP28 )
| ( ( sub @ sK602 @ id )
!= sK602 )
| ( hoasinduction_lem3a_lthm != $true ) )
& ( ( hoasinduction_lem3a_lthm = $true )
| ( ( $true != sP27 )
& ( $true != sP28 )
& ! [X178: term] :
( ( sub @ X178 @ id )
= X178 ) ) )
& ( hoasinduction_lem1v2 = $true )
& ( ! [X179: subst,X180: term > $o,X181: term > $o,X182: term] :
( ( ( X180 @ ( sub @ ( sK603 @ X182 @ X181 @ X180 @ X179 ) @ ( push @ X182 @ X179 ) ) )
!= ( X181 @ ( sK603 @ X182 @ X181 @ X180 @ X179 ) ) )
| ( ( X181 @ one )
= $true )
| ( $true
!= ( X180 @ X182 ) ) )
| ( pushprop_lem1v2 != $true ) )
& ( ( pushprop_lem1v2 = $true )
| ( ! [X188: term] :
( ( sK605 @ ( sub @ X188 @ ( push @ sK607 @ sK604 ) ) )
= ( sK606 @ X188 ) )
& ( $true
!= ( sK606 @ one ) )
& ( $true
= ( sK605 @ sK607 ) ) ) )
& ( lamnotap != $true )
& ( hoasapnotvar_gthm = $true )
& ( ! [X189: subst > term > subst > $o,X191: term] :
( ( X189 @ id @ X191 @ id )
= ( sK608 @ X189 @ X191 ) )
| ( hoasinduction_lem0_lthm != $true ) )
& ( ( hoasinduction_lem0_lthm = $true )
| ! [X193: term > $o] :
( ( sK609 @ id @ ( sK610 @ X193 ) @ id )
!= ( X193 @ ( sK610 @ X193 ) ) ) )
& ( ( d2subst @ d_id )
= sh )
& ( ( pushprop_lem1v2_lthm = $true )
| ( ! [X199: term] :
( ( sK614 @ X199 )
= ( sK613 @ ( sub @ X199 @ ( push @ sK611 @ sK612 ) ) ) )
& ( $true
!= ( sK614 @ one ) )
& ( $true
= ( sK613 @ sK611 ) )
& ! [X200: term,X201: subst] :
( ( sub @ one @ ( push @ X200 @ X201 ) )
= X200 ) ) )
& ( ! [X202: term,X203: subst,X204: term > $o,X205: term > $o] :
( ( ( X204 @ ( sub @ ( sK615 @ X205 @ X204 @ X203 @ X202 ) @ ( push @ X202 @ X203 ) ) )
!= ( X205 @ ( sK615 @ X205 @ X204 @ X203 @ X202 ) ) )
| ( ( X205 @ one )
= $true )
| ( ( X204 @ X202 )
!= $true ) )
| ( sK616
!= ( sub @ one @ ( push @ sK616 @ sK617 ) ) )
| ( pushprop_lem1v2_lthm != $true ) )
& ( hoasinduction_lem1_gthm = $true )
& ( pushprop_lem0_gthm = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ( axvarid = $true )
| ( ( sub @ sK618 @ id )
!= sK618 ) )
& ( ! [X210: term] :
( ( sub @ X210 @ id )
= X210 )
| ( axvarid != $true ) )
& ( ( sP24 = $true )
| ( hoasinduction_lem3v2a != $true ) )
& ( ( hoasinduction_lem3v2a = $true )
| ( sP24 != $true ) )
& ( ( hoasapinj1 = $true )
| ( ( ( ap @ ( sub @ sK622 @ id ) @ sK619 )
= ( ap @ ( sub @ sK621 @ id ) @ sK620 ) )
& ( sK621 != sK622 ) ) )
& ( ! [X215: term,X216: term,X217: term,X218: term] :
( ( ( ap @ ( sub @ X217 @ id ) @ X216 )
!= ( ap @ ( sub @ X218 @ id ) @ X215 ) )
| ( X217 = X218 ) )
| ( hoasapinj1 != $true ) )
& ( pushprop_gthm = $true )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( axscons = $true )
| ( sK623
!= ( push @ ( sub @ one @ sK623 ) @ ( comp @ sh @ sK623 ) ) ) )
& ( ! [X220: subst] :
( ( push @ ( sub @ one @ X220 ) @ ( comp @ sh @ X220 ) )
= X220 )
| ( axscons != $true ) )
& ( ( hoasinduction = $true )
| ( $true != sP22 ) )
& ( ( $true = sP22 )
| ( hoasinduction != $true ) )
& ( pushprop_lem2v2 = $true )
& ( ( hoasinduction_no_psi_cond = $true )
| ( ( ( sK625 @ id @ sK624 @ id )
!= $true )
& ( ( sP17 @ sK625 )
!= $true )
& ( ( sP16 @ sK625 )
!= $true ) ) )
& ( ! [X223: term,X224: subst > term > subst > $o] :
( ( $true
= ( X224 @ id @ X223 @ id ) )
| ( $true
= ( sP17 @ X224 ) )
| ( ( sP16 @ X224 )
= $true ) )
| ( hoasinduction_no_psi_cond != $true ) )
& ( hoasinduction_lem3_gthm = $true )
& ( ( termmset = $true )
| ( sK626
!= ( sub @ sK626 @ id ) ) )
& ( ! [X226: term] :
( ( sub @ X226 @ id )
= X226 )
| ( termmset != $true ) )
& ! [X227: d_term] : ( d_one = X227 )
& ( ulamvarsh = $true )
& ( hoasapinj2_gthm = $true )
& ( axmap = $true )
& ( ( sP15 = $true )
| ( hoasinduction_lem3 != $true ) )
& ( ( hoasinduction_lem3 = $true )
| ( sP15 != $true ) )
& ( ! [X228: term] :
( ( sub @ X228 @ id )
= X228 )
| ( sK627
!= ( sub @ sK627 @ id ) )
| ( termmset_lthm != $true ) )
& ( ( termmset_lthm = $true )
| ( ( ( sub @ sK628 @ id )
!= sK628 )
& ! [X231: term] :
( ( sub @ X231 @ id )
= X231 ) ) )
& ( ( pushprop_lem1 = $true )
| ( ( ( sK633 @ sK630 )
= $true )
& ( $true
!= ( sK631 @ ( sub @ sK630 @ ( push @ sK629 @ sK632 ) ) ) ) ) )
& ( ! [X237: term,X238: term,X239: term > $o,X240: subst,X241: term > $o] :
( ( $true
!= ( X241 @ X238 ) )
| ( ( X239 @ ( sub @ X238 @ ( push @ X237 @ X240 ) ) )
= $true ) )
| ( pushprop_lem1 != $true ) )
& ( ( axvarcons = $true )
| ( ( sub @ one @ ( push @ sK635 @ sK634 ) )
!= sK635 ) )
& ( ! [X244: subst,X245: term] :
( ( sub @ one @ ( push @ X245 @ X244 ) )
= X245 )
| ( axvarcons != $true ) )
& ( ( hoasinduction_lthm_3 = $true )
| ( ( $true != sP11 )
& ( $true != sP9 )
& ! [X246: term] :
( ( sub @ X246 @ id )
= X246 )
& ! [X247: subst > term > subst > $o,X249: term] :
( ( sK636 @ X247 @ X249 )
= ( X247 @ id @ X249 @ id ) )
& ( sP10 != $true ) ) )
& ( ( $true = sP11 )
| ( $true = sP9 )
| ( ( sub @ sK637 @ id )
!= sK637 )
| ! [X252: term > $o] :
( ( X252 @ ( sK639 @ X252 ) )
!= ( sK638 @ id @ ( sK639 @ X252 ) @ id ) )
| ( sP10 = $true )
| ( hoasinduction_lthm_3 != $true ) )
& ( pushprop_lthm = $true )
& ( ! [X254: subst] :
( ( comp @ id @ X254 )
= X254 )
| ( axidl != $true ) )
& ( ( axidl = $true )
| ( sK640
!= ( comp @ id @ sK640 ) ) )
& ( ( hoasinduction_lem3aa = $true )
| ( sP1 != $true ) )
& ( ( sP1 = $true )
| ( hoasinduction_lem3aa != $true ) )
& ( hoaslaminj_gthm = $true )
& ( ( hoasinduction_lem0 = $true )
| ! [X257: term > $o] :
( ( sK641 @ id @ ( sK642 @ X257 ) @ id )
!= ( X257 @ ( sK642 @ X257 ) ) ) )
& ( ! [X259: subst > term > subst > $o,X261: term] :
( ( X259 @ id @ X261 @ id )
= ( sK643 @ X259 @ X261 ) )
| ( hoasinduction_lem0 != $true ) )
& ! [X262: subst] :
( ( d2subst @ ( sK644 @ X262 ) )
= X262 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[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,sK591,sK592,sK593,sK594,sK595,sK596,sK597,sK598,sK599,sK600,sK601,sK602,sK603,sK604,sK605,sK606,sK607,sK608,sK609,sK610,sK611,sK612,sK613,sK614,sK615,sK616,sK617,sK618,sK619,sK620,sK621,sK622,sK623,sK624,sK625,sK626,sK627,sK628,sK629,sK630,sK631,sK632,sK633,sK634,sK635,sK636,sK637,sK638,sK639,sK640,sK641,sK642,sK643,sK644])],[f673,f748,f747,f746,f745,f744,f743,f742,f741,f740,f739,f738,f737,f736,f735,f734,f733,f732,f731,f730,f729,f728,f727,f726,f725,f724,f723,f722,f721,f720,f719,f718,f717,f716,f715,f714,f713,f712,f711,f710,f709,f708,f707,f706,f705,f704,f703,f702,f701,f700,f699,f698,f697,f696,f695,f694,f693,f692,f691,f690,f689,f688,f687,f686,f685,f684,f683,f682,f681,f680,f679,f678,f677,f676,f675,f674]) ).
thf(f674,plain,
( ? [X0: term,X1: term,X2: term,X3: term] :
( ( X1 != X3 )
& ( ( ap @ X1 @ X0 )
= ( ap @ X3 @ X2 ) ) )
=> ( ( sK517 != sK519 )
& ( ( ap @ sK519 @ sK518 )
= ( ap @ sK517 @ sK516 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f675,plain,
( ? [X9: subst] :
( ( comp @ X9 @ id )
!= X9 )
=> ( ( comp @ sK520 @ id )
!= sK520 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f676,plain,
( ? [X10: term] :
( ( sub @ X10 @ id )
!= X10 )
=> ( ( sub @ sK521 @ id )
!= sK521 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f677,plain,
( ? [X11: subst > term > subst > $o] :
! [X12: term > $o] :
? [X13: term] :
( ( X12 @ X13 )
!= ( X11 @ id @ X13 @ id ) )
=> ! [X12: term > $o] :
? [X13: term] :
( ( X12 @ X13 )
!= ( sK522 @ id @ X13 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f678,plain,
! [X12: term > $o] :
( ? [X13: term] :
( ( X12 @ X13 )
!= ( sK522 @ id @ X13 @ id ) )
=> ( ( X12 @ ( sK523 @ X12 ) )
!= ( sK522 @ id @ ( sK523 @ X12 ) @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f679,plain,
! [X15: subst > term > subst > $o] :
( ? [X16: term > $o] :
! [X17: term] :
( ( X15 @ id @ X17 @ id )
= ( X16 @ X17 ) )
=> ! [X17: term] :
( ( X15 @ id @ X17 @ id )
= ( sK524 @ X15 @ X17 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f680,plain,
( ? [X21: subst] :
( ( comp @ id @ X21 )
!= X21 )
=> ( ( comp @ id @ sK525 )
!= sK525 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f681,plain,
( ? [X22: subst] :
( ( comp @ X22 @ id )
!= X22 )
=> ( ( comp @ sK526 @ id )
!= sK526 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f682,plain,
( ? [X24: term] :
( ( sub @ X24 @ id )
!= X24 )
=> ( sK527
!= ( sub @ sK527 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f683,plain,
( ? [X31: term,X32: term,X33: term,X34: term] :
( ( ( ap @ ( sub @ X31 @ id ) @ X34 )
= ( ap @ ( sub @ X33 @ id ) @ X32 ) )
& ( X32 != X34 ) )
=> ( ( ( ap @ ( sub @ sK528 @ id ) @ sK531 )
= ( ap @ ( sub @ sK530 @ id ) @ sK529 ) )
& ( sK529 != sK531 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f684,plain,
( ? [X35: term] :
( ( sub @ X35 @ id )
!= X35 )
=> ( sK532
!= ( sub @ sK532 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f685,plain,
( ? [X37: term] :
! [X38: subst > term > term] :
? [X39: term,X40: subst] :
( ( sub @ X37 @ ( push @ X39 @ X40 ) )
!= ( X38 @ X40 @ X39 ) )
=> ! [X38: subst > term > term] :
? [X40: subst,X39: term] :
( ( X38 @ X40 @ X39 )
!= ( sub @ sK533 @ ( push @ X39 @ X40 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f686,plain,
! [X38: subst > term > term] :
( ? [X40: subst,X39: term] :
( ( X38 @ X40 @ X39 )
!= ( sub @ sK533 @ ( push @ X39 @ X40 ) ) )
=> ( ( sub @ sK533 @ ( push @ ( sK534 @ X38 ) @ ( sK535 @ X38 ) ) )
!= ( X38 @ ( sK535 @ X38 ) @ ( sK534 @ X38 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f687,plain,
! [X41: term] :
( ? [X42: subst > term > term] :
! [X43: term,X44: subst] :
( ( X42 @ X44 @ X43 )
= ( sub @ X41 @ ( push @ X43 @ X44 ) ) )
=> ! [X44: subst,X43: term] :
( ( sK536 @ X41 @ X44 @ X43 )
= ( sub @ X41 @ ( push @ X43 @ X44 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f688,plain,
( ? [X47: term,X48: term] :
( ( X47 != X48 )
& ( ( lam @ X48 )
= ( lam @ X47 ) ) )
=> ( ( sK537 != sK538 )
& ( ( lam @ sK538 )
= ( lam @ sK537 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f689,plain,
( ? [X49: term] :
! [X50: subst > term > term] :
( ( X50 @ sh @ one )
!= ( sub @ X49 @ ( push @ one @ sh ) ) )
=> ! [X50: subst > term > term] :
( ( sub @ sK539 @ ( push @ one @ sh ) )
!= ( X50 @ sh @ one ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f690,plain,
! [X51: term] :
( ? [X52: subst > term > term] :
( ( sub @ X51 @ ( push @ one @ sh ) )
= ( X52 @ sh @ one ) )
=> ( ( sK540 @ X51 @ sh @ one )
= ( sub @ X51 @ ( push @ one @ sh ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f691,plain,
( ? [X58: subst] :
( ( comp @ X58 @ id )
!= X58 )
=> ( sK541
!= ( comp @ sK541 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f692,plain,
( ? [X59: subst,X60: term] :
( ( comp @ sh @ ( push @ X60 @ X59 ) )
!= X59 )
=> ( sK542
!= ( comp @ sh @ ( push @ sK543 @ sK542 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f693,plain,
( ? [X61: term,X62: subst] :
( ( sub @ one @ ( push @ X61 @ X62 ) )
!= X61 )
=> ( sK544
!= ( sub @ one @ ( push @ sK544 @ sK545 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f694,plain,
! [X63: subst,X64: term > $o,X65: term] :
( ? [X66: term > $o] :
! [X67: term] :
( ( X64 @ ( sub @ X67 @ ( push @ X65 @ X63 ) ) )
= ( X66 @ X67 ) )
=> ! [X67: term] :
( ( sK546 @ X65 @ X64 @ X63 @ X67 )
= ( X64 @ ( sub @ X67 @ ( push @ X65 @ X63 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f695,plain,
( ? [X68: subst,X69: term > $o,X70: term] :
! [X71: term > $o] :
? [X72: term] :
( ( X71 @ X72 )
!= ( X69 @ ( sub @ X72 @ ( push @ X70 @ X68 ) ) ) )
=> ! [X71: term > $o] :
? [X72: term] :
( ( X71 @ X72 )
!= ( sK548 @ ( sub @ X72 @ ( push @ sK549 @ sK547 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f696,plain,
! [X71: term > $o] :
( ? [X72: term] :
( ( X71 @ X72 )
!= ( sK548 @ ( sub @ X72 @ ( push @ sK549 @ sK547 ) ) ) )
=> ( ( X71 @ ( sK550 @ X71 ) )
!= ( sK548 @ ( sub @ ( sK550 @ X71 ) @ ( push @ sK549 @ sK547 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f697,plain,
( ? [X74: term] :
( ( sub @ X74 @ id )
!= X74 )
=> ( ( sub @ sK551 @ id )
!= sK551 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f698,plain,
( ? [X75: term > $o,X76: subst,X77: term] :
! [X78: term > $o] :
? [X79: term] :
( ( X78 @ X79 )
!= ( X75 @ ( sub @ X79 @ ( push @ X77 @ X76 ) ) ) )
=> ! [X78: term > $o] :
? [X79: term] :
( ( X78 @ X79 )
!= ( sK552 @ ( sub @ X79 @ ( push @ sK554 @ sK553 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f699,plain,
! [X78: term > $o] :
( ? [X79: term] :
( ( X78 @ X79 )
!= ( sK552 @ ( sub @ X79 @ ( push @ sK554 @ sK553 ) ) ) )
=> ( ( X78 @ ( sK555 @ X78 ) )
!= ( sK552 @ ( sub @ ( sK555 @ X78 ) @ ( push @ sK554 @ sK553 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f700,plain,
! [X80: term > $o,X81: subst,X82: term] :
( ? [X83: term > $o] :
! [X84: term] :
( ( X83 @ X84 )
= ( X80 @ ( sub @ X84 @ ( push @ X82 @ X81 ) ) ) )
=> ! [X84: term] :
( ( sK556 @ X82 @ X81 @ X80 @ X84 )
= ( X80 @ ( sub @ X84 @ ( push @ X82 @ X81 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f701,plain,
! [X85: subst > term > term] :
( ? [X88: subst,X89: term,X90: subst] :
( ( sub @ ( X85 @ X90 @ X89 ) @ X88 )
!= ( X85 @ ( comp @ X90 @ X88 ) @ ( sub @ X89 @ X88 ) ) )
=> ( ( sub @ ( X85 @ ( sK559 @ X85 ) @ ( sK558 @ X85 ) ) @ ( sK557 @ X85 ) )
!= ( X85 @ ( comp @ ( sK559 @ X85 ) @ ( sK557 @ X85 ) ) @ ( sub @ ( sK558 @ X85 ) @ ( sK557 @ X85 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f702,plain,
( ? [X91: subst > term > term,X92: term,X93: term] :
( ( ( lam @ ( X91 @ sh @ one ) )
= ( ap @ ( sub @ X92 @ id ) @ X93 ) )
& ! [X94: subst,X95: term,X96: subst] :
( ( sub @ ( X91 @ X96 @ X95 ) @ X94 )
= ( X91 @ ( comp @ X96 @ X94 ) @ ( sub @ X95 @ X94 ) ) ) )
=> ( ( ( lam @ ( sK560 @ sh @ one ) )
= ( ap @ ( sub @ sK561 @ id ) @ sK562 ) )
& ! [X96: subst,X95: term,X94: subst] :
( ( sub @ ( sK560 @ X96 @ X95 ) @ X94 )
= ( sK560 @ ( comp @ X96 @ X94 ) @ ( sub @ X95 @ X94 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f703,plain,
! [X97: term] :
( ? [X98: d_term] :
( ( d2term @ X98 )
= X97 )
=> ( ( d2term @ ( sK563 @ X97 ) )
= X97 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f704,plain,
( ? [X101: term,X102: term] :
( ( X101 != X102 )
& ( ( sub @ X101 @ sh )
= ( sub @ X102 @ sh ) ) )
=> ( ( sK564 != sK565 )
& ( ( sub @ sK564 @ sh )
= ( sub @ sK565 @ sh ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f705,plain,
( ? [X105: term,X106: subst] :
( ( comp @ sh @ ( push @ X105 @ X106 ) )
!= X106 )
=> ( ( comp @ sh @ ( push @ sK566 @ sK567 ) )
!= sK567 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f706,plain,
( ? [X109: term] :
! [X110: subst > term > term] :
? [X111: term,X112: subst] :
( ( X110 @ X112 @ X111 )
!= ( sub @ X109 @ ( push @ X111 @ X112 ) ) )
=> ! [X110: subst > term > term] :
? [X112: subst,X111: term] :
( ( sub @ sK568 @ ( push @ X111 @ X112 ) )
!= ( X110 @ X112 @ X111 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f707,plain,
! [X110: subst > term > term] :
( ? [X112: subst,X111: term] :
( ( sub @ sK568 @ ( push @ X111 @ X112 ) )
!= ( X110 @ X112 @ X111 ) )
=> ( ( sub @ sK568 @ ( push @ ( sK569 @ X110 ) @ ( sK570 @ X110 ) ) )
!= ( X110 @ ( sK570 @ X110 ) @ ( sK569 @ X110 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f708,plain,
! [X113: term] :
( ? [X114: subst > term > term] :
! [X115: term,X116: subst] :
( ( X114 @ X116 @ X115 )
= ( sub @ X113 @ ( push @ X115 @ X116 ) ) )
=> ! [X116: subst,X115: term] :
( ( sK571 @ X113 @ X116 @ X115 )
= ( sub @ X113 @ ( push @ X115 @ X116 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f709,plain,
! [X117: term] :
( ? [X118: subst > term > term] :
( ( X118 @ sh @ one )
= ( sub @ X117 @ ( push @ one @ sh ) ) )
=> ( ( sK572 @ X117 @ sh @ one )
= ( sub @ X117 @ ( push @ one @ sh ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f710,plain,
( ? [X119: term] :
! [X120: subst > term > term] :
( ( X120 @ sh @ one )
!= ( sub @ X119 @ ( push @ one @ sh ) ) )
=> ! [X120: subst > term > term] :
( ( X120 @ sh @ one )
!= ( sub @ sK573 @ ( push @ one @ sh ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f711,plain,
! [X122: subst > term > term] :
( ? [X125: subst,X126: subst,X127: term] :
( ( X122 @ ( comp @ X126 @ X125 ) @ ( sub @ X127 @ X125 ) )
!= ( sub @ ( X122 @ X126 @ X127 ) @ X125 ) )
=> ( ( X122 @ ( comp @ ( sK575 @ X122 ) @ ( sK574 @ X122 ) ) @ ( sub @ ( sK576 @ X122 ) @ ( sK574 @ X122 ) ) )
!= ( sub @ ( X122 @ ( sK575 @ X122 ) @ ( sK576 @ X122 ) ) @ ( sK574 @ X122 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f712,plain,
! [X124: subst > term > term] :
( ? [X128: term,X129: subst,X130: subst] :
( ( sub @ ( X124 @ X129 @ X128 ) @ X130 )
!= ( X124 @ ( comp @ X129 @ X130 ) @ ( sub @ X128 @ X130 ) ) )
=> ( ( sub @ ( X124 @ ( sK578 @ X124 ) @ ( sK577 @ X124 ) ) @ ( sK579 @ X124 ) )
!= ( X124 @ ( comp @ ( sK578 @ X124 ) @ ( sK579 @ X124 ) ) @ ( sub @ ( sK577 @ X124 ) @ ( sK579 @ X124 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f713,plain,
( ? [X131: subst,X132: subst > term > term,X133: term,X134: subst > term > term] :
( ! [X135: subst,X136: subst,X137: term] :
( ( X132 @ ( comp @ X136 @ X135 ) @ ( sub @ X137 @ X135 ) )
= ( sub @ ( X132 @ X136 @ X137 ) @ X135 ) )
& ( ( lam @ ( X132 @ sh @ one ) )
= ( lam @ ( X134 @ sh @ one ) ) )
& ! [X138: term,X139: subst,X140: subst] :
( ( X134 @ ( comp @ X139 @ X140 ) @ ( sub @ X138 @ X140 ) )
= ( sub @ ( X134 @ X139 @ X138 ) @ X140 ) )
& ( ( X132 @ X131 @ X133 )
!= ( X134 @ X131 @ X133 ) ) )
=> ( ! [X137: term,X136: subst,X135: subst] :
( ( sK581 @ ( comp @ X136 @ X135 ) @ ( sub @ X137 @ X135 ) )
= ( sub @ ( sK581 @ X136 @ X137 ) @ X135 ) )
& ( ( lam @ ( sK583 @ sh @ one ) )
= ( lam @ ( sK581 @ sh @ one ) ) )
& ! [X140: subst,X139: subst,X138: term] :
( ( sub @ ( sK583 @ X139 @ X138 ) @ X140 )
= ( sK583 @ ( comp @ X139 @ X140 ) @ ( sub @ X138 @ X140 ) ) )
& ( ( sK583 @ sK580 @ sK582 )
!= ( sK581 @ sK580 @ sK582 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f714,plain,
( ? [X145: term,X146: term,X147: term,X148: term] :
( ( ( ap @ X147 @ X148 )
= ( ap @ X146 @ X145 ) )
& ( X145 != X148 ) )
=> ( ( ( ap @ sK586 @ sK587 )
= ( ap @ sK585 @ sK584 ) )
& ( sK587 != sK584 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f715,plain,
( ? [X149: term] :
( ( sub @ X149 @ id )
!= X149 )
=> ( ( sub @ sK588 @ id )
!= sK588 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f716,plain,
( ? [X150: term] :
! [X151: subst > term > term] :
? [X152: subst,X153: term] :
( ( sub @ X150 @ ( push @ X153 @ X152 ) )
!= ( X151 @ X152 @ X153 ) )
=> ! [X151: subst > term > term] :
? [X153: term,X152: subst] :
( ( sub @ sK589 @ ( push @ X153 @ X152 ) )
!= ( X151 @ X152 @ X153 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f717,plain,
! [X151: subst > term > term] :
( ? [X153: term,X152: subst] :
( ( sub @ sK589 @ ( push @ X153 @ X152 ) )
!= ( X151 @ X152 @ X153 ) )
=> ( ( sub @ sK589 @ ( push @ ( sK591 @ X151 ) @ ( sK590 @ X151 ) ) )
!= ( X151 @ ( sK590 @ X151 ) @ ( sK591 @ X151 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f718,plain,
! [X155: term] :
( ? [X156: subst > term > term] :
! [X157: subst,X158: term] :
( ( X156 @ X157 @ X158 )
= ( sub @ X155 @ ( push @ X158 @ X157 ) ) )
=> ! [X158: term,X157: subst] :
( ( sK592 @ X155 @ X157 @ X158 )
= ( sub @ X155 @ ( push @ X158 @ X157 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f719,plain,
( ? [X159: subst,X160: term] :
( ( comp @ sh @ ( push @ X160 @ X159 ) )
!= X159 )
=> ( ( comp @ sh @ ( push @ sK594 @ sK593 ) )
!= sK593 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f720,plain,
( ? [X161: term,X162: subst] :
( ( sub @ one @ ( push @ X161 @ X162 ) )
!= X161 )
=> ( ( sub @ one @ ( push @ sK595 @ sK596 ) )
!= sK595 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f721,plain,
( ? [X172: term,X173: term > $o,X174: subst,X175: term,X176: term > $o] :
( ( $true
!= ( X176 @ ( sub @ X172 @ ( push @ X175 @ X174 ) ) ) )
& ( ( X173 @ X172 )
= $true ) )
=> ( ( ( sK601 @ ( sub @ sK597 @ ( push @ sK600 @ sK599 ) ) )
!= $true )
& ( $true
= ( sK598 @ sK597 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f722,plain,
( ? [X177: term] :
( ( sub @ X177 @ id )
!= X177 )
=> ( ( sub @ sK602 @ id )
!= sK602 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f723,plain,
! [X179: subst,X180: term > $o,X181: term > $o,X182: term] :
( ? [X183: term] :
( ( X181 @ X183 )
!= ( X180 @ ( sub @ X183 @ ( push @ X182 @ X179 ) ) ) )
=> ( ( X180 @ ( sub @ ( sK603 @ X182 @ X181 @ X180 @ X179 ) @ ( push @ X182 @ X179 ) ) )
!= ( X181 @ ( sK603 @ X182 @ X181 @ X180 @ X179 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f724,plain,
( ? [X184: subst,X185: term > $o,X186: term > $o,X187: term] :
( ! [X188: term] :
( ( X185 @ ( sub @ X188 @ ( push @ X187 @ X184 ) ) )
= ( X186 @ X188 ) )
& ( $true
!= ( X186 @ one ) )
& ( ( X185 @ X187 )
= $true ) )
=> ( ! [X188: term] :
( ( sK605 @ ( sub @ X188 @ ( push @ sK607 @ sK604 ) ) )
= ( sK606 @ X188 ) )
& ( $true
!= ( sK606 @ one ) )
& ( $true
= ( sK605 @ sK607 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f725,plain,
! [X189: subst > term > subst > $o] :
( ? [X190: term > $o] :
! [X191: term] :
( ( X190 @ X191 )
= ( X189 @ id @ X191 @ id ) )
=> ! [X191: term] :
( ( X189 @ id @ X191 @ id )
= ( sK608 @ X189 @ X191 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f726,plain,
( ? [X192: subst > term > subst > $o] :
! [X193: term > $o] :
? [X194: term] :
( ( X193 @ X194 )
!= ( X192 @ id @ X194 @ id ) )
=> ! [X193: term > $o] :
? [X194: term] :
( ( X193 @ X194 )
!= ( sK609 @ id @ X194 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f727,plain,
! [X193: term > $o] :
( ? [X194: term] :
( ( X193 @ X194 )
!= ( sK609 @ id @ X194 @ id ) )
=> ( ( sK609 @ id @ ( sK610 @ X193 ) @ id )
!= ( X193 @ ( sK610 @ X193 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f728,plain,
( ? [X195: term,X196: subst,X197: term > $o,X198: term > $o] :
( ! [X199: term] :
( ( X198 @ X199 )
= ( X197 @ ( sub @ X199 @ ( push @ X195 @ X196 ) ) ) )
& ( $true
!= ( X198 @ one ) )
& ( ( X197 @ X195 )
= $true ) )
=> ( ! [X199: term] :
( ( sK614 @ X199 )
= ( sK613 @ ( sub @ X199 @ ( push @ sK611 @ sK612 ) ) ) )
& ( $true
!= ( sK614 @ one ) )
& ( $true
= ( sK613 @ sK611 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f729,plain,
! [X202: term,X203: subst,X204: term > $o,X205: term > $o] :
( ? [X206: term] :
( ( X205 @ X206 )
!= ( X204 @ ( sub @ X206 @ ( push @ X202 @ X203 ) ) ) )
=> ( ( X204 @ ( sub @ ( sK615 @ X205 @ X204 @ X203 @ X202 ) @ ( push @ X202 @ X203 ) ) )
!= ( X205 @ ( sK615 @ X205 @ X204 @ X203 @ X202 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f730,plain,
( ? [X207: term,X208: subst] :
( ( sub @ one @ ( push @ X207 @ X208 ) )
!= X207 )
=> ( sK616
!= ( sub @ one @ ( push @ sK616 @ sK617 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f731,plain,
( ? [X209: term] :
( ( sub @ X209 @ id )
!= X209 )
=> ( ( sub @ sK618 @ id )
!= sK618 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f732,plain,
( ? [X211: term,X212: term,X213: term,X214: term] :
( ( ( ap @ ( sub @ X213 @ id ) @ X212 )
= ( ap @ ( sub @ X214 @ id ) @ X211 ) )
& ( X213 != X214 ) )
=> ( ( ( ap @ ( sub @ sK622 @ id ) @ sK619 )
= ( ap @ ( sub @ sK621 @ id ) @ sK620 ) )
& ( sK621 != sK622 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f733,plain,
( ? [X219: subst] :
( ( push @ ( sub @ one @ X219 ) @ ( comp @ sh @ X219 ) )
!= X219 )
=> ( sK623
!= ( push @ ( sub @ one @ sK623 ) @ ( comp @ sh @ sK623 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f734,plain,
( ? [X221: term,X222: subst > term > subst > $o] :
( ( ( X222 @ id @ X221 @ id )
!= $true )
& ( $true
!= ( sP17 @ X222 ) )
& ( ( sP16 @ X222 )
!= $true ) )
=> ( ( ( sK625 @ id @ sK624 @ id )
!= $true )
& ( ( sP17 @ sK625 )
!= $true )
& ( ( sP16 @ sK625 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f735,plain,
( ? [X225: term] :
( ( sub @ X225 @ id )
!= X225 )
=> ( sK626
!= ( sub @ sK626 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f736,plain,
( ? [X229: term] :
( ( sub @ X229 @ id )
!= X229 )
=> ( sK627
!= ( sub @ sK627 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f737,plain,
( ? [X230: term] :
( ( sub @ X230 @ id )
!= X230 )
=> ( ( sub @ sK628 @ id )
!= sK628 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f738,plain,
( ? [X232: term,X233: term,X234: term > $o,X235: subst,X236: term > $o] :
( ( $true
= ( X236 @ X233 ) )
& ( $true
!= ( X234 @ ( sub @ X233 @ ( push @ X232 @ X235 ) ) ) ) )
=> ( ( ( sK633 @ sK630 )
= $true )
& ( $true
!= ( sK631 @ ( sub @ sK630 @ ( push @ sK629 @ sK632 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f739,plain,
( ? [X242: subst,X243: term] :
( ( sub @ one @ ( push @ X243 @ X242 ) )
!= X243 )
=> ( ( sub @ one @ ( push @ sK635 @ sK634 ) )
!= sK635 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f740,plain,
! [X247: subst > term > subst > $o] :
( ? [X248: term > $o] :
! [X249: term] :
( ( X248 @ X249 )
= ( X247 @ id @ X249 @ id ) )
=> ! [X249: term] :
( ( sK636 @ X247 @ X249 )
= ( X247 @ id @ X249 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f741,plain,
( ? [X250: term] :
( ( sub @ X250 @ id )
!= X250 )
=> ( ( sub @ sK637 @ id )
!= sK637 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f742,plain,
( ? [X251: subst > term > subst > $o] :
! [X252: term > $o] :
? [X253: term] :
( ( X251 @ id @ X253 @ id )
!= ( X252 @ X253 ) )
=> ! [X252: term > $o] :
? [X253: term] :
( ( sK638 @ id @ X253 @ id )
!= ( X252 @ X253 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f743,plain,
! [X252: term > $o] :
( ? [X253: term] :
( ( sK638 @ id @ X253 @ id )
!= ( X252 @ X253 ) )
=> ( ( X252 @ ( sK639 @ X252 ) )
!= ( sK638 @ id @ ( sK639 @ X252 ) @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f744,plain,
( ? [X255: subst] :
( ( comp @ id @ X255 )
!= X255 )
=> ( sK640
!= ( comp @ id @ sK640 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f745,plain,
( ? [X256: subst > term > subst > $o] :
! [X257: term > $o] :
? [X258: term] :
( ( X257 @ X258 )
!= ( X256 @ id @ X258 @ id ) )
=> ! [X257: term > $o] :
? [X258: term] :
( ( X257 @ X258 )
!= ( sK641 @ id @ X258 @ id ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f746,plain,
! [X257: term > $o] :
( ? [X258: term] :
( ( X257 @ X258 )
!= ( sK641 @ id @ X258 @ id ) )
=> ( ( sK641 @ id @ ( sK642 @ X257 ) @ id )
!= ( X257 @ ( sK642 @ X257 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f747,plain,
! [X259: subst > term > subst > $o] :
( ? [X260: term > $o] :
! [X261: term] :
( ( X259 @ id @ X261 @ id )
= ( X260 @ X261 ) )
=> ! [X261: term] :
( ( X259 @ id @ X261 @ id )
= ( sK643 @ X259 @ X261 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f748,plain,
! [X262: subst] :
( ? [X263: d_subst] :
( ( d2subst @ X263 )
= X262 )
=> ( ( d2subst @ ( sK644 @ X262 ) )
= X262 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f673,plain,
( ( hoasapnotvar = $true )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( apinj1 = $true )
| ? [X0: term,X1: term,X2: term,X3: term] :
( ( X1 != X3 )
& ( ( ap @ X1 @ X0 )
= ( ap @ X3 @ X2 ) ) ) )
& ( ! [X4: term,X5: term,X6: term,X7: term] :
( ( X5 = X7 )
| ( ( ap @ X5 @ X4 )
!= ( ap @ X7 @ X6 ) ) )
| ( apinj1 != $true ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( hoaslamnotvar_gthm = $true )
& ( ! [X8: subst] :
( ( comp @ X8 @ id )
= X8 )
| ( axidr != $true ) )
& ( ( axidr = $true )
| ? [X9: subst] :
( ( comp @ X9 @ id )
!= X9 ) )
& ( termmset_gthm = $true )
& ( ( sP108 = $true )
| ? [X10: term] :
( ( sub @ X10 @ id )
!= X10 )
| ? [X11: subst > term > subst > $o] :
! [X12: term > $o] :
? [X13: term] :
( ( X12 @ X13 )
!= ( X11 @ id @ X13 @ id ) )
| ( sP109 = $true )
| ( sP107 = $true )
| ( hoasinduction_no_psi_cond_lthm != $true ) )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
| ( ( sP108 != $true )
& ! [X14: term] :
( ( sub @ X14 @ id )
= X14 )
& ! [X15: subst > term > subst > $o] :
? [X16: term > $o] :
! [X17: term] :
( ( X15 @ id @ X17 @ id )
= ( X16 @ X17 ) )
& ( sP109 != $true )
& ( sP107 != $true ) ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ! [X18: d_subst] : ( d_id = X18 )
& ( ( ! [X19: subst] :
( ( comp @ id @ X19 )
= X19 )
& ! [X20: subst] :
( ( comp @ X20 @ id )
= X20 ) )
| ( substmonoid != $true ) )
& ( ( substmonoid = $true )
| ? [X21: subst] :
( ( comp @ id @ X21 )
!= X21 )
| ? [X22: subst] :
( ( comp @ X22 @ id )
!= X22 ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( one
= ( d2term @ d_one ) )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ( sP100 = $true )
| ( hoasinduction_lem3aa_lthm != $true ) )
& ( ( hoasinduction_lem3aa_lthm = $true )
| ( sP100 != $true ) )
& ( ( induction = $true )
| ( sP98 != $true ) )
& ( ( sP98 = $true )
| ( induction != $true ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
| ( ! [X23: term] :
( ( sub @ X23 @ id )
= X23 )
& ( $true != sP95 ) ) )
& ( ? [X24: term] :
( ( sub @ X24 @ id )
!= X24 )
| ( $true = sP95 )
| ( hoasinduction_lem3v2_lthm != $true ) )
& ( pushprop_lthm_orig = $true )
& ( hoaslamnotvar_lthm = $true )
& ( hoaslamnotap_lthm = $true )
& ! [X25: d_term,X26: d_term] :
( ( ( d2term @ X25 )
!= ( d2term @ X26 ) )
| ( X25 = X26 ) )
& ( hoaslamnotvar = $true )
& ( ( hoasinduction_lem2 = $true )
| ( $true != sP91 ) )
& ( ( $true = sP91 )
| ( hoasinduction_lem2 != $true ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( axabs = $true )
& ( ! [X27: term,X28: term,X29: term,X30: term] :
( ( ( ap @ ( sub @ X27 @ id ) @ X30 )
!= ( ap @ ( sub @ X29 @ id ) @ X28 ) )
| ( X28 = X30 ) )
| ( hoasapinj2 != $true ) )
& ( ( hoasapinj2 = $true )
| ? [X31: term,X32: term,X33: term,X34: term] :
( ( ( ap @ ( sub @ X31 @ id ) @ X34 )
= ( ap @ ( sub @ X33 @ id ) @ X32 ) )
& ( X32 != X34 ) ) )
& ( ( induction2 = $true )
| ( sP88 != $true ) )
& ( ( sP88 = $true )
| ( induction2 != $true ) )
& ( induction2_gthm = $true )
& ( ( $true = sP85 )
| ( induction2lem != $true ) )
& ( ( induction2lem = $true )
| ( $true != sP85 ) )
& ( hoasinduction_lem1v2_gthm = $true )
& ( ( sP81 = $true )
| ? [X35: term] :
( ( sub @ X35 @ id )
!= X35 )
| ( $true = sP82 )
| ( induction2_lthm != $true ) )
& ( ( induction2_lthm = $true )
| ( ( sP81 != $true )
& ! [X36: term] :
( ( sub @ X36 @ id )
= X36 )
& ( $true != sP82 ) ) )
& ( hoasapnotvar_lthm = $true )
& ( ( hoasinduction_lem3v2_f = $true )
| ? [X37: term] :
! [X38: subst > term > term] :
? [X39: term,X40: subst] :
( ( sub @ X37 @ ( push @ X39 @ X40 ) )
!= ( X38 @ X40 @ X39 ) ) )
& ( ! [X41: term] :
? [X42: subst > term > term] :
! [X43: term,X44: subst] :
( ( X42 @ X44 @ X43 )
= ( sub @ X41 @ ( push @ X43 @ X44 ) ) )
| ( hoasinduction_lem3v2_f != $true ) )
& ( axclos = $true )
& ( ! [X45: term,X46: term] :
( ( X45 = X46 )
| ( ( lam @ X46 )
!= ( lam @ X45 ) ) )
| ( laminj != $true ) )
& ( ( laminj = $true )
| ? [X47: term,X48: term] :
( ( X47 != X48 )
& ( ( lam @ X48 )
= ( lam @ X47 ) ) ) )
& ( pushprop_lem3v2_lthm = $true )
& ( axassoc = $true )
& ( ulamvar1 != $true )
& ( ( hoasinduction_lem3b_lthm = $true )
| ? [X49: term] :
! [X50: subst > term > term] :
( ( X50 @ sh @ one )
!= ( sub @ X49 @ ( push @ one @ sh ) ) ) )
& ( ! [X51: term] :
? [X52: subst > term > term] :
( ( sub @ X51 @ ( push @ one @ sh ) )
= ( X52 @ sh @ one ) )
| ( hoasinduction_lem3b_lthm != $true ) )
& ( ( sP72 = $true )
| ( $true = sP75 )
| ( sP74 = $true )
| ( $true = sP73 )
| ( hoasinduction_lthm != $true ) )
& ( ( hoasinduction_lthm = $true )
| ( ( sP72 != $true )
& ( $true != sP75 )
& ( sP74 != $true )
& ( $true != sP73 ) ) )
& ( ( induction2lem_lthm = $true )
| ( ( sP60 != $true )
& ( sP59 != $true )
& ! [X53: subst] :
( ( comp @ X53 @ id )
= X53 )
& ! [X54: subst,X55: term] :
( ( comp @ sh @ ( push @ X55 @ X54 ) )
= X54 )
& ! [X56: term,X57: subst] :
( ( sub @ one @ ( push @ X56 @ X57 ) )
= X56 ) ) )
& ( ( sP60 = $true )
| ( sP59 = $true )
| ? [X58: subst] :
( ( comp @ X58 @ id )
!= X58 )
| ? [X59: subst,X60: term] :
( ( comp @ sh @ ( push @ X60 @ X59 ) )
!= X59 )
| ? [X61: term,X62: subst] :
( ( sub @ one @ ( push @ X61 @ X62 ) )
!= X61 )
| ( induction2lem_lthm != $true ) )
& ( ! [X63: subst,X64: term > $o,X65: term] :
? [X66: term > $o] :
! [X67: term] :
( ( X64 @ ( sub @ X67 @ ( push @ X65 @ X63 ) ) )
= ( X66 @ X67 ) )
| ( pushprop_lem0_lthm != $true ) )
& ( ( pushprop_lem0_lthm = $true )
| ? [X68: subst,X69: term > $o,X70: term] :
! [X71: term > $o] :
? [X72: term] :
( ( X71 @ X72 )
!= ( X69 @ ( sub @ X72 @ ( push @ X70 @ X68 ) ) ) ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) )
= ( Y3 @ Y4 ) ) ) ) )
& ( apnotvar = $true )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( hoasinduction_gthm = $true )
& ( axapp = $true )
& ( ( hoasinduction_lem3_lthm = $true )
| ( ( sP54 != $true )
& ! [X73: term] :
( ( sub @ X73 @ id )
= X73 )
& ( $true != sP53 ) ) )
& ( ( sP54 = $true )
| ? [X74: term] :
( ( sub @ X74 @ id )
!= X74 )
| ( $true = sP53 )
| ( hoasinduction_lem3_lthm != $true ) )
& ( ( pushprop_lem0 = $true )
| ? [X75: term > $o,X76: subst,X77: term] :
! [X78: term > $o] :
? [X79: term] :
( ( X78 @ X79 )
!= ( X75 @ ( sub @ X79 @ ( push @ X77 @ X76 ) ) ) ) )
& ( ! [X80: term > $o,X81: subst,X82: term] :
? [X83: term > $o] :
! [X84: term] :
( ( X83 @ X84 )
= ( X80 @ ( sub @ X84 @ ( push @ X82 @ X81 ) ) ) )
| ( pushprop_lem0 != $true ) )
& ( induction2lem_gthm = $true )
& ( ( $true = sP48 )
| ( hoasinduction_lem2v2 != $true ) )
& ( ( hoasinduction_lem2v2 = $true )
| ( $true != sP48 ) )
& ( ( hoasinduction_lem3aaa = $true )
| ( $true != sP45 ) )
& ( ( $true = sP45 )
| ( hoasinduction_lem3aaa != $true ) )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ( hoasinduction_lem3a = $true )
| ( $true != sP43 ) )
& ( ( $true = sP43 )
| ( hoasinduction_lem3a != $true ) )
& ( ! [X85: subst > term > term,X86: term,X87: term] :
( ( ( ap @ ( sub @ X86 @ id ) @ X87 )
!= ( lam @ ( X85 @ sh @ one ) ) )
| ? [X88: subst,X89: term,X90: subst] :
( ( sub @ ( X85 @ X90 @ X89 ) @ X88 )
!= ( X85 @ ( comp @ X90 @ X88 ) @ ( sub @ X89 @ X88 ) ) ) )
| ( hoaslamnotap != $true ) )
& ( ( hoaslamnotap = $true )
| ? [X91: subst > term > term,X92: term,X93: term] :
( ( ( lam @ ( X91 @ sh @ one ) )
= ( ap @ ( sub @ X92 @ id ) @ X93 ) )
& ! [X94: subst,X95: term,X96: subst] :
( ( sub @ ( X91 @ X96 @ X95 ) @ X94 )
= ( X91 @ ( comp @ X96 @ X94 ) @ ( sub @ X95 @ X94 ) ) ) ) )
& ( hoasinduction_lem1 = $true )
& ( pushprop_lem2v2_gthm = $true )
& ! [X97: term] :
? [X98: d_term] :
( ( d2term @ X98 )
= X97 )
& ( ( sP41 = $true )
| ( hoasapinj2_lthm != $true ) )
& ( ( hoasapinj2_lthm = $true )
| ( sP41 != $true ) )
& ( lamnotvar = $true )
& ( axvarshift = $true )
& ( hoasinduction_lem3b_gthm = $true )
& ( pushprop = $true )
& ! [X99: d_subst,X100: d_subst] :
( ( X99 = X100 )
| ( ( d2subst @ X100 )
!= ( d2subst @ X99 ) ) )
& ( ulamvarind = $true )
& ( substmonoid_gthm = $true )
& ( hoasinduction_lem2_lthm = $true )
& ( pushprop_lem2v2_lthm = $true )
& ( ( shinj = $true )
| ? [X101: term,X102: term] :
( ( X101 != X102 )
& ( ( sub @ X101 @ sh )
= ( sub @ X102 @ sh ) ) ) )
& ( ! [X103: term,X104: term] :
( ( X103 = X104 )
| ( ( sub @ X104 @ sh )
!= ( sub @ X103 @ sh ) ) )
| ( shinj != $true ) )
& ( ( axshiftcons = $true )
| ? [X105: term,X106: subst] :
( ( comp @ sh @ ( push @ X105 @ X106 ) )
!= X106 ) )
& ( ! [X107: term,X108: subst] :
( ( comp @ sh @ ( push @ X107 @ X108 ) )
= X108 )
| ( axshiftcons != $true ) )
& ( hoasapinj1_gthm = $true )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( hoasinduction_lem1_lthm = $true )
& ( ( sP39 = $true )
| ( hoasinduction_lem3v2 != $true ) )
& ( ( hoasinduction_lem3v2 = $true )
| ( sP39 != $true ) )
& ( ( hoasinduction_lem3v2_f_lthm = $true )
| ? [X109: term] :
! [X110: subst > term > term] :
? [X111: term,X112: subst] :
( ( X110 @ X112 @ X111 )
!= ( sub @ X109 @ ( push @ X111 @ X112 ) ) ) )
& ( ! [X113: term] :
? [X114: subst > term > term] :
! [X115: term,X116: subst] :
( ( X114 @ X116 @ X115 )
= ( sub @ X113 @ ( push @ X115 @ X116 ) ) )
| ( hoasinduction_lem3v2_f_lthm != $true ) )
& ( ( d2subst @ d_id )
= id )
& ( pushprop_lem1v2_gthm = $true )
& ( ! [X117: term] :
? [X118: subst > term > term] :
( ( X118 @ sh @ one )
= ( sub @ X117 @ ( push @ one @ sh ) ) )
| ( hoasinduction_lem3b != $true ) )
& ( ( hoasinduction_lem3b = $true )
| ? [X119: term] :
! [X120: subst > term > term] :
( ( X120 @ sh @ one )
!= ( sub @ X119 @ ( push @ one @ sh ) ) ) )
& ( ( sP35 = $true )
| ( hoaslaminj_lthm != $true ) )
& ( ( hoaslaminj_lthm = $true )
| ( sP35 != $true ) )
& ( ! [X121: subst,X122: subst > term > term,X123: term,X124: subst > term > term] :
( ? [X125: subst,X126: subst,X127: term] :
( ( X122 @ ( comp @ X126 @ X125 ) @ ( sub @ X127 @ X125 ) )
!= ( sub @ ( X122 @ X126 @ X127 ) @ X125 ) )
| ( ( lam @ ( X124 @ sh @ one ) )
!= ( lam @ ( X122 @ sh @ one ) ) )
| ? [X128: term,X129: subst,X130: subst] :
( ( sub @ ( X124 @ X129 @ X128 ) @ X130 )
!= ( X124 @ ( comp @ X129 @ X130 ) @ ( sub @ X128 @ X130 ) ) )
| ( ( X124 @ X121 @ X123 )
= ( X122 @ X121 @ X123 ) ) )
| ( hoaslaminj != $true ) )
& ( ( hoaslaminj = $true )
| ? [X131: subst,X132: subst > term > term,X133: term,X134: subst > term > term] :
( ! [X135: subst,X136: subst,X137: term] :
( ( X132 @ ( comp @ X136 @ X135 ) @ ( sub @ X137 @ X135 ) )
= ( sub @ ( X132 @ X136 @ X137 ) @ X135 ) )
& ( ( lam @ ( X132 @ sh @ one ) )
= ( lam @ ( X134 @ sh @ one ) ) )
& ! [X138: term,X139: subst,X140: subst] :
( ( X134 @ ( comp @ X139 @ X140 ) @ ( sub @ X138 @ X140 ) )
= ( sub @ ( X134 @ X139 @ X138 ) @ X140 ) )
& ( ( X132 @ X131 @ X133 )
!= ( X134 @ X131 @ X133 ) ) ) )
& ( hoaslamnotap_gthm = $true )
& ( ( substmonoid_lthm = $true )
| ( $true != sP33 ) )
& ( ( $true = sP33 )
| ( substmonoid_lthm != $true ) )
& ( ! [X141: term,X142: term,X143: term,X144: term] :
( ( ( ap @ X142 @ X141 )
!= ( ap @ X143 @ X144 ) )
| ( X141 = X144 ) )
| ( apinj2 != $true ) )
& ( ( apinj2 = $true )
| ? [X145: term,X146: term,X147: term,X148: term] :
( ( ( ap @ X147 @ X148 )
= ( ap @ X146 @ X145 ) )
& ( X145 != X148 ) ) )
& ( hoasinduction_lem2_gthm = $true )
& ( pushprop_lem3v2 = $true )
& ( pushprop_lem1_gthm = $true )
& ( ( hoasapinj1_lthm = $true )
| ( $true != sP32 ) )
& ( ( $true = sP32 )
| ( hoasapinj1_lthm != $true ) )
& ( ( $true = sP30 )
| ? [X149: term] :
( ( sub @ X149 @ id )
!= X149 )
| ? [X150: term] :
! [X151: subst > term > term] :
? [X152: subst,X153: term] :
( ( sub @ X150 @ ( push @ X153 @ X152 ) )
!= ( X151 @ X152 @ X153 ) )
| ( hoasinduction_lem3v2a_lthm != $true ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
| ( ( $true != sP30 )
& ! [X154: term] :
( ( sub @ X154 @ id )
= X154 )
& ! [X155: term] :
? [X156: subst > term > term] :
! [X157: subst,X158: term] :
( ( X156 @ X157 @ X158 )
= ( sub @ X155 @ ( push @ X158 @ X157 ) ) ) ) )
& ( ? [X159: subst,X160: term] :
( ( comp @ sh @ ( push @ X160 @ X159 ) )
!= X159 )
| ? [X161: term,X162: subst] :
( ( sub @ one @ ( push @ X161 @ X162 ) )
!= X161 )
| ! [X163: term,X164: term > $o,X165: subst,X166: term,X167: term > $o] :
( ( ( X167 @ ( sub @ X163 @ ( push @ X166 @ X165 ) ) )
= $true )
| ( $true
!= ( X164 @ X163 ) ) )
| ( pushprop_lem1_lthm != $true ) )
& ( ( pushprop_lem1_lthm = $true )
| ( ! [X168: subst,X169: term] :
( ( comp @ sh @ ( push @ X169 @ X168 ) )
= X168 )
& ! [X170: term,X171: subst] :
( ( sub @ one @ ( push @ X170 @ X171 ) )
= X170 )
& ? [X172: term,X173: term > $o,X174: subst,X175: term,X176: term > $o] :
( ( $true
!= ( X176 @ ( sub @ X172 @ ( push @ X175 @ X174 ) ) ) )
& ( ( X173 @ X172 )
= $true ) ) ) )
& ( ( $true = sP27 )
| ( $true = sP28 )
| ? [X177: term] :
( ( sub @ X177 @ id )
!= X177 )
| ( hoasinduction_lem3a_lthm != $true ) )
& ( ( hoasinduction_lem3a_lthm = $true )
| ( ( $true != sP27 )
& ( $true != sP28 )
& ! [X178: term] :
( ( sub @ X178 @ id )
= X178 ) ) )
& ( hoasinduction_lem1v2 = $true )
& ( ! [X179: subst,X180: term > $o,X181: term > $o,X182: term] :
( ? [X183: term] :
( ( X181 @ X183 )
!= ( X180 @ ( sub @ X183 @ ( push @ X182 @ X179 ) ) ) )
| ( ( X181 @ one )
= $true )
| ( $true
!= ( X180 @ X182 ) ) )
| ( pushprop_lem1v2 != $true ) )
& ( ( pushprop_lem1v2 = $true )
| ? [X184: subst,X185: term > $o,X186: term > $o,X187: term] :
( ! [X188: term] :
( ( X185 @ ( sub @ X188 @ ( push @ X187 @ X184 ) ) )
= ( X186 @ X188 ) )
& ( $true
!= ( X186 @ one ) )
& ( ( X185 @ X187 )
= $true ) ) )
& ( lamnotap != $true )
& ( hoasapnotvar_gthm = $true )
& ( ! [X189: subst > term > subst > $o] :
? [X190: term > $o] :
! [X191: term] :
( ( X190 @ X191 )
= ( X189 @ id @ X191 @ id ) )
| ( hoasinduction_lem0_lthm != $true ) )
& ( ( hoasinduction_lem0_lthm = $true )
| ? [X192: subst > term > subst > $o] :
! [X193: term > $o] :
? [X194: term] :
( ( X193 @ X194 )
!= ( X192 @ id @ X194 @ id ) ) )
& ( ( d2subst @ d_id )
= sh )
& ( ( pushprop_lem1v2_lthm = $true )
| ( ? [X195: term,X196: subst,X197: term > $o,X198: term > $o] :
( ! [X199: term] :
( ( X198 @ X199 )
= ( X197 @ ( sub @ X199 @ ( push @ X195 @ X196 ) ) ) )
& ( $true
!= ( X198 @ one ) )
& ( ( X197 @ X195 )
= $true ) )
& ! [X200: term,X201: subst] :
( ( sub @ one @ ( push @ X200 @ X201 ) )
= X200 ) ) )
& ( ! [X202: term,X203: subst,X204: term > $o,X205: term > $o] :
( ? [X206: term] :
( ( X205 @ X206 )
!= ( X204 @ ( sub @ X206 @ ( push @ X202 @ X203 ) ) ) )
| ( ( X205 @ one )
= $true )
| ( ( X204 @ X202 )
!= $true ) )
| ? [X207: term,X208: subst] :
( ( sub @ one @ ( push @ X207 @ X208 ) )
!= X207 )
| ( pushprop_lem1v2_lthm != $true ) )
& ( hoasinduction_lem1_gthm = $true )
& ( pushprop_lem0_gthm = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ( axvarid = $true )
| ? [X209: term] :
( ( sub @ X209 @ id )
!= X209 ) )
& ( ! [X210: term] :
( ( sub @ X210 @ id )
= X210 )
| ( axvarid != $true ) )
& ( ( sP24 = $true )
| ( hoasinduction_lem3v2a != $true ) )
& ( ( hoasinduction_lem3v2a = $true )
| ( sP24 != $true ) )
& ( ( hoasapinj1 = $true )
| ? [X211: term,X212: term,X213: term,X214: term] :
( ( ( ap @ ( sub @ X213 @ id ) @ X212 )
= ( ap @ ( sub @ X214 @ id ) @ X211 ) )
& ( X213 != X214 ) ) )
& ( ! [X215: term,X216: term,X217: term,X218: term] :
( ( ( ap @ ( sub @ X217 @ id ) @ X216 )
!= ( ap @ ( sub @ X218 @ id ) @ X215 ) )
| ( X217 = X218 ) )
| ( hoasapinj1 != $true ) )
& ( pushprop_gthm = $true )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( axscons = $true )
| ? [X219: subst] :
( ( push @ ( sub @ one @ X219 ) @ ( comp @ sh @ X219 ) )
!= X219 ) )
& ( ! [X220: subst] :
( ( push @ ( sub @ one @ X220 ) @ ( comp @ sh @ X220 ) )
= X220 )
| ( axscons != $true ) )
& ( ( hoasinduction = $true )
| ( $true != sP22 ) )
& ( ( $true = sP22 )
| ( hoasinduction != $true ) )
& ( pushprop_lem2v2 = $true )
& ( ( hoasinduction_no_psi_cond = $true )
| ? [X221: term,X222: subst > term > subst > $o] :
( ( ( X222 @ id @ X221 @ id )
!= $true )
& ( $true
!= ( sP17 @ X222 ) )
& ( ( sP16 @ X222 )
!= $true ) ) )
& ( ! [X223: term,X224: subst > term > subst > $o] :
( ( $true
= ( X224 @ id @ X223 @ id ) )
| ( $true
= ( sP17 @ X224 ) )
| ( ( sP16 @ X224 )
= $true ) )
| ( hoasinduction_no_psi_cond != $true ) )
& ( hoasinduction_lem3_gthm = $true )
& ( ( termmset = $true )
| ? [X225: term] :
( ( sub @ X225 @ id )
!= X225 ) )
& ( ! [X226: term] :
( ( sub @ X226 @ id )
= X226 )
| ( termmset != $true ) )
& ! [X227: d_term] : ( d_one = X227 )
& ( ulamvarsh = $true )
& ( hoasapinj2_gthm = $true )
& ( axmap = $true )
& ( ( sP15 = $true )
| ( hoasinduction_lem3 != $true ) )
& ( ( hoasinduction_lem3 = $true )
| ( sP15 != $true ) )
& ( ! [X228: term] :
( ( sub @ X228 @ id )
= X228 )
| ? [X229: term] :
( ( sub @ X229 @ id )
!= X229 )
| ( termmset_lthm != $true ) )
& ( ( termmset_lthm = $true )
| ( ? [X230: term] :
( ( sub @ X230 @ id )
!= X230 )
& ! [X231: term] :
( ( sub @ X231 @ id )
= X231 ) ) )
& ( ( pushprop_lem1 = $true )
| ? [X232: term,X233: term,X234: term > $o,X235: subst,X236: term > $o] :
( ( $true
= ( X236 @ X233 ) )
& ( $true
!= ( X234 @ ( sub @ X233 @ ( push @ X232 @ X235 ) ) ) ) ) )
& ( ! [X237: term,X238: term,X239: term > $o,X240: subst,X241: term > $o] :
( ( $true
!= ( X241 @ X238 ) )
| ( ( X239 @ ( sub @ X238 @ ( push @ X237 @ X240 ) ) )
= $true ) )
| ( pushprop_lem1 != $true ) )
& ( ( axvarcons = $true )
| ? [X242: subst,X243: term] :
( ( sub @ one @ ( push @ X243 @ X242 ) )
!= X243 ) )
& ( ! [X244: subst,X245: term] :
( ( sub @ one @ ( push @ X245 @ X244 ) )
= X245 )
| ( axvarcons != $true ) )
& ( ( hoasinduction_lthm_3 = $true )
| ( ( $true != sP11 )
& ( $true != sP9 )
& ! [X246: term] :
( ( sub @ X246 @ id )
= X246 )
& ! [X247: subst > term > subst > $o] :
? [X248: term > $o] :
! [X249: term] :
( ( X248 @ X249 )
= ( X247 @ id @ X249 @ id ) )
& ( sP10 != $true ) ) )
& ( ( $true = sP11 )
| ( $true = sP9 )
| ? [X250: term] :
( ( sub @ X250 @ id )
!= X250 )
| ? [X251: subst > term > subst > $o] :
! [X252: term > $o] :
? [X253: term] :
( ( X251 @ id @ X253 @ id )
!= ( X252 @ X253 ) )
| ( sP10 = $true )
| ( hoasinduction_lthm_3 != $true ) )
& ( pushprop_lthm = $true )
& ( ! [X254: subst] :
( ( comp @ id @ X254 )
= X254 )
| ( axidl != $true ) )
& ( ( axidl = $true )
| ? [X255: subst] :
( ( comp @ id @ X255 )
!= X255 ) )
& ( ( hoasinduction_lem3aa = $true )
| ( sP1 != $true ) )
& ( ( sP1 = $true )
| ( hoasinduction_lem3aa != $true ) )
& ( hoaslaminj_gthm = $true )
& ( ( hoasinduction_lem0 = $true )
| ? [X256: subst > term > subst > $o] :
! [X257: term > $o] :
? [X258: term] :
( ( X257 @ X258 )
!= ( X256 @ id @ X258 @ id ) ) )
& ( ! [X259: subst > term > subst > $o] :
? [X260: term > $o] :
! [X261: term] :
( ( X259 @ id @ X261 @ id )
= ( X260 @ X261 ) )
| ( hoasinduction_lem0 != $true ) )
& ! [X262: subst] :
? [X263: d_subst] :
( ( d2subst @ X263 )
= X262 ) ),
inference(rectify,[status(thm)],[f672]) ).
thf(f672,plain,
( ( hoasapnotvar = $true )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( apinj1 = $true )
| ? [X261: term,X262: term,X263: term,X264: term] :
( ( X262 != X264 )
& ( ( ap @ X264 @ X263 )
= ( ap @ X262 @ X261 ) ) ) )
& ( ! [X261: term,X262: term,X263: term,X264: term] :
( ( X262 = X264 )
| ( ( ap @ X264 @ X263 )
!= ( ap @ X262 @ X261 ) ) )
| ( apinj1 != $true ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( hoaslamnotvar_gthm = $true )
& ( ! [X52: subst] :
( ( comp @ X52 @ id )
= X52 )
| ( axidr != $true ) )
& ( ( axidr = $true )
| ? [X52: subst] :
( ( comp @ X52 @ id )
!= X52 ) )
& ( termmset_gthm = $true )
& ( ( sP108 = $true )
| ? [X10: term] :
( ( sub @ X10 @ id )
!= X10 )
| ? [X0: subst > term > subst > $o] :
! [X1: term > $o] :
? [X2: term] :
( ( X0 @ id @ X2 @ id )
!= ( X1 @ X2 ) )
| ( sP109 = $true )
| ( sP107 = $true )
| ( hoasinduction_no_psi_cond_lthm != $true ) )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
| ( ( sP108 != $true )
& ! [X10: term] :
( ( sub @ X10 @ id )
= X10 )
& ! [X0: subst > term > subst > $o] :
? [X1: term > $o] :
! [X2: term] :
( ( X0 @ id @ X2 @ id )
= ( X1 @ X2 ) )
& ( sP109 != $true )
& ( sP107 != $true ) ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ! [X291: d_subst] : ( d_id = X291 )
& ( ( ! [X79: subst] :
( ( comp @ id @ X79 )
= X79 )
& ! [X80: subst] :
( ( comp @ X80 @ id )
= X80 ) )
| ( substmonoid != $true ) )
& ( ( substmonoid = $true )
| ? [X79: subst] :
( ( comp @ id @ X79 )
!= X79 )
| ? [X80: subst] :
( ( comp @ X80 @ id )
!= X80 ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( one
= ( d2term @ d_one ) )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ( sP100 = $true )
| ( hoasinduction_lem3aa_lthm != $true ) )
& ( ( hoasinduction_lem3aa_lthm = $true )
| ( sP100 != $true ) )
& ( ( induction = $true )
| ( sP98 != $true ) )
& ( ( sP98 = $true )
| ( induction != $true ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
| ( ! [X98: term] :
( ( sub @ X98 @ id )
= X98 )
& ( $true != sP95 ) ) )
& ( ? [X98: term] :
( ( sub @ X98 @ id )
!= X98 )
| ( $true = sP95 )
| ( hoasinduction_lem3v2_lthm != $true ) )
& ( pushprop_lthm_orig = $true )
& ( hoaslamnotvar_lthm = $true )
& ( hoaslamnotap_lthm = $true )
& ! [X234: d_term,X235: d_term] :
( ( ( d2term @ X234 )
!= ( d2term @ X235 ) )
| ( X234 = X235 ) )
& ( hoaslamnotvar = $true )
& ( ( hoasinduction_lem2 = $true )
| ( $true != sP91 ) )
& ( ( $true = sP91 )
| ( hoasinduction_lem2 != $true ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( axabs = $true )
& ( ! [X480: term,X481: term,X482: term,X483: term] :
( ( ( ap @ ( sub @ X482 @ id ) @ X481 )
!= ( ap @ ( sub @ X480 @ id ) @ X483 ) )
| ( X481 = X483 ) )
| ( hoasapinj2 != $true ) )
& ( ( hoasapinj2 = $true )
| ? [X480: term,X481: term,X482: term,X483: term] :
( ( ( ap @ ( sub @ X482 @ id ) @ X481 )
= ( ap @ ( sub @ X480 @ id ) @ X483 ) )
& ( X481 != X483 ) ) )
& ( ( induction2 = $true )
| ( sP88 != $true ) )
& ( ( sP88 = $true )
| ( induction2 != $true ) )
& ( induction2_gthm = $true )
& ( ( $true = sP85 )
| ( induction2lem != $true ) )
& ( ( induction2lem = $true )
| ( $true != sP85 ) )
& ( hoasinduction_lem1v2_gthm = $true )
& ( ( sP81 = $true )
| ? [X128: term] :
( ( sub @ X128 @ id )
!= X128 )
| ( $true = sP82 )
| ( induction2_lthm != $true ) )
& ( ( induction2_lthm = $true )
| ( ( sP81 != $true )
& ! [X128: term] :
( ( sub @ X128 @ id )
= X128 )
& ( $true != sP82 ) ) )
& ( hoasapnotvar_lthm = $true )
& ( ( hoasinduction_lem3v2_f = $true )
| ? [X280: term] :
! [X281: subst > term > term] :
? [X282: term,X283: subst] :
( ( X281 @ X283 @ X282 )
!= ( sub @ X280 @ ( push @ X282 @ X283 ) ) ) )
& ( ! [X280: term] :
? [X281: subst > term > term] :
! [X282: term,X283: subst] :
( ( X281 @ X283 @ X282 )
= ( sub @ X280 @ ( push @ X282 @ X283 ) ) )
| ( hoasinduction_lem3v2_f != $true ) )
& ( axclos = $true )
& ( ! [X30: term,X31: term] :
( ( X30 = X31 )
| ( ( lam @ X30 )
!= ( lam @ X31 ) ) )
| ( laminj != $true ) )
& ( ( laminj = $true )
| ? [X30: term,X31: term] :
( ( X30 != X31 )
& ( ( lam @ X30 )
= ( lam @ X31 ) ) ) )
& ( pushprop_lem3v2_lthm = $true )
& ( axassoc = $true )
& ( ulamvar1 != $true )
& ( ( hoasinduction_lem3b_lthm = $true )
| ? [X339: term] :
! [X340: subst > term > term] :
( ( X340 @ sh @ one )
!= ( sub @ X339 @ ( push @ one @ sh ) ) ) )
& ( ! [X339: term] :
? [X340: subst > term > term] :
( ( X340 @ sh @ one )
= ( sub @ X339 @ ( push @ one @ sh ) ) )
| ( hoasinduction_lem3b_lthm != $true ) )
& ( ( sP72 = $true )
| ( $true = sP75 )
| ( sP74 = $true )
| ( $true = sP73 )
| ( hoasinduction_lthm != $true ) )
& ( ( hoasinduction_lthm = $true )
| ( ( sP72 != $true )
& ( $true != sP75 )
& ( sP74 != $true )
& ( $true != sP73 ) ) )
& ( ( induction2lem_lthm = $true )
| ( ( sP60 != $true )
& ( sP59 != $true )
& ! [X510: subst] :
( ( comp @ X510 @ id )
= X510 )
& ! [X508: subst,X509: term] :
( ( comp @ sh @ ( push @ X509 @ X508 ) )
= X508 )
& ! [X506: term,X507: subst] :
( ( sub @ one @ ( push @ X506 @ X507 ) )
= X506 ) ) )
& ( ( sP60 = $true )
| ( sP59 = $true )
| ? [X510: subst] :
( ( comp @ X510 @ id )
!= X510 )
| ? [X508: subst,X509: term] :
( ( comp @ sh @ ( push @ X509 @ X508 ) )
!= X508 )
| ? [X506: term,X507: subst] :
( ( sub @ one @ ( push @ X506 @ X507 ) )
!= X506 )
| ( induction2lem_lthm != $true ) )
& ( ! [X144: subst,X145: term > $o,X146: term] :
? [X147: term > $o] :
! [X148: term] :
( ( X145 @ ( sub @ X148 @ ( push @ X146 @ X144 ) ) )
= ( X147 @ X148 ) )
| ( pushprop_lem0_lthm != $true ) )
& ( ( pushprop_lem0_lthm = $true )
| ? [X144: subst,X145: term > $o,X146: term] :
! [X147: term > $o] :
? [X148: term] :
( ( X145 @ ( sub @ X148 @ ( push @ X146 @ X144 ) ) )
!= ( X147 @ X148 ) ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) )
= ( Y3 @ Y4 ) ) ) ) )
& ( apnotvar = $true )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( hoasinduction_gthm = $true )
& ( axapp = $true )
& ( ( hoasinduction_lem3_lthm = $true )
| ( ( sP54 != $true )
& ! [X424: term] :
( ( sub @ X424 @ id )
= X424 )
& ( $true != sP53 ) ) )
& ( ( sP54 = $true )
| ? [X424: term] :
( ( sub @ X424 @ id )
!= X424 )
| ( $true = sP53 )
| ( hoasinduction_lem3_lthm != $true ) )
& ( ( pushprop_lem0 = $true )
| ? [X119: term > $o,X120: subst,X121: term] :
! [X122: term > $o] :
? [X123: term] :
( ( X122 @ X123 )
!= ( X119 @ ( sub @ X123 @ ( push @ X121 @ X120 ) ) ) ) )
& ( ! [X119: term > $o,X120: subst,X121: term] :
? [X122: term > $o] :
! [X123: term] :
( ( X122 @ X123 )
= ( X119 @ ( sub @ X123 @ ( push @ X121 @ X120 ) ) ) )
| ( pushprop_lem0 != $true ) )
& ( induction2lem_gthm = $true )
& ( ( $true = sP48 )
| ( hoasinduction_lem2v2 != $true ) )
& ( ( hoasinduction_lem2v2 = $true )
| ( $true != sP48 ) )
& ( ( hoasinduction_lem3aaa = $true )
| ( $true != sP45 ) )
& ( ( $true = sP45 )
| ( hoasinduction_lem3aaa != $true ) )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ( hoasinduction_lem3a = $true )
| ( $true != sP43 ) )
& ( ( $true = sP43 )
| ( hoasinduction_lem3a != $true ) )
& ( ! [X341: subst > term > term,X342: term,X343: term] :
( ( ( ap @ ( sub @ X342 @ id ) @ X343 )
!= ( lam @ ( X341 @ sh @ one ) ) )
| ? [X344: subst,X345: term,X346: subst] :
( ( sub @ ( X341 @ X346 @ X345 ) @ X344 )
!= ( X341 @ ( comp @ X346 @ X344 ) @ ( sub @ X345 @ X344 ) ) ) )
| ( hoaslamnotap != $true ) )
& ( ( hoaslamnotap = $true )
| ? [X341: subst > term > term,X342: term,X343: term] :
( ( ( ap @ ( sub @ X342 @ id ) @ X343 )
= ( lam @ ( X341 @ sh @ one ) ) )
& ! [X344: subst,X345: term,X346: subst] :
( ( sub @ ( X341 @ X346 @ X345 ) @ X344 )
= ( X341 @ ( comp @ X346 @ X344 ) @ ( sub @ X345 @ X344 ) ) ) ) )
& ( hoasinduction_lem1 = $true )
& ( pushprop_lem2v2_gthm = $true )
& ! [X422: term] :
? [X423: d_term] :
( ( d2term @ X423 )
= X422 )
& ( ( sP41 = $true )
| ( hoasapinj2_lthm != $true ) )
& ( ( hoasapinj2_lthm = $true )
| ( sP41 != $true ) )
& ( lamnotvar = $true )
& ( axvarshift = $true )
& ( hoasinduction_lem3b_gthm = $true )
& ( pushprop = $true )
& ! [X265: d_subst,X266: d_subst] :
( ( X265 = X266 )
| ( ( d2subst @ X266 )
!= ( d2subst @ X265 ) ) )
& ( ulamvarind = $true )
& ( substmonoid_gthm = $true )
& ( hoasinduction_lem2_lthm = $true )
& ( pushprop_lem2v2_lthm = $true )
& ( ( shinj = $true )
| ? [X328: term,X329: term] :
( ( X328 != X329 )
& ( ( sub @ X329 @ sh )
= ( sub @ X328 @ sh ) ) ) )
& ( ! [X328: term,X329: term] :
( ( X328 = X329 )
| ( ( sub @ X329 @ sh )
!= ( sub @ X328 @ sh ) ) )
| ( shinj != $true ) )
& ( ( axshiftcons = $true )
| ? [X117: term,X118: subst] :
( ( comp @ sh @ ( push @ X117 @ X118 ) )
!= X118 ) )
& ( ! [X117: term,X118: subst] :
( ( comp @ sh @ ( push @ X117 @ X118 ) )
= X118 )
| ( axshiftcons != $true ) )
& ( hoasapinj1_gthm = $true )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( hoasinduction_lem1_lthm = $true )
& ( ( sP39 = $true )
| ( hoasinduction_lem3v2 != $true ) )
& ( ( hoasinduction_lem3v2 = $true )
| ( sP39 != $true ) )
& ( ( hoasinduction_lem3v2_f_lthm = $true )
| ? [X124: term] :
! [X125: subst > term > term] :
? [X126: term,X127: subst] :
( ( sub @ X124 @ ( push @ X126 @ X127 ) )
!= ( X125 @ X127 @ X126 ) ) )
& ( ! [X124: term] :
? [X125: subst > term > term] :
! [X126: term,X127: subst] :
( ( sub @ X124 @ ( push @ X126 @ X127 ) )
= ( X125 @ X127 @ X126 ) )
| ( hoasinduction_lem3v2_f_lthm != $true ) )
& ( ( d2subst @ d_id )
= id )
& ( pushprop_lem1v2_gthm = $true )
& ( ! [X529: term] :
? [X530: subst > term > term] :
( ( X530 @ sh @ one )
= ( sub @ X529 @ ( push @ one @ sh ) ) )
| ( hoasinduction_lem3b != $true ) )
& ( ( hoasinduction_lem3b = $true )
| ? [X529: term] :
! [X530: subst > term > term] :
( ( X530 @ sh @ one )
!= ( sub @ X529 @ ( push @ one @ sh ) ) ) )
& ( ( sP35 = $true )
| ( hoaslaminj_lthm != $true ) )
& ( ( hoaslaminj_lthm = $true )
| ( sP35 != $true ) )
& ( ! [X404: subst,X405: subst > term > term,X406: term,X407: subst > term > term] :
( ? [X411: subst,X412: subst,X413: term] :
( ( X405 @ ( comp @ X412 @ X411 ) @ ( sub @ X413 @ X411 ) )
!= ( sub @ ( X405 @ X412 @ X413 ) @ X411 ) )
| ( ( lam @ ( X407 @ sh @ one ) )
!= ( lam @ ( X405 @ sh @ one ) ) )
| ? [X408: term,X409: subst,X410: subst] :
( ( X407 @ ( comp @ X409 @ X410 ) @ ( sub @ X408 @ X410 ) )
!= ( sub @ ( X407 @ X409 @ X408 ) @ X410 ) )
| ( ( X407 @ X404 @ X406 )
= ( X405 @ X404 @ X406 ) ) )
| ( hoaslaminj != $true ) )
& ( ( hoaslaminj = $true )
| ? [X404: subst,X405: subst > term > term,X406: term,X407: subst > term > term] :
( ! [X411: subst,X412: subst,X413: term] :
( ( X405 @ ( comp @ X412 @ X411 ) @ ( sub @ X413 @ X411 ) )
= ( sub @ ( X405 @ X412 @ X413 ) @ X411 ) )
& ( ( lam @ ( X407 @ sh @ one ) )
= ( lam @ ( X405 @ sh @ one ) ) )
& ! [X408: term,X409: subst,X410: subst] :
( ( X407 @ ( comp @ X409 @ X410 ) @ ( sub @ X408 @ X410 ) )
= ( sub @ ( X407 @ X409 @ X408 ) @ X410 ) )
& ( ( X407 @ X404 @ X406 )
!= ( X405 @ X404 @ X406 ) ) ) )
& ( hoaslamnotap_gthm = $true )
& ( ( substmonoid_lthm = $true )
| ( $true != sP33 ) )
& ( ( $true = sP33 )
| ( substmonoid_lthm != $true ) )
& ( ! [X48: term,X49: term,X50: term,X51: term] :
( ( ( ap @ X49 @ X48 )
!= ( ap @ X50 @ X51 ) )
| ( X48 = X51 ) )
| ( apinj2 != $true ) )
& ( ( apinj2 = $true )
| ? [X48: term,X49: term,X50: term,X51: term] :
( ( ( ap @ X49 @ X48 )
= ( ap @ X50 @ X51 ) )
& ( X48 != X51 ) ) )
& ( hoasinduction_lem2_gthm = $true )
& ( pushprop_lem3v2 = $true )
& ( pushprop_lem1_gthm = $true )
& ( ( hoasapinj1_lthm = $true )
| ( $true != sP32 ) )
& ( ( $true = sP32 )
| ( hoasapinj1_lthm != $true ) )
& ( ( $true = sP30 )
| ? [X469: term] :
( ( sub @ X469 @ id )
!= X469 )
| ? [X465: term] :
! [X466: subst > term > term] :
? [X467: subst,X468: term] :
( ( sub @ X465 @ ( push @ X468 @ X467 ) )
!= ( X466 @ X467 @ X468 ) )
| ( hoasinduction_lem3v2a_lthm != $true ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
| ( ( $true != sP30 )
& ! [X469: term] :
( ( sub @ X469 @ id )
= X469 )
& ! [X465: term] :
? [X466: subst > term > term] :
! [X467: subst,X468: term] :
( ( sub @ X465 @ ( push @ X468 @ X467 ) )
= ( X466 @ X467 @ X468 ) ) ) )
& ( ? [X151: subst,X152: term] :
( ( comp @ sh @ ( push @ X152 @ X151 ) )
!= X151 )
| ? [X149: term,X150: subst] :
( ( sub @ one @ ( push @ X149 @ X150 ) )
!= X149 )
| ! [X153: term,X154: term > $o,X155: subst,X156: term,X157: term > $o] :
( ( ( X157 @ ( sub @ X153 @ ( push @ X156 @ X155 ) ) )
= $true )
| ( $true
!= ( X154 @ X153 ) ) )
| ( pushprop_lem1_lthm != $true ) )
& ( ( pushprop_lem1_lthm = $true )
| ( ! [X151: subst,X152: term] :
( ( comp @ sh @ ( push @ X152 @ X151 ) )
= X151 )
& ! [X149: term,X150: subst] :
( ( sub @ one @ ( push @ X149 @ X150 ) )
= X149 )
& ? [X153: term,X154: term > $o,X155: subst,X156: term,X157: term > $o] :
( ( ( X157 @ ( sub @ X153 @ ( push @ X156 @ X155 ) ) )
!= $true )
& ( $true
= ( X154 @ X153 ) ) ) ) )
& ( ( $true = sP27 )
| ( $true = sP28 )
| ? [X81: term] :
( ( sub @ X81 @ id )
!= X81 )
| ( hoasinduction_lem3a_lthm != $true ) )
& ( ( hoasinduction_lem3a_lthm = $true )
| ( ( $true != sP27 )
& ( $true != sP28 )
& ! [X81: term] :
( ( sub @ X81 @ id )
= X81 ) ) )
& ( hoasinduction_lem1v2 = $true )
& ( ! [X399: subst,X400: term > $o,X401: term > $o,X402: term] :
( ? [X403: term] :
( ( X400 @ ( sub @ X403 @ ( push @ X402 @ X399 ) ) )
!= ( X401 @ X403 ) )
| ( $true
= ( X401 @ one ) )
| ( $true
!= ( X400 @ X402 ) ) )
| ( pushprop_lem1v2 != $true ) )
& ( ( pushprop_lem1v2 = $true )
| ? [X399: subst,X400: term > $o,X401: term > $o,X402: term] :
( ! [X403: term] :
( ( X400 @ ( sub @ X403 @ ( push @ X402 @ X399 ) ) )
= ( X401 @ X403 ) )
& ( $true
!= ( X401 @ one ) )
& ( $true
= ( X400 @ X402 ) ) ) )
& ( lamnotap != $true )
& ( hoasapnotvar_gthm = $true )
& ( ! [X449: subst > term > subst > $o] :
? [X450: term > $o] :
! [X451: term] :
( ( X449 @ id @ X451 @ id )
= ( X450 @ X451 ) )
| ( hoasinduction_lem0_lthm != $true ) )
& ( ( hoasinduction_lem0_lthm = $true )
| ? [X449: subst > term > subst > $o] :
! [X450: term > $o] :
? [X451: term] :
( ( X449 @ id @ X451 @ id )
!= ( X450 @ X451 ) ) )
& ( ( d2subst @ d_id )
= sh )
& ( ( pushprop_lem1v2_lthm = $true )
| ( ? [X286: term,X287: subst,X288: term > $o,X289: term > $o] :
( ! [X290: term] :
( ( X288 @ ( sub @ X290 @ ( push @ X286 @ X287 ) ) )
= ( X289 @ X290 ) )
& ( ( X289 @ one )
!= $true )
& ( $true
= ( X288 @ X286 ) ) )
& ! [X284: term,X285: subst] :
( ( sub @ one @ ( push @ X284 @ X285 ) )
= X284 ) ) )
& ( ! [X286: term,X287: subst,X288: term > $o,X289: term > $o] :
( ? [X290: term] :
( ( X288 @ ( sub @ X290 @ ( push @ X286 @ X287 ) ) )
!= ( X289 @ X290 ) )
| ( ( X289 @ one )
= $true )
| ( $true
!= ( X288 @ X286 ) ) )
| ? [X284: term,X285: subst] :
( ( sub @ one @ ( push @ X284 @ X285 ) )
!= X284 )
| ( pushprop_lem1v2_lthm != $true ) )
& ( hoasinduction_lem1_gthm = $true )
& ( pushprop_lem0_gthm = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ( axvarid = $true )
| ? [X236: term] :
( ( sub @ X236 @ id )
!= X236 ) )
& ( ! [X236: term] :
( ( sub @ X236 @ id )
= X236 )
| ( axvarid != $true ) )
& ( ( sP24 = $true )
| ( hoasinduction_lem3v2a != $true ) )
& ( ( hoasinduction_lem3v2a = $true )
| ( sP24 != $true ) )
& ( ( hoasapinj1 = $true )
| ? [X486: term,X487: term,X488: term,X489: term] :
( ( ( ap @ ( sub @ X489 @ id ) @ X486 )
= ( ap @ ( sub @ X488 @ id ) @ X487 ) )
& ( X488 != X489 ) ) )
& ( ! [X486: term,X487: term,X488: term,X489: term] :
( ( ( ap @ ( sub @ X489 @ id ) @ X486 )
!= ( ap @ ( sub @ X488 @ id ) @ X487 ) )
| ( X488 = X489 ) )
| ( hoasapinj1 != $true ) )
& ( pushprop_gthm = $true )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( axscons = $true )
| ? [X267: subst] :
( ( push @ ( sub @ one @ X267 ) @ ( comp @ sh @ X267 ) )
!= X267 ) )
& ( ! [X267: subst] :
( ( push @ ( sub @ one @ X267 ) @ ( comp @ sh @ X267 ) )
= X267 )
| ( axscons != $true ) )
& ( ( hoasinduction = $true )
| ( $true != sP22 ) )
& ( ( $true = sP22 )
| ( hoasinduction != $true ) )
& ( pushprop_lem2v2 = $true )
& ( ( hoasinduction_no_psi_cond = $true )
| ? [X330: term,X331: subst > term > subst > $o] :
( ( ( X331 @ id @ X330 @ id )
!= $true )
& ( ( sP17 @ X331 )
!= $true )
& ( ( sP16 @ X331 )
!= $true ) ) )
& ( ! [X330: term,X331: subst > term > subst > $o] :
( ( ( X331 @ id @ X330 @ id )
= $true )
| ( ( sP17 @ X331 )
= $true )
| ( ( sP16 @ X331 )
= $true ) )
| ( hoasinduction_no_psi_cond != $true ) )
& ( hoasinduction_lem3_gthm = $true )
& ( ( termmset = $true )
| ? [X394: term] :
( ( sub @ X394 @ id )
!= X394 ) )
& ( ! [X394: term] :
( ( sub @ X394 @ id )
= X394 )
| ( termmset != $true ) )
& ! [X531: d_term] : ( d_one = X531 )
& ( ulamvarsh = $true )
& ( hoasapinj2_gthm = $true )
& ( axmap = $true )
& ( ( sP15 = $true )
| ( hoasinduction_lem3 != $true ) )
& ( ( hoasinduction_lem3 = $true )
| ( sP15 != $true ) )
& ( ! [X254: term] :
( ( sub @ X254 @ id )
= X254 )
| ? [X253: term] :
( ( sub @ X253 @ id )
!= X253 )
| ( termmset_lthm != $true ) )
& ( ( termmset_lthm = $true )
| ( ? [X254: term] :
( ( sub @ X254 @ id )
!= X254 )
& ! [X253: term] :
( ( sub @ X253 @ id )
= X253 ) ) )
& ( ( pushprop_lem1 = $true )
| ? [X275: term,X276: term,X277: term > $o,X278: subst,X279: term > $o] :
( ( ( X279 @ X276 )
= $true )
& ( ( X277 @ ( sub @ X276 @ ( push @ X275 @ X278 ) ) )
!= $true ) ) )
& ( ! [X275: term,X276: term,X277: term > $o,X278: subst,X279: term > $o] :
( ( ( X279 @ X276 )
!= $true )
| ( ( X277 @ ( sub @ X276 @ ( push @ X275 @ X278 ) ) )
= $true ) )
| ( pushprop_lem1 != $true ) )
& ( ( axvarcons = $true )
| ? [X77: subst,X78: term] :
( ( sub @ one @ ( push @ X78 @ X77 ) )
!= X78 ) )
& ( ! [X77: subst,X78: term] :
( ( sub @ one @ ( push @ X78 @ X77 ) )
= X78 )
| ( axvarcons != $true ) )
& ( ( hoasinduction_lthm_3 = $true )
| ( ( $true != sP11 )
& ( $true != sP9 )
& ! [X357: term] :
( ( sub @ X357 @ id )
= X357 )
& ! [X347: subst > term > subst > $o] :
? [X348: term > $o] :
! [X349: term] :
( ( X347 @ id @ X349 @ id )
= ( X348 @ X349 ) )
& ( sP10 != $true ) ) )
& ( ( $true = sP11 )
| ( $true = sP9 )
| ? [X357: term] :
( ( sub @ X357 @ id )
!= X357 )
| ? [X347: subst > term > subst > $o] :
! [X348: term > $o] :
? [X349: term] :
( ( X347 @ id @ X349 @ id )
!= ( X348 @ X349 ) )
| ( sP10 = $true )
| ( hoasinduction_lthm_3 != $true ) )
& ( pushprop_lthm = $true )
& ( ! [X528: subst] :
( ( comp @ id @ X528 )
= X528 )
| ( axidl != $true ) )
& ( ( axidl = $true )
| ? [X528: subst] :
( ( comp @ id @ X528 )
!= X528 ) )
& ( ( hoasinduction_lem3aa = $true )
| ( sP1 != $true ) )
& ( ( sP1 = $true )
| ( hoasinduction_lem3aa != $true ) )
& ( hoaslaminj_gthm = $true )
& ( ( hoasinduction_lem0 = $true )
| ? [X525: subst > term > subst > $o] :
! [X526: term > $o] :
? [X527: term] :
( ( X525 @ id @ X527 @ id )
!= ( X526 @ X527 ) ) )
& ( ! [X525: subst > term > subst > $o] :
? [X526: term > $o] :
! [X527: term] :
( ( X525 @ id @ X527 @ id )
= ( X526 @ X527 ) )
| ( hoasinduction_lem0 != $true ) )
& ! [X484: subst] :
? [X485: d_subst] :
( ( d2subst @ X485 )
= X484 ) ),
inference(flattening,[status(thm)],[f671]) ).
thf(f671,plain,
( ( hoasapnotvar = $true )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( apinj1 = $true )
| ? [X261: term,X262: term,X263: term,X264: term] :
( ( X262 != X264 )
& ( ( ap @ X264 @ X263 )
= ( ap @ X262 @ X261 ) ) ) )
& ( ! [X261: term,X262: term,X263: term,X264: term] :
( ( X262 = X264 )
| ( ( ap @ X264 @ X263 )
!= ( ap @ X262 @ X261 ) ) )
| ( apinj1 != $true ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( hoaslamnotvar_gthm = $true )
& ( ! [X52: subst] :
( ( comp @ X52 @ id )
= X52 )
| ( axidr != $true ) )
& ( ( axidr = $true )
| ? [X52: subst] :
( ( comp @ X52 @ id )
!= X52 ) )
& ( termmset_gthm = $true )
& ( ( sP108 = $true )
| ? [X10: term] :
( ( sub @ X10 @ id )
!= X10 )
| ? [X0: subst > term > subst > $o] :
! [X1: term > $o] :
? [X2: term] :
( ( X0 @ id @ X2 @ id )
!= ( X1 @ X2 ) )
| ( sP109 = $true )
| ( sP107 = $true )
| ( hoasinduction_no_psi_cond_lthm != $true ) )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
| ( ( sP108 != $true )
& ! [X10: term] :
( ( sub @ X10 @ id )
= X10 )
& ! [X0: subst > term > subst > $o] :
? [X1: term > $o] :
! [X2: term] :
( ( X0 @ id @ X2 @ id )
= ( X1 @ X2 ) )
& ( sP109 != $true )
& ( sP107 != $true ) ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ! [X291: d_subst] : ( d_id = X291 )
& ( ( ! [X79: subst] :
( ( comp @ id @ X79 )
= X79 )
& ! [X80: subst] :
( ( comp @ X80 @ id )
= X80 ) )
| ( substmonoid != $true ) )
& ( ( substmonoid = $true )
| ? [X79: subst] :
( ( comp @ id @ X79 )
!= X79 )
| ? [X80: subst] :
( ( comp @ X80 @ id )
!= X80 ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( one
= ( d2term @ d_one ) )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ( sP100 = $true )
| ( hoasinduction_lem3aa_lthm != $true ) )
& ( ( hoasinduction_lem3aa_lthm = $true )
| ( sP100 != $true ) )
& ( ( induction = $true )
| ( sP98 != $true ) )
& ( ( sP98 = $true )
| ( induction != $true ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
| ( ! [X98: term] :
( ( sub @ X98 @ id )
= X98 )
& ( $true != sP95 ) ) )
& ( ? [X98: term] :
( ( sub @ X98 @ id )
!= X98 )
| ( $true = sP95 )
| ( hoasinduction_lem3v2_lthm != $true ) )
& ( pushprop_lthm_orig = $true )
& ( hoaslamnotvar_lthm = $true )
& ( hoaslamnotap_lthm = $true )
& ! [X234: d_term,X235: d_term] :
( ( ( d2term @ X234 )
!= ( d2term @ X235 ) )
| ( X234 = X235 ) )
& ( hoaslamnotvar = $true )
& ( ( hoasinduction_lem2 = $true )
| ( $true != sP91 ) )
& ( ( $true = sP91 )
| ( hoasinduction_lem2 != $true ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( axabs = $true )
& ( ! [X480: term,X481: term,X482: term,X483: term] :
( ( ( ap @ ( sub @ X482 @ id ) @ X481 )
!= ( ap @ ( sub @ X480 @ id ) @ X483 ) )
| ( X481 = X483 ) )
| ( hoasapinj2 != $true ) )
& ( ( hoasapinj2 = $true )
| ? [X480: term,X481: term,X482: term,X483: term] :
( ( ( ap @ ( sub @ X482 @ id ) @ X481 )
= ( ap @ ( sub @ X480 @ id ) @ X483 ) )
& ( X481 != X483 ) ) )
& ( ( induction2 = $true )
| ( sP88 != $true ) )
& ( ( sP88 = $true )
| ( induction2 != $true ) )
& ( induction2_gthm = $true )
& ( ( $true = sP85 )
| ( induction2lem != $true ) )
& ( ( induction2lem = $true )
| ( $true != sP85 ) )
& ( hoasinduction_lem1v2_gthm = $true )
& ( ( sP81 = $true )
| ? [X128: term] :
( ( sub @ X128 @ id )
!= X128 )
| ( $true = sP82 )
| ( induction2_lthm != $true ) )
& ( ( induction2_lthm = $true )
| ( ( sP81 != $true )
& ! [X128: term] :
( ( sub @ X128 @ id )
= X128 )
& ( $true != sP82 ) ) )
& ( hoasapnotvar_lthm = $true )
& ( ( hoasinduction_lem3v2_f = $true )
| ? [X280: term] :
! [X281: subst > term > term] :
? [X282: term,X283: subst] :
( ( X281 @ X283 @ X282 )
!= ( sub @ X280 @ ( push @ X282 @ X283 ) ) ) )
& ( ! [X280: term] :
? [X281: subst > term > term] :
! [X282: term,X283: subst] :
( ( X281 @ X283 @ X282 )
= ( sub @ X280 @ ( push @ X282 @ X283 ) ) )
| ( hoasinduction_lem3v2_f != $true ) )
& ( axclos = $true )
& ( ! [X30: term,X31: term] :
( ( X30 = X31 )
| ( ( lam @ X30 )
!= ( lam @ X31 ) ) )
| ( laminj != $true ) )
& ( ( laminj = $true )
| ? [X30: term,X31: term] :
( ( X30 != X31 )
& ( ( lam @ X30 )
= ( lam @ X31 ) ) ) )
& ( pushprop_lem3v2_lthm = $true )
& ( axassoc = $true )
& ( ulamvar1 != $true )
& ( ( hoasinduction_lem3b_lthm = $true )
| ? [X339: term] :
! [X340: subst > term > term] :
( ( X340 @ sh @ one )
!= ( sub @ X339 @ ( push @ one @ sh ) ) ) )
& ( ! [X339: term] :
? [X340: subst > term > term] :
( ( X340 @ sh @ one )
= ( sub @ X339 @ ( push @ one @ sh ) ) )
| ( hoasinduction_lem3b_lthm != $true ) )
& ( ( sP72 = $true )
| ( $true = sP75 )
| ( sP74 = $true )
| ( $true = sP73 )
| ( hoasinduction_lthm != $true ) )
& ( ( hoasinduction_lthm = $true )
| ( ( sP72 != $true )
& ( $true != sP75 )
& ( sP74 != $true )
& ( $true != sP73 ) ) )
& ( ( induction2lem_lthm = $true )
| ( ( sP60 != $true )
& ( sP59 != $true )
& ! [X510: subst] :
( ( comp @ X510 @ id )
= X510 )
& ! [X508: subst,X509: term] :
( ( comp @ sh @ ( push @ X509 @ X508 ) )
= X508 )
& ! [X506: term,X507: subst] :
( ( sub @ one @ ( push @ X506 @ X507 ) )
= X506 ) ) )
& ( ( sP60 = $true )
| ( sP59 = $true )
| ? [X510: subst] :
( ( comp @ X510 @ id )
!= X510 )
| ? [X508: subst,X509: term] :
( ( comp @ sh @ ( push @ X509 @ X508 ) )
!= X508 )
| ? [X506: term,X507: subst] :
( ( sub @ one @ ( push @ X506 @ X507 ) )
!= X506 )
| ( induction2lem_lthm != $true ) )
& ( ! [X144: subst,X145: term > $o,X146: term] :
? [X147: term > $o] :
! [X148: term] :
( ( X145 @ ( sub @ X148 @ ( push @ X146 @ X144 ) ) )
= ( X147 @ X148 ) )
| ( pushprop_lem0_lthm != $true ) )
& ( ( pushprop_lem0_lthm = $true )
| ? [X144: subst,X145: term > $o,X146: term] :
! [X147: term > $o] :
? [X148: term] :
( ( X145 @ ( sub @ X148 @ ( push @ X146 @ X144 ) ) )
!= ( X147 @ X148 ) ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) )
= ( Y3 @ Y4 ) ) ) ) )
& ( apnotvar = $true )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( hoasinduction_gthm = $true )
& ( axapp = $true )
& ( ( hoasinduction_lem3_lthm = $true )
| ( ( sP54 != $true )
& ! [X424: term] :
( ( sub @ X424 @ id )
= X424 )
& ( $true != sP53 ) ) )
& ( ( sP54 = $true )
| ? [X424: term] :
( ( sub @ X424 @ id )
!= X424 )
| ( $true = sP53 )
| ( hoasinduction_lem3_lthm != $true ) )
& ( ( pushprop_lem0 = $true )
| ? [X119: term > $o,X120: subst,X121: term] :
! [X122: term > $o] :
? [X123: term] :
( ( X122 @ X123 )
!= ( X119 @ ( sub @ X123 @ ( push @ X121 @ X120 ) ) ) ) )
& ( ! [X119: term > $o,X120: subst,X121: term] :
? [X122: term > $o] :
! [X123: term] :
( ( X122 @ X123 )
= ( X119 @ ( sub @ X123 @ ( push @ X121 @ X120 ) ) ) )
| ( pushprop_lem0 != $true ) )
& ( induction2lem_gthm = $true )
& ( ( $true = sP48 )
| ( hoasinduction_lem2v2 != $true ) )
& ( ( hoasinduction_lem2v2 = $true )
| ( $true != sP48 ) )
& ( ( hoasinduction_lem3aaa = $true )
| ( $true != sP45 ) )
& ( ( $true = sP45 )
| ( hoasinduction_lem3aaa != $true ) )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ( hoasinduction_lem3a = $true )
| ( $true != sP43 ) )
& ( ( $true = sP43 )
| ( hoasinduction_lem3a != $true ) )
& ( ! [X341: subst > term > term,X342: term,X343: term] :
( ( ( ap @ ( sub @ X342 @ id ) @ X343 )
!= ( lam @ ( X341 @ sh @ one ) ) )
| ? [X344: subst,X345: term,X346: subst] :
( ( sub @ ( X341 @ X346 @ X345 ) @ X344 )
!= ( X341 @ ( comp @ X346 @ X344 ) @ ( sub @ X345 @ X344 ) ) ) )
| ( hoaslamnotap != $true ) )
& ( ( hoaslamnotap = $true )
| ? [X341: subst > term > term,X342: term,X343: term] :
( ( ( ap @ ( sub @ X342 @ id ) @ X343 )
= ( lam @ ( X341 @ sh @ one ) ) )
& ! [X344: subst,X345: term,X346: subst] :
( ( sub @ ( X341 @ X346 @ X345 ) @ X344 )
= ( X341 @ ( comp @ X346 @ X344 ) @ ( sub @ X345 @ X344 ) ) ) ) )
& ( hoasinduction_lem1 = $true )
& ( pushprop_lem2v2_gthm = $true )
& ! [X422: term] :
? [X423: d_term] :
( ( d2term @ X423 )
= X422 )
& ( ( sP41 = $true )
| ( hoasapinj2_lthm != $true ) )
& ( ( hoasapinj2_lthm = $true )
| ( sP41 != $true ) )
& ( lamnotvar = $true )
& ( axvarshift = $true )
& ( hoasinduction_lem3b_gthm = $true )
& ( pushprop = $true )
& ! [X265: d_subst,X266: d_subst] :
( ( X265 = X266 )
| ( ( d2subst @ X266 )
!= ( d2subst @ X265 ) ) )
& ( ulamvarind = $true )
& ( substmonoid_gthm = $true )
& ( hoasinduction_lem2_lthm = $true )
& ( pushprop_lem2v2_lthm = $true )
& ( ( shinj = $true )
| ? [X328: term,X329: term] :
( ( X328 != X329 )
& ( ( sub @ X329 @ sh )
= ( sub @ X328 @ sh ) ) ) )
& ( ! [X328: term,X329: term] :
( ( X328 = X329 )
| ( ( sub @ X329 @ sh )
!= ( sub @ X328 @ sh ) ) )
| ( shinj != $true ) )
& ( ( axshiftcons = $true )
| ? [X117: term,X118: subst] :
( ( comp @ sh @ ( push @ X117 @ X118 ) )
!= X118 ) )
& ( ! [X117: term,X118: subst] :
( ( comp @ sh @ ( push @ X117 @ X118 ) )
= X118 )
| ( axshiftcons != $true ) )
& ( hoasapinj1_gthm = $true )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( hoasinduction_lem1_lthm = $true )
& ( ( sP39 = $true )
| ( hoasinduction_lem3v2 != $true ) )
& ( ( hoasinduction_lem3v2 = $true )
| ( sP39 != $true ) )
& ( ( hoasinduction_lem3v2_f_lthm = $true )
| ? [X124: term] :
! [X125: subst > term > term] :
? [X126: term,X127: subst] :
( ( sub @ X124 @ ( push @ X126 @ X127 ) )
!= ( X125 @ X127 @ X126 ) ) )
& ( ! [X124: term] :
? [X125: subst > term > term] :
! [X126: term,X127: subst] :
( ( sub @ X124 @ ( push @ X126 @ X127 ) )
= ( X125 @ X127 @ X126 ) )
| ( hoasinduction_lem3v2_f_lthm != $true ) )
& ( ( d2subst @ d_id )
= id )
& ( pushprop_lem1v2_gthm = $true )
& ( ! [X529: term] :
? [X530: subst > term > term] :
( ( X530 @ sh @ one )
= ( sub @ X529 @ ( push @ one @ sh ) ) )
| ( hoasinduction_lem3b != $true ) )
& ( ( hoasinduction_lem3b = $true )
| ? [X529: term] :
! [X530: subst > term > term] :
( ( X530 @ sh @ one )
!= ( sub @ X529 @ ( push @ one @ sh ) ) ) )
& ( ( sP35 = $true )
| ( hoaslaminj_lthm != $true ) )
& ( ( hoaslaminj_lthm = $true )
| ( sP35 != $true ) )
& ( ! [X404: subst,X405: subst > term > term,X406: term,X407: subst > term > term] :
( ? [X411: subst,X412: subst,X413: term] :
( ( X405 @ ( comp @ X412 @ X411 ) @ ( sub @ X413 @ X411 ) )
!= ( sub @ ( X405 @ X412 @ X413 ) @ X411 ) )
| ( ( lam @ ( X407 @ sh @ one ) )
!= ( lam @ ( X405 @ sh @ one ) ) )
| ? [X408: term,X409: subst,X410: subst] :
( ( X407 @ ( comp @ X409 @ X410 ) @ ( sub @ X408 @ X410 ) )
!= ( sub @ ( X407 @ X409 @ X408 ) @ X410 ) )
| ( ( X407 @ X404 @ X406 )
= ( X405 @ X404 @ X406 ) ) )
| ( hoaslaminj != $true ) )
& ( ( hoaslaminj = $true )
| ? [X404: subst,X405: subst > term > term,X406: term,X407: subst > term > term] :
( ! [X411: subst,X412: subst,X413: term] :
( ( X405 @ ( comp @ X412 @ X411 ) @ ( sub @ X413 @ X411 ) )
= ( sub @ ( X405 @ X412 @ X413 ) @ X411 ) )
& ( ( lam @ ( X407 @ sh @ one ) )
= ( lam @ ( X405 @ sh @ one ) ) )
& ! [X408: term,X409: subst,X410: subst] :
( ( X407 @ ( comp @ X409 @ X410 ) @ ( sub @ X408 @ X410 ) )
= ( sub @ ( X407 @ X409 @ X408 ) @ X410 ) )
& ( ( X407 @ X404 @ X406 )
!= ( X405 @ X404 @ X406 ) ) ) )
& ( hoaslamnotap_gthm = $true )
& ( ( substmonoid_lthm = $true )
| ( $true != sP33 ) )
& ( ( $true = sP33 )
| ( substmonoid_lthm != $true ) )
& ( ! [X48: term,X49: term,X50: term,X51: term] :
( ( ( ap @ X49 @ X48 )
!= ( ap @ X50 @ X51 ) )
| ( X48 = X51 ) )
| ( apinj2 != $true ) )
& ( ( apinj2 = $true )
| ? [X48: term,X49: term,X50: term,X51: term] :
( ( ( ap @ X49 @ X48 )
= ( ap @ X50 @ X51 ) )
& ( X48 != X51 ) ) )
& ( hoasinduction_lem2_gthm = $true )
& ( pushprop_lem3v2 = $true )
& ( pushprop_lem1_gthm = $true )
& ( ( hoasapinj1_lthm = $true )
| ( $true != sP32 ) )
& ( ( $true = sP32 )
| ( hoasapinj1_lthm != $true ) )
& ( ( $true = sP30 )
| ? [X469: term] :
( ( sub @ X469 @ id )
!= X469 )
| ? [X465: term] :
! [X466: subst > term > term] :
? [X467: subst,X468: term] :
( ( sub @ X465 @ ( push @ X468 @ X467 ) )
!= ( X466 @ X467 @ X468 ) )
| ( hoasinduction_lem3v2a_lthm != $true ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
| ( ( $true != sP30 )
& ! [X469: term] :
( ( sub @ X469 @ id )
= X469 )
& ! [X465: term] :
? [X466: subst > term > term] :
! [X467: subst,X468: term] :
( ( sub @ X465 @ ( push @ X468 @ X467 ) )
= ( X466 @ X467 @ X468 ) ) ) )
& ( ? [X151: subst,X152: term] :
( ( comp @ sh @ ( push @ X152 @ X151 ) )
!= X151 )
| ? [X149: term,X150: subst] :
( ( sub @ one @ ( push @ X149 @ X150 ) )
!= X149 )
| ! [X153: term,X154: term > $o,X155: subst,X156: term,X157: term > $o] :
( ( ( X157 @ ( sub @ X153 @ ( push @ X156 @ X155 ) ) )
= $true )
| ( $true
!= ( X154 @ X153 ) ) )
| ( pushprop_lem1_lthm != $true ) )
& ( ( pushprop_lem1_lthm = $true )
| ( ! [X151: subst,X152: term] :
( ( comp @ sh @ ( push @ X152 @ X151 ) )
= X151 )
& ! [X149: term,X150: subst] :
( ( sub @ one @ ( push @ X149 @ X150 ) )
= X149 )
& ? [X153: term,X154: term > $o,X155: subst,X156: term,X157: term > $o] :
( ( ( X157 @ ( sub @ X153 @ ( push @ X156 @ X155 ) ) )
!= $true )
& ( $true
= ( X154 @ X153 ) ) ) ) )
& ( ( $true = sP27 )
| ( $true = sP28 )
| ? [X81: term] :
( ( sub @ X81 @ id )
!= X81 )
| ( hoasinduction_lem3a_lthm != $true ) )
& ( ( hoasinduction_lem3a_lthm = $true )
| ( ( $true != sP27 )
& ( $true != sP28 )
& ! [X81: term] :
( ( sub @ X81 @ id )
= X81 ) ) )
& ( hoasinduction_lem1v2 = $true )
& ( ! [X399: subst,X400: term > $o,X401: term > $o,X402: term] :
( ? [X403: term] :
( ( X400 @ ( sub @ X403 @ ( push @ X402 @ X399 ) ) )
!= ( X401 @ X403 ) )
| ( $true
= ( X401 @ one ) )
| ( $true
!= ( X400 @ X402 ) ) )
| ( pushprop_lem1v2 != $true ) )
& ( ( pushprop_lem1v2 = $true )
| ? [X399: subst,X400: term > $o,X401: term > $o,X402: term] :
( ! [X403: term] :
( ( X400 @ ( sub @ X403 @ ( push @ X402 @ X399 ) ) )
= ( X401 @ X403 ) )
& ( $true
!= ( X401 @ one ) )
& ( $true
= ( X400 @ X402 ) ) ) )
& ( lamnotap != $true )
& ( hoasapnotvar_gthm = $true )
& ( ! [X449: subst > term > subst > $o] :
? [X450: term > $o] :
! [X451: term] :
( ( X449 @ id @ X451 @ id )
= ( X450 @ X451 ) )
| ( hoasinduction_lem0_lthm != $true ) )
& ( ( hoasinduction_lem0_lthm = $true )
| ? [X449: subst > term > subst > $o] :
! [X450: term > $o] :
? [X451: term] :
( ( X449 @ id @ X451 @ id )
!= ( X450 @ X451 ) ) )
& ( ( d2subst @ d_id )
= sh )
& ( ( pushprop_lem1v2_lthm = $true )
| ( ? [X286: term,X287: subst,X288: term > $o,X289: term > $o] :
( ! [X290: term] :
( ( X288 @ ( sub @ X290 @ ( push @ X286 @ X287 ) ) )
= ( X289 @ X290 ) )
& ( ( X289 @ one )
!= $true )
& ( $true
= ( X288 @ X286 ) ) )
& ! [X284: term,X285: subst] :
( ( sub @ one @ ( push @ X284 @ X285 ) )
= X284 ) ) )
& ( ! [X286: term,X287: subst,X288: term > $o,X289: term > $o] :
( ? [X290: term] :
( ( X288 @ ( sub @ X290 @ ( push @ X286 @ X287 ) ) )
!= ( X289 @ X290 ) )
| ( ( X289 @ one )
= $true )
| ( $true
!= ( X288 @ X286 ) ) )
| ? [X284: term,X285: subst] :
( ( sub @ one @ ( push @ X284 @ X285 ) )
!= X284 )
| ( pushprop_lem1v2_lthm != $true ) )
& ( hoasinduction_lem1_gthm = $true )
& ( pushprop_lem0_gthm = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ( axvarid = $true )
| ? [X236: term] :
( ( sub @ X236 @ id )
!= X236 ) )
& ( ! [X236: term] :
( ( sub @ X236 @ id )
= X236 )
| ( axvarid != $true ) )
& ( ( sP24 = $true )
| ( hoasinduction_lem3v2a != $true ) )
& ( ( hoasinduction_lem3v2a = $true )
| ( sP24 != $true ) )
& ( ( hoasapinj1 = $true )
| ? [X486: term,X487: term,X488: term,X489: term] :
( ( ( ap @ ( sub @ X489 @ id ) @ X486 )
= ( ap @ ( sub @ X488 @ id ) @ X487 ) )
& ( X488 != X489 ) ) )
& ( ! [X486: term,X487: term,X488: term,X489: term] :
( ( ( ap @ ( sub @ X489 @ id ) @ X486 )
!= ( ap @ ( sub @ X488 @ id ) @ X487 ) )
| ( X488 = X489 ) )
| ( hoasapinj1 != $true ) )
& ( pushprop_gthm = $true )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( axscons = $true )
| ? [X267: subst] :
( ( push @ ( sub @ one @ X267 ) @ ( comp @ sh @ X267 ) )
!= X267 ) )
& ( ! [X267: subst] :
( ( push @ ( sub @ one @ X267 ) @ ( comp @ sh @ X267 ) )
= X267 )
| ( axscons != $true ) )
& ( ( hoasinduction = $true )
| ( $true != sP22 ) )
& ( ( $true = sP22 )
| ( hoasinduction != $true ) )
& ( pushprop_lem2v2 = $true )
& ( ( hoasinduction_no_psi_cond = $true )
| ? [X330: term,X331: subst > term > subst > $o] :
( ( ( X331 @ id @ X330 @ id )
!= $true )
& ( ( sP17 @ X331 )
!= $true )
& ( ( sP16 @ X331 )
!= $true ) ) )
& ( ! [X330: term,X331: subst > term > subst > $o] :
( ( ( X331 @ id @ X330 @ id )
= $true )
| ( ( sP17 @ X331 )
= $true )
| ( ( sP16 @ X331 )
= $true ) )
| ( hoasinduction_no_psi_cond != $true ) )
& ( hoasinduction_lem3_gthm = $true )
& ( ( termmset = $true )
| ? [X394: term] :
( ( sub @ X394 @ id )
!= X394 ) )
& ( ! [X394: term] :
( ( sub @ X394 @ id )
= X394 )
| ( termmset != $true ) )
& ! [X531: d_term] : ( d_one = X531 )
& ( ulamvarsh = $true )
& ( hoasapinj2_gthm = $true )
& ( axmap = $true )
& ( ( sP15 = $true )
| ( hoasinduction_lem3 != $true ) )
& ( ( hoasinduction_lem3 = $true )
| ( sP15 != $true ) )
& ( ! [X254: term] :
( ( sub @ X254 @ id )
= X254 )
| ? [X253: term] :
( ( sub @ X253 @ id )
!= X253 )
| ( termmset_lthm != $true ) )
& ( ( termmset_lthm = $true )
| ( ? [X254: term] :
( ( sub @ X254 @ id )
!= X254 )
& ! [X253: term] :
( ( sub @ X253 @ id )
= X253 ) ) )
& ( ( pushprop_lem1 = $true )
| ? [X275: term,X276: term,X277: term > $o,X278: subst,X279: term > $o] :
( ( ( X279 @ X276 )
= $true )
& ( ( X277 @ ( sub @ X276 @ ( push @ X275 @ X278 ) ) )
!= $true ) ) )
& ( ! [X275: term,X276: term,X277: term > $o,X278: subst,X279: term > $o] :
( ( ( X279 @ X276 )
!= $true )
| ( ( X277 @ ( sub @ X276 @ ( push @ X275 @ X278 ) ) )
= $true ) )
| ( pushprop_lem1 != $true ) )
& ( ( axvarcons = $true )
| ? [X77: subst,X78: term] :
( ( sub @ one @ ( push @ X78 @ X77 ) )
!= X78 ) )
& ( ! [X77: subst,X78: term] :
( ( sub @ one @ ( push @ X78 @ X77 ) )
= X78 )
| ( axvarcons != $true ) )
& ( ( hoasinduction_lthm_3 = $true )
| ( ( $true != sP11 )
& ( $true != sP9 )
& ! [X357: term] :
( ( sub @ X357 @ id )
= X357 )
& ! [X347: subst > term > subst > $o] :
? [X348: term > $o] :
! [X349: term] :
( ( X347 @ id @ X349 @ id )
= ( X348 @ X349 ) )
& ( sP10 != $true ) ) )
& ( ( $true = sP11 )
| ( $true = sP9 )
| ? [X357: term] :
( ( sub @ X357 @ id )
!= X357 )
| ? [X347: subst > term > subst > $o] :
! [X348: term > $o] :
? [X349: term] :
( ( X347 @ id @ X349 @ id )
!= ( X348 @ X349 ) )
| ( sP10 = $true )
| ( hoasinduction_lthm_3 != $true ) )
& ( pushprop_lthm = $true )
& ( ! [X528: subst] :
( ( comp @ id @ X528 )
= X528 )
| ( axidl != $true ) )
& ( ( axidl = $true )
| ? [X528: subst] :
( ( comp @ id @ X528 )
!= X528 ) )
& ( ( hoasinduction_lem3aa = $true )
| ( sP1 != $true ) )
& ( ( sP1 = $true )
| ( hoasinduction_lem3aa != $true ) )
& ( hoaslaminj_gthm = $true )
& ( ( hoasinduction_lem0 = $true )
| ? [X525: subst > term > subst > $o] :
! [X526: term > $o] :
? [X527: term] :
( ( X525 @ id @ X527 @ id )
!= ( X526 @ X527 ) ) )
& ( ! [X525: subst > term > subst > $o] :
? [X526: term > $o] :
! [X527: term] :
( ( X525 @ id @ X527 @ id )
= ( X526 @ X527 ) )
| ( hoasinduction_lem0 != $true ) )
& ! [X484: subst] :
? [X485: d_subst] :
( ( d2subst @ X485 )
= X484 ) ),
inference(nnf_transformation,[status(thm)],[f126]) ).
thf(f126,plain,
( ( hoasapnotvar = $true )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( apinj1 = $true )
<=> ! [X261: term,X262: term,X263: term,X264: term] :
( ( X262 = X264 )
| ( ( ap @ X264 @ X263 )
!= ( ap @ X262 @ X261 ) ) ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( hoaslamnotvar_gthm = $true )
& ( ! [X52: subst] :
( ( comp @ X52 @ id )
= X52 )
<=> ( axidr = $true ) )
& ( termmset_gthm = $true )
& ( ( ( sP108 = $true )
| ? [X10: term] :
( ( sub @ X10 @ id )
!= X10 )
| ? [X0: subst > term > subst > $o] :
! [X1: term > $o] :
? [X2: term] :
( ( X0 @ id @ X2 @ id )
!= ( X1 @ X2 ) )
| ( sP109 = $true )
| ( sP107 = $true ) )
<=> ( hoasinduction_no_psi_cond_lthm = $true ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ! [X291: d_subst] : ( d_id = X291 )
& ( ( ! [X79: subst] :
( ( comp @ id @ X79 )
= X79 )
& ! [X80: subst] :
( ( comp @ X80 @ id )
= X80 ) )
<=> ( substmonoid = $true ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( one
= ( d2term @ d_one ) )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ( sP100 = $true )
<=> ( hoasinduction_lem3aa_lthm = $true ) )
& ( ( induction = $true )
<=> ( sP98 = $true ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
<=> ( ? [X98: term] :
( ( sub @ X98 @ id )
!= X98 )
| ( $true = sP95 ) ) )
& ( pushprop_lthm_orig = $true )
& ( hoaslamnotvar_lthm = $true )
& ( hoaslamnotap_lthm = $true )
& ! [X234: d_term,X235: d_term] :
( ( ( d2term @ X234 )
!= ( d2term @ X235 ) )
| ( X234 = X235 ) )
& ( hoaslamnotvar = $true )
& ( ( hoasinduction_lem2 = $true )
<=> ( $true = sP91 ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( axabs = $true )
& ( ! [X480: term,X481: term,X482: term,X483: term] :
( ( ( ap @ ( sub @ X482 @ id ) @ X481 )
!= ( ap @ ( sub @ X480 @ id ) @ X483 ) )
| ( X481 = X483 ) )
<=> ( hoasapinj2 = $true ) )
& ( ( induction2 = $true )
<=> ( sP88 = $true ) )
& ( induction2_gthm = $true )
& ( ( $true = sP85 )
<=> ( induction2lem = $true ) )
& ( hoasinduction_lem1v2_gthm = $true )
& ( ( ( sP81 = $true )
| ? [X128: term] :
( ( sub @ X128 @ id )
!= X128 )
| ( $true = sP82 ) )
<=> ( induction2_lthm = $true ) )
& ( hoasapnotvar_lthm = $true )
& ( ( hoasinduction_lem3v2_f = $true )
<=> ! [X280: term] :
? [X281: subst > term > term] :
! [X282: term,X283: subst] :
( ( X281 @ X283 @ X282 )
= ( sub @ X280 @ ( push @ X282 @ X283 ) ) ) )
& ( axclos = $true )
& ( ! [X30: term,X31: term] :
( ( X30 = X31 )
| ( ( lam @ X30 )
!= ( lam @ X31 ) ) )
<=> ( laminj = $true ) )
& ( pushprop_lem3v2_lthm = $true )
& ( axassoc = $true )
& ( ulamvar1 != $true )
& ( ( hoasinduction_lem3b_lthm = $true )
<=> ! [X339: term] :
? [X340: subst > term > term] :
( ( X340 @ sh @ one )
= ( sub @ X339 @ ( push @ one @ sh ) ) ) )
& ( ( ( sP72 = $true )
| ( $true = sP75 )
| ( sP74 = $true )
| ( $true = sP73 ) )
<=> ( hoasinduction_lthm = $true ) )
& ( ( induction2lem_lthm = $true )
<=> ( ( sP60 = $true )
| ( sP59 = $true )
| ? [X510: subst] :
( ( comp @ X510 @ id )
!= X510 )
| ? [X508: subst,X509: term] :
( ( comp @ sh @ ( push @ X509 @ X508 ) )
!= X508 )
| ? [X506: term,X507: subst] :
( ( sub @ one @ ( push @ X506 @ X507 ) )
!= X506 ) ) )
& ( ! [X144: subst,X145: term > $o,X146: term] :
? [X147: term > $o] :
! [X148: term] :
( ( X145 @ ( sub @ X148 @ ( push @ X146 @ X144 ) ) )
= ( X147 @ X148 ) )
<=> ( pushprop_lem0_lthm = $true ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) )
= ( Y3 @ Y4 ) ) ) ) )
& ( apnotvar = $true )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( hoasinduction_gthm = $true )
& ( axapp = $true )
& ( ( hoasinduction_lem3_lthm = $true )
<=> ( ( sP54 = $true )
| ? [X424: term] :
( ( sub @ X424 @ id )
!= X424 )
| ( $true = sP53 ) ) )
& ( ( pushprop_lem0 = $true )
<=> ! [X119: term > $o,X120: subst,X121: term] :
? [X122: term > $o] :
! [X123: term] :
( ( X122 @ X123 )
= ( X119 @ ( sub @ X123 @ ( push @ X121 @ X120 ) ) ) ) )
& ( induction2lem_gthm = $true )
& ( ( $true = sP48 )
<=> ( hoasinduction_lem2v2 = $true ) )
& ( ( hoasinduction_lem3aaa = $true )
<=> ( $true = sP45 ) )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ( hoasinduction_lem3a = $true )
<=> ( $true = sP43 ) )
& ( ! [X341: subst > term > term,X342: term,X343: term] :
( ( ( ap @ ( sub @ X342 @ id ) @ X343 )
!= ( lam @ ( X341 @ sh @ one ) ) )
| ? [X344: subst,X345: term,X346: subst] :
( ( sub @ ( X341 @ X346 @ X345 ) @ X344 )
!= ( X341 @ ( comp @ X346 @ X344 ) @ ( sub @ X345 @ X344 ) ) ) )
<=> ( hoaslamnotap = $true ) )
& ( hoasinduction_lem1 = $true )
& ( pushprop_lem2v2_gthm = $true )
& ! [X422: term] :
? [X423: d_term] :
( ( d2term @ X423 )
= X422 )
& ( ( sP41 = $true )
<=> ( hoasapinj2_lthm = $true ) )
& ( lamnotvar = $true )
& ( axvarshift = $true )
& ( hoasinduction_lem3b_gthm = $true )
& ( pushprop = $true )
& ! [X265: d_subst,X266: d_subst] :
( ( X265 = X266 )
| ( ( d2subst @ X266 )
!= ( d2subst @ X265 ) ) )
& ( ulamvarind = $true )
& ( substmonoid_gthm = $true )
& ( hoasinduction_lem2_lthm = $true )
& ( pushprop_lem2v2_lthm = $true )
& ( ( shinj = $true )
<=> ! [X328: term,X329: term] :
( ( X328 = X329 )
| ( ( sub @ X329 @ sh )
!= ( sub @ X328 @ sh ) ) ) )
& ( ( axshiftcons = $true )
<=> ! [X117: term,X118: subst] :
( ( comp @ sh @ ( push @ X117 @ X118 ) )
= X118 ) )
& ( hoasapinj1_gthm = $true )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( hoasinduction_lem1_lthm = $true )
& ( ( sP39 = $true )
<=> ( hoasinduction_lem3v2 = $true ) )
& ( ( hoasinduction_lem3v2_f_lthm = $true )
<=> ! [X124: term] :
? [X125: subst > term > term] :
! [X126: term,X127: subst] :
( ( sub @ X124 @ ( push @ X126 @ X127 ) )
= ( X125 @ X127 @ X126 ) ) )
& ( ( d2subst @ d_id )
= id )
& ( pushprop_lem1v2_gthm = $true )
& ( ! [X529: term] :
? [X530: subst > term > term] :
( ( X530 @ sh @ one )
= ( sub @ X529 @ ( push @ one @ sh ) ) )
<=> ( hoasinduction_lem3b = $true ) )
& ( ( sP35 = $true )
<=> ( hoaslaminj_lthm = $true ) )
& ( ! [X404: subst,X405: subst > term > term,X406: term,X407: subst > term > term] :
( ? [X411: subst,X412: subst,X413: term] :
( ( X405 @ ( comp @ X412 @ X411 ) @ ( sub @ X413 @ X411 ) )
!= ( sub @ ( X405 @ X412 @ X413 ) @ X411 ) )
| ( ( lam @ ( X407 @ sh @ one ) )
!= ( lam @ ( X405 @ sh @ one ) ) )
| ? [X408: term,X409: subst,X410: subst] :
( ( X407 @ ( comp @ X409 @ X410 ) @ ( sub @ X408 @ X410 ) )
!= ( sub @ ( X407 @ X409 @ X408 ) @ X410 ) )
| ( ( X407 @ X404 @ X406 )
= ( X405 @ X404 @ X406 ) ) )
<=> ( hoaslaminj = $true ) )
& ( hoaslamnotap_gthm = $true )
& ( ( substmonoid_lthm = $true )
<=> ( $true = sP33 ) )
& ( ! [X48: term,X49: term,X50: term,X51: term] :
( ( ( ap @ X49 @ X48 )
!= ( ap @ X50 @ X51 ) )
| ( X48 = X51 ) )
<=> ( apinj2 = $true ) )
& ( hoasinduction_lem2_gthm = $true )
& ( pushprop_lem3v2 = $true )
& ( pushprop_lem1_gthm = $true )
& ( ( hoasapinj1_lthm = $true )
<=> ( $true = sP32 ) )
& ( ( ( $true = sP30 )
| ? [X469: term] :
( ( sub @ X469 @ id )
!= X469 )
| ? [X465: term] :
! [X466: subst > term > term] :
? [X467: subst,X468: term] :
( ( sub @ X465 @ ( push @ X468 @ X467 ) )
!= ( X466 @ X467 @ X468 ) ) )
<=> ( hoasinduction_lem3v2a_lthm = $true ) )
& ( ( ? [X151: subst,X152: term] :
( ( comp @ sh @ ( push @ X152 @ X151 ) )
!= X151 )
| ? [X149: term,X150: subst] :
( ( sub @ one @ ( push @ X149 @ X150 ) )
!= X149 )
| ! [X153: term,X154: term > $o,X155: subst,X156: term,X157: term > $o] :
( ( ( X157 @ ( sub @ X153 @ ( push @ X156 @ X155 ) ) )
= $true )
| ( $true
!= ( X154 @ X153 ) ) ) )
<=> ( pushprop_lem1_lthm = $true ) )
& ( ( ( $true = sP27 )
| ( $true = sP28 )
| ? [X81: term] :
( ( sub @ X81 @ id )
!= X81 ) )
<=> ( hoasinduction_lem3a_lthm = $true ) )
& ( hoasinduction_lem1v2 = $true )
& ( ! [X399: subst,X400: term > $o,X401: term > $o,X402: term] :
( ? [X403: term] :
( ( X400 @ ( sub @ X403 @ ( push @ X402 @ X399 ) ) )
!= ( X401 @ X403 ) )
| ( $true
= ( X401 @ one ) )
| ( $true
!= ( X400 @ X402 ) ) )
<=> ( pushprop_lem1v2 = $true ) )
& ( lamnotap != $true )
& ( hoasapnotvar_gthm = $true )
& ( ! [X449: subst > term > subst > $o] :
? [X450: term > $o] :
! [X451: term] :
( ( X449 @ id @ X451 @ id )
= ( X450 @ X451 ) )
<=> ( hoasinduction_lem0_lthm = $true ) )
& ( ( d2subst @ d_id )
= sh )
& ( ( pushprop_lem1v2_lthm = $true )
<=> ( ! [X286: term,X287: subst,X288: term > $o,X289: term > $o] :
( ? [X290: term] :
( ( X288 @ ( sub @ X290 @ ( push @ X286 @ X287 ) ) )
!= ( X289 @ X290 ) )
| ( ( X289 @ one )
= $true )
| ( $true
!= ( X288 @ X286 ) ) )
| ? [X284: term,X285: subst] :
( ( sub @ one @ ( push @ X284 @ X285 ) )
!= X284 ) ) )
& ( hoasinduction_lem1_gthm = $true )
& ( pushprop_lem0_gthm = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ( axvarid = $true )
<=> ! [X236: term] :
( ( sub @ X236 @ id )
= X236 ) )
& ( ( sP24 = $true )
<=> ( hoasinduction_lem3v2a = $true ) )
& ( ( hoasapinj1 = $true )
<=> ! [X486: term,X487: term,X488: term,X489: term] :
( ( ( ap @ ( sub @ X489 @ id ) @ X486 )
!= ( ap @ ( sub @ X488 @ id ) @ X487 ) )
| ( X488 = X489 ) ) )
& ( pushprop_gthm = $true )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( axscons = $true )
<=> ! [X267: subst] :
( ( push @ ( sub @ one @ X267 ) @ ( comp @ sh @ X267 ) )
= X267 ) )
& ( ( hoasinduction = $true )
<=> ( $true = sP22 ) )
& ( pushprop_lem2v2 = $true )
& ( ( hoasinduction_no_psi_cond = $true )
<=> ! [X330: term,X331: subst > term > subst > $o] :
( ( ( X331 @ id @ X330 @ id )
= $true )
| ( ( sP17 @ X331 )
= $true )
| ( ( sP16 @ X331 )
= $true ) ) )
& ( hoasinduction_lem3_gthm = $true )
& ( ( termmset = $true )
<=> ! [X394: term] :
( ( sub @ X394 @ id )
= X394 ) )
& ! [X531: d_term] : ( d_one = X531 )
& ( ulamvarsh = $true )
& ( hoasapinj2_gthm = $true )
& ( axmap = $true )
& ( ( sP15 = $true )
<=> ( hoasinduction_lem3 = $true ) )
& ( ( ! [X254: term] :
( ( sub @ X254 @ id )
= X254 )
| ? [X253: term] :
( ( sub @ X253 @ id )
!= X253 ) )
<=> ( termmset_lthm = $true ) )
& ( ( pushprop_lem1 = $true )
<=> ! [X275: term,X276: term,X277: term > $o,X278: subst,X279: term > $o] :
( ( ( X279 @ X276 )
!= $true )
| ( ( X277 @ ( sub @ X276 @ ( push @ X275 @ X278 ) ) )
= $true ) ) )
& ( ( axvarcons = $true )
<=> ! [X77: subst,X78: term] :
( ( sub @ one @ ( push @ X78 @ X77 ) )
= X78 ) )
& ( ( hoasinduction_lthm_3 = $true )
<=> ( ( $true = sP11 )
| ( $true = sP9 )
| ? [X357: term] :
( ( sub @ X357 @ id )
!= X357 )
| ? [X347: subst > term > subst > $o] :
! [X348: term > $o] :
? [X349: term] :
( ( X347 @ id @ X349 @ id )
!= ( X348 @ X349 ) )
| ( sP10 = $true ) ) )
& ( pushprop_lthm = $true )
& ( ! [X528: subst] :
( ( comp @ id @ X528 )
= X528 )
<=> ( axidl = $true ) )
& ( ( hoasinduction_lem3aa = $true )
<=> ( sP1 = $true ) )
& ( hoaslaminj_gthm = $true )
& ( ( hoasinduction_lem0 = $true )
<=> ! [X525: subst > term > subst > $o] :
? [X526: term > $o] :
! [X527: term] :
( ( X525 @ id @ X527 @ id )
= ( X526 @ X527 ) ) )
& ! [X484: subst] :
? [X485: d_subst] :
( ( d2subst @ X485 )
= X484 ) ),
inference(definition_folding,[status(thm)],[f13,f125,f124,f123,f122,f121,f120,f119,f118,f117,f116,f115,f114,f113,f112,f111,f110,f109,f108,f107,f106,f105,f104,f103,f102,f101,f100,f99,f98,f97,f96,f95,f94,f93,f92,f91,f90,f89,f88,f87,f86,f85,f84,f83,f82,f81,f80,f79,f78,f77,f76,f75,f74,f73,f72,f71,f70,f69,f68,f67,f66,f65,f64,f63,f62,f61,f60,f59,f58,f57,f56,f55,f54,f53,f52,f51,f50,f49,f48,f47,f46,f45,f44,f43,f42,f41,f40,f39,f38,f37,f36,f35,f34,f33,f32,f31,f30,f29,f28,f27,f26,f25,f24,f23,f22,f21,f20,f19,f18,f17,f16]) ).
thf(f16,plain,
! [X498: subst > term > subst > $o] :
( ( $true
= ( sP0 @ X498 ) )
<=> ? [X501: subst > term > term] :
( ! [X505: term] :
( ( $true
!= ( X498 @ id @ X505 @ id ) )
| ( $true
= ( X498 @ id @ ( X501 @ id @ X505 ) @ id ) ) )
& ( $true
!= ( X498 @ id @ ( lam @ ( X501 @ sh @ one ) ) @ id ) )
& ! [X502: subst,X503: subst,X504: term] :
( ( X501 @ ( comp @ X502 @ X503 ) @ ( sub @ X504 @ X503 ) )
= ( sub @ ( X501 @ X502 @ X504 ) @ X503 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f17,plain,
( ( sP1 = $true )
<=> ! [X498: subst > term > subst > $o,X499: term] :
( ( $true
= ( sP0 @ X498 ) )
| ? [X500: term] :
( ( $true
!= ( X498 @ id @ ( sub @ X499 @ ( push @ X500 @ id ) ) @ id ) )
& ( $true
= ( X498 @ id @ X500 @ id ) ) )
| ( $true
= ( X498 @ id @ ( lam @ ( sub @ X499 @ ( push @ one @ sh ) ) ) @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f18,plain,
! [X358: subst > term > subst > $o] :
( ( $true
= ( sP2 @ X358 ) )
<=> ! [X362: subst > term > term] :
( ? [X363: term] :
( ( ( X358 @ id @ ( X362 @ id @ X363 ) @ id )
!= $true )
& ( ( X358 @ id @ X363 @ id )
= $true ) )
| ( $true
= ( X358 @ id @ ( lam @ ( X362 @ sh @ one ) ) @ id ) )
| ? [X364: subst,X365: subst,X366: term] :
( ( sub @ ( X362 @ X364 @ X366 ) @ X365 )
!= ( X362 @ ( comp @ X364 @ X365 ) @ ( sub @ X366 @ X365 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f19,plain,
! [X369: subst > term > subst > $o] :
( ( ( sP3 @ X369 )
= $true )
<=> ? [X380: subst > term > term] :
( ! [X381: term] :
( ( $true
!= ( X369 @ id @ X381 @ id ) )
| ( ( X369 @ id @ ( X380 @ id @ X381 ) @ id )
= $true ) )
& ! [X382: subst,X383: term,X384: subst] :
( ( X380 @ ( comp @ X382 @ X384 ) @ ( sub @ X383 @ X384 ) )
= ( sub @ ( X380 @ X382 @ X383 ) @ X384 ) )
& ( $true
!= ( X369 @ id @ ( lam @ ( X380 @ sh @ one ) ) @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f20,plain,
! [X369: subst > term > subst > $o] :
( ( ( sP4 @ X369 )
= $true )
<=> ? [X374: term,X375: term] :
( ( ( X369 @ id @ X375 @ id )
= $true )
& ( $true
= ( X369 @ id @ X374 @ id ) )
& ( ( X369 @ id @ ( ap @ ( sub @ X374 @ id ) @ X375 ) @ id )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f21,plain,
! [X369: subst > term > subst > $o] :
( ( $true
= ( sP5 @ X369 ) )
<=> ? [X385: term] :
( ( $true
!= ( X369 @ id @ X385 @ id ) )
& ( $true
= ( var @ ( sub @ X385 @ id ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f22,plain,
! [X369: subst > term > subst > $o] :
( ( $true
= ( sP6 @ X369 ) )
<=> ? [X370: term,X371: subst,X372: subst,X373: subst] :
( ( $true
!= ( X369 @ X373 @ X370 @ ( comp @ X372 @ X371 ) ) )
& ( $true
= ( X369 @ ( comp @ X373 @ X372 ) @ ( sub @ X370 @ X372 ) @ X371 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f23,plain,
! [X351: term > $o] :
( ( $true
= ( sP7 @ X351 ) )
<=> ! [X353: term,X354: term] :
( ( ( X351 @ X353 )
!= $true )
| ( $true
= ( X351 @ ( ap @ X354 @ X353 ) ) )
| ( $true
!= ( X351 @ X354 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f24,plain,
! [X351: term > $o] :
( ( $true
= ( sP8 @ X351 ) )
<=> ! [X355: term] :
( ( $true
= ( X351 @ ( lam @ X355 ) ) )
| ? [X356: term] :
( ( ( X351 @ ( sub @ X355 @ ( push @ X356 @ id ) ) )
!= $true )
& ( ( X351 @ X356 )
= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f25,plain,
( ( $true = sP9 )
<=> ! [X368: term,X369: subst > term > subst > $o] :
( ( ( sP4 @ X369 )
= $true )
| ? [X376: subst,X377: subst,X378: subst,X379: term] :
( ( ( X369 @ X378 @ X379 @ ( comp @ X376 @ X377 ) )
= $true )
& ( ( X369 @ ( comp @ X378 @ X376 ) @ ( sub @ X379 @ X376 ) @ X377 )
!= $true ) )
| ( ( sP3 @ X369 )
= $true )
| ( $true
= ( sP6 @ X369 ) )
| ( $true
= ( X369 @ id @ X368 @ id ) )
| ( $true
= ( sP5 @ X369 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f26,plain,
( ( sP10 = $true )
<=> ? [X358: subst > term > subst > $o,X359: term,X360: term > $o] :
( ( $true
!= ( X360 @ ( lam @ X359 ) ) )
& ! [X361: term] :
( ( X360 @ X361 )
= ( X358 @ id @ X361 @ id ) )
& ! [X367: term] :
( ( ( X360 @ X367 )
!= $true )
| ( $true
= ( X360 @ ( sub @ X359 @ ( push @ X367 @ id ) ) ) ) )
& ( $true
= ( sP2 @ X358 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f27,plain,
( ( $true = sP11 )
<=> ? [X350: term,X351: term > $o] :
( ( $true
!= ( X351 @ X350 ) )
& ( $true
= ( sP7 @ X351 ) )
& ! [X352: term] :
( ( ( X351 @ X352 )
= $true )
| ( ( var @ X352 )
!= $true ) )
& ( $true
= ( sP8 @ X351 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f28,plain,
! [X33: subst > term > subst > $o] :
( ( ( sP12 @ X33 )
= $true )
<=> ? [X42: subst > term > term] :
( ( ( X33 @ id @ ( lam @ ( X42 @ sh @ one ) ) @ id )
!= $true )
& ! [X43: term] :
( ( $true
!= ( X33 @ id @ X43 @ id ) )
| ( ( X33 @ id @ ( X42 @ id @ X43 ) @ id )
= $true ) )
& ! [X44: term,X45: subst,X46: subst] :
( ( X42 @ ( comp @ X46 @ X45 ) @ ( sub @ X44 @ X45 ) )
= ( sub @ ( X42 @ X46 @ X44 ) @ X45 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f29,plain,
! [X33: subst > term > subst > $o] :
( ( $true
= ( sP13 @ X33 ) )
<=> ? [X34: term,X35: subst,X36: subst,X37: subst] :
( ( ( X33 @ X36 @ X34 @ ( comp @ X37 @ X35 ) )
!= $true )
& ( ( X33 @ ( comp @ X36 @ X37 ) @ ( sub @ X34 @ X37 ) @ X35 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f30,plain,
! [X32: term,X33: subst > term > subst > $o] :
( ( ( sP14 @ X33 @ X32 )
= $true )
<=> ? [X47: term] :
( ( ( X33 @ id @ ( sub @ X32 @ ( push @ X47 @ id ) ) @ id )
!= $true )
& ( $true
= ( X33 @ id @ X47 @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f31,plain,
( ( sP15 = $true )
<=> ! [X32: term,X33: subst > term > subst > $o] :
( ( ( sP12 @ X33 )
= $true )
| ? [X38: subst,X39: subst,X40: subst,X41: term] :
( ( $true
!= ( X33 @ ( comp @ X39 @ X40 ) @ ( sub @ X41 @ X40 ) @ X38 ) )
& ( $true
= ( X33 @ X39 @ X41 @ ( comp @ X40 @ X38 ) ) ) )
| ( $true
= ( X33 @ id @ ( lam @ X32 ) @ id ) )
| ( ( sP14 @ X33 @ X32 )
= $true )
| ( $true
= ( sP13 @ X33 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f32,plain,
! [X331: subst > term > subst > $o] :
( ( ( sP16 @ X331 )
= $true )
<=> ? [X332: subst > term > term] :
( ( $true
!= ( X331 @ id @ ( lam @ ( X332 @ sh @ one ) ) @ id ) )
& ! [X333: term] :
( ( ( X331 @ id @ X333 @ id )
!= $true )
| ( ( X331 @ id @ ( X332 @ id @ X333 ) @ id )
= $true ) )
& ! [X334: subst,X335: subst,X336: term] :
( ( sub @ ( X332 @ X335 @ X336 ) @ X334 )
= ( X332 @ ( comp @ X335 @ X334 ) @ ( sub @ X336 @ X334 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f33,plain,
! [X331: subst > term > subst > $o] :
( ( ( sP17 @ X331 )
= $true )
<=> ? [X337: term,X338: term] :
( ( ( X331 @ id @ ( ap @ ( sub @ X337 @ id ) @ X338 ) @ id )
!= $true )
& ( ( X331 @ id @ X338 @ id )
= $true )
& ( ( X331 @ id @ X337 @ id )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f34,plain,
! [X293: subst > term > subst > $o] :
( ( $true
= ( sP18 @ X293 ) )
<=> ? [X294: subst > term > term] :
( ( $true
!= ( X293 @ id @ ( lam @ ( X294 @ sh @ one ) ) @ id ) )
& ! [X298: term] :
( ( $true
!= ( X293 @ id @ X298 @ id ) )
| ( $true
= ( X293 @ id @ ( X294 @ id @ X298 ) @ id ) ) )
& ! [X295: subst,X296: term,X297: subst] :
( ( X294 @ ( comp @ X295 @ X297 ) @ ( sub @ X296 @ X297 ) )
= ( sub @ ( X294 @ X295 @ X296 ) @ X297 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f35,plain,
! [X293: subst > term > subst > $o] :
( ( $true
= ( sP19 @ X293 ) )
<=> ? [X304: term,X305: term] :
( ( $true
!= ( X293 @ id @ ( ap @ ( sub @ X304 @ id ) @ X305 ) @ id ) )
& ( $true
= ( X293 @ id @ X305 @ id ) )
& ( $true
= ( X293 @ id @ X304 @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f36,plain,
! [X293: subst > term > subst > $o] :
( ( $true
= ( sP20 @ X293 ) )
<=> ? [X299: subst,X300: subst,X301: term,X302: subst] :
( ( $true
!= ( X293 @ ( comp @ X302 @ X300 ) @ ( sub @ X301 @ X300 ) @ X299 ) )
& ( ( X293 @ X302 @ X301 @ ( comp @ X300 @ X299 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f37,plain,
! [X293: subst > term > subst > $o] :
( ( ( sP21 @ X293 )
= $true )
<=> ? [X303: term] :
( ( $true
= ( var @ ( sub @ X303 @ id ) ) )
& ( ( X293 @ id @ X303 @ id )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f38,plain,
( ( $true = sP22 )
<=> ! [X292: term,X293: subst > term > subst > $o] :
( ? [X306: term,X307: subst,X308: subst,X309: subst] :
( ( $true
= ( X293 @ ( comp @ X308 @ X307 ) @ ( sub @ X306 @ X307 ) @ X309 ) )
& ( ( X293 @ X308 @ X306 @ ( comp @ X307 @ X309 ) )
!= $true ) )
| ( ( sP21 @ X293 )
= $true )
| ( ( X293 @ id @ X292 @ id )
= $true )
| ( $true
= ( sP19 @ X293 ) )
| ( $true
= ( sP18 @ X293 ) )
| ( $true
= ( sP20 @ X293 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f39,plain,
! [X159: subst > term > subst > $o] :
( ( ( sP23 @ X159 )
= $true )
<=> ? [X162: subst > term > term] :
( ! [X163: term] :
( ( $true
!= ( X159 @ id @ X163 @ id ) )
| ( $true
= ( X159 @ id @ ( X162 @ id @ X163 ) @ id ) ) )
& ( ( X159 @ id @ ( lam @ ( X162 @ sh @ one ) ) @ id )
!= $true )
& ! [X164: subst,X165: term,X166: subst] :
( ( sub @ ( X162 @ X166 @ X165 ) @ X164 )
= ( X162 @ ( comp @ X166 @ X164 ) @ ( sub @ X165 @ X164 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f40,plain,
( ( sP24 = $true )
<=> ! [X158: term > $o,X159: subst > term > subst > $o,X160: term] :
( ? [X167: term] :
( ( $true
!= ( X158 @ ( sub @ X160 @ ( push @ X167 @ id ) ) ) )
& ( ( X158 @ X167 )
= $true ) )
| ? [X161: term] :
( ( X158 @ X161 )
!= ( X159 @ id @ X161 @ id ) )
| ( $true
= ( X158 @ ( lam @ X160 ) ) )
| ( ( sP23 @ X159 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f41,plain,
! [X82: subst > term > subst > $o] :
( ( $true
= ( sP25 @ X82 ) )
<=> ! [X84: subst > term > term] :
( ? [X85: term,X86: subst,X87: subst] :
( ( sub @ ( X84 @ X87 @ X85 ) @ X86 )
!= ( X84 @ ( comp @ X87 @ X86 ) @ ( sub @ X85 @ X86 ) ) )
| ( $true
= ( X82 @ id @ ( lam @ ( X84 @ sh @ one ) ) @ id ) )
| ? [X88: term] :
( ( ( X82 @ id @ ( X84 @ id @ X88 ) @ id )
!= $true )
& ( $true
= ( X82 @ id @ X88 @ id ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f42,plain,
! [X90: subst > term > subst > $o] :
( ( $true
= ( sP26 @ X90 ) )
<=> ? [X92: subst > term > term] :
( ! [X94: term,X95: subst,X96: subst] :
( ( sub @ ( X92 @ X96 @ X94 ) @ X95 )
= ( X92 @ ( comp @ X96 @ X95 ) @ ( sub @ X94 @ X95 ) ) )
& ! [X93: term] :
( ( $true
= ( X90 @ id @ ( X92 @ id @ X93 ) @ id ) )
| ( $true
!= ( X90 @ id @ X93 @ id ) ) )
& ( $true
!= ( X90 @ id @ ( lam @ ( X92 @ sh @ one ) ) @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f43,plain,
( ( $true = sP27 )
<=> ! [X90: subst > term > subst > $o,X91: term] :
( ? [X97: term] :
( ( $true
= ( X90 @ id @ X97 @ id ) )
& ( $true
!= ( X90 @ id @ ( sub @ X91 @ ( push @ X97 @ id ) ) @ id ) ) )
| ( ( X90 @ id @ ( lam @ X91 ) @ id )
= $true )
| ( $true
= ( sP26 @ X90 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f44,plain,
( ( $true = sP28 )
<=> ? [X82: subst > term > subst > $o,X83: term] :
( ( ( X82 @ id @ ( lam @ ( sub @ X83 @ ( push @ one @ sh ) ) ) @ id )
!= $true )
& ! [X89: term] :
( ( $true
= ( X82 @ id @ ( sub @ X83 @ ( push @ X89 @ id ) ) @ id ) )
| ( ( X82 @ id @ X89 @ id )
!= $true ) )
& ( $true
= ( sP25 @ X82 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f45,plain,
! [X470: subst > term > subst > $o] :
( ( $true
= ( sP29 @ X470 ) )
<=> ? [X473: subst > term > term] :
( ! [X475: subst,X476: subst,X477: term] :
( ( X473 @ ( comp @ X476 @ X475 ) @ ( sub @ X477 @ X475 ) )
= ( sub @ ( X473 @ X476 @ X477 ) @ X475 ) )
& ( ( X470 @ id @ ( lam @ ( X473 @ sh @ one ) ) @ id )
!= $true )
& ! [X474: term] :
( ( ( X470 @ id @ X474 @ id )
!= $true )
| ( ( X470 @ id @ ( X473 @ id @ X474 ) @ id )
= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f46,plain,
( ( $true = sP30 )
<=> ! [X470: subst > term > subst > $o,X471: term,X472: term > $o] :
( ( $true
= ( sP29 @ X470 ) )
| ? [X479: term] :
( ( ( X472 @ ( sub @ X471 @ ( push @ X479 @ id ) ) )
!= $true )
& ( $true
= ( X472 @ X479 ) ) )
| ? [X478: term] :
( ( X470 @ id @ X478 @ id )
!= ( X472 @ X478 ) )
| ( ( X472 @ ( lam @ X471 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f47,plain,
( ( sP31 = $true )
<=> ! [X73: term,X74: term,X75: term,X76: term] :
( ( X73 = X74 )
| ( ( ap @ ( sub @ X74 @ id ) @ X76 )
!= ( ap @ ( sub @ X73 @ id ) @ X75 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f48,plain,
( ( $true = sP32 )
<=> ( ( sP31 = $true )
| ? [X69: term,X70: term,X71: term,X72: term] :
( ( ( ap @ X69 @ X70 )
= ( ap @ X71 @ X72 ) )
& ( X69 != X71 ) )
| ? [X68: term] :
( ( sub @ X68 @ id )
!= X68 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f49,plain,
( ( $true = sP33 )
<=> ( ? [X396: subst] :
( ( comp @ X396 @ id )
!= X396 )
| ? [X395: subst] :
( ( comp @ id @ X395 )
!= X395 )
| ( ! [X397: subst] :
( ( comp @ id @ X397 )
= X397 )
& ! [X398: subst] :
( ( comp @ X398 @ id )
= X398 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f50,plain,
( ( sP34 = $true )
<=> ! [X243: subst,X244: term,X245: subst > term > term,X246: subst > term > term] :
( ( ( lam @ ( X246 @ sh @ one ) )
!= ( lam @ ( X245 @ sh @ one ) ) )
| ( ( X246 @ X243 @ X244 )
= ( X245 @ X243 @ X244 ) )
| ? [X250: subst,X251: term,X252: subst] :
( ( X245 @ ( comp @ X250 @ X252 ) @ ( sub @ X251 @ X252 ) )
!= ( sub @ ( X245 @ X250 @ X251 ) @ X252 ) )
| ? [X247: term,X248: subst,X249: subst] :
( ( sub @ ( X246 @ X248 @ X247 ) @ X249 )
!= ( X246 @ ( comp @ X248 @ X249 ) @ ( sub @ X247 @ X249 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f51,plain,
( ( sP35 = $true )
<=> ( ? [X237: subst,X238: term] :
( ( sub @ one @ ( push @ X238 @ X237 ) )
!= X238 )
| ( sP34 = $true )
| ? [X239: term,X240: subst] :
( ( comp @ sh @ ( push @ X239 @ X240 ) )
!= X240 )
| ? [X241: term,X242: term] :
( ( X241 != X242 )
& ( ( lam @ X241 )
= ( lam @ X242 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f52,plain,
! [X311: subst > term > subst > $o] :
( ( ( sP36 @ X311 )
= $true )
<=> ? [X323: subst > term > term] :
( ( ( X311 @ id @ ( lam @ ( X323 @ sh @ one ) ) @ id )
!= $true )
& ! [X325: term,X326: subst,X327: subst] :
( ( X323 @ ( comp @ X327 @ X326 ) @ ( sub @ X325 @ X326 ) )
= ( sub @ ( X323 @ X327 @ X325 ) @ X326 ) )
& ! [X324: term] :
( ( ( X311 @ id @ ( X323 @ id @ X324 ) @ id )
= $true )
| ( $true
!= ( X311 @ id @ X324 @ id ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f53,plain,
! [X311: subst > term > subst > $o] :
( ( ( sP37 @ X311 )
= $true )
<=> ? [X319: subst,X320: subst,X321: term,X322: subst] :
( ( ( X311 @ X322 @ X321 @ ( comp @ X319 @ X320 ) )
= $true )
& ( ( X311 @ ( comp @ X322 @ X319 ) @ ( sub @ X321 @ X319 ) @ X320 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f54,plain,
! [X312: term > $o,X310: term] :
( ( $true
= ( sP38 @ X310 @ X312 ) )
<=> ? [X314: term] :
( ( ( X312 @ X314 )
= $true )
& ( ( X312 @ ( sub @ X310 @ ( push @ X314 @ id ) ) )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f55,plain,
( ( sP39 = $true )
<=> ! [X310: term,X311: subst > term > subst > $o,X312: term > $o] :
( ( ( sP36 @ X311 )
= $true )
| ? [X315: subst,X316: subst,X317: subst,X318: term] :
( ( $true
!= ( X311 @ X316 @ X318 @ ( comp @ X317 @ X315 ) ) )
& ( ( X311 @ ( comp @ X316 @ X317 ) @ ( sub @ X318 @ X317 ) @ X315 )
= $true ) )
| ( $true
= ( sP38 @ X310 @ X312 ) )
| ( ( X312 @ ( lam @ X310 ) )
= $true )
| ( ( sP37 @ X311 )
= $true )
| ? [X313: term] :
( ( X312 @ X313 )
!= ( X311 @ id @ X313 @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f56,plain,
( ( sP40 = $true )
<=> ! [X536: term,X537: term,X538: term,X539: term] :
( ( ( ap @ ( sub @ X536 @ id ) @ X539 )
!= ( ap @ ( sub @ X537 @ id ) @ X538 ) )
| ( X538 = X539 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f57,plain,
( ( sP41 = $true )
<=> ( ? [X532: term,X533: term,X534: term,X535: term] :
( ( ( ap @ X532 @ X534 )
= ( ap @ X535 @ X533 ) )
& ( X533 != X534 ) )
| ( sP40 = $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f58,plain,
! [X491: subst > term > subst > $o] :
( ( $true
= ( sP42 @ X491 ) )
<=> ? [X493: subst > term > term] :
( ! [X497: term] :
( ( ( X491 @ id @ ( X493 @ id @ X497 ) @ id )
= $true )
| ( ( X491 @ id @ X497 @ id )
!= $true ) )
& ( ( X491 @ id @ ( lam @ ( X493 @ sh @ one ) ) @ id )
!= $true )
& ! [X494: subst,X495: subst,X496: term] :
( ( X493 @ ( comp @ X494 @ X495 ) @ ( sub @ X496 @ X495 ) )
= ( sub @ ( X493 @ X494 @ X496 ) @ X495 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f59,plain,
( ( $true = sP43 )
<=> ! [X490: term,X491: subst > term > subst > $o] :
( ( $true
= ( sP42 @ X491 ) )
| ? [X492: term] :
( ( ( X491 @ id @ ( sub @ X490 @ ( push @ X492 @ id ) ) @ id )
!= $true )
& ( ( X491 @ id @ X492 @ id )
= $true ) )
| ( $true
= ( X491 @ id @ ( lam @ X490 ) @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f60,plain,
! [X223: subst > term > subst > $o] :
( ( ( sP44 @ X223 )
= $true )
<=> ? [X225: term,X226: subst > term > term] :
( ! [X233: term] :
( ( ( X223 @ id @ ( X226 @ id @ X233 ) @ id )
= $true )
| ( $true
!= ( X223 @ id @ X233 @ id ) ) )
& ! [X227: subst,X228: term,X229: subst] :
( ( sub @ ( sub @ X225 @ ( push @ X228 @ X229 ) ) @ X227 )
= ( sub @ ( X226 @ X229 @ X228 ) @ X227 ) )
& ( $true
!= ( X223 @ id @ ( lam @ ( X226 @ sh @ one ) ) @ id ) )
& ! [X230: subst,X231: term,X232: subst] :
( ( sub @ X225 @ ( push @ ( sub @ X231 @ X232 ) @ ( comp @ X230 @ X232 ) ) )
= ( X226 @ ( comp @ X230 @ X232 ) @ ( sub @ X231 @ X232 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f61,plain,
( ( $true = sP45 )
<=> ! [X222: term,X223: subst > term > subst > $o] :
( ( ( sP44 @ X223 )
= $true )
| ? [X224: term] :
( ( ( X223 @ id @ X224 @ id )
= $true )
& ( $true
!= ( X223 @ id @ ( sub @ X222 @ ( push @ X224 @ id ) ) @ id ) ) )
| ( $true
= ( X223 @ id @ ( lam @ ( sub @ X222 @ ( push @ one @ sh ) ) ) @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f62,plain,
! [X55: subst > term > subst > $o] :
( ( ( sP46 @ X55 )
= $true )
<=> ? [X61: term,X62: term] :
( ( ( X55 @ id @ X62 @ id )
= $true )
& ( ( X55 @ id @ ( ap @ ( sub @ X62 @ id ) @ X61 ) @ id )
!= $true )
& ( $true
= ( X55 @ id @ X61 @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f63,plain,
! [X55: subst > term > subst > $o] :
( ( ( sP47 @ X55 )
= $true )
<=> ? [X57: subst,X58: term,X59: subst,X60: subst] :
( ( ( X55 @ ( comp @ X60 @ X57 ) @ ( sub @ X58 @ X57 ) @ X59 )
!= $true )
& ( $true
= ( X55 @ X60 @ X58 @ ( comp @ X57 @ X59 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f64,plain,
( ( $true = sP48 )
<=> ! [X53: term,X54: term > $o,X55: subst > term > subst > $o,X56: term] :
( ? [X64: subst,X65: term,X66: subst,X67: subst] :
( ( ( X55 @ X66 @ X65 @ ( comp @ X67 @ X64 ) )
!= $true )
& ( ( X55 @ ( comp @ X66 @ X67 ) @ ( sub @ X65 @ X67 ) @ X64 )
= $true ) )
| ( ( sP46 @ X55 )
= $true )
| ( ( X54 @ ( ap @ X53 @ X56 ) )
= $true )
| ( ( X54 @ X53 )
!= $true )
| ? [X63: term] :
( ( X55 @ id @ X63 @ id )
!= ( X54 @ X63 ) )
| ( ( X54 @ X56 )
!= $true )
| ( ( sP47 @ X55 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f65,plain,
! [X434: subst > term > subst > $o] :
( ( ( sP49 @ X434 )
= $true )
<=> ? [X444: subst > term > term] :
( ! [X445: term] :
( ( ( X434 @ id @ ( X444 @ id @ X445 ) @ id )
= $true )
| ( ( X434 @ id @ X445 @ id )
!= $true ) )
& ( ( X434 @ id @ ( lam @ ( X444 @ sh @ one ) ) @ id )
!= $true )
& ! [X446: subst,X447: term,X448: subst] :
( ( X444 @ ( comp @ X448 @ X446 ) @ ( sub @ X447 @ X446 ) )
= ( sub @ ( X444 @ X448 @ X447 ) @ X446 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f66,plain,
! [X434: subst > term > subst > $o,X433: term] :
( ( $true
= ( sP50 @ X433 @ X434 ) )
<=> ? [X435: term] :
( ( $true
= ( X434 @ id @ X435 @ id ) )
& ( ( X434 @ id @ ( sub @ X433 @ ( push @ X435 @ id ) ) @ id )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f67,plain,
! [X434: subst > term > subst > $o] :
( ( $true
= ( sP51 @ X434 ) )
<=> ? [X436: subst,X437: term,X438: subst,X439: subst] :
( ( $true
!= ( X434 @ ( comp @ X436 @ X439 ) @ ( sub @ X437 @ X439 ) @ X438 ) )
& ( ( X434 @ X436 @ X437 @ ( comp @ X439 @ X438 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f68,plain,
! [X425: subst > term > subst > $o] :
( ( ( sP52 @ X425 )
= $true )
<=> ! [X427: subst > term > term] :
( ? [X428: subst,X429: term,X430: subst] :
( ( X427 @ ( comp @ X430 @ X428 ) @ ( sub @ X429 @ X428 ) )
!= ( sub @ ( X427 @ X430 @ X429 ) @ X428 ) )
| ( $true
= ( X425 @ id @ ( lam @ ( X427 @ sh @ one ) ) @ id ) )
| ? [X431: term] :
( ( $true
= ( X425 @ id @ X431 @ id ) )
& ( ( X425 @ id @ ( X427 @ id @ X431 ) @ id )
!= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f69,plain,
( ( $true = sP53 )
<=> ! [X433: term,X434: subst > term > subst > $o] :
( ( ( sP49 @ X434 )
= $true )
| ( ( X434 @ id @ ( lam @ X433 ) @ id )
= $true )
| ? [X440: subst,X441: term,X442: subst,X443: subst] :
( ( ( X434 @ ( comp @ X442 @ X440 ) @ ( sub @ X441 @ X440 ) @ X443 )
= $true )
& ( ( X434 @ X442 @ X441 @ ( comp @ X440 @ X443 ) )
!= $true ) )
| ( $true
= ( sP51 @ X434 ) )
| ( $true
= ( sP50 @ X433 @ X434 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f70,plain,
( ( sP54 = $true )
<=> ? [X425: subst > term > subst > $o,X426: term] :
( ( $true
!= ( X425 @ id @ ( lam @ ( sub @ X426 @ ( push @ one @ sh ) ) ) @ id ) )
& ! [X432: term] :
( ( $true
= ( X425 @ id @ ( sub @ X426 @ ( push @ X432 @ id ) ) @ id ) )
| ( ( X425 @ id @ X432 @ id )
!= $true ) )
& ( ( sP52 @ X425 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f71,plain,
! [X518: term > $o] :
( ( ( sP55 @ X518 )
= $true )
<=> ? [X520: term] :
( ! [X521: term] :
( ( $true
!= ( X518 @ X521 ) )
| ( $true
= ( X518 @ ( sub @ X520 @ ( push @ X521 @ id ) ) ) ) )
& ( ( X518 @ ( lam @ X520 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f72,plain,
! [X518: term > $o] :
( ( ( sP56 @ X518 )
= $true )
<=> ? [X522: term,X523: term] :
( ( $true
!= ( X518 @ ( ap @ X523 @ X522 ) ) )
& ( ( X518 @ X522 )
= $true )
& ( ( X518 @ X523 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f73,plain,
! [X512: term > $o] :
( ( $true
= ( sP57 @ X512 ) )
<=> ! [X515: term,X516: term] :
( ( ( X512 @ ( ap @ X516 @ X515 ) )
= $true )
| ( ( X512 @ X515 )
!= $true )
| ( $true
!= ( X512 @ X516 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f74,plain,
! [X512: term > $o] :
( ( ( sP58 @ X512 )
= $true )
<=> ! [X514: term] :
( ( ( X512 @ X514 )
= $true )
| ( ( var @ X514 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f75,plain,
( ( sP59 = $true )
<=> ! [X517: subst,X518: term > $o,X519: term] :
( ( ( sP56 @ X518 )
= $true )
| ( $true
= ( X518 @ ( sub @ X519 @ X517 ) ) )
| ? [X524: term] :
( ( $true
!= ( X518 @ ( sub @ X524 @ X517 ) ) )
& ( ( var @ X524 )
= $true ) )
| ( ( sP55 @ X518 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f76,plain,
( ( sP60 = $true )
<=> ? [X511: term,X512: term > $o] :
( ( $true
= ( sP57 @ X512 ) )
& ( ( X512 @ X511 )
!= $true )
& ! [X513: term] :
( ( $true
!= ( X512 @ X513 ) )
| ( ( X512 @ ( lam @ X513 ) )
= $true ) )
& ( ( sP58 @ X512 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f77,plain,
! [X168: term > $o] :
( ( $true
= ( sP61 @ X168 ) )
<=> ! [X172: term,X173: term] :
( ( ( X168 @ X172 )
!= $true )
| ( ( X168 @ ( ap @ X173 @ X172 ) )
= $true )
| ( $true
!= ( X168 @ X173 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f78,plain,
! [X168: term > $o] :
( ( ( sP62 @ X168 )
= $true )
<=> ! [X170: term] :
( ( ( X168 @ ( lam @ X170 ) )
= $true )
| ? [X171: term] :
( ( ( X168 @ X171 )
= $true )
& ( $true
!= ( X168 @ ( sub @ X170 @ ( push @ X171 @ id ) ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f79,plain,
! [X177: subst > term > subst > $o] :
( ( $true
= ( sP63 @ X177 ) )
<=> ! [X186: term,X187: term] :
( ( $true
!= ( X177 @ id @ X187 @ id ) )
| ( $true
!= ( X177 @ id @ X186 @ id ) )
| ( $true
= ( X177 @ id @ ( ap @ ( sub @ X187 @ id ) @ X186 ) @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f80,plain,
! [X177: subst > term > subst > $o] :
( ( $true
= ( sP64 @ X177 ) )
<=> ! [X178: subst,X179: subst,X180: term,X181: subst] :
( ( ( X177 @ X179 @ X180 @ ( comp @ X181 @ X178 ) )
!= $true )
| ( ( X177 @ ( comp @ X179 @ X181 ) @ ( sub @ X180 @ X181 ) @ X178 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f81,plain,
! [X189: subst > term > subst > $o] :
( ( $true
= ( sP65 @ X189 ) )
<=> ! [X199: subst > term > term] :
( ? [X200: term,X201: subst,X202: subst] :
( ( sub @ ( X199 @ X201 @ X200 ) @ X202 )
!= ( X199 @ ( comp @ X201 @ X202 ) @ ( sub @ X200 @ X202 ) ) )
| ? [X203: term] :
( ( ( X189 @ id @ X203 @ id )
= $true )
& ( ( X189 @ id @ ( X199 @ id @ X203 ) @ id )
!= $true ) )
| ( ( X189 @ id @ ( lam @ ( X199 @ sh @ one ) ) @ id )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f82,plain,
! [X189: subst > term > subst > $o] :
( ( ( sP66 @ X189 )
= $true )
<=> ! [X194: subst,X195: subst,X196: term,X197: subst] :
( ( ( X189 @ ( comp @ X197 @ X195 ) @ ( sub @ X196 @ X195 ) @ X194 )
!= $true )
| ( ( X189 @ X197 @ X196 @ ( comp @ X195 @ X194 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f83,plain,
! [X189: subst > term > subst > $o] :
( ( $true
= ( sP67 @ X189 ) )
<=> ! [X190: subst,X191: term,X192: subst,X193: subst] :
( ( ( X189 @ X193 @ X191 @ ( comp @ X190 @ X192 ) )
!= $true )
| ( ( X189 @ ( comp @ X193 @ X190 ) @ ( sub @ X191 @ X190 ) @ X192 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f84,plain,
! [X204: subst > term > subst > $o] :
( ( ( sP68 @ X204 )
= $true )
<=> ? [X217: subst > term > term] :
( ! [X218: subst,X219: term,X220: subst] :
( ( sub @ ( X217 @ X220 @ X219 ) @ X218 )
= ( X217 @ ( comp @ X220 @ X218 ) @ ( sub @ X219 @ X218 ) ) )
& ! [X221: term] :
( ( $true
!= ( X204 @ id @ X221 @ id ) )
| ( ( X204 @ id @ ( X217 @ id @ X221 ) @ id )
= $true ) )
& ( ( X204 @ id @ ( lam @ ( X217 @ sh @ one ) ) @ id )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f85,plain,
! [X204: subst > term > subst > $o] :
( ( $true
= ( sP69 @ X204 ) )
<=> ? [X206: term,X207: term] :
( ( $true
= ( X204 @ id @ X206 @ id ) )
& ( $true
!= ( X204 @ id @ ( ap @ ( sub @ X207 @ id ) @ X206 ) @ id ) )
& ( $true
= ( X204 @ id @ X207 @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f86,plain,
! [X204: subst > term > subst > $o] :
( ( $true
= ( sP70 @ X204 ) )
<=> ? [X212: subst,X213: subst,X214: term,X215: subst] :
( ( ( X204 @ ( comp @ X213 @ X212 ) @ ( sub @ X214 @ X212 ) @ X215 )
!= $true )
& ( $true
= ( X204 @ X213 @ X214 @ ( comp @ X212 @ X215 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f87,plain,
! [X204: subst > term > subst > $o] :
( ( $true
= ( sP71 @ X204 ) )
<=> ? [X208: subst,X209: subst,X210: subst,X211: term] :
( ( $true
= ( X204 @ ( comp @ X210 @ X208 ) @ ( sub @ X211 @ X208 ) @ X209 ) )
& ( ( X204 @ X210 @ X211 @ ( comp @ X208 @ X209 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f88,plain,
( ( sP72 = $true )
<=> ! [X204: subst > term > subst > $o,X205: term] :
( ? [X216: term] :
( ( $true
= ( var @ ( sub @ X216 @ id ) ) )
& ( ( X204 @ id @ X216 @ id )
!= $true ) )
| ( $true
= ( sP71 @ X204 ) )
| ( ( sP68 @ X204 )
= $true )
| ( $true
= ( sP70 @ X204 ) )
| ( $true
= ( X204 @ id @ X205 @ id ) )
| ( $true
= ( sP69 @ X204 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f89,plain,
( ( $true = sP73 )
<=> ? [X168: term > $o,X169: term] :
( ( $true
!= ( X168 @ X169 ) )
& ( $true
= ( sP61 @ X168 ) )
& ! [X174: term] :
( ( ( var @ X174 )
!= $true )
| ( ( X168 @ X174 )
= $true ) )
& ( ( sP62 @ X168 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f90,plain,
( ( sP74 = $true )
<=> ? [X175: term,X176: term,X177: subst > term > subst > $o] :
( ( $true
= ( X177 @ id @ X175 @ id ) )
& ! [X182: subst,X183: subst,X184: term,X185: subst] :
( ( $true
= ( X177 @ X185 @ X184 @ ( comp @ X183 @ X182 ) ) )
| ( $true
!= ( X177 @ ( comp @ X185 @ X183 ) @ ( sub @ X184 @ X183 ) @ X182 ) ) )
& ( $true
= ( sP63 @ X177 ) )
& ( $true
= ( X177 @ id @ X176 @ id ) )
& ( $true
= ( sP64 @ X177 ) )
& ( ( X177 @ id @ ( ap @ X175 @ X176 ) @ id )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f91,plain,
( ( $true = sP75 )
<=> ? [X188: term,X189: subst > term > subst > $o] :
( ! [X198: term] :
( ( ( X189 @ id @ ( sub @ X188 @ ( push @ X198 @ id ) ) @ id )
= $true )
| ( $true
!= ( X189 @ id @ X198 @ id ) ) )
& ( $true
= ( sP67 @ X189 ) )
& ( ( X189 @ id @ ( lam @ X188 ) @ id )
!= $true )
& ( ( sP66 @ X189 )
= $true )
& ( $true
= ( sP65 @ X189 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f92,plain,
! [X130: term > $o] :
( ( ( sP76 @ X130 )
= $true )
<=> ! [X134: term,X135: term] :
( ( ( X130 @ X134 )
!= $true )
| ( $true
!= ( X130 @ X135 ) )
| ( ( X130 @ ( ap @ X134 @ X135 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f93,plain,
! [X129: subst,X130: term > $o] :
( ( ( sP77 @ X130 @ X129 )
= $true )
<=> ! [X136: term] :
( ( ( var @ X136 )
!= $true )
| ( $true
= ( X130 @ ( sub @ X136 @ X129 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f94,plain,
! [X130: term > $o] :
( ( $true
= ( sP78 @ X130 ) )
<=> ! [X132: term] :
( ? [X133: term] :
( ( $true
!= ( X130 @ ( sub @ X132 @ ( push @ X133 @ id ) ) ) )
& ( ( X130 @ X133 )
= $true ) )
| ( ( X130 @ ( lam @ X132 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f95,plain,
! [X138: term > $o] :
( ( $true
= ( sP79 @ X138 ) )
<=> ? [X142: term] :
( ! [X143: term] :
( ( ( X138 @ X143 )
!= $true )
| ( ( X138 @ ( sub @ X142 @ ( push @ X143 @ id ) ) )
= $true ) )
& ( $true
!= ( X138 @ ( lam @ X142 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f96,plain,
! [X138: term > $o] :
( ( ( sP80 @ X138 )
= $true )
<=> ? [X140: term,X141: term] :
( ( ( X138 @ X140 )
= $true )
& ( ( X138 @ ( ap @ X140 @ X141 ) )
!= $true )
& ( $true
= ( X138 @ X141 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f97,plain,
( ( sP81 = $true )
<=> ! [X137: term,X138: term > $o] :
( ? [X139: term] :
( ( ( var @ X139 )
= $true )
& ( ( X138 @ X139 )
!= $true ) )
| ( $true
= ( sP79 @ X138 ) )
| ( ( sP80 @ X138 )
= $true )
| ( $true
= ( X138 @ X137 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f98,plain,
( ( $true = sP82 )
<=> ? [X129: subst,X130: term > $o,X131: term] :
( ( $true
= ( sP78 @ X130 ) )
& ( ( sP77 @ X130 @ X129 )
= $true )
& ( $true
!= ( X130 @ ( sub @ X131 @ X129 ) ) )
& ( ( sP76 @ X130 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f99,plain,
! [X388: term > $o] :
( ( $true
= ( sP83 @ X388 ) )
<=> ? [X392: term] :
( ( ( X388 @ ( lam @ X392 ) )
!= $true )
& ! [X393: term] :
( ( $true
!= ( X388 @ X393 ) )
| ( ( X388 @ ( sub @ X392 @ ( push @ X393 @ id ) ) )
= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f100,plain,
! [X388: term > $o] :
( ( $true
= ( sP84 @ X388 ) )
<=> ? [X390: term,X391: term] :
( ( ( X388 @ X390 )
= $true )
& ( ( X388 @ ( ap @ X391 @ X390 ) )
!= $true )
& ( $true
= ( X388 @ X391 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f101,plain,
( ( $true = sP85 )
<=> ! [X386: term,X387: subst,X388: term > $o] :
( ( $true
= ( sP83 @ X388 ) )
| ( $true
= ( X388 @ ( sub @ X386 @ X387 ) ) )
| ? [X389: term] :
( ( $true
= ( var @ X389 ) )
& ( ( X388 @ ( sub @ X389 @ X387 ) )
!= $true ) )
| ( $true
= ( sP84 @ X388 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f102,plain,
! [X268: term > $o] :
( ( $true
= ( sP86 @ X268 ) )
<=> ? [X270: term] :
( ! [X271: term] :
( ( $true
= ( X268 @ ( sub @ X270 @ ( push @ X271 @ id ) ) ) )
| ( $true
!= ( X268 @ X271 ) ) )
& ( ( X268 @ ( lam @ X270 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f103,plain,
! [X268: term > $o] :
( ( $true
= ( sP87 @ X268 ) )
<=> ? [X272: term,X273: term] :
( ( $true
= ( X268 @ X272 ) )
& ( ( X268 @ ( ap @ X273 @ X272 ) )
!= $true )
& ( ( X268 @ X273 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f104,plain,
( ( sP88 = $true )
<=> ! [X268: term > $o,X269: term] :
( ? [X274: term] :
( ( $true
!= ( X268 @ X274 ) )
& ( ( var @ X274 )
= $true ) )
| ( $true
= ( sP87 @ X268 ) )
| ( ( X268 @ X269 )
= $true )
| ( $true
= ( sP86 @ X268 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f105,plain,
! [X454: subst > term > subst > $o] :
( ( $true
= ( sP89 @ X454 ) )
<=> ? [X463: term,X464: term] :
( ( $true
= ( X454 @ id @ X463 @ id ) )
& ( $true
!= ( X454 @ id @ ( ap @ ( sub @ X463 @ id ) @ X464 ) @ id ) )
& ( ( X454 @ id @ X464 @ id )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f106,plain,
! [X454: subst > term > subst > $o] :
( ( $true
= ( sP90 @ X454 ) )
<=> ? [X459: subst,X460: term,X461: subst,X462: subst] :
( ( ( X454 @ X461 @ X460 @ ( comp @ X459 @ X462 ) )
= $true )
& ( ( X454 @ ( comp @ X461 @ X459 ) @ ( sub @ X460 @ X459 ) @ X462 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f107,plain,
( ( $true = sP91 )
<=> ! [X452: term,X453: term,X454: subst > term > subst > $o] :
( ( ( X454 @ id @ X453 @ id )
!= $true )
| ( $true
= ( sP89 @ X454 ) )
| ( ( X454 @ id @ X452 @ id )
!= $true )
| ? [X455: subst,X456: subst,X457: term,X458: subst] :
( ( ( X454 @ X458 @ X457 @ ( comp @ X455 @ X456 ) )
!= $true )
& ( $true
= ( X454 @ ( comp @ X458 @ X455 ) @ ( sub @ X457 @ X455 ) @ X456 ) ) )
| ( ( X454 @ id @ ( ap @ X452 @ X453 ) @ id )
= $true )
| ( $true
= ( sP90 @ X454 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f108,plain,
! [X100: subst > term > subst > $o] :
( ( $true
= ( sP92 @ X100 ) )
<=> ? [X103: subst > term > term] :
( ! [X104: subst,X105: subst,X106: term] :
( ( X103 @ ( comp @ X105 @ X104 ) @ ( sub @ X106 @ X104 ) )
= ( sub @ ( X103 @ X105 @ X106 ) @ X104 ) )
& ! [X107: term] :
( ( ( X100 @ id @ X107 @ id )
!= $true )
| ( $true
= ( X100 @ id @ ( X103 @ id @ X107 ) @ id ) ) )
& ( $true
!= ( X100 @ id @ ( lam @ ( X103 @ sh @ one ) ) @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f109,plain,
! [X100: subst > term > subst > $o] :
( ( ( sP93 @ X100 )
= $true )
<=> ? [X108: subst,X109: term,X110: subst,X111: subst] :
( ( ( X100 @ ( comp @ X108 @ X110 ) @ ( sub @ X109 @ X110 ) @ X111 )
!= $true )
& ( ( X100 @ X108 @ X109 @ ( comp @ X110 @ X111 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f110,plain,
! [X100: subst > term > subst > $o] :
( ( ( sP94 @ X100 )
= $true )
<=> ? [X113: subst,X114: subst,X115: term,X116: subst] :
( ( $true
= ( X100 @ ( comp @ X114 @ X113 ) @ ( sub @ X115 @ X113 ) @ X116 ) )
& ( $true
!= ( X100 @ X114 @ X115 @ ( comp @ X113 @ X116 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f111,plain,
( ( $true = sP95 )
<=> ! [X99: term > $o,X100: subst > term > subst > $o,X101: term] :
( ( ( X99 @ ( lam @ X101 ) )
= $true )
| ? [X102: term] :
( ( ( X99 @ ( sub @ X101 @ ( push @ X102 @ id ) ) )
!= $true )
& ( ( X99 @ X102 )
= $true ) )
| ( $true
= ( sP92 @ X100 ) )
| ( ( sP94 @ X100 )
= $true )
| ? [X112: term] :
( ( X100 @ id @ X112 @ id )
!= ( X99 @ X112 ) )
| ( ( sP93 @ X100 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f112,plain,
! [X256: term > $o] :
( ( ( sP96 @ X256 )
= $true )
<=> ? [X258: term,X259: term] :
( ( ( X256 @ X258 )
= $true )
& ( ( X256 @ ( ap @ X259 @ X258 ) )
!= $true )
& ( $true
= ( X256 @ X259 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f113,plain,
! [X256: term > $o] :
( ( ( sP97 @ X256 )
= $true )
<=> ? [X260: term] :
( ( $true
!= ( X256 @ X260 ) )
& ( ( var @ X260 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f114,plain,
( ( sP98 = $true )
<=> ! [X255: term,X256: term > $o] :
( ( ( sP96 @ X256 )
= $true )
| ? [X257: term] :
( ( $true
= ( X256 @ X257 ) )
& ( ( X256 @ ( lam @ X257 ) )
!= $true ) )
| ( ( X256 @ X255 )
= $true )
| ( ( sP97 @ X256 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f115,plain,
! [X415: subst > term > subst > $o] :
( ( $true
= ( sP99 @ X415 ) )
<=> ? [X417: subst > term > term] :
( ! [X421: term] :
( ( $true
!= ( X415 @ id @ X421 @ id ) )
| ( ( X415 @ id @ ( X417 @ id @ X421 ) @ id )
= $true ) )
& ( ( X415 @ id @ ( lam @ ( X417 @ sh @ one ) ) @ id )
!= $true )
& ! [X418: subst,X419: term,X420: subst] :
( ( sub @ ( X417 @ X418 @ X419 ) @ X420 )
= ( X417 @ ( comp @ X418 @ X420 ) @ ( sub @ X419 @ X420 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f116,plain,
( ( sP100 = $true )
<=> ! [X414: term,X415: subst > term > subst > $o] :
( ( $true
= ( sP99 @ X415 ) )
| ( ( X415 @ id @ ( lam @ ( sub @ X414 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ? [X416: term] :
( ( ( X415 @ id @ X416 @ id )
= $true )
& ( ( X415 @ id @ ( sub @ X414 @ ( push @ X416 @ id ) ) @ id )
!= $true ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f117,plain,
! [X21: subst > term > subst > $o] :
( ( $true
= ( sP101 @ X21 ) )
<=> ? [X25: subst > term > term] :
( ( ( X21 @ id @ ( lam @ ( X25 @ sh @ one ) ) @ id )
!= $true )
& ! [X26: term] :
( ( ( X21 @ id @ X26 @ id )
!= $true )
| ( ( X21 @ id @ ( X25 @ id @ X26 ) @ id )
= $true ) )
& ! [X27: term,X28: subst,X29: subst] :
( ( X25 @ ( comp @ X28 @ X29 ) @ ( sub @ X27 @ X29 ) )
= ( sub @ ( X25 @ X28 @ X27 ) @ X29 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f118,plain,
! [X21: subst > term > subst > $o] :
( ( $true
= ( sP102 @ X21 ) )
<=> ? [X23: term,X24: term] :
( ( ( X21 @ id @ X24 @ id )
= $true )
& ( $true
!= ( X21 @ id @ ( ap @ ( sub @ X23 @ id ) @ X24 ) @ id ) )
& ( $true
= ( X21 @ id @ X23 @ id ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f119,plain,
! [X4: term > $o] :
( ( $true
= ( sP103 @ X4 ) )
<=> ! [X5: term,X6: term] :
( ( ( X4 @ X5 )
!= $true )
| ( ( X4 @ X6 )
!= $true )
| ( $true
= ( X4 @ ( ap @ X5 @ X6 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f120,plain,
! [X4: term > $o] :
( ( $true
= ( sP104 @ X4 ) )
<=> ! [X7: term] :
( ( $true
!= ( var @ X7 ) )
| ( ( X4 @ X7 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f121,plain,
! [X4: term > $o] :
( ( ( sP105 @ X4 )
= $true )
<=> ! [X8: term] :
( ( ( X4 @ ( lam @ X8 ) )
= $true )
| ? [X9: term] :
( ( $true
!= ( X4 @ ( sub @ X8 @ ( push @ X9 @ id ) ) ) )
& ( $true
= ( X4 @ X9 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f122,plain,
! [X12: subst > term > subst > $o] :
( ( ( sP106 @ X12 )
= $true )
<=> ! [X15: subst > term > term] :
( ? [X16: term] :
( ( ( X12 @ id @ ( X15 @ id @ X16 ) @ id )
!= $true )
& ( $true
= ( X12 @ id @ X16 @ id ) ) )
| ( $true
= ( X12 @ id @ ( lam @ ( X15 @ sh @ one ) ) @ id ) )
| ? [X17: term,X18: subst,X19: subst] :
( ( sub @ ( X15 @ X19 @ X17 ) @ X18 )
!= ( X15 @ ( comp @ X19 @ X18 ) @ ( sub @ X17 @ X18 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f123,plain,
( ( sP107 = $true )
<=> ! [X21: subst > term > subst > $o,X22: term] :
( ( $true
= ( sP102 @ X21 ) )
| ( $true
= ( X21 @ id @ X22 @ id ) )
| ( $true
= ( sP101 @ X21 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f124,plain,
( ( sP108 = $true )
<=> ? [X11: term,X12: subst > term > subst > $o,X13: term > $o] :
( ! [X14: term] :
( ( X13 @ X14 )
= ( X12 @ id @ X14 @ id ) )
& ! [X20: term] :
( ( $true
= ( X13 @ ( sub @ X11 @ ( push @ X20 @ id ) ) ) )
| ( ( X13 @ X20 )
!= $true ) )
& ( ( X13 @ ( lam @ X11 ) )
!= $true )
& ( ( sP106 @ X12 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f125,plain,
( ( sP109 = $true )
<=> ? [X3: term,X4: term > $o] :
( ( ( sP105 @ X4 )
= $true )
& ( $true
= ( sP104 @ X4 ) )
& ( $true
!= ( X4 @ X3 ) )
& ( $true
= ( sP103 @ X4 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f13,plain,
( ( hoasapnotvar = $true )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( apinj1 = $true )
<=> ! [X261: term,X262: term,X263: term,X264: term] :
( ( X262 = X264 )
| ( ( ap @ X264 @ X263 )
!= ( ap @ X262 @ X261 ) ) ) )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( hoaslamnotvar_gthm = $true )
& ( ! [X52: subst] :
( ( comp @ X52 @ id )
= X52 )
<=> ( axidr = $true ) )
& ( termmset_gthm = $true )
& ( ( ? [X11: term,X12: subst > term > subst > $o,X13: term > $o] :
( ! [X14: term] :
( ( X13 @ X14 )
= ( X12 @ id @ X14 @ id ) )
& ! [X20: term] :
( ( $true
= ( X13 @ ( sub @ X11 @ ( push @ X20 @ id ) ) ) )
| ( ( X13 @ X20 )
!= $true ) )
& ( ( X13 @ ( lam @ X11 ) )
!= $true )
& ! [X15: subst > term > term] :
( ? [X16: term] :
( ( ( X12 @ id @ ( X15 @ id @ X16 ) @ id )
!= $true )
& ( $true
= ( X12 @ id @ X16 @ id ) ) )
| ( $true
= ( X12 @ id @ ( lam @ ( X15 @ sh @ one ) ) @ id ) )
| ? [X17: term,X18: subst,X19: subst] :
( ( sub @ ( X15 @ X19 @ X17 ) @ X18 )
!= ( X15 @ ( comp @ X19 @ X18 ) @ ( sub @ X17 @ X18 ) ) ) ) )
| ? [X10: term] :
( ( sub @ X10 @ id )
!= X10 )
| ? [X0: subst > term > subst > $o] :
! [X1: term > $o] :
? [X2: term] :
( ( X0 @ id @ X2 @ id )
!= ( X1 @ X2 ) )
| ? [X3: term,X4: term > $o] :
( ! [X8: term] :
( ( ( X4 @ ( lam @ X8 ) )
= $true )
| ? [X9: term] :
( ( $true
!= ( X4 @ ( sub @ X8 @ ( push @ X9 @ id ) ) ) )
& ( $true
= ( X4 @ X9 ) ) ) )
& ! [X7: term] :
( ( $true
!= ( var @ X7 ) )
| ( ( X4 @ X7 )
= $true ) )
& ( $true
!= ( X4 @ X3 ) )
& ! [X5: term,X6: term] :
( ( ( X4 @ X5 )
!= $true )
| ( ( X4 @ X6 )
!= $true )
| ( $true
= ( X4 @ ( ap @ X5 @ X6 ) ) ) ) )
| ! [X21: subst > term > subst > $o,X22: term] :
( ? [X23: term,X24: term] :
( ( ( X21 @ id @ X24 @ id )
= $true )
& ( $true
!= ( X21 @ id @ ( ap @ ( sub @ X23 @ id ) @ X24 ) @ id ) )
& ( $true
= ( X21 @ id @ X23 @ id ) ) )
| ( $true
= ( X21 @ id @ X22 @ id ) )
| ? [X25: subst > term > term] :
( ( ( X21 @ id @ ( lam @ ( X25 @ sh @ one ) ) @ id )
!= $true )
& ! [X26: term] :
( ( ( X21 @ id @ X26 @ id )
!= $true )
| ( ( X21 @ id @ ( X25 @ id @ X26 ) @ id )
= $true ) )
& ! [X27: term,X28: subst,X29: subst] :
( ( X25 @ ( comp @ X28 @ X29 ) @ ( sub @ X27 @ X29 ) )
= ( sub @ ( X25 @ X28 @ X27 ) @ X29 ) ) ) ) )
<=> ( hoasinduction_no_psi_cond_lthm = $true ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ! [X291: d_subst] : ( d_id = X291 )
& ( ( ! [X79: subst] :
( ( comp @ id @ X79 )
= X79 )
& ! [X80: subst] :
( ( comp @ X80 @ id )
= X80 ) )
<=> ( substmonoid = $true ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( one
= ( d2term @ d_one ) )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ! [X414: term,X415: subst > term > subst > $o] :
( ? [X417: subst > term > term] :
( ! [X421: term] :
( ( $true
!= ( X415 @ id @ X421 @ id ) )
| ( ( X415 @ id @ ( X417 @ id @ X421 ) @ id )
= $true ) )
& ( ( X415 @ id @ ( lam @ ( X417 @ sh @ one ) ) @ id )
!= $true )
& ! [X418: subst,X419: term,X420: subst] :
( ( sub @ ( X417 @ X418 @ X419 ) @ X420 )
= ( X417 @ ( comp @ X418 @ X420 ) @ ( sub @ X419 @ X420 ) ) ) )
| ( ( X415 @ id @ ( lam @ ( sub @ X414 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ? [X416: term] :
( ( ( X415 @ id @ X416 @ id )
= $true )
& ( ( X415 @ id @ ( sub @ X414 @ ( push @ X416 @ id ) ) @ id )
!= $true ) ) )
<=> ( hoasinduction_lem3aa_lthm = $true ) )
& ( ( induction = $true )
<=> ! [X255: term,X256: term > $o] :
( ? [X258: term,X259: term] :
( ( ( X256 @ X258 )
= $true )
& ( ( X256 @ ( ap @ X259 @ X258 ) )
!= $true )
& ( $true
= ( X256 @ X259 ) ) )
| ? [X257: term] :
( ( $true
= ( X256 @ X257 ) )
& ( ( X256 @ ( lam @ X257 ) )
!= $true ) )
| ( ( X256 @ X255 )
= $true )
| ? [X260: term] :
( ( $true
!= ( X256 @ X260 ) )
& ( ( var @ X260 )
= $true ) ) ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
<=> ( ? [X98: term] :
( ( sub @ X98 @ id )
!= X98 )
| ! [X99: term > $o,X100: subst > term > subst > $o,X101: term] :
( ( ( X99 @ ( lam @ X101 ) )
= $true )
| ? [X102: term] :
( ( ( X99 @ ( sub @ X101 @ ( push @ X102 @ id ) ) )
!= $true )
& ( ( X99 @ X102 )
= $true ) )
| ? [X103: subst > term > term] :
( ! [X104: subst,X105: subst,X106: term] :
( ( X103 @ ( comp @ X105 @ X104 ) @ ( sub @ X106 @ X104 ) )
= ( sub @ ( X103 @ X105 @ X106 ) @ X104 ) )
& ! [X107: term] :
( ( ( X100 @ id @ X107 @ id )
!= $true )
| ( $true
= ( X100 @ id @ ( X103 @ id @ X107 ) @ id ) ) )
& ( $true
!= ( X100 @ id @ ( lam @ ( X103 @ sh @ one ) ) @ id ) ) )
| ? [X113: subst,X114: subst,X115: term,X116: subst] :
( ( $true
= ( X100 @ ( comp @ X114 @ X113 ) @ ( sub @ X115 @ X113 ) @ X116 ) )
& ( $true
!= ( X100 @ X114 @ X115 @ ( comp @ X113 @ X116 ) ) ) )
| ? [X112: term] :
( ( X100 @ id @ X112 @ id )
!= ( X99 @ X112 ) )
| ? [X108: subst,X109: term,X110: subst,X111: subst] :
( ( ( X100 @ ( comp @ X108 @ X110 ) @ ( sub @ X109 @ X110 ) @ X111 )
!= $true )
& ( ( X100 @ X108 @ X109 @ ( comp @ X110 @ X111 ) )
= $true ) ) ) ) )
& ( pushprop_lthm_orig = $true )
& ( hoaslamnotvar_lthm = $true )
& ( hoaslamnotap_lthm = $true )
& ! [X234: d_term,X235: d_term] :
( ( ( d2term @ X234 )
!= ( d2term @ X235 ) )
| ( X234 = X235 ) )
& ( hoaslamnotvar = $true )
& ( ( hoasinduction_lem2 = $true )
<=> ! [X452: term,X453: term,X454: subst > term > subst > $o] :
( ( ( X454 @ id @ X453 @ id )
!= $true )
| ? [X463: term,X464: term] :
( ( $true
= ( X454 @ id @ X463 @ id ) )
& ( $true
!= ( X454 @ id @ ( ap @ ( sub @ X463 @ id ) @ X464 ) @ id ) )
& ( ( X454 @ id @ X464 @ id )
= $true ) )
| ( ( X454 @ id @ X452 @ id )
!= $true )
| ? [X455: subst,X456: subst,X457: term,X458: subst] :
( ( ( X454 @ X458 @ X457 @ ( comp @ X455 @ X456 ) )
!= $true )
& ( $true
= ( X454 @ ( comp @ X458 @ X455 ) @ ( sub @ X457 @ X455 ) @ X456 ) ) )
| ( ( X454 @ id @ ( ap @ X452 @ X453 ) @ id )
= $true )
| ? [X459: subst,X460: term,X461: subst,X462: subst] :
( ( ( X454 @ X461 @ X460 @ ( comp @ X459 @ X462 ) )
= $true )
& ( ( X454 @ ( comp @ X461 @ X459 ) @ ( sub @ X460 @ X459 ) @ X462 )
!= $true ) ) ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( axabs = $true )
& ( ! [X480: term,X481: term,X482: term,X483: term] :
( ( ( ap @ ( sub @ X482 @ id ) @ X481 )
!= ( ap @ ( sub @ X480 @ id ) @ X483 ) )
| ( X481 = X483 ) )
<=> ( hoasapinj2 = $true ) )
& ( ( induction2 = $true )
<=> ! [X268: term > $o,X269: term] :
( ? [X274: term] :
( ( $true
!= ( X268 @ X274 ) )
& ( ( var @ X274 )
= $true ) )
| ? [X272: term,X273: term] :
( ( $true
= ( X268 @ X272 ) )
& ( ( X268 @ ( ap @ X273 @ X272 ) )
!= $true )
& ( ( X268 @ X273 )
= $true ) )
| ( ( X268 @ X269 )
= $true )
| ? [X270: term] :
( ! [X271: term] :
( ( $true
= ( X268 @ ( sub @ X270 @ ( push @ X271 @ id ) ) ) )
| ( $true
!= ( X268 @ X271 ) ) )
& ( ( X268 @ ( lam @ X270 ) )
!= $true ) ) ) )
& ( induction2_gthm = $true )
& ( ! [X386: term,X387: subst,X388: term > $o] :
( ? [X392: term] :
( ( ( X388 @ ( lam @ X392 ) )
!= $true )
& ! [X393: term] :
( ( $true
!= ( X388 @ X393 ) )
| ( ( X388 @ ( sub @ X392 @ ( push @ X393 @ id ) ) )
= $true ) ) )
| ( $true
= ( X388 @ ( sub @ X386 @ X387 ) ) )
| ? [X389: term] :
( ( $true
= ( var @ X389 ) )
& ( ( X388 @ ( sub @ X389 @ X387 ) )
!= $true ) )
| ? [X390: term,X391: term] :
( ( ( X388 @ X390 )
= $true )
& ( ( X388 @ ( ap @ X391 @ X390 ) )
!= $true )
& ( $true
= ( X388 @ X391 ) ) ) )
<=> ( induction2lem = $true ) )
& ( hoasinduction_lem1v2_gthm = $true )
& ( ( ! [X137: term,X138: term > $o] :
( ? [X139: term] :
( ( ( var @ X139 )
= $true )
& ( ( X138 @ X139 )
!= $true ) )
| ? [X142: term] :
( ! [X143: term] :
( ( ( X138 @ X143 )
!= $true )
| ( ( X138 @ ( sub @ X142 @ ( push @ X143 @ id ) ) )
= $true ) )
& ( $true
!= ( X138 @ ( lam @ X142 ) ) ) )
| ? [X140: term,X141: term] :
( ( ( X138 @ X140 )
= $true )
& ( ( X138 @ ( ap @ X140 @ X141 ) )
!= $true )
& ( $true
= ( X138 @ X141 ) ) )
| ( $true
= ( X138 @ X137 ) ) )
| ? [X128: term] :
( ( sub @ X128 @ id )
!= X128 )
| ? [X129: subst,X130: term > $o,X131: term] :
( ! [X132: term] :
( ? [X133: term] :
( ( $true
!= ( X130 @ ( sub @ X132 @ ( push @ X133 @ id ) ) ) )
& ( ( X130 @ X133 )
= $true ) )
| ( ( X130 @ ( lam @ X132 ) )
= $true ) )
& ! [X136: term] :
( ( ( var @ X136 )
!= $true )
| ( $true
= ( X130 @ ( sub @ X136 @ X129 ) ) ) )
& ( $true
!= ( X130 @ ( sub @ X131 @ X129 ) ) )
& ! [X134: term,X135: term] :
( ( ( X130 @ X134 )
!= $true )
| ( $true
!= ( X130 @ X135 ) )
| ( ( X130 @ ( ap @ X134 @ X135 ) )
= $true ) ) ) )
<=> ( induction2_lthm = $true ) )
& ( hoasapnotvar_lthm = $true )
& ( ( hoasinduction_lem3v2_f = $true )
<=> ! [X280: term] :
? [X281: subst > term > term] :
! [X282: term,X283: subst] :
( ( X281 @ X283 @ X282 )
= ( sub @ X280 @ ( push @ X282 @ X283 ) ) ) )
& ( axclos = $true )
& ( ! [X30: term,X31: term] :
( ( X30 = X31 )
| ( ( lam @ X30 )
!= ( lam @ X31 ) ) )
<=> ( laminj = $true ) )
& ( pushprop_lem3v2_lthm = $true )
& ( axassoc = $true )
& ( ulamvar1 != $true )
& ( ( hoasinduction_lem3b_lthm = $true )
<=> ! [X339: term] :
? [X340: subst > term > term] :
( ( X340 @ sh @ one )
= ( sub @ X339 @ ( push @ one @ sh ) ) ) )
& ( ( ! [X204: subst > term > subst > $o,X205: term] :
( ? [X216: term] :
( ( $true
= ( var @ ( sub @ X216 @ id ) ) )
& ( ( X204 @ id @ X216 @ id )
!= $true ) )
| ? [X208: subst,X209: subst,X210: subst,X211: term] :
( ( $true
= ( X204 @ ( comp @ X210 @ X208 ) @ ( sub @ X211 @ X208 ) @ X209 ) )
& ( ( X204 @ X210 @ X211 @ ( comp @ X208 @ X209 ) )
!= $true ) )
| ? [X217: subst > term > term] :
( ! [X218: subst,X219: term,X220: subst] :
( ( sub @ ( X217 @ X220 @ X219 ) @ X218 )
= ( X217 @ ( comp @ X220 @ X218 ) @ ( sub @ X219 @ X218 ) ) )
& ! [X221: term] :
( ( $true
!= ( X204 @ id @ X221 @ id ) )
| ( ( X204 @ id @ ( X217 @ id @ X221 ) @ id )
= $true ) )
& ( ( X204 @ id @ ( lam @ ( X217 @ sh @ one ) ) @ id )
!= $true ) )
| ? [X212: subst,X213: subst,X214: term,X215: subst] :
( ( ( X204 @ ( comp @ X213 @ X212 ) @ ( sub @ X214 @ X212 ) @ X215 )
!= $true )
& ( $true
= ( X204 @ X213 @ X214 @ ( comp @ X212 @ X215 ) ) ) )
| ( $true
= ( X204 @ id @ X205 @ id ) )
| ? [X206: term,X207: term] :
( ( $true
= ( X204 @ id @ X206 @ id ) )
& ( $true
!= ( X204 @ id @ ( ap @ ( sub @ X207 @ id ) @ X206 ) @ id ) )
& ( $true
= ( X204 @ id @ X207 @ id ) ) ) )
| ? [X188: term,X189: subst > term > subst > $o] :
( ! [X198: term] :
( ( ( X189 @ id @ ( sub @ X188 @ ( push @ X198 @ id ) ) @ id )
= $true )
| ( $true
!= ( X189 @ id @ X198 @ id ) ) )
& ! [X190: subst,X191: term,X192: subst,X193: subst] :
( ( ( X189 @ X193 @ X191 @ ( comp @ X190 @ X192 ) )
!= $true )
| ( ( X189 @ ( comp @ X193 @ X190 ) @ ( sub @ X191 @ X190 ) @ X192 )
= $true ) )
& ( ( X189 @ id @ ( lam @ X188 ) @ id )
!= $true )
& ! [X194: subst,X195: subst,X196: term,X197: subst] :
( ( ( X189 @ ( comp @ X197 @ X195 ) @ ( sub @ X196 @ X195 ) @ X194 )
!= $true )
| ( ( X189 @ X197 @ X196 @ ( comp @ X195 @ X194 ) )
= $true ) )
& ! [X199: subst > term > term] :
( ? [X200: term,X201: subst,X202: subst] :
( ( sub @ ( X199 @ X201 @ X200 ) @ X202 )
!= ( X199 @ ( comp @ X201 @ X202 ) @ ( sub @ X200 @ X202 ) ) )
| ? [X203: term] :
( ( ( X189 @ id @ X203 @ id )
= $true )
& ( ( X189 @ id @ ( X199 @ id @ X203 ) @ id )
!= $true ) )
| ( ( X189 @ id @ ( lam @ ( X199 @ sh @ one ) ) @ id )
= $true ) ) )
| ? [X175: term,X176: term,X177: subst > term > subst > $o] :
( ( $true
= ( X177 @ id @ X175 @ id ) )
& ! [X182: subst,X183: subst,X184: term,X185: subst] :
( ( $true
= ( X177 @ X185 @ X184 @ ( comp @ X183 @ X182 ) ) )
| ( $true
!= ( X177 @ ( comp @ X185 @ X183 ) @ ( sub @ X184 @ X183 ) @ X182 ) ) )
& ! [X186: term,X187: term] :
( ( $true
!= ( X177 @ id @ X187 @ id ) )
| ( $true
!= ( X177 @ id @ X186 @ id ) )
| ( $true
= ( X177 @ id @ ( ap @ ( sub @ X187 @ id ) @ X186 ) @ id ) ) )
& ( $true
= ( X177 @ id @ X176 @ id ) )
& ! [X178: subst,X179: subst,X180: term,X181: subst] :
( ( ( X177 @ X179 @ X180 @ ( comp @ X181 @ X178 ) )
!= $true )
| ( ( X177 @ ( comp @ X179 @ X181 ) @ ( sub @ X180 @ X181 ) @ X178 )
= $true ) )
& ( ( X177 @ id @ ( ap @ X175 @ X176 ) @ id )
!= $true ) )
| ? [X168: term > $o,X169: term] :
( ( $true
!= ( X168 @ X169 ) )
& ! [X172: term,X173: term] :
( ( ( X168 @ X172 )
!= $true )
| ( ( X168 @ ( ap @ X173 @ X172 ) )
= $true )
| ( $true
!= ( X168 @ X173 ) ) )
& ! [X174: term] :
( ( ( var @ X174 )
!= $true )
| ( ( X168 @ X174 )
= $true ) )
& ! [X170: term] :
( ( ( X168 @ ( lam @ X170 ) )
= $true )
| ? [X171: term] :
( ( ( X168 @ X171 )
= $true )
& ( $true
!= ( X168 @ ( sub @ X170 @ ( push @ X171 @ id ) ) ) ) ) ) ) )
<=> ( hoasinduction_lthm = $true ) )
& ( ( induction2lem_lthm = $true )
<=> ( ? [X511: term,X512: term > $o] :
( ! [X515: term,X516: term] :
( ( ( X512 @ ( ap @ X516 @ X515 ) )
= $true )
| ( ( X512 @ X515 )
!= $true )
| ( $true
!= ( X512 @ X516 ) ) )
& ( ( X512 @ X511 )
!= $true )
& ! [X513: term] :
( ( $true
!= ( X512 @ X513 ) )
| ( ( X512 @ ( lam @ X513 ) )
= $true ) )
& ! [X514: term] :
( ( ( X512 @ X514 )
= $true )
| ( ( var @ X514 )
!= $true ) ) )
| ! [X517: subst,X518: term > $o,X519: term] :
( ? [X522: term,X523: term] :
( ( $true
!= ( X518 @ ( ap @ X523 @ X522 ) ) )
& ( ( X518 @ X522 )
= $true )
& ( ( X518 @ X523 )
= $true ) )
| ( $true
= ( X518 @ ( sub @ X519 @ X517 ) ) )
| ? [X524: term] :
( ( $true
!= ( X518 @ ( sub @ X524 @ X517 ) ) )
& ( ( var @ X524 )
= $true ) )
| ? [X520: term] :
( ! [X521: term] :
( ( $true
!= ( X518 @ X521 ) )
| ( $true
= ( X518 @ ( sub @ X520 @ ( push @ X521 @ id ) ) ) ) )
& ( ( X518 @ ( lam @ X520 ) )
!= $true ) ) )
| ? [X510: subst] :
( ( comp @ X510 @ id )
!= X510 )
| ? [X508: subst,X509: term] :
( ( comp @ sh @ ( push @ X509 @ X508 ) )
!= X508 )
| ? [X506: term,X507: subst] :
( ( sub @ one @ ( push @ X506 @ X507 ) )
!= X506 ) ) )
& ( ! [X144: subst,X145: term > $o,X146: term] :
? [X147: term > $o] :
! [X148: term] :
( ( X145 @ ( sub @ X148 @ ( push @ X146 @ X144 ) ) )
= ( X147 @ X148 ) )
<=> ( pushprop_lem0_lthm = $true ) )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( pushprop_p_and_p_prime
= ( ^ [Y0: term,Y1: subst,Y2: term > $o,Y3: term > $o] :
( !! @ term
@ ^ [Y4: term] :
( ( Y2 @ ( sub @ Y4 @ ( push @ Y0 @ Y1 ) ) )
= ( Y3 @ Y4 ) ) ) ) )
& ( apnotvar = $true )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( hoasinduction_gthm = $true )
& ( axapp = $true )
& ( ( hoasinduction_lem3_lthm = $true )
<=> ( ? [X425: subst > term > subst > $o,X426: term] :
( ( $true
!= ( X425 @ id @ ( lam @ ( sub @ X426 @ ( push @ one @ sh ) ) ) @ id ) )
& ! [X432: term] :
( ( $true
= ( X425 @ id @ ( sub @ X426 @ ( push @ X432 @ id ) ) @ id ) )
| ( ( X425 @ id @ X432 @ id )
!= $true ) )
& ! [X427: subst > term > term] :
( ? [X428: subst,X429: term,X430: subst] :
( ( X427 @ ( comp @ X430 @ X428 ) @ ( sub @ X429 @ X428 ) )
!= ( sub @ ( X427 @ X430 @ X429 ) @ X428 ) )
| ( $true
= ( X425 @ id @ ( lam @ ( X427 @ sh @ one ) ) @ id ) )
| ? [X431: term] :
( ( $true
= ( X425 @ id @ X431 @ id ) )
& ( ( X425 @ id @ ( X427 @ id @ X431 ) @ id )
!= $true ) ) ) )
| ? [X424: term] :
( ( sub @ X424 @ id )
!= X424 )
| ! [X433: term,X434: subst > term > subst > $o] :
( ? [X444: subst > term > term] :
( ! [X445: term] :
( ( ( X434 @ id @ ( X444 @ id @ X445 ) @ id )
= $true )
| ( ( X434 @ id @ X445 @ id )
!= $true ) )
& ( ( X434 @ id @ ( lam @ ( X444 @ sh @ one ) ) @ id )
!= $true )
& ! [X446: subst,X447: term,X448: subst] :
( ( X444 @ ( comp @ X448 @ X446 ) @ ( sub @ X447 @ X446 ) )
= ( sub @ ( X444 @ X448 @ X447 ) @ X446 ) ) )
| ( ( X434 @ id @ ( lam @ X433 ) @ id )
= $true )
| ? [X440: subst,X441: term,X442: subst,X443: subst] :
( ( ( X434 @ ( comp @ X442 @ X440 ) @ ( sub @ X441 @ X440 ) @ X443 )
= $true )
& ( ( X434 @ X442 @ X441 @ ( comp @ X440 @ X443 ) )
!= $true ) )
| ? [X436: subst,X437: term,X438: subst,X439: subst] :
( ( $true
!= ( X434 @ ( comp @ X436 @ X439 ) @ ( sub @ X437 @ X439 ) @ X438 ) )
& ( ( X434 @ X436 @ X437 @ ( comp @ X439 @ X438 ) )
= $true ) )
| ? [X435: term] :
( ( $true
= ( X434 @ id @ X435 @ id ) )
& ( ( X434 @ id @ ( sub @ X433 @ ( push @ X435 @ id ) ) @ id )
!= $true ) ) ) ) )
& ( ( pushprop_lem0 = $true )
<=> ! [X119: term > $o,X120: subst,X121: term] :
? [X122: term > $o] :
! [X123: term] :
( ( X122 @ X123 )
= ( X119 @ ( sub @ X123 @ ( push @ X121 @ X120 ) ) ) ) )
& ( induction2lem_gthm = $true )
& ( ! [X53: term,X54: term > $o,X55: subst > term > subst > $o,X56: term] :
( ? [X64: subst,X65: term,X66: subst,X67: subst] :
( ( ( X55 @ X66 @ X65 @ ( comp @ X67 @ X64 ) )
!= $true )
& ( ( X55 @ ( comp @ X66 @ X67 ) @ ( sub @ X65 @ X67 ) @ X64 )
= $true ) )
| ? [X61: term,X62: term] :
( ( ( X55 @ id @ X62 @ id )
= $true )
& ( ( X55 @ id @ ( ap @ ( sub @ X62 @ id ) @ X61 ) @ id )
!= $true )
& ( $true
= ( X55 @ id @ X61 @ id ) ) )
| ( ( X54 @ ( ap @ X53 @ X56 ) )
= $true )
| ( ( X54 @ X53 )
!= $true )
| ? [X63: term] :
( ( X55 @ id @ X63 @ id )
!= ( X54 @ X63 ) )
| ( ( X54 @ X56 )
!= $true )
| ? [X57: subst,X58: term,X59: subst,X60: subst] :
( ( ( X55 @ ( comp @ X60 @ X57 ) @ ( sub @ X58 @ X57 ) @ X59 )
!= $true )
& ( $true
= ( X55 @ X60 @ X58 @ ( comp @ X57 @ X59 ) ) ) ) )
<=> ( hoasinduction_lem2v2 = $true ) )
& ( ( hoasinduction_lem3aaa = $true )
<=> ! [X222: term,X223: subst > term > subst > $o] :
( ? [X225: term,X226: subst > term > term] :
( ! [X233: term] :
( ( ( X223 @ id @ ( X226 @ id @ X233 ) @ id )
= $true )
| ( $true
!= ( X223 @ id @ X233 @ id ) ) )
& ! [X227: subst,X228: term,X229: subst] :
( ( sub @ ( sub @ X225 @ ( push @ X228 @ X229 ) ) @ X227 )
= ( sub @ ( X226 @ X229 @ X228 ) @ X227 ) )
& ( $true
!= ( X223 @ id @ ( lam @ ( X226 @ sh @ one ) ) @ id ) )
& ! [X230: subst,X231: term,X232: subst] :
( ( sub @ X225 @ ( push @ ( sub @ X231 @ X232 ) @ ( comp @ X230 @ X232 ) ) )
= ( X226 @ ( comp @ X230 @ X232 ) @ ( sub @ X231 @ X232 ) ) ) )
| ? [X224: term] :
( ( ( X223 @ id @ X224 @ id )
= $true )
& ( $true
!= ( X223 @ id @ ( sub @ X222 @ ( push @ X224 @ id ) ) @ id ) ) )
| ( $true
= ( X223 @ id @ ( lam @ ( sub @ X222 @ ( push @ one @ sh ) ) ) @ id ) ) ) )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ( hoasinduction_lem3a = $true )
<=> ! [X490: term,X491: subst > term > subst > $o] :
( ? [X493: subst > term > term] :
( ! [X497: term] :
( ( ( X491 @ id @ ( X493 @ id @ X497 ) @ id )
= $true )
| ( ( X491 @ id @ X497 @ id )
!= $true ) )
& ( ( X491 @ id @ ( lam @ ( X493 @ sh @ one ) ) @ id )
!= $true )
& ! [X494: subst,X495: subst,X496: term] :
( ( X493 @ ( comp @ X494 @ X495 ) @ ( sub @ X496 @ X495 ) )
= ( sub @ ( X493 @ X494 @ X496 ) @ X495 ) ) )
| ? [X492: term] :
( ( ( X491 @ id @ ( sub @ X490 @ ( push @ X492 @ id ) ) @ id )
!= $true )
& ( ( X491 @ id @ X492 @ id )
= $true ) )
| ( $true
= ( X491 @ id @ ( lam @ X490 ) @ id ) ) ) )
& ( ! [X341: subst > term > term,X342: term,X343: term] :
( ( ( ap @ ( sub @ X342 @ id ) @ X343 )
!= ( lam @ ( X341 @ sh @ one ) ) )
| ? [X344: subst,X345: term,X346: subst] :
( ( sub @ ( X341 @ X346 @ X345 ) @ X344 )
!= ( X341 @ ( comp @ X346 @ X344 ) @ ( sub @ X345 @ X344 ) ) ) )
<=> ( hoaslamnotap = $true ) )
& ( hoasinduction_lem1 = $true )
& ( pushprop_lem2v2_gthm = $true )
& ! [X422: term] :
? [X423: d_term] :
( ( d2term @ X423 )
= X422 )
& ( ( ? [X532: term,X533: term,X534: term,X535: term] :
( ( ( ap @ X532 @ X534 )
= ( ap @ X535 @ X533 ) )
& ( X533 != X534 ) )
| ! [X536: term,X537: term,X538: term,X539: term] :
( ( ( ap @ ( sub @ X536 @ id ) @ X539 )
!= ( ap @ ( sub @ X537 @ id ) @ X538 ) )
| ( X538 = X539 ) ) )
<=> ( hoasapinj2_lthm = $true ) )
& ( lamnotvar = $true )
& ( axvarshift = $true )
& ( hoasinduction_lem3b_gthm = $true )
& ( pushprop = $true )
& ! [X265: d_subst,X266: d_subst] :
( ( X265 = X266 )
| ( ( d2subst @ X266 )
!= ( d2subst @ X265 ) ) )
& ( ulamvarind = $true )
& ( substmonoid_gthm = $true )
& ( hoasinduction_lem2_lthm = $true )
& ( pushprop_lem2v2_lthm = $true )
& ( ( shinj = $true )
<=> ! [X328: term,X329: term] :
( ( X328 = X329 )
| ( ( sub @ X329 @ sh )
!= ( sub @ X328 @ sh ) ) ) )
& ( ( axshiftcons = $true )
<=> ! [X117: term,X118: subst] :
( ( comp @ sh @ ( push @ X117 @ X118 ) )
= X118 ) )
& ( hoasapinj1_gthm = $true )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( hoasinduction_lem1_lthm = $true )
& ( ! [X310: term,X311: subst > term > subst > $o,X312: term > $o] :
( ? [X323: subst > term > term] :
( ( ( X311 @ id @ ( lam @ ( X323 @ sh @ one ) ) @ id )
!= $true )
& ! [X325: term,X326: subst,X327: subst] :
( ( X323 @ ( comp @ X327 @ X326 ) @ ( sub @ X325 @ X326 ) )
= ( sub @ ( X323 @ X327 @ X325 ) @ X326 ) )
& ! [X324: term] :
( ( ( X311 @ id @ ( X323 @ id @ X324 ) @ id )
= $true )
| ( $true
!= ( X311 @ id @ X324 @ id ) ) ) )
| ? [X315: subst,X316: subst,X317: subst,X318: term] :
( ( $true
!= ( X311 @ X316 @ X318 @ ( comp @ X317 @ X315 ) ) )
& ( ( X311 @ ( comp @ X316 @ X317 ) @ ( sub @ X318 @ X317 ) @ X315 )
= $true ) )
| ? [X314: term] :
( ( ( X312 @ X314 )
= $true )
& ( ( X312 @ ( sub @ X310 @ ( push @ X314 @ id ) ) )
!= $true ) )
| ( ( X312 @ ( lam @ X310 ) )
= $true )
| ? [X319: subst,X320: subst,X321: term,X322: subst] :
( ( ( X311 @ X322 @ X321 @ ( comp @ X319 @ X320 ) )
= $true )
& ( ( X311 @ ( comp @ X322 @ X319 ) @ ( sub @ X321 @ X319 ) @ X320 )
!= $true ) )
| ? [X313: term] :
( ( X312 @ X313 )
!= ( X311 @ id @ X313 @ id ) ) )
<=> ( hoasinduction_lem3v2 = $true ) )
& ( ( hoasinduction_lem3v2_f_lthm = $true )
<=> ! [X124: term] :
? [X125: subst > term > term] :
! [X126: term,X127: subst] :
( ( sub @ X124 @ ( push @ X126 @ X127 ) )
= ( X125 @ X127 @ X126 ) ) )
& ( ( d2subst @ d_id )
= id )
& ( pushprop_lem1v2_gthm = $true )
& ( ! [X529: term] :
? [X530: subst > term > term] :
( ( X530 @ sh @ one )
= ( sub @ X529 @ ( push @ one @ sh ) ) )
<=> ( hoasinduction_lem3b = $true ) )
& ( ( ? [X237: subst,X238: term] :
( ( sub @ one @ ( push @ X238 @ X237 ) )
!= X238 )
| ! [X243: subst,X244: term,X245: subst > term > term,X246: subst > term > term] :
( ( ( lam @ ( X246 @ sh @ one ) )
!= ( lam @ ( X245 @ sh @ one ) ) )
| ( ( X246 @ X243 @ X244 )
= ( X245 @ X243 @ X244 ) )
| ? [X250: subst,X251: term,X252: subst] :
( ( X245 @ ( comp @ X250 @ X252 ) @ ( sub @ X251 @ X252 ) )
!= ( sub @ ( X245 @ X250 @ X251 ) @ X252 ) )
| ? [X247: term,X248: subst,X249: subst] :
( ( sub @ ( X246 @ X248 @ X247 ) @ X249 )
!= ( X246 @ ( comp @ X248 @ X249 ) @ ( sub @ X247 @ X249 ) ) ) )
| ? [X239: term,X240: subst] :
( ( comp @ sh @ ( push @ X239 @ X240 ) )
!= X240 )
| ? [X241: term,X242: term] :
( ( X241 != X242 )
& ( ( lam @ X241 )
= ( lam @ X242 ) ) ) )
<=> ( hoaslaminj_lthm = $true ) )
& ( ! [X404: subst,X405: subst > term > term,X406: term,X407: subst > term > term] :
( ? [X411: subst,X412: subst,X413: term] :
( ( X405 @ ( comp @ X412 @ X411 ) @ ( sub @ X413 @ X411 ) )
!= ( sub @ ( X405 @ X412 @ X413 ) @ X411 ) )
| ( ( lam @ ( X407 @ sh @ one ) )
!= ( lam @ ( X405 @ sh @ one ) ) )
| ? [X408: term,X409: subst,X410: subst] :
( ( X407 @ ( comp @ X409 @ X410 ) @ ( sub @ X408 @ X410 ) )
!= ( sub @ ( X407 @ X409 @ X408 ) @ X410 ) )
| ( ( X407 @ X404 @ X406 )
= ( X405 @ X404 @ X406 ) ) )
<=> ( hoaslaminj = $true ) )
& ( hoaslamnotap_gthm = $true )
& ( ( substmonoid_lthm = $true )
<=> ( ? [X396: subst] :
( ( comp @ X396 @ id )
!= X396 )
| ? [X395: subst] :
( ( comp @ id @ X395 )
!= X395 )
| ( ! [X397: subst] :
( ( comp @ id @ X397 )
= X397 )
& ! [X398: subst] :
( ( comp @ X398 @ id )
= X398 ) ) ) )
& ( ! [X48: term,X49: term,X50: term,X51: term] :
( ( ( ap @ X49 @ X48 )
!= ( ap @ X50 @ X51 ) )
| ( X48 = X51 ) )
<=> ( apinj2 = $true ) )
& ( hoasinduction_lem2_gthm = $true )
& ( pushprop_lem3v2 = $true )
& ( pushprop_lem1_gthm = $true )
& ( ( hoasapinj1_lthm = $true )
<=> ( ! [X73: term,X74: term,X75: term,X76: term] :
( ( X73 = X74 )
| ( ( ap @ ( sub @ X74 @ id ) @ X76 )
!= ( ap @ ( sub @ X73 @ id ) @ X75 ) ) )
| ? [X69: term,X70: term,X71: term,X72: term] :
( ( ( ap @ X69 @ X70 )
= ( ap @ X71 @ X72 ) )
& ( X69 != X71 ) )
| ? [X68: term] :
( ( sub @ X68 @ id )
!= X68 ) ) )
& ( ( ! [X470: subst > term > subst > $o,X471: term,X472: term > $o] :
( ? [X473: subst > term > term] :
( ! [X475: subst,X476: subst,X477: term] :
( ( X473 @ ( comp @ X476 @ X475 ) @ ( sub @ X477 @ X475 ) )
= ( sub @ ( X473 @ X476 @ X477 ) @ X475 ) )
& ( ( X470 @ id @ ( lam @ ( X473 @ sh @ one ) ) @ id )
!= $true )
& ! [X474: term] :
( ( ( X470 @ id @ X474 @ id )
!= $true )
| ( ( X470 @ id @ ( X473 @ id @ X474 ) @ id )
= $true ) ) )
| ? [X479: term] :
( ( ( X472 @ ( sub @ X471 @ ( push @ X479 @ id ) ) )
!= $true )
& ( $true
= ( X472 @ X479 ) ) )
| ? [X478: term] :
( ( X470 @ id @ X478 @ id )
!= ( X472 @ X478 ) )
| ( ( X472 @ ( lam @ X471 ) )
= $true ) )
| ? [X469: term] :
( ( sub @ X469 @ id )
!= X469 )
| ? [X465: term] :
! [X466: subst > term > term] :
? [X467: subst,X468: term] :
( ( sub @ X465 @ ( push @ X468 @ X467 ) )
!= ( X466 @ X467 @ X468 ) ) )
<=> ( hoasinduction_lem3v2a_lthm = $true ) )
& ( ( ? [X151: subst,X152: term] :
( ( comp @ sh @ ( push @ X152 @ X151 ) )
!= X151 )
| ? [X149: term,X150: subst] :
( ( sub @ one @ ( push @ X149 @ X150 ) )
!= X149 )
| ! [X153: term,X154: term > $o,X155: subst,X156: term,X157: term > $o] :
( ( ( X157 @ ( sub @ X153 @ ( push @ X156 @ X155 ) ) )
= $true )
| ( $true
!= ( X154 @ X153 ) ) ) )
<=> ( pushprop_lem1_lthm = $true ) )
& ( ( ! [X90: subst > term > subst > $o,X91: term] :
( ? [X97: term] :
( ( $true
= ( X90 @ id @ X97 @ id ) )
& ( $true
!= ( X90 @ id @ ( sub @ X91 @ ( push @ X97 @ id ) ) @ id ) ) )
| ( ( X90 @ id @ ( lam @ X91 ) @ id )
= $true )
| ? [X92: subst > term > term] :
( ! [X94: term,X95: subst,X96: subst] :
( ( sub @ ( X92 @ X96 @ X94 ) @ X95 )
= ( X92 @ ( comp @ X96 @ X95 ) @ ( sub @ X94 @ X95 ) ) )
& ! [X93: term] :
( ( $true
= ( X90 @ id @ ( X92 @ id @ X93 ) @ id ) )
| ( $true
!= ( X90 @ id @ X93 @ id ) ) )
& ( $true
!= ( X90 @ id @ ( lam @ ( X92 @ sh @ one ) ) @ id ) ) ) )
| ? [X82: subst > term > subst > $o,X83: term] :
( ( ( X82 @ id @ ( lam @ ( sub @ X83 @ ( push @ one @ sh ) ) ) @ id )
!= $true )
& ! [X89: term] :
( ( $true
= ( X82 @ id @ ( sub @ X83 @ ( push @ X89 @ id ) ) @ id ) )
| ( ( X82 @ id @ X89 @ id )
!= $true ) )
& ! [X84: subst > term > term] :
( ? [X85: term,X86: subst,X87: subst] :
( ( sub @ ( X84 @ X87 @ X85 ) @ X86 )
!= ( X84 @ ( comp @ X87 @ X86 ) @ ( sub @ X85 @ X86 ) ) )
| ( $true
= ( X82 @ id @ ( lam @ ( X84 @ sh @ one ) ) @ id ) )
| ? [X88: term] :
( ( ( X82 @ id @ ( X84 @ id @ X88 ) @ id )
!= $true )
& ( $true
= ( X82 @ id @ X88 @ id ) ) ) ) )
| ? [X81: term] :
( ( sub @ X81 @ id )
!= X81 ) )
<=> ( hoasinduction_lem3a_lthm = $true ) )
& ( hoasinduction_lem1v2 = $true )
& ( ! [X399: subst,X400: term > $o,X401: term > $o,X402: term] :
( ? [X403: term] :
( ( X400 @ ( sub @ X403 @ ( push @ X402 @ X399 ) ) )
!= ( X401 @ X403 ) )
| ( $true
= ( X401 @ one ) )
| ( $true
!= ( X400 @ X402 ) ) )
<=> ( pushprop_lem1v2 = $true ) )
& ( lamnotap != $true )
& ( hoasapnotvar_gthm = $true )
& ( ! [X449: subst > term > subst > $o] :
? [X450: term > $o] :
! [X451: term] :
( ( X449 @ id @ X451 @ id )
= ( X450 @ X451 ) )
<=> ( hoasinduction_lem0_lthm = $true ) )
& ( ( d2subst @ d_id )
= sh )
& ( ( pushprop_lem1v2_lthm = $true )
<=> ( ! [X286: term,X287: subst,X288: term > $o,X289: term > $o] :
( ? [X290: term] :
( ( X288 @ ( sub @ X290 @ ( push @ X286 @ X287 ) ) )
!= ( X289 @ X290 ) )
| ( ( X289 @ one )
= $true )
| ( $true
!= ( X288 @ X286 ) ) )
| ? [X284: term,X285: subst] :
( ( sub @ one @ ( push @ X284 @ X285 ) )
!= X284 ) ) )
& ( hoasinduction_lem1_gthm = $true )
& ( pushprop_lem0_gthm = $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ( axvarid = $true )
<=> ! [X236: term] :
( ( sub @ X236 @ id )
= X236 ) )
& ( ! [X158: term > $o,X159: subst > term > subst > $o,X160: term] :
( ? [X167: term] :
( ( $true
!= ( X158 @ ( sub @ X160 @ ( push @ X167 @ id ) ) ) )
& ( ( X158 @ X167 )
= $true ) )
| ? [X161: term] :
( ( X158 @ X161 )
!= ( X159 @ id @ X161 @ id ) )
| ( $true
= ( X158 @ ( lam @ X160 ) ) )
| ? [X162: subst > term > term] :
( ! [X163: term] :
( ( $true
!= ( X159 @ id @ X163 @ id ) )
| ( $true
= ( X159 @ id @ ( X162 @ id @ X163 ) @ id ) ) )
& ( ( X159 @ id @ ( lam @ ( X162 @ sh @ one ) ) @ id )
!= $true )
& ! [X164: subst,X165: term,X166: subst] :
( ( sub @ ( X162 @ X166 @ X165 ) @ X164 )
= ( X162 @ ( comp @ X166 @ X164 ) @ ( sub @ X165 @ X164 ) ) ) ) )
<=> ( hoasinduction_lem3v2a = $true ) )
& ( ( hoasapinj1 = $true )
<=> ! [X486: term,X487: term,X488: term,X489: term] :
( ( ( ap @ ( sub @ X489 @ id ) @ X486 )
!= ( ap @ ( sub @ X488 @ id ) @ X487 ) )
| ( X488 = X489 ) ) )
& ( pushprop_gthm = $true )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( axscons = $true )
<=> ! [X267: subst] :
( ( push @ ( sub @ one @ X267 ) @ ( comp @ sh @ X267 ) )
= X267 ) )
& ( ( hoasinduction = $true )
<=> ! [X292: term,X293: subst > term > subst > $o] :
( ? [X306: term,X307: subst,X308: subst,X309: subst] :
( ( $true
= ( X293 @ ( comp @ X308 @ X307 ) @ ( sub @ X306 @ X307 ) @ X309 ) )
& ( ( X293 @ X308 @ X306 @ ( comp @ X307 @ X309 ) )
!= $true ) )
| ? [X303: term] :
( ( $true
= ( var @ ( sub @ X303 @ id ) ) )
& ( ( X293 @ id @ X303 @ id )
!= $true ) )
| ( ( X293 @ id @ X292 @ id )
= $true )
| ? [X304: term,X305: term] :
( ( $true
!= ( X293 @ id @ ( ap @ ( sub @ X304 @ id ) @ X305 ) @ id ) )
& ( $true
= ( X293 @ id @ X305 @ id ) )
& ( $true
= ( X293 @ id @ X304 @ id ) ) )
| ? [X294: subst > term > term] :
( ( $true
!= ( X293 @ id @ ( lam @ ( X294 @ sh @ one ) ) @ id ) )
& ! [X298: term] :
( ( $true
!= ( X293 @ id @ X298 @ id ) )
| ( $true
= ( X293 @ id @ ( X294 @ id @ X298 ) @ id ) ) )
& ! [X295: subst,X296: term,X297: subst] :
( ( X294 @ ( comp @ X295 @ X297 ) @ ( sub @ X296 @ X297 ) )
= ( sub @ ( X294 @ X295 @ X296 ) @ X297 ) ) )
| ? [X299: subst,X300: subst,X301: term,X302: subst] :
( ( $true
!= ( X293 @ ( comp @ X302 @ X300 ) @ ( sub @ X301 @ X300 ) @ X299 ) )
& ( ( X293 @ X302 @ X301 @ ( comp @ X300 @ X299 ) )
= $true ) ) ) )
& ( pushprop_lem2v2 = $true )
& ( ( hoasinduction_no_psi_cond = $true )
<=> ! [X330: term,X331: subst > term > subst > $o] :
( ( ( X331 @ id @ X330 @ id )
= $true )
| ? [X337: term,X338: term] :
( ( ( X331 @ id @ ( ap @ ( sub @ X337 @ id ) @ X338 ) @ id )
!= $true )
& ( ( X331 @ id @ X338 @ id )
= $true )
& ( ( X331 @ id @ X337 @ id )
= $true ) )
| ? [X332: subst > term > term] :
( ( $true
!= ( X331 @ id @ ( lam @ ( X332 @ sh @ one ) ) @ id ) )
& ! [X333: term] :
( ( ( X331 @ id @ X333 @ id )
!= $true )
| ( ( X331 @ id @ ( X332 @ id @ X333 ) @ id )
= $true ) )
& ! [X334: subst,X335: subst,X336: term] :
( ( sub @ ( X332 @ X335 @ X336 ) @ X334 )
= ( X332 @ ( comp @ X335 @ X334 ) @ ( sub @ X336 @ X334 ) ) ) ) ) )
& ( hoasinduction_lem3_gthm = $true )
& ( ( termmset = $true )
<=> ! [X394: term] :
( ( sub @ X394 @ id )
= X394 ) )
& ! [X531: d_term] : ( d_one = X531 )
& ( ulamvarsh = $true )
& ( hoasapinj2_gthm = $true )
& ( axmap = $true )
& ( ! [X32: term,X33: subst > term > subst > $o] :
( ? [X42: subst > term > term] :
( ( ( X33 @ id @ ( lam @ ( X42 @ sh @ one ) ) @ id )
!= $true )
& ! [X43: term] :
( ( $true
!= ( X33 @ id @ X43 @ id ) )
| ( ( X33 @ id @ ( X42 @ id @ X43 ) @ id )
= $true ) )
& ! [X44: term,X45: subst,X46: subst] :
( ( X42 @ ( comp @ X46 @ X45 ) @ ( sub @ X44 @ X45 ) )
= ( sub @ ( X42 @ X46 @ X44 ) @ X45 ) ) )
| ? [X38: subst,X39: subst,X40: subst,X41: term] :
( ( $true
!= ( X33 @ ( comp @ X39 @ X40 ) @ ( sub @ X41 @ X40 ) @ X38 ) )
& ( $true
= ( X33 @ X39 @ X41 @ ( comp @ X40 @ X38 ) ) ) )
| ( $true
= ( X33 @ id @ ( lam @ X32 ) @ id ) )
| ? [X47: term] :
( ( ( X33 @ id @ ( sub @ X32 @ ( push @ X47 @ id ) ) @ id )
!= $true )
& ( $true
= ( X33 @ id @ X47 @ id ) ) )
| ? [X34: term,X35: subst,X36: subst,X37: subst] :
( ( ( X33 @ X36 @ X34 @ ( comp @ X37 @ X35 ) )
!= $true )
& ( ( X33 @ ( comp @ X36 @ X37 ) @ ( sub @ X34 @ X37 ) @ X35 )
= $true ) ) )
<=> ( hoasinduction_lem3 = $true ) )
& ( ( ! [X254: term] :
( ( sub @ X254 @ id )
= X254 )
| ? [X253: term] :
( ( sub @ X253 @ id )
!= X253 ) )
<=> ( termmset_lthm = $true ) )
& ( ( pushprop_lem1 = $true )
<=> ! [X275: term,X276: term,X277: term > $o,X278: subst,X279: term > $o] :
( ( ( X279 @ X276 )
!= $true )
| ( ( X277 @ ( sub @ X276 @ ( push @ X275 @ X278 ) ) )
= $true ) ) )
& ( ( axvarcons = $true )
<=> ! [X77: subst,X78: term] :
( ( sub @ one @ ( push @ X78 @ X77 ) )
= X78 ) )
& ( ( hoasinduction_lthm_3 = $true )
<=> ( ? [X350: term,X351: term > $o] :
( ( $true
!= ( X351 @ X350 ) )
& ! [X353: term,X354: term] :
( ( ( X351 @ X353 )
!= $true )
| ( $true
= ( X351 @ ( ap @ X354 @ X353 ) ) )
| ( $true
!= ( X351 @ X354 ) ) )
& ! [X352: term] :
( ( ( X351 @ X352 )
= $true )
| ( ( var @ X352 )
!= $true ) )
& ! [X355: term] :
( ( $true
= ( X351 @ ( lam @ X355 ) ) )
| ? [X356: term] :
( ( ( X351 @ ( sub @ X355 @ ( push @ X356 @ id ) ) )
!= $true )
& ( ( X351 @ X356 )
= $true ) ) ) )
| ! [X368: term,X369: subst > term > subst > $o] :
( ? [X374: term,X375: term] :
( ( ( X369 @ id @ X375 @ id )
= $true )
& ( $true
= ( X369 @ id @ X374 @ id ) )
& ( ( X369 @ id @ ( ap @ ( sub @ X374 @ id ) @ X375 ) @ id )
!= $true ) )
| ? [X376: subst,X377: subst,X378: subst,X379: term] :
( ( ( X369 @ X378 @ X379 @ ( comp @ X376 @ X377 ) )
= $true )
& ( ( X369 @ ( comp @ X378 @ X376 ) @ ( sub @ X379 @ X376 ) @ X377 )
!= $true ) )
| ? [X380: subst > term > term] :
( ! [X381: term] :
( ( $true
!= ( X369 @ id @ X381 @ id ) )
| ( ( X369 @ id @ ( X380 @ id @ X381 ) @ id )
= $true ) )
& ! [X382: subst,X383: term,X384: subst] :
( ( X380 @ ( comp @ X382 @ X384 ) @ ( sub @ X383 @ X384 ) )
= ( sub @ ( X380 @ X382 @ X383 ) @ X384 ) )
& ( $true
!= ( X369 @ id @ ( lam @ ( X380 @ sh @ one ) ) @ id ) ) )
| ? [X370: term,X371: subst,X372: subst,X373: subst] :
( ( $true
!= ( X369 @ X373 @ X370 @ ( comp @ X372 @ X371 ) ) )
& ( $true
= ( X369 @ ( comp @ X373 @ X372 ) @ ( sub @ X370 @ X372 ) @ X371 ) ) )
| ( $true
= ( X369 @ id @ X368 @ id ) )
| ? [X385: term] :
( ( $true
!= ( X369 @ id @ X385 @ id ) )
& ( $true
= ( var @ ( sub @ X385 @ id ) ) ) ) )
| ? [X357: term] :
( ( sub @ X357 @ id )
!= X357 )
| ? [X347: subst > term > subst > $o] :
! [X348: term > $o] :
? [X349: term] :
( ( X347 @ id @ X349 @ id )
!= ( X348 @ X349 ) )
| ? [X358: subst > term > subst > $o,X359: term,X360: term > $o] :
( ( $true
!= ( X360 @ ( lam @ X359 ) ) )
& ! [X361: term] :
( ( X360 @ X361 )
= ( X358 @ id @ X361 @ id ) )
& ! [X367: term] :
( ( ( X360 @ X367 )
!= $true )
| ( $true
= ( X360 @ ( sub @ X359 @ ( push @ X367 @ id ) ) ) ) )
& ! [X362: subst > term > term] :
( ? [X363: term] :
( ( ( X358 @ id @ ( X362 @ id @ X363 ) @ id )
!= $true )
& ( ( X358 @ id @ X363 @ id )
= $true ) )
| ( $true
= ( X358 @ id @ ( lam @ ( X362 @ sh @ one ) ) @ id ) )
| ? [X364: subst,X365: subst,X366: term] :
( ( sub @ ( X362 @ X364 @ X366 ) @ X365 )
!= ( X362 @ ( comp @ X364 @ X365 ) @ ( sub @ X366 @ X365 ) ) ) ) ) ) )
& ( pushprop_lthm = $true )
& ( ! [X528: subst] :
( ( comp @ id @ X528 )
= X528 )
<=> ( axidl = $true ) )
& ( ( hoasinduction_lem3aa = $true )
<=> ! [X498: subst > term > subst > $o,X499: term] :
( ? [X501: subst > term > term] :
( ! [X505: term] :
( ( $true
!= ( X498 @ id @ X505 @ id ) )
| ( $true
= ( X498 @ id @ ( X501 @ id @ X505 ) @ id ) ) )
& ( $true
!= ( X498 @ id @ ( lam @ ( X501 @ sh @ one ) ) @ id ) )
& ! [X502: subst,X503: subst,X504: term] :
( ( X501 @ ( comp @ X502 @ X503 ) @ ( sub @ X504 @ X503 ) )
= ( sub @ ( X501 @ X502 @ X504 ) @ X503 ) ) )
| ? [X500: term] :
( ( $true
!= ( X498 @ id @ ( sub @ X499 @ ( push @ X500 @ id ) ) @ id ) )
& ( $true
= ( X498 @ id @ X500 @ id ) ) )
| ( $true
= ( X498 @ id @ ( lam @ ( sub @ X499 @ ( push @ one @ sh ) ) ) @ id ) ) ) )
& ( hoaslaminj_gthm = $true )
& ( ( hoasinduction_lem0 = $true )
<=> ! [X525: subst > term > subst > $o] :
? [X526: term > $o] :
! [X527: term] :
( ( X525 @ id @ X527 @ id )
= ( X526 @ X527 ) ) )
& ! [X484: subst] :
? [X485: d_subst] :
( ( d2subst @ X485 )
= X484 ) ),
inference(flattening,[status(thm)],[f12]) ).
thf(f12,plain,
( ( ( pushprop_lem1 = $true )
<=> ! [X275: term,X276: term,X277: term > $o,X278: subst,X279: term > $o] :
( ( ( X279 @ X276 )
!= $true )
| ( ( X277 @ ( sub @ X276 @ ( push @ X275 @ X278 ) ) )
= $true ) ) )
& ( induction2_gthm = $true )
& ( ! [X404: subst,X405: subst > term > term,X406: term,X407: subst > term > term] :
( ? [X411: subst,X412: subst,X413: term] :
( ( X405 @ ( comp @ X412 @ X411 ) @ ( sub @ X413 @ X411 ) )
!= ( sub @ ( X405 @ X412 @ X413 ) @ X411 ) )
| ( ( lam @ ( X407 @ sh @ one ) )
!= ( lam @ ( X405 @ sh @ one ) ) )
| ? [X408: term,X409: subst,X410: subst] :
( ( X407 @ ( comp @ X409 @ X410 ) @ ( sub @ X408 @ X410 ) )
!= ( sub @ ( X407 @ X409 @ X408 ) @ X410 ) )
| ( ( X407 @ X404 @ X406 )
= ( X405 @ X404 @ X406 ) ) )
<=> ( hoaslaminj = $true ) )
& ( ( axshiftcons = $true )
<=> ! [X117: term,X118: subst] :
( ( comp @ sh @ ( push @ X117 @ X118 ) )
= X118 ) )
& ( ( hoasinduction_lem3a = $true )
<=> ! [X490: term,X491: subst > term > subst > $o] :
( ? [X493: subst > term > term] :
( ! [X497: term] :
( ( ( X491 @ id @ ( X493 @ id @ X497 ) @ id )
= $true )
| ( ( X491 @ id @ X497 @ id )
!= $true ) )
& ( ( X491 @ id @ ( lam @ ( X493 @ sh @ one ) ) @ id )
!= $true )
& ! [X494: subst,X495: subst,X496: term] :
( ( X493 @ ( comp @ X494 @ X495 ) @ ( sub @ X496 @ X495 ) )
= ( sub @ ( X493 @ X494 @ X496 ) @ X495 ) ) )
| ? [X492: term] :
( ( ( X491 @ id @ ( sub @ X490 @ ( push @ X492 @ id ) ) @ id )
!= $true )
& ( ( X491 @ id @ X492 @ id )
= $true ) )
| ( $true
= ( X491 @ id @ ( lam @ X490 ) @ id ) ) ) )
& ( pushprop_lem2v2 = $true )
& ( ! [X53: term,X54: term > $o,X55: subst > term > subst > $o,X56: term] :
( ? [X64: subst,X65: term,X66: subst,X67: subst] :
( ( ( X55 @ X66 @ X65 @ ( comp @ X67 @ X64 ) )
!= $true )
& ( ( X55 @ ( comp @ X66 @ X67 ) @ ( sub @ X65 @ X67 ) @ X64 )
= $true ) )
| ? [X61: term,X62: term] :
( ( ( X55 @ id @ X62 @ id )
= $true )
& ( ( X55 @ id @ ( ap @ ( sub @ X62 @ id ) @ X61 ) @ id )
!= $true )
& ( $true
= ( X55 @ id @ X61 @ id ) ) )
| ( ( X54 @ ( ap @ X53 @ X56 ) )
= $true )
| ( ( X54 @ X53 )
!= $true )
| ? [X63: term] :
( ( X55 @ id @ X63 @ id )
!= ( X54 @ X63 ) )
| ( ( X54 @ X56 )
!= $true )
| ? [X57: subst,X58: term,X59: subst,X60: subst] :
( ( ( X55 @ ( comp @ X60 @ X57 ) @ ( sub @ X58 @ X57 ) @ X59 )
!= $true )
& ( $true
= ( X55 @ X60 @ X58 @ ( comp @ X57 @ X59 ) ) ) ) )
<=> ( hoasinduction_lem2v2 = $true ) )
& ( ! [X386: term,X387: subst,X388: term > $o] :
( ? [X392: term] :
( ( ( X388 @ ( lam @ X392 ) )
!= $true )
& ! [X393: term] :
( ( $true
!= ( X388 @ X393 ) )
| ( ( X388 @ ( sub @ X392 @ ( push @ X393 @ id ) ) )
= $true ) ) )
| ( $true
= ( X388 @ ( sub @ X386 @ X387 ) ) )
| ? [X389: term] :
( ( $true
= ( var @ X389 ) )
& ( ( X388 @ ( sub @ X389 @ X387 ) )
!= $true ) )
| ? [X390: term,X391: term] :
( ( ( X388 @ X390 )
= $true )
& ( ( X388 @ ( ap @ X391 @ X390 ) )
!= $true )
& ( $true
= ( X388 @ X391 ) ) ) )
<=> ( induction2lem = $true ) )
& ( ( ! [X470: subst > term > subst > $o,X471: term,X472: term > $o] :
( ? [X473: subst > term > term] :
( ! [X475: subst,X476: subst,X477: term] :
( ( X473 @ ( comp @ X476 @ X475 ) @ ( sub @ X477 @ X475 ) )
= ( sub @ ( X473 @ X476 @ X477 ) @ X475 ) )
& ( ( X470 @ id @ ( lam @ ( X473 @ sh @ one ) ) @ id )
!= $true )
& ! [X474: term] :
( ( ( X470 @ id @ X474 @ id )
!= $true )
| ( ( X470 @ id @ ( X473 @ id @ X474 ) @ id )
= $true ) ) )
| ? [X479: term] :
( ( ( X472 @ ( sub @ X471 @ ( push @ X479 @ id ) ) )
!= $true )
& ( $true
= ( X472 @ X479 ) ) )
| ? [X478: term] :
( ( X470 @ id @ X478 @ id )
!= ( X472 @ X478 ) )
| ( ( X472 @ ( lam @ X471 ) )
= $true ) )
| ? [X469: term] :
( ( sub @ X469 @ id )
!= X469 )
| ? [X465: term] :
! [X466: subst > term > term] :
? [X467: subst,X468: term] :
( ( sub @ X465 @ ( push @ X468 @ X467 ) )
!= ( X466 @ X467 @ X468 ) ) )
<=> ( hoasinduction_lem3v2a_lthm = $true ) )
& ( hoasapnotvar_gthm = $true )
& ( ! [X144: subst,X145: term > $o,X146: term] :
? [X147: term > $o] :
! [X148: term] :
( ( X145 @ ( sub @ X148 @ ( push @ X146 @ X144 ) ) )
= ( X147 @ X148 ) )
<=> ( pushprop_lem0_lthm = $true ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( hoasinduction_lem3v2_gthm = $true )
& ( ( hoasinduction_lem3v2_f = $true )
<=> ! [X280: term] :
? [X281: subst > term > term] :
! [X282: term,X283: subst] :
( ( X281 @ X283 @ X282 )
= ( sub @ X280 @ ( push @ X282 @ X283 ) ) ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( termmset_gthm = $true )
& ( ( hoasinduction_lem3v2_f_lthm = $true )
<=> ! [X124: term] :
? [X125: subst > term > term] :
! [X126: term,X127: subst] :
( ( sub @ X124 @ ( push @ X126 @ X127 ) )
= ( X125 @ X127 @ X126 ) ) )
& ( ( pushprop_lem1v2_lthm = $true )
<=> ( ! [X286: term,X287: subst,X288: term > $o,X289: term > $o] :
( ? [X290: term] :
( ( X288 @ ( sub @ X290 @ ( push @ X286 @ X287 ) ) )
!= ( X289 @ X290 ) )
| ( ( X289 @ one )
= $true )
| ( $true
!= ( X288 @ X286 ) ) )
| ? [X284: term,X285: subst] :
( ( sub @ one @ ( push @ X284 @ X285 ) )
!= X284 ) ) )
& ( ! [X30: term,X31: term] :
( ( X30 = X31 )
| ( ( lam @ X30 )
!= ( lam @ X31 ) ) )
<=> ( laminj = $true ) )
& ( ( hoasinduction_lem0 = $true )
<=> ! [X525: subst > term > subst > $o] :
? [X526: term > $o] :
! [X527: term] :
( ( X525 @ id @ X527 @ id )
= ( X526 @ X527 ) ) )
& ( ! [X399: subst,X400: term > $o,X401: term > $o,X402: term] :
( ? [X403: term] :
( ( X400 @ ( sub @ X403 @ ( push @ X402 @ X399 ) ) )
!= ( X401 @ X403 ) )
| ( $true
= ( X401 @ one ) )
| ( $true
!= ( X400 @ X402 ) ) )
<=> ( pushprop_lem1v2 = $true ) )
& ( ( apinj1 = $true )
<=> ! [X261: term,X262: term,X263: term,X264: term] :
( ( X262 = X264 )
| ( ( ap @ X264 @ X263 )
!= ( ap @ X262 @ X261 ) ) ) )
& ( one
= ( d2term @ d_one ) )
& ( ! [X528: subst] :
( ( comp @ id @ X528 )
= X528 )
<=> ( axidl = $true ) )
& ( ( hoasinduction_lem3_lthm = $true )
<=> ( ! [X433: term,X434: subst > term > subst > $o] :
( ? [X444: subst > term > term] :
( ! [X445: term] :
( ( ( X434 @ id @ ( X444 @ id @ X445 ) @ id )
= $true )
| ( ( X434 @ id @ X445 @ id )
!= $true ) )
& ( ( X434 @ id @ ( lam @ ( X444 @ sh @ one ) ) @ id )
!= $true )
& ! [X446: subst,X447: term,X448: subst] :
( ( X444 @ ( comp @ X448 @ X446 ) @ ( sub @ X447 @ X446 ) )
= ( sub @ ( X444 @ X448 @ X447 ) @ X446 ) ) )
| ( ( X434 @ id @ ( lam @ X433 ) @ id )
= $true )
| ? [X440: subst,X441: term,X442: subst,X443: subst] :
( ( ( X434 @ ( comp @ X442 @ X440 ) @ ( sub @ X441 @ X440 ) @ X443 )
= $true )
& ( ( X434 @ X442 @ X441 @ ( comp @ X440 @ X443 ) )
!= $true ) )
| ? [X436: subst,X437: term,X438: subst,X439: subst] :
( ( $true
!= ( X434 @ ( comp @ X436 @ X439 ) @ ( sub @ X437 @ X439 ) @ X438 ) )
& ( ( X434 @ X436 @ X437 @ ( comp @ X439 @ X438 ) )
= $true ) )
| ? [X435: term] :
( ( $true
= ( X434 @ id @ X435 @ id ) )
& ( ( X434 @ id @ ( sub @ X433 @ ( push @ X435 @ id ) ) @ id )
!= $true ) ) )
| ? [X425: subst > term > subst > $o,X426: term] :
( ( $true
!= ( X425 @ id @ ( lam @ ( sub @ X426 @ ( push @ one @ sh ) ) ) @ id ) )
& ! [X432: term] :
( ( $true
= ( X425 @ id @ ( sub @ X426 @ ( push @ X432 @ id ) ) @ id ) )
| ( ( X425 @ id @ X432 @ id )
!= $true ) )
& ! [X427: subst > term > term] :
( ? [X428: subst,X429: term,X430: subst] :
( ( X427 @ ( comp @ X430 @ X428 ) @ ( sub @ X429 @ X428 ) )
!= ( sub @ ( X427 @ X430 @ X429 ) @ X428 ) )
| ( $true
= ( X425 @ id @ ( lam @ ( X427 @ sh @ one ) ) @ id ) )
| ? [X431: term] :
( ( $true
= ( X425 @ id @ X431 @ id ) )
& ( ( X425 @ id @ ( X427 @ id @ X431 ) @ id )
!= $true ) ) ) )
| ? [X424: term] :
( ( sub @ X424 @ id )
!= X424 ) ) )
& ( apnotvar = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ( hoasinduction = $true )
<=> ! [X292: term,X293: subst > term > subst > $o] :
( ? [X306: term,X307: subst,X308: subst,X309: subst] :
( ( $true
= ( X293 @ ( comp @ X308 @ X307 ) @ ( sub @ X306 @ X307 ) @ X309 ) )
& ( ( X293 @ X308 @ X306 @ ( comp @ X307 @ X309 ) )
!= $true ) )
| ? [X303: term] :
( ( $true
= ( var @ ( sub @ X303 @ id ) ) )
& ( ( X293 @ id @ X303 @ id )
!= $true ) )
| ( ( X293 @ id @ X292 @ id )
= $true )
| ? [X304: term,X305: term] :
( ( $true
!= ( X293 @ id @ ( ap @ ( sub @ X304 @ id ) @ X305 ) @ id ) )
& ( $true
= ( X293 @ id @ X305 @ id ) )
& ( $true
= ( X293 @ id @ X304 @ id ) ) )
| ? [X294: subst > term > term] :
( ( $true
!= ( X293 @ id @ ( lam @ ( X294 @ sh @ one ) ) @ id ) )
& ! [X298: term] :
( ( $true
!= ( X293 @ id @ X298 @ id ) )
| ( $true
= ( X293 @ id @ ( X294 @ id @ X298 ) @ id ) ) )
& ! [X295: subst,X296: term,X297: subst] :
( ( X294 @ ( comp @ X295 @ X297 ) @ ( sub @ X296 @ X297 ) )
= ( sub @ ( X294 @ X295 @ X296 ) @ X297 ) ) )
| ? [X299: subst,X300: subst,X301: term,X302: subst] :
( ( $true
!= ( X293 @ ( comp @ X302 @ X300 ) @ ( sub @ X301 @ X300 ) @ X299 ) )
& ( ( X293 @ X302 @ X301 @ ( comp @ X300 @ X299 ) )
= $true ) ) ) )
& ( ( d2subst @ d_id )
= sh )
& ( lamnotap != $true )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( ! [X368: term,X369: subst > term > subst > $o] :
( ? [X374: term,X375: term] :
( ( ( X369 @ id @ X375 @ id )
= $true )
& ( $true
= ( X369 @ id @ X374 @ id ) )
& ( ( X369 @ id @ ( ap @ ( sub @ X374 @ id ) @ X375 ) @ id )
!= $true ) )
| ? [X376: subst,X377: subst,X378: subst,X379: term] :
( ( ( X369 @ X378 @ X379 @ ( comp @ X376 @ X377 ) )
= $true )
& ( ( X369 @ ( comp @ X378 @ X376 ) @ ( sub @ X379 @ X376 ) @ X377 )
!= $true ) )
| ? [X380: subst > term > term] :
( ! [X381: term] :
( ( $true
!= ( X369 @ id @ X381 @ id ) )
| ( ( X369 @ id @ ( X380 @ id @ X381 ) @ id )
= $true ) )
& ! [X382: subst,X383: term,X384: subst] :
( ( X380 @ ( comp @ X382 @ X384 ) @ ( sub @ X383 @ X384 ) )
= ( sub @ ( X380 @ X382 @ X383 ) @ X384 ) )
& ( $true
!= ( X369 @ id @ ( lam @ ( X380 @ sh @ one ) ) @ id ) ) )
| ? [X370: term,X371: subst,X372: subst,X373: subst] :
( ( $true
!= ( X369 @ X373 @ X370 @ ( comp @ X372 @ X371 ) ) )
& ( $true
= ( X369 @ ( comp @ X373 @ X372 ) @ ( sub @ X370 @ X372 ) @ X371 ) ) )
| ( $true
= ( X369 @ id @ X368 @ id ) )
| ? [X385: term] :
( ( $true
!= ( X369 @ id @ X385 @ id ) )
& ( $true
= ( var @ ( sub @ X385 @ id ) ) ) ) )
| ? [X358: subst > term > subst > $o,X359: term,X360: term > $o] :
( ( $true
!= ( X360 @ ( lam @ X359 ) ) )
& ! [X361: term] :
( ( X360 @ X361 )
= ( X358 @ id @ X361 @ id ) )
& ! [X367: term] :
( ( ( X360 @ X367 )
!= $true )
| ( $true
= ( X360 @ ( sub @ X359 @ ( push @ X367 @ id ) ) ) ) )
& ! [X362: subst > term > term] :
( ? [X363: term] :
( ( ( X358 @ id @ ( X362 @ id @ X363 ) @ id )
!= $true )
& ( ( X358 @ id @ X363 @ id )
= $true ) )
| ( $true
= ( X358 @ id @ ( lam @ ( X362 @ sh @ one ) ) @ id ) )
| ? [X364: subst,X365: subst,X366: term] :
( ( sub @ ( X362 @ X364 @ X366 ) @ X365 )
!= ( X362 @ ( comp @ X364 @ X365 ) @ ( sub @ X366 @ X365 ) ) ) ) )
| ? [X357: term] :
( ( sub @ X357 @ id )
!= X357 )
| ? [X350: term,X351: term > $o] :
( ( $true
!= ( X351 @ X350 ) )
& ! [X353: term,X354: term] :
( ( ( X351 @ X353 )
!= $true )
| ( $true
= ( X351 @ ( ap @ X354 @ X353 ) ) )
| ( $true
!= ( X351 @ X354 ) ) )
& ! [X352: term] :
( ( ( X351 @ X352 )
= $true )
| ( ( var @ X352 )
!= $true ) )
& ! [X355: term] :
( ( $true
= ( X351 @ ( lam @ X355 ) ) )
| ? [X356: term] :
( ( ( X351 @ ( sub @ X355 @ ( push @ X356 @ id ) ) )
!= $true )
& ( ( X351 @ X356 )
= $true ) ) ) )
| ? [X347: subst > term > subst > $o] :
! [X348: term > $o] :
? [X349: term] :
( ( X347 @ id @ X349 @ id )
!= ( X348 @ X349 ) ) )
<=> ( hoasinduction_lthm_3 = $true ) )
& ( ( axvarcons = $true )
<=> ! [X77: subst,X78: term] :
( ( sub @ one @ ( push @ X78 @ X77 ) )
= X78 ) )
& ( pushprop_lem1v2_gthm = $true )
& ( ! [X48: term,X49: term,X50: term,X51: term] :
( ( ( ap @ X49 @ X48 )
!= ( ap @ X50 @ X51 ) )
| ( X48 = X51 ) )
<=> ( apinj2 = $true ) )
& ( hoasinduction_lem2v2_gthm = $true )
& ( pushprop_lem3v2 = $true )
& ( hoasapinj1_gthm = $true )
& ( hoasapnotvar_lthm = $true )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
<=> ( ! [X21: subst > term > subst > $o,X22: term] :
( ? [X23: term,X24: term] :
( ( ( X21 @ id @ X24 @ id )
= $true )
& ( $true
!= ( X21 @ id @ ( ap @ ( sub @ X23 @ id ) @ X24 ) @ id ) )
& ( $true
= ( X21 @ id @ X23 @ id ) ) )
| ( $true
= ( X21 @ id @ X22 @ id ) )
| ? [X25: subst > term > term] :
( ( ( X21 @ id @ ( lam @ ( X25 @ sh @ one ) ) @ id )
!= $true )
& ! [X26: term] :
( ( ( X21 @ id @ X26 @ id )
!= $true )
| ( ( X21 @ id @ ( X25 @ id @ X26 ) @ id )
= $true ) )
& ! [X27: term,X28: subst,X29: subst] :
( ( X25 @ ( comp @ X28 @ X29 ) @ ( sub @ X27 @ X29 ) )
= ( sub @ ( X25 @ X28 @ X27 ) @ X29 ) ) ) )
| ? [X11: term,X12: subst > term > subst > $o,X13: term > $o] :
( ! [X14: term] :
( ( X13 @ X14 )
= ( X12 @ id @ X14 @ id ) )
& ! [X20: term] :
( ( $true
= ( X13 @ ( sub @ X11 @ ( push @ X20 @ id ) ) ) )
| ( ( X13 @ X20 )
!= $true ) )
& ( ( X13 @ ( lam @ X11 ) )
!= $true )
& ! [X15: subst > term > term] :
( ? [X16: term] :
( ( ( X12 @ id @ ( X15 @ id @ X16 ) @ id )
!= $true )
& ( $true
= ( X12 @ id @ X16 @ id ) ) )
| ( $true
= ( X12 @ id @ ( lam @ ( X15 @ sh @ one ) ) @ id ) )
| ? [X17: term,X18: subst,X19: subst] :
( ( sub @ ( X15 @ X19 @ X17 ) @ X18 )
!= ( X15 @ ( comp @ X19 @ X18 ) @ ( sub @ X17 @ X18 ) ) ) ) )
| ? [X10: term] :
( ( sub @ X10 @ id )
!= X10 )
| ? [X3: term,X4: term > $o] :
( ! [X8: term] :
( ( ( X4 @ ( lam @ X8 ) )
= $true )
| ? [X9: term] :
( ( $true
!= ( X4 @ ( sub @ X8 @ ( push @ X9 @ id ) ) ) )
& ( $true
= ( X4 @ X9 ) ) ) )
& ! [X7: term] :
( ( $true
!= ( var @ X7 ) )
| ( ( X4 @ X7 )
= $true ) )
& ( $true
!= ( X4 @ X3 ) )
& ! [X5: term,X6: term] :
( ( ( X4 @ X5 )
!= $true )
| ( ( X4 @ X6 )
!= $true )
| ( $true
= ( X4 @ ( ap @ X5 @ X6 ) ) ) ) )
| ? [X0: subst > term > subst > $o] :
! [X1: term > $o] :
? [X2: term] :
( ( X0 @ id @ X2 @ id )
!= ( X1 @ X2 ) ) ) )
& ( hoaslamnotap_gthm = $true )
& ( pushprop = $true )
& ( hoaslamnotvar_lthm = $true )
& ( ! [X32: term,X33: subst > term > subst > $o] :
( ? [X42: subst > term > term] :
( ( ( X33 @ id @ ( lam @ ( X42 @ sh @ one ) ) @ id )
!= $true )
& ! [X43: term] :
( ( $true
!= ( X33 @ id @ X43 @ id ) )
| ( ( X33 @ id @ ( X42 @ id @ X43 ) @ id )
= $true ) )
& ! [X44: term,X45: subst,X46: subst] :
( ( X42 @ ( comp @ X46 @ X45 ) @ ( sub @ X44 @ X45 ) )
= ( sub @ ( X42 @ X46 @ X44 ) @ X45 ) ) )
| ? [X38: subst,X39: subst,X40: subst,X41: term] :
( ( $true
!= ( X33 @ ( comp @ X39 @ X40 ) @ ( sub @ X41 @ X40 ) @ X38 ) )
& ( $true
= ( X33 @ X39 @ X41 @ ( comp @ X40 @ X38 ) ) ) )
| ( $true
= ( X33 @ id @ ( lam @ X32 ) @ id ) )
| ? [X47: term] :
( ( ( X33 @ id @ ( sub @ X32 @ ( push @ X47 @ id ) ) @ id )
!= $true )
& ( $true
= ( X33 @ id @ X47 @ id ) ) )
| ? [X34: term,X35: subst,X36: subst,X37: subst] :
( ( ( X33 @ X36 @ X34 @ ( comp @ X37 @ X35 ) )
!= $true )
& ( ( X33 @ ( comp @ X36 @ X37 ) @ ( sub @ X34 @ X37 ) @ X35 )
= $true ) ) )
<=> ( hoasinduction_lem3 = $true ) )
& ( ( axvarid = $true )
<=> ! [X236: term] :
( ( sub @ X236 @ id )
= X236 ) )
& ( ( ! [X254: term] :
( ( sub @ X254 @ id )
= X254 )
| ? [X253: term] :
( ( sub @ X253 @ id )
!= X253 ) )
<=> ( termmset_lthm = $true ) )
& ( axapp = $true )
& ( lamnotvar = $true )
& ( ( termmset = $true )
<=> ! [X394: term] :
( ( sub @ X394 @ id )
= X394 ) )
& ( ! [X158: term > $o,X159: subst > term > subst > $o,X160: term] :
( ? [X167: term] :
( ( $true
!= ( X158 @ ( sub @ X160 @ ( push @ X167 @ id ) ) ) )
& ( ( X158 @ X167 )
= $true ) )
| ? [X161: term] :
( ( X158 @ X161 )
!= ( X159 @ id @ X161 @ id ) )
| ( $true
= ( X158 @ ( lam @ X160 ) ) )
| ? [X162: subst > term > term] :
( ! [X163: term] :
( ( $true
!= ( X159 @ id @ X163 @ id ) )
| ( $true
= ( X159 @ id @ ( X162 @ id @ X163 ) @ id ) ) )
& ( ( X159 @ id @ ( lam @ ( X162 @ sh @ one ) ) @ id )
!= $true )
& ! [X164: subst,X165: term,X166: subst] :
( ( sub @ ( X162 @ X166 @ X165 ) @ X164 )
= ( X162 @ ( comp @ X166 @ X164 ) @ ( sub @ X165 @ X164 ) ) ) ) )
<=> ( hoasinduction_lem3v2a = $true ) )
& ( hoaslamnotvar_gthm = $true )
& ( ( hoasinduction_lem2 = $true )
<=> ! [X452: term,X453: term,X454: subst > term > subst > $o] :
( ( ( X454 @ id @ X453 @ id )
!= $true )
| ? [X463: term,X464: term] :
( ( $true
= ( X454 @ id @ X463 @ id ) )
& ( $true
!= ( X454 @ id @ ( ap @ ( sub @ X463 @ id ) @ X464 ) @ id ) )
& ( ( X454 @ id @ X464 @ id )
= $true ) )
| ( ( X454 @ id @ X452 @ id )
!= $true )
| ? [X455: subst,X456: subst,X457: term,X458: subst] :
( ( ( X454 @ X458 @ X457 @ ( comp @ X455 @ X456 ) )
!= $true )
& ( $true
= ( X454 @ ( comp @ X458 @ X455 ) @ ( sub @ X457 @ X455 ) @ X456 ) ) )
| ( ( X454 @ id @ ( ap @ X452 @ X453 ) @ id )
= $true )
| ? [X459: subst,X460: term,X461: subst,X462: subst] :
( ( ( X454 @ X461 @ X460 @ ( comp @ X459 @ X462 ) )
= $true )
& ( ( X454 @ ( comp @ X461 @ X459 ) @ ( sub @ X460 @ X459 ) @ X462 )
!= $true ) ) ) )
& ( ( hoasinduction_lem3aa = $true )
<=> ! [X498: subst > term > subst > $o,X499: term] :
( ? [X501: subst > term > term] :
( ! [X505: term] :
( ( $true
!= ( X498 @ id @ X505 @ id ) )
| ( $true
= ( X498 @ id @ ( X501 @ id @ X505 ) @ id ) ) )
& ( $true
!= ( X498 @ id @ ( lam @ ( X501 @ sh @ one ) ) @ id ) )
& ! [X502: subst,X503: subst,X504: term] :
( ( X501 @ ( comp @ X502 @ X503 ) @ ( sub @ X504 @ X503 ) )
= ( sub @ ( X501 @ X502 @ X504 ) @ X503 ) ) )
| ? [X500: term] :
( ( $true
!= ( X498 @ id @ ( sub @ X499 @ ( push @ X500 @ id ) ) @ id ) )
& ( $true
= ( X498 @ id @ X500 @ id ) ) )
| ( $true
= ( X498 @ id @ ( lam @ ( sub @ X499 @ ( push @ one @ sh ) ) ) @ id ) ) ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ! [X480: term,X481: term,X482: term,X483: term] :
( ( ( ap @ ( sub @ X482 @ id ) @ X481 )
!= ( ap @ ( sub @ X480 @ id ) @ X483 ) )
| ( X481 = X483 ) )
<=> ( hoasapinj2 = $true ) )
& ! [X422: term] :
? [X423: d_term] :
( ( d2term @ X423 )
= X422 )
& ( substmonoid_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 ) ) ) ) )
& ( hoaslaminj_gthm = $true )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( pushprop_lthm_orig = $true )
& ( pushprop_lthm = $true )
& ( pushprop_lem1_gthm = $true )
& ( hoasinduction_lem1_gthm = $true )
& ( ( induction2_lthm = $true )
<=> ( ! [X137: term,X138: term > $o] :
( ? [X139: term] :
( ( ( var @ X139 )
= $true )
& ( ( X138 @ X139 )
!= $true ) )
| ? [X142: term] :
( ! [X143: term] :
( ( ( X138 @ X143 )
!= $true )
| ( ( X138 @ ( sub @ X142 @ ( push @ X143 @ id ) ) )
= $true ) )
& ( $true
!= ( X138 @ ( lam @ X142 ) ) ) )
| ? [X140: term,X141: term] :
( ( ( X138 @ X140 )
= $true )
& ( ( X138 @ ( ap @ X140 @ X141 ) )
!= $true )
& ( $true
= ( X138 @ X141 ) ) )
| ( $true
= ( X138 @ X137 ) ) )
| ? [X129: subst,X130: term > $o,X131: term] :
( ! [X132: term] :
( ? [X133: term] :
( ( $true
!= ( X130 @ ( sub @ X132 @ ( push @ X133 @ id ) ) ) )
& ( ( X130 @ X133 )
= $true ) )
| ( ( X130 @ ( lam @ X132 ) )
= $true ) )
& ! [X136: term] :
( ( ( var @ X136 )
!= $true )
| ( $true
= ( X130 @ ( sub @ X136 @ X129 ) ) ) )
& ( $true
!= ( X130 @ ( sub @ X131 @ X129 ) ) )
& ! [X134: term,X135: term] :
( ( ( X130 @ X134 )
!= $true )
| ( $true
!= ( X130 @ X135 ) )
| ( ( X130 @ ( ap @ X134 @ X135 ) )
= $true ) ) )
| ? [X128: term] :
( ( sub @ X128 @ id )
!= X128 ) ) )
& ( ! [X529: term] :
? [X530: subst > term > term] :
( ( X530 @ sh @ one )
= ( sub @ X529 @ ( push @ one @ sh ) ) )
<=> ( hoasinduction_lem3b = $true ) )
& ( pushprop_gthm = $true )
& ( pushprop_lem2v2_gthm = $true )
& ( hoasinduction_lem1 = $true )
& ( hoasapinj2_gthm = $true )
& ! [X265: d_subst,X266: d_subst] :
( ( X265 = X266 )
| ( ( d2subst @ X266 )
!= ( d2subst @ X265 ) ) )
& ( pushprop_lem0_gthm = $true )
& ( ! [X341: subst > term > term,X342: term,X343: term] :
( ( ( ap @ ( sub @ X342 @ id ) @ X343 )
!= ( lam @ ( X341 @ sh @ one ) ) )
| ? [X344: subst,X345: term,X346: subst] :
( ( sub @ ( X341 @ X346 @ X345 ) @ X344 )
!= ( X341 @ ( comp @ X346 @ X344 ) @ ( sub @ X345 @ X344 ) ) ) )
<=> ( hoaslamnotap = $true ) )
& ( axvarshift = $true )
& ( ( pushprop_lem0 = $true )
<=> ! [X119: term > $o,X120: subst,X121: term] :
? [X122: term > $o] :
! [X123: term] :
( ( X122 @ X123 )
= ( X119 @ ( sub @ X123 @ ( push @ X121 @ X120 ) ) ) ) )
& ( ( ! [X73: term,X74: term,X75: term,X76: term] :
( ( X73 = X74 )
| ( ( ap @ ( sub @ X74 @ id ) @ X76 )
!= ( ap @ ( sub @ X73 @ id ) @ X75 ) ) )
| ? [X69: term,X70: term,X71: term,X72: term] :
( ( ( ap @ X69 @ X70 )
= ( ap @ X71 @ X72 ) )
& ( X69 != X71 ) )
| ? [X68: term] :
( ( sub @ X68 @ id )
!= X68 ) )
<=> ( hoasapinj1_lthm = $true ) )
& ( ( axscons = $true )
<=> ! [X267: subst] :
( ( push @ ( sub @ one @ X267 ) @ ( comp @ sh @ X267 ) )
= X267 ) )
& ( ( ! [X517: subst,X518: term > $o,X519: term] :
( ? [X522: term,X523: term] :
( ( $true
!= ( X518 @ ( ap @ X523 @ X522 ) ) )
& ( ( X518 @ X522 )
= $true )
& ( ( X518 @ X523 )
= $true ) )
| ( $true
= ( X518 @ ( sub @ X519 @ X517 ) ) )
| ? [X524: term] :
( ( $true
!= ( X518 @ ( sub @ X524 @ X517 ) ) )
& ( ( var @ X524 )
= $true ) )
| ? [X520: term] :
( ! [X521: term] :
( ( $true
!= ( X518 @ X521 ) )
| ( $true
= ( X518 @ ( sub @ X520 @ ( push @ X521 @ id ) ) ) ) )
& ( ( X518 @ ( lam @ X520 ) )
!= $true ) ) )
| ? [X511: term,X512: term > $o] :
( ! [X515: term,X516: term] :
( ( ( X512 @ ( ap @ X516 @ X515 ) )
= $true )
| ( ( X512 @ X515 )
!= $true )
| ( $true
!= ( X512 @ X516 ) ) )
& ( ( X512 @ X511 )
!= $true )
& ! [X513: term] :
( ( $true
!= ( X512 @ X513 ) )
| ( ( X512 @ ( lam @ X513 ) )
= $true ) )
& ! [X514: term] :
( ( ( X512 @ X514 )
= $true )
| ( ( var @ X514 )
!= $true ) ) )
| ? [X510: subst] :
( ( comp @ X510 @ id )
!= X510 )
| ? [X508: subst,X509: term] :
( ( comp @ sh @ ( push @ X509 @ X508 ) )
!= X508 )
| ? [X506: term,X507: subst] :
( ( sub @ one @ ( push @ X506 @ X507 ) )
!= X506 ) )
<=> ( induction2lem_lthm = $true ) )
& ( ( shinj = $true )
<=> ! [X328: term,X329: term] :
( ( X328 = X329 )
| ( ( sub @ X329 @ sh )
!= ( sub @ X328 @ sh ) ) ) )
& ( axassoc = $true )
& ( hoasinduction_lem1v2 = $true )
& ( ! [X52: subst] :
( ( comp @ X52 @ id )
= X52 )
<=> ( axidr = $true ) )
& ( ! [X414: term,X415: subst > term > subst > $o] :
( ? [X417: subst > term > term] :
( ! [X421: term] :
( ( $true
!= ( X415 @ id @ X421 @ id ) )
| ( ( X415 @ id @ ( X417 @ id @ X421 ) @ id )
= $true ) )
& ( ( X415 @ id @ ( lam @ ( X417 @ sh @ one ) ) @ id )
!= $true )
& ! [X418: subst,X419: term,X420: subst] :
( ( sub @ ( X417 @ X418 @ X419 ) @ X420 )
= ( X417 @ ( comp @ X418 @ X420 ) @ ( sub @ X419 @ X420 ) ) ) )
| ( ( X415 @ id @ ( lam @ ( sub @ X414 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ? [X416: term] :
( ( ( X415 @ id @ X416 @ id )
= $true )
& ( ( X415 @ id @ ( sub @ X414 @ ( push @ X416 @ id ) ) @ id )
!= $true ) ) )
<=> ( hoasinduction_lem3aa_lthm = $true ) )
& ! [X234: d_term,X235: d_term] :
( ( ( d2term @ X234 )
!= ( d2term @ X235 ) )
| ( X234 = X235 ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( ( ! [X204: subst > term > subst > $o,X205: term] :
( ? [X216: term] :
( ( $true
= ( var @ ( sub @ X216 @ id ) ) )
& ( ( X204 @ id @ X216 @ id )
!= $true ) )
| ? [X208: subst,X209: subst,X210: subst,X211: term] :
( ( $true
= ( X204 @ ( comp @ X210 @ X208 ) @ ( sub @ X211 @ X208 ) @ X209 ) )
& ( ( X204 @ X210 @ X211 @ ( comp @ X208 @ X209 ) )
!= $true ) )
| ? [X217: subst > term > term] :
( ! [X218: subst,X219: term,X220: subst] :
( ( sub @ ( X217 @ X220 @ X219 ) @ X218 )
= ( X217 @ ( comp @ X220 @ X218 ) @ ( sub @ X219 @ X218 ) ) )
& ! [X221: term] :
( ( $true
!= ( X204 @ id @ X221 @ id ) )
| ( ( X204 @ id @ ( X217 @ id @ X221 ) @ id )
= $true ) )
& ( ( X204 @ id @ ( lam @ ( X217 @ sh @ one ) ) @ id )
!= $true ) )
| ? [X212: subst,X213: subst,X214: term,X215: subst] :
( ( ( X204 @ ( comp @ X213 @ X212 ) @ ( sub @ X214 @ X212 ) @ X215 )
!= $true )
& ( $true
= ( X204 @ X213 @ X214 @ ( comp @ X212 @ X215 ) ) ) )
| ( $true
= ( X204 @ id @ X205 @ id ) )
| ? [X206: term,X207: term] :
( ( $true
= ( X204 @ id @ X206 @ id ) )
& ( $true
!= ( X204 @ id @ ( ap @ ( sub @ X207 @ id ) @ X206 ) @ id ) )
& ( $true
= ( X204 @ id @ X207 @ id ) ) ) )
| ? [X188: term,X189: subst > term > subst > $o] :
( ! [X198: term] :
( ( ( X189 @ id @ ( sub @ X188 @ ( push @ X198 @ id ) ) @ id )
= $true )
| ( $true
!= ( X189 @ id @ X198 @ id ) ) )
& ! [X190: subst,X191: term,X192: subst,X193: subst] :
( ( ( X189 @ X193 @ X191 @ ( comp @ X190 @ X192 ) )
!= $true )
| ( ( X189 @ ( comp @ X193 @ X190 ) @ ( sub @ X191 @ X190 ) @ X192 )
= $true ) )
& ( ( X189 @ id @ ( lam @ X188 ) @ id )
!= $true )
& ! [X194: subst,X195: subst,X196: term,X197: subst] :
( ( ( X189 @ ( comp @ X197 @ X195 ) @ ( sub @ X196 @ X195 ) @ X194 )
!= $true )
| ( ( X189 @ X197 @ X196 @ ( comp @ X195 @ X194 ) )
= $true ) )
& ! [X199: subst > term > term] :
( ? [X200: term,X201: subst,X202: subst] :
( ( sub @ ( X199 @ X201 @ X200 ) @ X202 )
!= ( X199 @ ( comp @ X201 @ X202 ) @ ( sub @ X200 @ X202 ) ) )
| ? [X203: term] :
( ( ( X189 @ id @ X203 @ id )
= $true )
& ( ( X189 @ id @ ( X199 @ id @ X203 ) @ id )
!= $true ) )
| ( ( X189 @ id @ ( lam @ ( X199 @ sh @ one ) ) @ id )
= $true ) ) )
| ? [X175: term,X176: term,X177: subst > term > subst > $o] :
( ( $true
= ( X177 @ id @ X175 @ id ) )
& ! [X182: subst,X183: subst,X184: term,X185: subst] :
( ( $true
= ( X177 @ X185 @ X184 @ ( comp @ X183 @ X182 ) ) )
| ( $true
!= ( X177 @ ( comp @ X185 @ X183 ) @ ( sub @ X184 @ X183 ) @ X182 ) ) )
& ! [X186: term,X187: term] :
( ( $true
!= ( X177 @ id @ X187 @ id ) )
| ( $true
!= ( X177 @ id @ X186 @ id ) )
| ( $true
= ( X177 @ id @ ( ap @ ( sub @ X187 @ id ) @ X186 ) @ id ) ) )
& ( $true
= ( X177 @ id @ X176 @ id ) )
& ! [X178: subst,X179: subst,X180: term,X181: subst] :
( ( ( X177 @ X179 @ X180 @ ( comp @ X181 @ X178 ) )
!= $true )
| ( ( X177 @ ( comp @ X179 @ X181 ) @ ( sub @ X180 @ X181 ) @ X178 )
= $true ) )
& ( ( X177 @ id @ ( ap @ X175 @ X176 ) @ id )
!= $true ) )
| ? [X168: term > $o,X169: term] :
( ( $true
!= ( X168 @ X169 ) )
& ! [X172: term,X173: term] :
( ( ( X168 @ X172 )
!= $true )
| ( ( X168 @ ( ap @ X173 @ X172 ) )
= $true )
| ( $true
!= ( X168 @ X173 ) ) )
& ! [X174: term] :
( ( ( var @ X174 )
!= $true )
| ( ( X168 @ X174 )
= $true ) )
& ! [X170: term] :
( ( ( X168 @ ( lam @ X170 ) )
= $true )
| ? [X171: term] :
( ( ( X168 @ X171 )
= $true )
& ( $true
!= ( X168 @ ( sub @ X170 @ ( push @ X171 @ id ) ) ) ) ) ) ) )
<=> ( hoasinduction_lthm = $true ) )
& ( axmap = $true )
& ( ( hoasapinj1 = $true )
<=> ! [X486: term,X487: term,X488: term,X489: term] :
( ( ( ap @ ( sub @ X489 @ id ) @ X486 )
!= ( ap @ ( sub @ X488 @ id ) @ X487 ) )
| ( X488 = X489 ) ) )
& ( hoaslamnotvar = $true )
& ( hoasinduction_lem1v2_gthm = $true )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( hoasinduction_lem3aaa = $true )
<=> ! [X222: term,X223: subst > term > subst > $o] :
( ? [X225: term,X226: subst > term > term] :
( ! [X233: term] :
( ( ( X223 @ id @ ( X226 @ id @ X233 ) @ id )
= $true )
| ( $true
!= ( X223 @ id @ X233 @ id ) ) )
& ! [X227: subst,X228: term,X229: subst] :
( ( sub @ ( sub @ X225 @ ( push @ X228 @ X229 ) ) @ X227 )
= ( sub @ ( X226 @ X229 @ X228 ) @ X227 ) )
& ( $true
!= ( X223 @ id @ ( lam @ ( X226 @ sh @ one ) ) @ id ) )
& ! [X230: subst,X231: term,X232: subst] :
( ( sub @ X225 @ ( push @ ( sub @ X231 @ X232 ) @ ( comp @ X230 @ X232 ) ) )
= ( X226 @ ( comp @ X230 @ X232 ) @ ( sub @ X231 @ X232 ) ) ) )
| ? [X224: term] :
( ( ( X223 @ id @ X224 @ id )
= $true )
& ( $true
!= ( X223 @ id @ ( sub @ X222 @ ( push @ X224 @ id ) ) @ id ) ) )
| ( $true
= ( X223 @ id @ ( lam @ ( sub @ X222 @ ( push @ one @ sh ) ) ) @ id ) ) ) )
& ( ( hoasinduction_lem3a_lthm = $true )
<=> ( ! [X90: subst > term > subst > $o,X91: term] :
( ? [X97: term] :
( ( $true
= ( X90 @ id @ X97 @ id ) )
& ( $true
!= ( X90 @ id @ ( sub @ X91 @ ( push @ X97 @ id ) ) @ id ) ) )
| ( ( X90 @ id @ ( lam @ X91 ) @ id )
= $true )
| ? [X92: subst > term > term] :
( ! [X94: term,X95: subst,X96: subst] :
( ( sub @ ( X92 @ X96 @ X94 ) @ X95 )
= ( X92 @ ( comp @ X96 @ X95 ) @ ( sub @ X94 @ X95 ) ) )
& ! [X93: term] :
( ( $true
= ( X90 @ id @ ( X92 @ id @ X93 ) @ id ) )
| ( $true
!= ( X90 @ id @ X93 @ id ) ) )
& ( $true
!= ( X90 @ id @ ( lam @ ( X92 @ sh @ one ) ) @ id ) ) ) )
| ? [X82: subst > term > subst > $o,X83: term] :
( ( ( X82 @ id @ ( lam @ ( sub @ X83 @ ( push @ one @ sh ) ) ) @ id )
!= $true )
& ! [X89: term] :
( ( $true
= ( X82 @ id @ ( sub @ X83 @ ( push @ X89 @ id ) ) @ id ) )
| ( ( X82 @ id @ X89 @ id )
!= $true ) )
& ! [X84: subst > term > term] :
( ? [X85: term,X86: subst,X87: subst] :
( ( sub @ ( X84 @ X87 @ X85 ) @ X86 )
!= ( X84 @ ( comp @ X87 @ X86 ) @ ( sub @ X85 @ X86 ) ) )
| ( $true
= ( X82 @ id @ ( lam @ ( X84 @ sh @ one ) ) @ id ) )
| ? [X88: term] :
( ( ( X82 @ id @ ( X84 @ id @ X88 ) @ id )
!= $true )
& ( $true
= ( X82 @ id @ X88 @ id ) ) ) ) )
| ? [X81: term] :
( ( sub @ X81 @ id )
!= X81 ) ) )
& ! [X484: subst] :
? [X485: d_subst] :
( ( d2subst @ X485 )
= X484 )
& ( pushprop_lem3v2_lthm = $true )
& ( hoasinduction_lem2_lthm = $true )
& ( axabs = $true )
& ( hoasapnotvar = $true )
& ( ( hoaslaminj_lthm = $true )
<=> ( ! [X243: subst,X244: term,X245: subst > term > term,X246: subst > term > term] :
( ( ( lam @ ( X246 @ sh @ one ) )
!= ( lam @ ( X245 @ sh @ one ) ) )
| ( ( X246 @ X243 @ X244 )
= ( X245 @ X243 @ X244 ) )
| ? [X250: subst,X251: term,X252: subst] :
( ( X245 @ ( comp @ X250 @ X252 ) @ ( sub @ X251 @ X252 ) )
!= ( sub @ ( X245 @ X250 @ X251 ) @ X252 ) )
| ? [X247: term,X248: subst,X249: subst] :
( ( sub @ ( X246 @ X248 @ X247 ) @ X249 )
!= ( X246 @ ( comp @ X248 @ X249 ) @ ( sub @ X247 @ X249 ) ) ) )
| ? [X241: term,X242: term] :
( ( X241 != X242 )
& ( ( lam @ X241 )
= ( lam @ X242 ) ) )
| ? [X239: term,X240: subst] :
( ( comp @ sh @ ( push @ X239 @ X240 ) )
!= X240 )
| ? [X237: subst,X238: term] :
( ( sub @ one @ ( push @ X238 @ X237 ) )
!= X238 ) ) )
& ( ulamvarsh = $true )
& ( hoasinduction_lem2_gthm = $true )
& ( ( induction = $true )
<=> ! [X255: term,X256: term > $o] :
( ? [X258: term,X259: term] :
( ( ( X256 @ X258 )
= $true )
& ( ( X256 @ ( ap @ X259 @ X258 ) )
!= $true )
& ( $true
= ( X256 @ X259 ) ) )
| ? [X257: term] :
( ( $true
= ( X256 @ X257 ) )
& ( ( X256 @ ( lam @ X257 ) )
!= $true ) )
| ( ( X256 @ X255 )
= $true )
| ? [X260: term] :
( ( $true
!= ( X256 @ X260 ) )
& ( ( var @ X260 )
= $true ) ) ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
<=> ( ? [X98: term] :
( ( sub @ X98 @ id )
!= X98 )
| ! [X99: term > $o,X100: subst > term > subst > $o,X101: term] :
( ( ( X99 @ ( lam @ X101 ) )
= $true )
| ? [X102: term] :
( ( ( X99 @ ( sub @ X101 @ ( push @ X102 @ id ) ) )
!= $true )
& ( ( X99 @ X102 )
= $true ) )
| ? [X103: subst > term > term] :
( ! [X104: subst,X105: subst,X106: term] :
( ( X103 @ ( comp @ X105 @ X104 ) @ ( sub @ X106 @ X104 ) )
= ( sub @ ( X103 @ X105 @ X106 ) @ X104 ) )
& ! [X107: term] :
( ( ( X100 @ id @ X107 @ id )
!= $true )
| ( $true
= ( X100 @ id @ ( X103 @ id @ X107 ) @ id ) ) )
& ( $true
!= ( X100 @ id @ ( lam @ ( X103 @ sh @ one ) ) @ id ) ) )
| ? [X113: subst,X114: subst,X115: term,X116: subst] :
( ( $true
= ( X100 @ ( comp @ X114 @ X113 ) @ ( sub @ X115 @ X113 ) @ X116 ) )
& ( $true
!= ( X100 @ X114 @ X115 @ ( comp @ X113 @ X116 ) ) ) )
| ? [X112: term] :
( ( X100 @ id @ X112 @ id )
!= ( X99 @ X112 ) )
| ? [X108: subst,X109: term,X110: subst,X111: subst] :
( ( ( X100 @ ( comp @ X108 @ X110 ) @ ( sub @ X109 @ X110 ) @ X111 )
!= $true )
& ( ( X100 @ X108 @ X109 @ ( comp @ X110 @ X111 ) )
= $true ) ) ) ) )
& ( hoasinduction_lem1_lthm = $true )
& ( hoasinduction_lem3_gthm = $true )
& ( ulamvarind = $true )
& ( ( ! [X153: term,X154: term > $o,X155: subst,X156: term,X157: term > $o] :
( ( ( X157 @ ( sub @ X153 @ ( push @ X156 @ X155 ) ) )
= $true )
| ( $true
!= ( X154 @ X153 ) ) )
| ? [X151: subst,X152: term] :
( ( comp @ sh @ ( push @ X152 @ X151 ) )
!= X151 )
| ? [X149: term,X150: subst] :
( ( sub @ one @ ( push @ X149 @ X150 ) )
!= X149 ) )
<=> ( pushprop_lem1_lthm = $true ) )
& ( induction2lem_gthm = $true )
& ( ( ? [X532: term,X533: term,X534: term,X535: term] :
( ( ( ap @ X532 @ X534 )
= ( ap @ X535 @ X533 ) )
& ( X533 != X534 ) )
| ! [X536: term,X537: term,X538: term,X539: term] :
( ( ( ap @ ( sub @ X536 @ id ) @ X539 )
!= ( ap @ ( sub @ X537 @ id ) @ X538 ) )
| ( X538 = X539 ) ) )
<=> ( hoasapinj2_lthm = $true ) )
& ( ( hoasinduction_lem3b_lthm = $true )
<=> ! [X339: term] :
? [X340: subst > term > term] :
( ( X340 @ sh @ one )
= ( sub @ X339 @ ( push @ one @ sh ) ) ) )
& ( ( hoasinduction_no_psi_cond = $true )
<=> ! [X330: term,X331: subst > term > subst > $o] :
( ( ( X331 @ id @ X330 @ id )
= $true )
| ? [X337: term,X338: term] :
( ( ( X331 @ id @ ( ap @ ( sub @ X337 @ id ) @ X338 ) @ id )
!= $true )
& ( ( X331 @ id @ X338 @ id )
= $true )
& ( ( X331 @ id @ X337 @ id )
= $true ) )
| ? [X332: subst > term > term] :
( ( $true
!= ( X331 @ id @ ( lam @ ( X332 @ sh @ one ) ) @ id ) )
& ! [X333: term] :
( ( ( X331 @ id @ X333 @ id )
!= $true )
| ( ( X331 @ id @ ( X332 @ id @ X333 ) @ id )
= $true ) )
& ! [X334: subst,X335: subst,X336: term] :
( ( sub @ ( X332 @ X335 @ X336 ) @ X334 )
= ( X332 @ ( comp @ X335 @ X334 ) @ ( sub @ X336 @ X334 ) ) ) ) ) )
& ( ( substmonoid_lthm = $true )
<=> ( ( ! [X397: subst] :
( ( comp @ id @ X397 )
= X397 )
& ! [X398: subst] :
( ( comp @ X398 @ id )
= X398 ) )
| ? [X396: subst] :
( ( comp @ X396 @ id )
!= X396 )
| ? [X395: subst] :
( ( comp @ id @ X395 )
!= X395 ) ) )
& ! [X291: d_subst] : ( d_id = X291 )
& ( ( induction2 = $true )
<=> ! [X268: term > $o,X269: term] :
( ? [X274: term] :
( ( $true
!= ( X268 @ X274 ) )
& ( ( var @ X274 )
= $true ) )
| ? [X272: term,X273: term] :
( ( $true
= ( X268 @ X272 ) )
& ( ( X268 @ ( ap @ X273 @ X272 ) )
!= $true )
& ( ( X268 @ X273 )
= $true ) )
| ( ( X268 @ X269 )
= $true )
| ? [X270: term] :
( ! [X271: term] :
( ( $true
= ( X268 @ ( sub @ X270 @ ( push @ X271 @ id ) ) ) )
| ( $true
!= ( X268 @ X271 ) ) )
& ( ( X268 @ ( lam @ X270 ) )
!= $true ) ) ) )
& ( hoasinduction_gthm = $true )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( pushprop_lem2v2_lthm = $true )
& ( ! [X310: term,X311: subst > term > subst > $o,X312: term > $o] :
( ? [X323: subst > term > term] :
( ( ( X311 @ id @ ( lam @ ( X323 @ sh @ one ) ) @ id )
!= $true )
& ! [X325: term,X326: subst,X327: subst] :
( ( X323 @ ( comp @ X327 @ X326 ) @ ( sub @ X325 @ X326 ) )
= ( sub @ ( X323 @ X327 @ X325 ) @ X326 ) )
& ! [X324: term] :
( ( ( X311 @ id @ ( X323 @ id @ X324 ) @ id )
= $true )
| ( $true
!= ( X311 @ id @ X324 @ id ) ) ) )
| ? [X315: subst,X316: subst,X317: subst,X318: term] :
( ( $true
!= ( X311 @ X316 @ X318 @ ( comp @ X317 @ X315 ) ) )
& ( ( X311 @ ( comp @ X316 @ X317 ) @ ( sub @ X318 @ X317 ) @ X315 )
= $true ) )
| ? [X314: term] :
( ( ( X312 @ X314 )
= $true )
& ( ( X312 @ ( sub @ X310 @ ( push @ X314 @ id ) ) )
!= $true ) )
| ( ( X312 @ ( lam @ X310 ) )
= $true )
| ? [X319: subst,X320: subst,X321: term,X322: subst] :
( ( ( X311 @ X322 @ X321 @ ( comp @ X319 @ X320 ) )
= $true )
& ( ( X311 @ ( comp @ X322 @ X319 ) @ ( sub @ X321 @ X319 ) @ X320 )
!= $true ) )
| ? [X313: term] :
( ( X312 @ X313 )
!= ( X311 @ id @ X313 @ id ) ) )
<=> ( hoasinduction_lem3v2 = $true ) )
& ( hoaslamnotap_lthm = $true )
& ( axclos = $true )
& ( ulamvar1 != $true )
& ( ( d2subst @ d_id )
= id )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ( ! [X79: subst] :
( ( comp @ id @ X79 )
= X79 )
& ! [X80: subst] :
( ( comp @ X80 @ id )
= X80 ) )
<=> ( substmonoid = $true ) )
& ( ! [X449: subst > term > subst > $o] :
? [X450: term > $o] :
! [X451: term] :
( ( X449 @ id @ X451 @ id )
= ( X450 @ X451 ) )
<=> ( hoasinduction_lem0_lthm = $true ) )
& ( hoasinduction_lem3b_gthm = $true )
& ! [X531: d_term] : ( d_one = X531 ) ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
( ( ( pushprop_lem1 = $true )
<=> ! [X275: term,X276: term,X277: term > $o,X278: subst,X279: term > $o] :
( ( ( X279 @ X276 )
!= $true )
| ( ( X277 @ ( sub @ X276 @ ( push @ X275 @ X278 ) ) )
= $true ) ) )
& ( induction2_gthm = $true )
& ( ( hoaslaminj = $true )
<=> ! [X404: subst,X405: subst > term > term,X406: term,X407: subst > term > term] :
( ~ ! [X408: term,X409: subst,X410: subst] :
( ( X407 @ ( comp @ X409 @ X410 ) @ ( sub @ X408 @ X410 ) )
= ( sub @ ( X407 @ X409 @ X408 ) @ X410 ) )
| ( ( X407 @ X404 @ X406 )
= ( X405 @ X404 @ X406 ) )
| ~ ! [X411: subst,X412: subst,X413: term] :
( ( X405 @ ( comp @ X412 @ X411 ) @ ( sub @ X413 @ X411 ) )
= ( sub @ ( X405 @ X412 @ X413 ) @ X411 ) )
| ( ( lam @ ( X407 @ sh @ one ) )
!= ( lam @ ( X405 @ sh @ one ) ) ) ) )
& ( ( axshiftcons = $true )
<=> ! [X117: term,X118: subst] :
( ( comp @ sh @ ( push @ X117 @ X118 ) )
= X118 ) )
& ( ! [X490: term,X491: subst > term > subst > $o] :
( ~ ! [X492: term] :
( ( ( X491 @ id @ X492 @ id )
!= $true )
| ( ( X491 @ id @ ( sub @ X490 @ ( push @ X492 @ id ) ) @ id )
= $true ) )
| ~ ! [X493: subst > term > term] :
( ~ ! [X494: subst,X495: subst,X496: term] :
( ( X493 @ ( comp @ X494 @ X495 ) @ ( sub @ X496 @ X495 ) )
= ( sub @ ( X493 @ X494 @ X496 ) @ X495 ) )
| ( ( X491 @ id @ ( lam @ ( X493 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X497: term] :
( ( ( X491 @ id @ ( X493 @ id @ X497 ) @ id )
= $true )
| ( ( X491 @ id @ X497 @ id )
!= $true ) ) )
| ( $true
= ( X491 @ id @ ( lam @ X490 ) @ id ) ) )
<=> ( hoasinduction_lem3a = $true ) )
& ( pushprop_lem2v2 = $true )
& ( ! [X53: term,X54: term > $o,X55: subst > term > subst > $o,X56: term] :
( ( ( X54 @ X56 )
!= $true )
| ( ( X54 @ ( ap @ X53 @ X56 ) )
= $true )
| ~ ! [X64: subst,X65: term,X66: subst,X67: subst] :
( ( ( X55 @ X66 @ X65 @ ( comp @ X67 @ X64 ) )
= $true )
| ( ( X55 @ ( comp @ X66 @ X67 ) @ ( sub @ X65 @ X67 ) @ X64 )
!= $true ) )
| ~ ! [X61: term,X62: term] :
( ( ( X55 @ id @ X62 @ id )
!= $true )
| ( $true
!= ( X55 @ id @ X61 @ id ) )
| ( ( X55 @ id @ ( ap @ ( sub @ X62 @ id ) @ X61 ) @ id )
= $true ) )
| ~ ! [X57: subst,X58: term,X59: subst,X60: subst] :
( ( $true
!= ( X55 @ X60 @ X58 @ ( comp @ X57 @ X59 ) ) )
| ( ( X55 @ ( comp @ X60 @ X57 ) @ ( sub @ X58 @ X57 ) @ X59 )
= $true ) )
| ~ ! [X63: term] :
( ( X55 @ id @ X63 @ id )
= ( X54 @ X63 ) )
| ( ( X54 @ X53 )
!= $true ) )
<=> ( hoasinduction_lem2v2 = $true ) )
& ( ( induction2lem = $true )
<=> ! [X386: term,X387: subst,X388: term > $o] :
( ~ ! [X389: term] :
( ( $true
!= ( var @ X389 ) )
| ( ( X388 @ ( sub @ X389 @ X387 ) )
= $true ) )
| ~ ! [X392: term] :
( ( ( X388 @ ( lam @ X392 ) )
= $true )
| ~ ! [X393: term] :
( ( $true
!= ( X388 @ X393 ) )
| ( ( X388 @ ( sub @ X392 @ ( push @ X393 @ id ) ) )
= $true ) ) )
| ( $true
= ( X388 @ ( sub @ X386 @ X387 ) ) )
| ~ ! [X390: term,X391: term] :
( ( ( X388 @ X390 )
!= $true )
| ( ( X388 @ ( ap @ X391 @ X390 ) )
= $true )
| ( $true
!= ( X388 @ X391 ) ) ) ) )
& ( ( ! [X465: term] :
~ ! [X466: subst > term > term] :
~ ! [X467: subst,X468: term] :
( ( sub @ X465 @ ( push @ X468 @ X467 ) )
= ( X466 @ X467 @ X468 ) )
=> ( ! [X469: term] :
( ( sub @ X469 @ id )
= X469 )
=> ! [X470: subst > term > subst > $o,X471: term,X472: term > $o] :
( ~ ! [X479: term] :
( ( $true
!= ( X472 @ X479 ) )
| ( ( X472 @ ( sub @ X471 @ ( push @ X479 @ id ) ) )
= $true ) )
| ~ ! [X473: subst > term > term] :
( ~ ! [X475: subst,X476: subst,X477: term] :
( ( X473 @ ( comp @ X476 @ X475 ) @ ( sub @ X477 @ X475 ) )
= ( sub @ ( X473 @ X476 @ X477 ) @ X475 ) )
| ( ( X470 @ id @ ( lam @ ( X473 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X474: term] :
( ( ( X470 @ id @ X474 @ id )
!= $true )
| ( ( X470 @ id @ ( X473 @ id @ X474 ) @ id )
= $true ) ) )
| ~ ! [X478: term] :
( ( X470 @ id @ X478 @ id )
= ( X472 @ X478 ) )
| ( ( X472 @ ( lam @ X471 ) )
= $true ) ) ) )
<=> ( hoasinduction_lem3v2a_lthm = $true ) )
& ( hoasapnotvar_gthm = $true )
& ( ! [X144: subst,X145: term > $o,X146: term] :
~ ! [X147: term > $o] :
~ ! [X148: term] :
( ( X145 @ ( sub @ X148 @ ( push @ X146 @ X144 ) ) )
= ( X147 @ X148 ) )
<=> ( pushprop_lem0_lthm = $true ) )
& ( hoasinduction_lem3a_gthm = $true )
& ( hoasinduction_lem3v2_gthm = $true )
& ( ( hoasinduction_lem3v2_f = $true )
<=> ! [X280: term] :
~ ! [X281: subst > term > term] :
~ ! [X282: term,X283: subst] :
( ( X281 @ X283 @ X282 )
= ( sub @ X280 @ ( push @ X282 @ X283 ) ) ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( termmset_gthm = $true )
& ( ! [X124: term] :
~ ! [X125: subst > term > term] :
~ ! [X126: term,X127: subst] :
( ( sub @ X124 @ ( push @ X126 @ X127 ) )
= ( X125 @ X127 @ X126 ) )
<=> ( hoasinduction_lem3v2_f_lthm = $true ) )
& ( ( ! [X284: term,X285: subst] :
( ( sub @ one @ ( push @ X284 @ X285 ) )
= X284 )
=> ! [X286: term,X287: subst,X288: term > $o,X289: term > $o] :
( ~ ! [X290: term] :
( ( X288 @ ( sub @ X290 @ ( push @ X286 @ X287 ) ) )
= ( X289 @ X290 ) )
| ( ( X289 @ one )
= $true )
| ( $true
!= ( X288 @ X286 ) ) ) )
<=> ( pushprop_lem1v2_lthm = $true ) )
& ( ! [X30: term,X31: term] :
( ( X30 = X31 )
| ( ( lam @ X30 )
!= ( lam @ X31 ) ) )
<=> ( laminj = $true ) )
& ( ! [X525: subst > term > subst > $o] :
~ ! [X526: term > $o] :
~ ! [X527: term] :
( ( X525 @ id @ X527 @ id )
= ( X526 @ X527 ) )
<=> ( hoasinduction_lem0 = $true ) )
& ( ! [X399: subst,X400: term > $o,X401: term > $o,X402: term] :
( ( $true
!= ( X400 @ X402 ) )
| ~ ! [X403: term] :
( ( X400 @ ( sub @ X403 @ ( push @ X402 @ X399 ) ) )
= ( X401 @ X403 ) )
| ( $true
= ( X401 @ one ) ) )
<=> ( pushprop_lem1v2 = $true ) )
& ( ( apinj1 = $true )
<=> ! [X261: term,X262: term,X263: term,X264: term] :
( ( X262 = X264 )
| ( ( ap @ X264 @ X263 )
!= ( ap @ X262 @ X261 ) ) ) )
& ( one
= ( d2term @ d_one ) )
& ( ! [X528: subst] :
( ( comp @ id @ X528 )
= X528 )
<=> ( axidl = $true ) )
& ( ( hoasinduction_lem3_lthm = $true )
<=> ( ! [X424: term] :
( ( sub @ X424 @ id )
= X424 )
=> ( ! [X425: subst > term > subst > $o,X426: term] :
( ~ ! [X432: term] :
( ( $true
= ( X425 @ id @ ( sub @ X426 @ ( push @ X432 @ id ) ) @ id ) )
| ( ( X425 @ id @ X432 @ id )
!= $true ) )
| ~ ! [X427: subst > term > term] :
( ( $true
= ( X425 @ id @ ( lam @ ( X427 @ sh @ one ) ) @ id ) )
| ~ ! [X428: subst,X429: term,X430: subst] :
( ( X427 @ ( comp @ X430 @ X428 ) @ ( sub @ X429 @ X428 ) )
= ( sub @ ( X427 @ X430 @ X429 ) @ X428 ) )
| ~ ! [X431: term] :
( ( $true
!= ( X425 @ id @ X431 @ id ) )
| ( ( X425 @ id @ ( X427 @ id @ X431 ) @ id )
= $true ) ) )
| ( $true
= ( X425 @ id @ ( lam @ ( sub @ X426 @ ( push @ one @ sh ) ) ) @ id ) ) )
=> ! [X433: term,X434: subst > term > subst > $o] :
( ~ ! [X435: term] :
( ( $true
!= ( X434 @ id @ X435 @ id ) )
| ( ( X434 @ id @ ( sub @ X433 @ ( push @ X435 @ id ) ) @ id )
= $true ) )
| ~ ! [X440: subst,X441: term,X442: subst,X443: subst] :
( ( ( X434 @ X442 @ X441 @ ( comp @ X440 @ X443 ) )
= $true )
| ( ( X434 @ ( comp @ X442 @ X440 ) @ ( sub @ X441 @ X440 ) @ X443 )
!= $true ) )
| ~ ! [X444: subst > term > term] :
( ( ( X434 @ id @ ( lam @ ( X444 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X446: subst,X447: term,X448: subst] :
( ( X444 @ ( comp @ X448 @ X446 ) @ ( sub @ X447 @ X446 ) )
= ( sub @ ( X444 @ X448 @ X447 ) @ X446 ) )
| ~ ! [X445: term] :
( ( ( X434 @ id @ ( X444 @ id @ X445 ) @ id )
= $true )
| ( ( X434 @ id @ X445 @ id )
!= $true ) ) )
| ~ ! [X436: subst,X437: term,X438: subst,X439: subst] :
( ( ( X434 @ X436 @ X437 @ ( comp @ X439 @ X438 ) )
!= $true )
| ( $true
= ( X434 @ ( comp @ X436 @ X439 ) @ ( sub @ X437 @ X439 ) @ X438 ) ) )
| ( ( X434 @ id @ ( lam @ X433 ) @ id )
= $true ) ) ) ) )
& ( apnotvar = $true )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ! [X292: term,X293: subst > term > subst > $o] :
( ~ ! [X299: subst,X300: subst,X301: term,X302: subst] :
( ( ( X293 @ X302 @ X301 @ ( comp @ X300 @ X299 ) )
!= $true )
| ( $true
= ( X293 @ ( comp @ X302 @ X300 ) @ ( sub @ X301 @ X300 ) @ X299 ) ) )
| ~ ! [X294: subst > term > term] :
( ~ ! [X298: term] :
( ( $true
!= ( X293 @ id @ X298 @ id ) )
| ( $true
= ( X293 @ id @ ( X294 @ id @ X298 ) @ id ) ) )
| ~ ! [X295: subst,X296: term,X297: subst] :
( ( X294 @ ( comp @ X295 @ X297 ) @ ( sub @ X296 @ X297 ) )
= ( sub @ ( X294 @ X295 @ X296 ) @ X297 ) )
| ( $true
= ( X293 @ id @ ( lam @ ( X294 @ sh @ one ) ) @ id ) ) )
| ~ ! [X304: term,X305: term] :
( ( $true
= ( X293 @ id @ ( ap @ ( sub @ X304 @ id ) @ X305 ) @ id ) )
| ( $true
!= ( X293 @ id @ X305 @ id ) )
| ( $true
!= ( X293 @ id @ X304 @ id ) ) )
| ( ( X293 @ id @ X292 @ id )
= $true )
| ~ ! [X306: term,X307: subst,X308: subst,X309: subst] :
( ( ( X293 @ X308 @ X306 @ ( comp @ X307 @ X309 ) )
= $true )
| ( $true
!= ( X293 @ ( comp @ X308 @ X307 ) @ ( sub @ X306 @ X307 ) @ X309 ) ) )
| ~ ! [X303: term] :
( ( $true
!= ( var @ ( sub @ X303 @ id ) ) )
| ( ( X293 @ id @ X303 @ id )
= $true ) ) )
<=> ( hoasinduction = $true ) )
& ( ( d2subst @ d_id )
= sh )
& ( lamnotap != $true )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( ! [X347: subst > term > subst > $o] :
~ ! [X348: term > $o] :
~ ! [X349: term] :
( ( X347 @ id @ X349 @ id )
= ( X348 @ X349 ) )
=> ( ! [X350: term,X351: term > $o] :
( ~ ! [X355: term] :
( ( $true
= ( X351 @ ( lam @ X355 ) ) )
| ~ ! [X356: term] :
( ( ( X351 @ ( sub @ X355 @ ( push @ X356 @ id ) ) )
= $true )
| ( ( X351 @ X356 )
!= $true ) ) )
| ( $true
= ( X351 @ X350 ) )
| ~ ! [X353: term,X354: term] :
( ( ( X351 @ X353 )
!= $true )
| ( $true
= ( X351 @ ( ap @ X354 @ X353 ) ) )
| ( $true
!= ( X351 @ X354 ) ) )
| ~ ! [X352: term] :
( ( ( X351 @ X352 )
= $true )
| ( ( var @ X352 )
!= $true ) ) )
=> ( ! [X357: term] :
( ( sub @ X357 @ id )
= X357 )
=> ( ! [X358: subst > term > subst > $o,X359: term,X360: term > $o] :
( ~ ! [X362: subst > term > term] :
( ( $true
= ( X358 @ id @ ( lam @ ( X362 @ sh @ one ) ) @ id ) )
| ~ ! [X364: subst,X365: subst,X366: term] :
( ( sub @ ( X362 @ X364 @ X366 ) @ X365 )
= ( X362 @ ( comp @ X364 @ X365 ) @ ( sub @ X366 @ X365 ) ) )
| ~ ! [X363: term] :
( ( ( X358 @ id @ X363 @ id )
!= $true )
| ( ( X358 @ id @ ( X362 @ id @ X363 ) @ id )
= $true ) ) )
| ~ ! [X361: term] :
( ( X360 @ X361 )
= ( X358 @ id @ X361 @ id ) )
| ( $true
= ( X360 @ ( lam @ X359 ) ) )
| ~ ! [X367: term] :
( ( ( X360 @ X367 )
!= $true )
| ( $true
= ( X360 @ ( sub @ X359 @ ( push @ X367 @ id ) ) ) ) ) )
=> ! [X368: term,X369: subst > term > subst > $o] :
( ~ ! [X380: subst > term > term] :
( ( $true
= ( X369 @ id @ ( lam @ ( X380 @ sh @ one ) ) @ id ) )
| ~ ! [X382: subst,X383: term,X384: subst] :
( ( X380 @ ( comp @ X382 @ X384 ) @ ( sub @ X383 @ X384 ) )
= ( sub @ ( X380 @ X382 @ X383 ) @ X384 ) )
| ~ ! [X381: term] :
( ( $true
!= ( X369 @ id @ X381 @ id ) )
| ( ( X369 @ id @ ( X380 @ id @ X381 ) @ id )
= $true ) ) )
| ~ ! [X374: term,X375: term] :
( ( ( X369 @ id @ ( ap @ ( sub @ X374 @ id ) @ X375 ) @ id )
= $true )
| ( ( X369 @ id @ X375 @ id )
!= $true )
| ( $true
!= ( X369 @ id @ X374 @ id ) ) )
| ~ ! [X376: subst,X377: subst,X378: subst,X379: term] :
( ( ( X369 @ ( comp @ X378 @ X376 ) @ ( sub @ X379 @ X376 ) @ X377 )
= $true )
| ( ( X369 @ X378 @ X379 @ ( comp @ X376 @ X377 ) )
!= $true ) )
| ~ ! [X370: term,X371: subst,X372: subst,X373: subst] :
( ( $true
= ( X369 @ X373 @ X370 @ ( comp @ X372 @ X371 ) ) )
| ( $true
!= ( X369 @ ( comp @ X373 @ X372 ) @ ( sub @ X370 @ X372 ) @ X371 ) ) )
| ~ ! [X385: term] :
( ( $true
!= ( var @ ( sub @ X385 @ id ) ) )
| ( $true
= ( X369 @ id @ X385 @ id ) ) )
| ( $true
= ( X369 @ id @ X368 @ id ) ) ) ) ) ) )
<=> ( hoasinduction_lthm_3 = $true ) )
& ( ( axvarcons = $true )
<=> ! [X77: subst,X78: term] :
( ( sub @ one @ ( push @ X78 @ X77 ) )
= X78 ) )
& ( pushprop_lem1v2_gthm = $true )
& ( ! [X48: term,X49: term,X50: term,X51: term] :
( ( ( ap @ X49 @ X48 )
!= ( ap @ X50 @ X51 ) )
| ( X48 = X51 ) )
<=> ( apinj2 = $true ) )
& ( hoasinduction_lem2v2_gthm = $true )
& ( pushprop_lem3v2 = $true )
& ( hoasapinj1_gthm = $true )
& ( hoasapnotvar_lthm = $true )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
<=> ( ! [X0: subst > term > subst > $o] :
~ ! [X1: term > $o] :
~ ! [X2: term] :
( ( X0 @ id @ X2 @ id )
= ( X1 @ X2 ) )
=> ( ! [X3: term,X4: term > $o] :
( ~ ! [X7: term] :
( ( $true
!= ( var @ X7 ) )
| ( ( X4 @ X7 )
= $true ) )
| ~ ! [X5: term,X6: term] :
( ( ( X4 @ X5 )
!= $true )
| ( ( X4 @ X6 )
!= $true )
| ( $true
= ( X4 @ ( ap @ X5 @ X6 ) ) ) )
| ~ ! [X8: term] :
( ( ( X4 @ ( lam @ X8 ) )
= $true )
| ~ ! [X9: term] :
( ( $true
= ( X4 @ ( sub @ X8 @ ( push @ X9 @ id ) ) ) )
| ( $true
!= ( X4 @ X9 ) ) ) )
| ( $true
= ( X4 @ X3 ) ) )
=> ( ! [X10: term] :
( ( sub @ X10 @ id )
= X10 )
=> ( ! [X11: term,X12: subst > term > subst > $o,X13: term > $o] :
( ~ ! [X15: subst > term > term] :
( ~ ! [X17: term,X18: subst,X19: subst] :
( ( sub @ ( X15 @ X19 @ X17 ) @ X18 )
= ( X15 @ ( comp @ X19 @ X18 ) @ ( sub @ X17 @ X18 ) ) )
| ~ ! [X16: term] :
( ( ( X12 @ id @ ( X15 @ id @ X16 ) @ id )
= $true )
| ( $true
!= ( X12 @ id @ X16 @ id ) ) )
| ( $true
= ( X12 @ id @ ( lam @ ( X15 @ sh @ one ) ) @ id ) ) )
| ~ ! [X14: term] :
( ( X13 @ X14 )
= ( X12 @ id @ X14 @ id ) )
| ~ ! [X20: term] :
( ( $true
= ( X13 @ ( sub @ X11 @ ( push @ X20 @ id ) ) ) )
| ( ( X13 @ X20 )
!= $true ) )
| ( ( X13 @ ( lam @ X11 ) )
= $true ) )
=> ! [X21: subst > term > subst > $o,X22: term] :
( ( $true
= ( X21 @ id @ X22 @ id ) )
| ~ ! [X25: subst > term > term] :
( ( ( X21 @ id @ ( lam @ ( X25 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X27: term,X28: subst,X29: subst] :
( ( X25 @ ( comp @ X28 @ X29 ) @ ( sub @ X27 @ X29 ) )
= ( sub @ ( X25 @ X28 @ X27 ) @ X29 ) )
| ~ ! [X26: term] :
( ( ( X21 @ id @ X26 @ id )
!= $true )
| ( ( X21 @ id @ ( X25 @ id @ X26 ) @ id )
= $true ) ) )
| ~ ! [X23: term,X24: term] :
( ( $true
!= ( X21 @ id @ X23 @ id ) )
| ( $true
= ( X21 @ id @ ( ap @ ( sub @ X23 @ id ) @ X24 ) @ id ) )
| ( ( X21 @ id @ X24 @ id )
!= $true ) ) ) ) ) ) ) )
& ( hoaslamnotap_gthm = $true )
& ( pushprop = $true )
& ( hoaslamnotvar_lthm = $true )
& ( ( hoasinduction_lem3 = $true )
<=> ! [X32: term,X33: subst > term > subst > $o] :
( ~ ! [X34: term,X35: subst,X36: subst,X37: subst] :
( ( ( X33 @ ( comp @ X36 @ X37 ) @ ( sub @ X34 @ X37 ) @ X35 )
!= $true )
| ( ( X33 @ X36 @ X34 @ ( comp @ X37 @ X35 ) )
= $true ) )
| ~ ! [X42: subst > term > term] :
( ~ ! [X44: term,X45: subst,X46: subst] :
( ( X42 @ ( comp @ X46 @ X45 ) @ ( sub @ X44 @ X45 ) )
= ( sub @ ( X42 @ X46 @ X44 ) @ X45 ) )
| ~ ! [X43: term] :
( ( $true
!= ( X33 @ id @ X43 @ id ) )
| ( ( X33 @ id @ ( X42 @ id @ X43 ) @ id )
= $true ) )
| ( ( X33 @ id @ ( lam @ ( X42 @ sh @ one ) ) @ id )
= $true ) )
| ( $true
= ( X33 @ id @ ( lam @ X32 ) @ id ) )
| ~ ! [X38: subst,X39: subst,X40: subst,X41: term] :
( ( $true
= ( X33 @ ( comp @ X39 @ X40 ) @ ( sub @ X41 @ X40 ) @ X38 ) )
| ( $true
!= ( X33 @ X39 @ X41 @ ( comp @ X40 @ X38 ) ) ) )
| ~ ! [X47: term] :
( ( $true
!= ( X33 @ id @ X47 @ id ) )
| ( ( X33 @ id @ ( sub @ X32 @ ( push @ X47 @ id ) ) @ id )
= $true ) ) ) )
& ( ( axvarid = $true )
<=> ! [X236: term] :
( ( sub @ X236 @ id )
= X236 ) )
& ( ( ! [X253: term] :
( ( sub @ X253 @ id )
= X253 )
=> ! [X254: term] :
( ( sub @ X254 @ id )
= X254 ) )
<=> ( termmset_lthm = $true ) )
& ( axapp = $true )
& ( lamnotvar = $true )
& ( ( termmset = $true )
<=> ! [X394: term] :
( ( sub @ X394 @ id )
= X394 ) )
& ( ! [X158: term > $o,X159: subst > term > subst > $o,X160: term] :
( ~ ! [X167: term] :
( ( ( X158 @ X167 )
!= $true )
| ( $true
= ( X158 @ ( sub @ X160 @ ( push @ X167 @ id ) ) ) ) )
| ~ ! [X162: subst > term > term] :
( ( ( X159 @ id @ ( lam @ ( X162 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X163: term] :
( ( $true
!= ( X159 @ id @ X163 @ id ) )
| ( $true
= ( X159 @ id @ ( X162 @ id @ X163 ) @ id ) ) )
| ~ ! [X164: subst,X165: term,X166: subst] :
( ( sub @ ( X162 @ X166 @ X165 ) @ X164 )
= ( X162 @ ( comp @ X166 @ X164 ) @ ( sub @ X165 @ X164 ) ) ) )
| ( $true
= ( X158 @ ( lam @ X160 ) ) )
| ~ ! [X161: term] :
( ( X158 @ X161 )
= ( X159 @ id @ X161 @ id ) ) )
<=> ( hoasinduction_lem3v2a = $true ) )
& ( hoaslamnotvar_gthm = $true )
& ( ! [X452: term,X453: term,X454: subst > term > subst > $o] :
( ( ( X454 @ id @ X453 @ id )
!= $true )
| ~ ! [X463: term,X464: term] :
( ( $true
= ( X454 @ id @ ( ap @ ( sub @ X463 @ id ) @ X464 ) @ id ) )
| ( $true
!= ( X454 @ id @ X463 @ id ) )
| ( ( X454 @ id @ X464 @ id )
!= $true ) )
| ~ ! [X459: subst,X460: term,X461: subst,X462: subst] :
( ( ( X454 @ ( comp @ X461 @ X459 ) @ ( sub @ X460 @ X459 ) @ X462 )
= $true )
| ( ( X454 @ X461 @ X460 @ ( comp @ X459 @ X462 ) )
!= $true ) )
| ~ ! [X455: subst,X456: subst,X457: term,X458: subst] :
( ( ( X454 @ X458 @ X457 @ ( comp @ X455 @ X456 ) )
= $true )
| ( $true
!= ( X454 @ ( comp @ X458 @ X455 ) @ ( sub @ X457 @ X455 ) @ X456 ) ) )
| ( ( X454 @ id @ X452 @ id )
!= $true )
| ( ( X454 @ id @ ( ap @ X452 @ X453 ) @ id )
= $true ) )
<=> ( hoasinduction_lem2 = $true ) )
& ( ( hoasinduction_lem3aa = $true )
<=> ! [X498: subst > term > subst > $o,X499: term] :
( ~ ! [X500: term] :
( ( $true
= ( X498 @ id @ ( sub @ X499 @ ( push @ X500 @ id ) ) @ id ) )
| ( $true
!= ( X498 @ id @ X500 @ id ) ) )
| ~ ! [X501: subst > term > term] :
( ~ ! [X502: subst,X503: subst,X504: term] :
( ( X501 @ ( comp @ X502 @ X503 ) @ ( sub @ X504 @ X503 ) )
= ( sub @ ( X501 @ X502 @ X504 ) @ X503 ) )
| ~ ! [X505: term] :
( ( $true
!= ( X498 @ id @ X505 @ id ) )
| ( $true
= ( X498 @ id @ ( X501 @ id @ X505 ) @ id ) ) )
| ( $true
= ( X498 @ id @ ( lam @ ( X501 @ sh @ one ) ) @ id ) ) )
| ( $true
= ( X498 @ id @ ( lam @ ( sub @ X499 @ ( push @ one @ sh ) ) ) @ id ) ) ) )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ! [X480: term,X481: term,X482: term,X483: term] :
( ( ( ap @ ( sub @ X482 @ id ) @ X481 )
!= ( ap @ ( sub @ X480 @ id ) @ X483 ) )
| ( X481 = X483 ) )
<=> ( hoasapinj2 = $true ) )
& ! [X422: term] :
? [X423: d_term] :
( ( d2term @ X423 )
= X422 )
& ( substmonoid_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 ) ) ) ) )
& ( hoaslaminj_gthm = $true )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( pushprop_lthm_orig = $true )
& ( pushprop_lthm = $true )
& ( pushprop_lem1_gthm = $true )
& ( hoasinduction_lem1_gthm = $true )
& ( ( induction2_lthm = $true )
<=> ( ! [X128: term] :
( ( sub @ X128 @ id )
= X128 )
=> ( ! [X129: subst,X130: term > $o,X131: term] :
( ~ ! [X134: term,X135: term] :
( ( ( X130 @ X134 )
!= $true )
| ( $true
!= ( X130 @ X135 ) )
| ( ( X130 @ ( ap @ X134 @ X135 ) )
= $true ) )
| ~ ! [X136: term] :
( ( ( var @ X136 )
!= $true )
| ( $true
= ( X130 @ ( sub @ X136 @ X129 ) ) ) )
| ( $true
= ( X130 @ ( sub @ X131 @ X129 ) ) )
| ~ ! [X132: term] :
( ~ ! [X133: term] :
( ( ( X130 @ X133 )
!= $true )
| ( $true
= ( X130 @ ( sub @ X132 @ ( push @ X133 @ id ) ) ) ) )
| ( ( X130 @ ( lam @ X132 ) )
= $true ) ) )
=> ! [X137: term,X138: term > $o] :
( ~ ! [X142: term] :
( ( $true
= ( X138 @ ( lam @ X142 ) ) )
| ~ ! [X143: term] :
( ( ( X138 @ X143 )
!= $true )
| ( ( X138 @ ( sub @ X142 @ ( push @ X143 @ id ) ) )
= $true ) ) )
| ~ ! [X140: term,X141: term] :
( ( ( X138 @ ( ap @ X140 @ X141 ) )
= $true )
| ( ( X138 @ X140 )
!= $true )
| ( $true
!= ( X138 @ X141 ) ) )
| ( $true
= ( X138 @ X137 ) )
| ~ ! [X139: term] :
( ( ( var @ X139 )
!= $true )
| ( ( X138 @ X139 )
= $true ) ) ) ) ) )
& ( ! [X529: term] :
~ ! [X530: subst > term > term] :
( ( X530 @ sh @ one )
!= ( sub @ X529 @ ( push @ one @ sh ) ) )
<=> ( hoasinduction_lem3b = $true ) )
& ( pushprop_gthm = $true )
& ( pushprop_lem2v2_gthm = $true )
& ( hoasinduction_lem1 = $true )
& ( hoasapinj2_gthm = $true )
& ! [X265: d_subst,X266: d_subst] :
( ( ( d2subst @ X266 )
= ( d2subst @ X265 ) )
=> ( X265 = X266 ) )
& ( pushprop_lem0_gthm = $true )
& ( ( hoaslamnotap = $true )
<=> ! [X341: subst > term > term,X342: term,X343: term] :
( ( ( ap @ ( sub @ X342 @ id ) @ X343 )
!= ( lam @ ( X341 @ sh @ one ) ) )
| ~ ! [X344: subst,X345: term,X346: subst] :
( ( sub @ ( X341 @ X346 @ X345 ) @ X344 )
= ( X341 @ ( comp @ X346 @ X344 ) @ ( sub @ X345 @ X344 ) ) ) ) )
& ( axvarshift = $true )
& ( ( pushprop_lem0 = $true )
<=> ! [X119: term > $o,X120: subst,X121: term] :
~ ! [X122: term > $o] :
~ ! [X123: term] :
( ( X122 @ X123 )
= ( X119 @ ( sub @ X123 @ ( push @ X121 @ X120 ) ) ) ) )
& ( ( ! [X68: term] :
( ( sub @ X68 @ id )
= X68 )
=> ( ! [X69: term,X70: term,X71: term,X72: term] :
( ( X69 = X71 )
| ( ( ap @ X69 @ X70 )
!= ( ap @ X71 @ X72 ) ) )
=> ! [X73: term,X74: term,X75: term,X76: term] :
( ( X73 = X74 )
| ( ( ap @ ( sub @ X74 @ id ) @ X76 )
!= ( ap @ ( sub @ X73 @ id ) @ X75 ) ) ) ) )
<=> ( hoasapinj1_lthm = $true ) )
& ( ( axscons = $true )
<=> ! [X267: subst] :
( ( push @ ( sub @ one @ X267 ) @ ( comp @ sh @ X267 ) )
= X267 ) )
& ( ( ! [X506: term,X507: subst] :
( ( sub @ one @ ( push @ X506 @ X507 ) )
= X506 )
=> ( ! [X508: subst,X509: term] :
( ( comp @ sh @ ( push @ X509 @ X508 ) )
= X508 )
=> ( ! [X510: subst] :
( ( comp @ X510 @ id )
= X510 )
=> ( ! [X511: term,X512: term > $o] :
( ~ ! [X513: term] :
( ( $true
!= ( X512 @ X513 ) )
| ( ( X512 @ ( lam @ X513 ) )
= $true ) )
| ~ ! [X515: term,X516: term] :
( ( ( X512 @ ( ap @ X516 @ X515 ) )
= $true )
| ( ( X512 @ X515 )
!= $true )
| ( $true
!= ( X512 @ X516 ) ) )
| ~ ! [X514: term] :
( ( ( X512 @ X514 )
= $true )
| ( ( var @ X514 )
!= $true ) )
| ( ( X512 @ X511 )
= $true ) )
=> ! [X517: subst,X518: term > $o,X519: term] :
( ~ ! [X522: term,X523: term] :
( ( ( X518 @ X523 )
!= $true )
| ( ( X518 @ X522 )
!= $true )
| ( $true
= ( X518 @ ( ap @ X523 @ X522 ) ) ) )
| ( $true
= ( X518 @ ( sub @ X519 @ X517 ) ) )
| ~ ! [X520: term] :
( ~ ! [X521: term] :
( ( $true
!= ( X518 @ X521 ) )
| ( $true
= ( X518 @ ( sub @ X520 @ ( push @ X521 @ id ) ) ) ) )
| ( ( X518 @ ( lam @ X520 ) )
= $true ) )
| ~ ! [X524: term] :
( ( ( var @ X524 )
!= $true )
| ( $true
= ( X518 @ ( sub @ X524 @ X517 ) ) ) ) ) ) ) ) )
<=> ( induction2lem_lthm = $true ) )
& ( ( shinj = $true )
<=> ! [X328: term,X329: term] :
( ( X328 = X329 )
| ( ( sub @ X329 @ sh )
!= ( sub @ X328 @ sh ) ) ) )
& ( axassoc = $true )
& ( hoasinduction_lem1v2 = $true )
& ( ! [X52: subst] :
( ( comp @ X52 @ id )
= X52 )
<=> ( axidr = $true ) )
& ( ! [X414: term,X415: subst > term > subst > $o] :
( ~ ! [X417: subst > term > term] :
( ~ ! [X421: term] :
( ( $true
!= ( X415 @ id @ X421 @ id ) )
| ( ( X415 @ id @ ( X417 @ id @ X421 ) @ id )
= $true ) )
| ~ ! [X418: subst,X419: term,X420: subst] :
( ( sub @ ( X417 @ X418 @ X419 ) @ X420 )
= ( X417 @ ( comp @ X418 @ X420 ) @ ( sub @ X419 @ X420 ) ) )
| ( ( X415 @ id @ ( lam @ ( X417 @ sh @ one ) ) @ id )
= $true ) )
| ( ( X415 @ id @ ( lam @ ( sub @ X414 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X416: term] :
( ( ( X415 @ id @ X416 @ id )
!= $true )
| ( ( X415 @ id @ ( sub @ X414 @ ( push @ X416 @ id ) ) @ id )
= $true ) ) )
<=> ( hoasinduction_lem3aa_lthm = $true ) )
& ! [X234: d_term,X235: d_term] :
( ( ( d2term @ X234 )
= ( d2term @ X235 ) )
=> ( X234 = X235 ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( ( ! [X168: term > $o,X169: term] :
( ~ ! [X170: term] :
( ~ ! [X171: term] :
( ( ( X168 @ X171 )
!= $true )
| ( $true
= ( X168 @ ( sub @ X170 @ ( push @ X171 @ id ) ) ) ) )
| ( ( X168 @ ( lam @ X170 ) )
= $true ) )
| ~ ! [X172: term,X173: term] :
( ( ( X168 @ X172 )
!= $true )
| ( ( X168 @ ( ap @ X173 @ X172 ) )
= $true )
| ( $true
!= ( X168 @ X173 ) ) )
| ~ ! [X174: term] :
( ( ( var @ X174 )
!= $true )
| ( ( X168 @ X174 )
= $true ) )
| ( $true
= ( X168 @ X169 ) ) )
=> ( ! [X175: term,X176: term,X177: subst > term > subst > $o] :
( ( $true
!= ( X177 @ id @ X176 @ id ) )
| ~ ! [X186: term,X187: term] :
( ( $true
!= ( X177 @ id @ X187 @ id ) )
| ( $true
!= ( X177 @ id @ X186 @ id ) )
| ( $true
= ( X177 @ id @ ( ap @ ( sub @ X187 @ id ) @ X186 ) @ id ) ) )
| ~ ! [X178: subst,X179: subst,X180: term,X181: subst] :
( ( ( X177 @ X179 @ X180 @ ( comp @ X181 @ X178 ) )
!= $true )
| ( ( X177 @ ( comp @ X179 @ X181 ) @ ( sub @ X180 @ X181 ) @ X178 )
= $true ) )
| ~ ! [X182: subst,X183: subst,X184: term,X185: subst] :
( ( $true
= ( X177 @ X185 @ X184 @ ( comp @ X183 @ X182 ) ) )
| ( $true
!= ( X177 @ ( comp @ X185 @ X183 ) @ ( sub @ X184 @ X183 ) @ X182 ) ) )
| ( ( X177 @ id @ ( ap @ X175 @ X176 ) @ id )
= $true )
| ( $true
!= ( X177 @ id @ X175 @ id ) ) )
=> ( ! [X188: term,X189: subst > term > subst > $o] :
( ~ ! [X198: term] :
( ( ( X189 @ id @ ( sub @ X188 @ ( push @ X198 @ id ) ) @ id )
= $true )
| ( $true
!= ( X189 @ id @ X198 @ id ) ) )
| ~ ! [X194: subst,X195: subst,X196: term,X197: subst] :
( ( ( X189 @ ( comp @ X197 @ X195 ) @ ( sub @ X196 @ X195 ) @ X194 )
!= $true )
| ( ( X189 @ X197 @ X196 @ ( comp @ X195 @ X194 ) )
= $true ) )
| ~ ! [X199: subst > term > term] :
( ( ( X189 @ id @ ( lam @ ( X199 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X203: term] :
( ( ( X189 @ id @ X203 @ id )
!= $true )
| ( ( X189 @ id @ ( X199 @ id @ X203 ) @ id )
= $true ) )
| ~ ! [X200: term,X201: subst,X202: subst] :
( ( sub @ ( X199 @ X201 @ X200 ) @ X202 )
= ( X199 @ ( comp @ X201 @ X202 ) @ ( sub @ X200 @ X202 ) ) ) )
| ~ ! [X190: subst,X191: term,X192: subst,X193: subst] :
( ( ( X189 @ X193 @ X191 @ ( comp @ X190 @ X192 ) )
!= $true )
| ( ( X189 @ ( comp @ X193 @ X190 ) @ ( sub @ X191 @ X190 ) @ X192 )
= $true ) )
| ( ( X189 @ id @ ( lam @ X188 ) @ id )
= $true ) )
=> ! [X204: subst > term > subst > $o,X205: term] :
( ~ ! [X216: term] :
( ( ( X204 @ id @ X216 @ id )
= $true )
| ( $true
!= ( var @ ( sub @ X216 @ id ) ) ) )
| ~ ! [X206: term,X207: term] :
( ( $true
!= ( X204 @ id @ X206 @ id ) )
| ( $true
!= ( X204 @ id @ X207 @ id ) )
| ( $true
= ( X204 @ id @ ( ap @ ( sub @ X207 @ id ) @ X206 ) @ id ) ) )
| ~ ! [X217: subst > term > term] :
( ~ ! [X221: term] :
( ( $true
!= ( X204 @ id @ X221 @ id ) )
| ( ( X204 @ id @ ( X217 @ id @ X221 ) @ id )
= $true ) )
| ( ( X204 @ id @ ( lam @ ( X217 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X218: subst,X219: term,X220: subst] :
( ( sub @ ( X217 @ X220 @ X219 ) @ X218 )
= ( X217 @ ( comp @ X220 @ X218 ) @ ( sub @ X219 @ X218 ) ) ) )
| ( $true
= ( X204 @ id @ X205 @ id ) )
| ~ ! [X208: subst,X209: subst,X210: subst,X211: term] :
( ( ( X204 @ X210 @ X211 @ ( comp @ X208 @ X209 ) )
= $true )
| ( $true
!= ( X204 @ ( comp @ X210 @ X208 ) @ ( sub @ X211 @ X208 ) @ X209 ) ) )
| ~ ! [X212: subst,X213: subst,X214: term,X215: subst] :
( ( ( X204 @ ( comp @ X213 @ X212 ) @ ( sub @ X214 @ X212 ) @ X215 )
= $true )
| ( $true
!= ( X204 @ X213 @ X214 @ ( comp @ X212 @ X215 ) ) ) ) ) ) ) )
<=> ( hoasinduction_lthm = $true ) )
& ( axmap = $true )
& ( ( hoasapinj1 = $true )
<=> ! [X486: term,X487: term,X488: term,X489: term] :
( ( ( ap @ ( sub @ X489 @ id ) @ X486 )
!= ( ap @ ( sub @ X488 @ id ) @ X487 ) )
| ( X488 = X489 ) ) )
& ( hoaslamnotvar = $true )
& ( hoasinduction_lem1v2_gthm = $true )
& ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ! [X222: term,X223: subst > term > subst > $o] :
( ~ ! [X224: term] :
( ( $true
= ( X223 @ id @ ( sub @ X222 @ ( push @ X224 @ id ) ) @ id ) )
| ( ( X223 @ id @ X224 @ id )
!= $true ) )
| ( $true
= ( X223 @ id @ ( lam @ ( sub @ X222 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X225: term,X226: subst > term > term] :
( ~ ! [X227: subst,X228: term,X229: subst] :
( ( sub @ ( sub @ X225 @ ( push @ X228 @ X229 ) ) @ X227 )
= ( sub @ ( X226 @ X229 @ X228 ) @ X227 ) )
| ~ ! [X233: term] :
( ( ( X223 @ id @ ( X226 @ id @ X233 ) @ id )
= $true )
| ( $true
!= ( X223 @ id @ X233 @ id ) ) )
| ( $true
= ( X223 @ id @ ( lam @ ( X226 @ sh @ one ) ) @ id ) )
| ~ ! [X230: subst,X231: term,X232: subst] :
( ( sub @ X225 @ ( push @ ( sub @ X231 @ X232 ) @ ( comp @ X230 @ X232 ) ) )
= ( X226 @ ( comp @ X230 @ X232 ) @ ( sub @ X231 @ X232 ) ) ) ) )
<=> ( hoasinduction_lem3aaa = $true ) )
& ( ( hoasinduction_lem3a_lthm = $true )
<=> ( ! [X81: term] :
( ( sub @ X81 @ id )
= X81 )
=> ( ! [X82: subst > term > subst > $o,X83: term] :
( ~ ! [X84: subst > term > term] :
( ~ ! [X85: term,X86: subst,X87: subst] :
( ( sub @ ( X84 @ X87 @ X85 ) @ X86 )
= ( X84 @ ( comp @ X87 @ X86 ) @ ( sub @ X85 @ X86 ) ) )
| ~ ! [X88: term] :
( ( $true
!= ( X82 @ id @ X88 @ id ) )
| ( ( X82 @ id @ ( X84 @ id @ X88 ) @ id )
= $true ) )
| ( $true
= ( X82 @ id @ ( lam @ ( X84 @ sh @ one ) ) @ id ) ) )
| ( ( X82 @ id @ ( lam @ ( sub @ X83 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X89: term] :
( ( $true
= ( X82 @ id @ ( sub @ X83 @ ( push @ X89 @ id ) ) @ id ) )
| ( ( X82 @ id @ X89 @ id )
!= $true ) ) )
=> ! [X90: subst > term > subst > $o,X91: term] :
( ~ ! [X97: term] :
( ( $true
!= ( X90 @ id @ X97 @ id ) )
| ( $true
= ( X90 @ id @ ( sub @ X91 @ ( push @ X97 @ id ) ) @ id ) ) )
| ~ ! [X92: subst > term > term] :
( ( $true
= ( X90 @ id @ ( lam @ ( X92 @ sh @ one ) ) @ id ) )
| ~ ! [X94: term,X95: subst,X96: subst] :
( ( sub @ ( X92 @ X96 @ X94 ) @ X95 )
= ( X92 @ ( comp @ X96 @ X95 ) @ ( sub @ X94 @ X95 ) ) )
| ~ ! [X93: term] :
( ( $true
= ( X90 @ id @ ( X92 @ id @ X93 ) @ id ) )
| ( $true
!= ( X90 @ id @ X93 @ id ) ) ) )
| ( ( X90 @ id @ ( lam @ X91 ) @ id )
= $true ) ) ) ) )
& ! [X484: subst] :
? [X485: d_subst] :
( ( d2subst @ X485 )
= X484 )
& ( pushprop_lem3v2_lthm = $true )
& ( hoasinduction_lem2_lthm = $true )
& ( axabs = $true )
& ( hoasapnotvar = $true )
& ( ( hoaslaminj_lthm = $true )
<=> ( ! [X237: subst,X238: term] :
( ( sub @ one @ ( push @ X238 @ X237 ) )
= X238 )
=> ( ! [X239: term,X240: subst] :
( ( comp @ sh @ ( push @ X239 @ X240 ) )
= X240 )
=> ( ! [X241: term,X242: term] :
( ( X241 = X242 )
| ( ( lam @ X241 )
!= ( lam @ X242 ) ) )
=> ! [X243: subst,X244: term,X245: subst > term > term,X246: subst > term > term] :
( ( ( lam @ ( X246 @ sh @ one ) )
!= ( lam @ ( X245 @ sh @ one ) ) )
| ~ ! [X247: term,X248: subst,X249: subst] :
( ( sub @ ( X246 @ X248 @ X247 ) @ X249 )
= ( X246 @ ( comp @ X248 @ X249 ) @ ( sub @ X247 @ X249 ) ) )
| ~ ! [X250: subst,X251: term,X252: subst] :
( ( X245 @ ( comp @ X250 @ X252 ) @ ( sub @ X251 @ X252 ) )
= ( sub @ ( X245 @ X250 @ X251 ) @ X252 ) )
| ( ( X246 @ X243 @ X244 )
= ( X245 @ X243 @ X244 ) ) ) ) ) ) )
& ( ulamvarsh = $true )
& ( hoasinduction_lem2_gthm = $true )
& ( ! [X255: term,X256: term > $o] :
( ~ ! [X260: term] :
( ( ( var @ X260 )
!= $true )
| ( $true
= ( X256 @ X260 ) ) )
| ~ ! [X257: term] :
( ( ( X256 @ ( lam @ X257 ) )
= $true )
| ( $true
!= ( X256 @ X257 ) ) )
| ~ ! [X258: term,X259: term] :
( ( ( X256 @ ( ap @ X259 @ X258 ) )
= $true )
| ( $true
!= ( X256 @ X259 ) )
| ( ( X256 @ X258 )
!= $true ) )
| ( ( X256 @ X255 )
= $true ) )
<=> ( induction = $true ) )
& ( ( ! [X98: term] :
( ( sub @ X98 @ id )
= X98 )
=> ! [X99: term > $o,X100: subst > term > subst > $o,X101: term] :
( ~ ! [X108: subst,X109: term,X110: subst,X111: subst] :
( ( ( X100 @ ( comp @ X108 @ X110 ) @ ( sub @ X109 @ X110 ) @ X111 )
= $true )
| ( ( X100 @ X108 @ X109 @ ( comp @ X110 @ X111 ) )
!= $true ) )
| ~ ! [X112: term] :
( ( X100 @ id @ X112 @ id )
= ( X99 @ X112 ) )
| ( ( X99 @ ( lam @ X101 ) )
= $true )
| ~ ! [X103: subst > term > term] :
( ~ ! [X104: subst,X105: subst,X106: term] :
( ( X103 @ ( comp @ X105 @ X104 ) @ ( sub @ X106 @ X104 ) )
= ( sub @ ( X103 @ X105 @ X106 ) @ X104 ) )
| ~ ! [X107: term] :
( ( ( X100 @ id @ X107 @ id )
!= $true )
| ( $true
= ( X100 @ id @ ( X103 @ id @ X107 ) @ id ) ) )
| ( $true
= ( X100 @ id @ ( lam @ ( X103 @ sh @ one ) ) @ id ) ) )
| ~ ! [X113: subst,X114: subst,X115: term,X116: subst] :
( ( $true
= ( X100 @ X114 @ X115 @ ( comp @ X113 @ X116 ) ) )
| ( $true
!= ( X100 @ ( comp @ X114 @ X113 ) @ ( sub @ X115 @ X113 ) @ X116 ) ) )
| ~ ! [X102: term] :
( ( ( X99 @ ( sub @ X101 @ ( push @ X102 @ id ) ) )
= $true )
| ( ( X99 @ X102 )
!= $true ) ) ) )
<=> ( hoasinduction_lem3v2_lthm = $true ) )
& ( hoasinduction_lem1_lthm = $true )
& ( hoasinduction_lem3_gthm = $true )
& ( ulamvarind = $true )
& ( ( ! [X149: term,X150: subst] :
( ( sub @ one @ ( push @ X149 @ X150 ) )
= X149 )
=> ( ! [X151: subst,X152: term] :
( ( comp @ sh @ ( push @ X152 @ X151 ) )
= X151 )
=> ! [X153: term,X154: term > $o,X155: subst,X156: term,X157: term > $o] :
( ( ( X157 @ ( sub @ X153 @ ( push @ X156 @ X155 ) ) )
= $true )
| ( $true
!= ( X154 @ X153 ) ) ) ) )
<=> ( pushprop_lem1_lthm = $true ) )
& ( induction2lem_gthm = $true )
& ( ( hoasapinj2_lthm = $true )
<=> ( ! [X532: term,X533: term,X534: term,X535: term] :
( ( X533 = X534 )
| ( ( ap @ X532 @ X534 )
!= ( ap @ X535 @ X533 ) ) )
=> ! [X536: term,X537: term,X538: term,X539: term] :
( ( ( ap @ ( sub @ X536 @ id ) @ X539 )
!= ( ap @ ( sub @ X537 @ id ) @ X538 ) )
| ( X538 = X539 ) ) ) )
& ( ! [X339: term] :
~ ! [X340: subst > term > term] :
( ( X340 @ sh @ one )
!= ( sub @ X339 @ ( push @ one @ sh ) ) )
<=> ( hoasinduction_lem3b_lthm = $true ) )
& ( ( hoasinduction_no_psi_cond = $true )
<=> ! [X330: term,X331: subst > term > subst > $o] :
( ~ ! [X337: term,X338: term] :
( ( ( X331 @ id @ ( ap @ ( sub @ X337 @ id ) @ X338 ) @ id )
= $true )
| ( ( X331 @ id @ X337 @ id )
!= $true )
| ( ( X331 @ id @ X338 @ id )
!= $true ) )
| ( ( X331 @ id @ X330 @ id )
= $true )
| ~ ! [X332: subst > term > term] :
( ~ ! [X334: subst,X335: subst,X336: term] :
( ( sub @ ( X332 @ X335 @ X336 ) @ X334 )
= ( X332 @ ( comp @ X335 @ X334 ) @ ( sub @ X336 @ X334 ) ) )
| ~ ! [X333: term] :
( ( ( X331 @ id @ X333 @ id )
!= $true )
| ( ( X331 @ id @ ( X332 @ id @ X333 ) @ id )
= $true ) )
| ( $true
= ( X331 @ id @ ( lam @ ( X332 @ sh @ one ) ) @ id ) ) ) ) )
& ( ( substmonoid_lthm = $true )
<=> ( ! [X395: subst] :
( ( comp @ id @ X395 )
= X395 )
=> ( ! [X396: subst] :
( ( comp @ X396 @ id )
= X396 )
=> ( ! [X397: subst] :
( ( comp @ id @ X397 )
= X397 )
& ! [X398: subst] :
( ( comp @ X398 @ id )
= X398 ) ) ) ) )
& ! [X291: d_subst] : ( d_id = X291 )
& ( ! [X268: term > $o,X269: term] :
( ~ ! [X270: term] :
( ( ( X268 @ ( lam @ X270 ) )
= $true )
| ~ ! [X271: term] :
( ( $true
= ( X268 @ ( sub @ X270 @ ( push @ X271 @ id ) ) ) )
| ( $true
!= ( X268 @ X271 ) ) ) )
| ~ ! [X274: term] :
( ( ( var @ X274 )
!= $true )
| ( $true
= ( X268 @ X274 ) ) )
| ( ( X268 @ X269 )
= $true )
| ~ ! [X272: term,X273: term] :
( ( ( X268 @ ( ap @ X273 @ X272 ) )
= $true )
| ( ( X268 @ X273 )
!= $true )
| ( $true
!= ( X268 @ X272 ) ) ) )
<=> ( induction2 = $true ) )
& ( hoasinduction_gthm = $true )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( pushprop_lem2v2_lthm = $true )
& ( ! [X310: term,X311: subst > term > subst > $o,X312: term > $o] :
( ~ ! [X315: subst,X316: subst,X317: subst,X318: term] :
( ( ( X311 @ ( comp @ X316 @ X317 ) @ ( sub @ X318 @ X317 ) @ X315 )
!= $true )
| ( $true
= ( X311 @ X316 @ X318 @ ( comp @ X317 @ X315 ) ) ) )
| ~ ! [X319: subst,X320: subst,X321: term,X322: subst] :
( ( ( X311 @ X322 @ X321 @ ( comp @ X319 @ X320 ) )
!= $true )
| ( ( X311 @ ( comp @ X322 @ X319 ) @ ( sub @ X321 @ X319 ) @ X320 )
= $true ) )
| ( ( X312 @ ( lam @ X310 ) )
= $true )
| ~ ! [X313: term] :
( ( X312 @ X313 )
= ( X311 @ id @ X313 @ id ) )
| ~ ! [X314: term] :
( ( ( X312 @ X314 )
!= $true )
| ( ( X312 @ ( sub @ X310 @ ( push @ X314 @ id ) ) )
= $true ) )
| ~ ! [X323: subst > term > term] :
( ~ ! [X325: term,X326: subst,X327: subst] :
( ( X323 @ ( comp @ X327 @ X326 ) @ ( sub @ X325 @ X326 ) )
= ( sub @ ( X323 @ X327 @ X325 ) @ X326 ) )
| ( ( X311 @ id @ ( lam @ ( X323 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X324: term] :
( ( ( X311 @ id @ ( X323 @ id @ X324 ) @ id )
= $true )
| ( $true
!= ( X311 @ id @ X324 @ id ) ) ) ) )
<=> ( hoasinduction_lem3v2 = $true ) )
& ( hoaslamnotap_lthm = $true )
& ( axclos = $true )
& ( ulamvar1 != $true )
& ( ( d2subst @ d_id )
= id )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( ( ! [X79: subst] :
( ( comp @ id @ X79 )
= X79 )
& ! [X80: subst] :
( ( comp @ X80 @ id )
= X80 ) )
<=> ( substmonoid = $true ) )
& ( ! [X449: subst > term > subst > $o] :
~ ! [X450: term > $o] :
~ ! [X451: term] :
( ( X449 @ id @ X451 @ id )
= ( X450 @ X451 ) )
<=> ( hoasinduction_lem0_lthm = $true ) )
& ( hoasinduction_lem3b_gthm = $true )
& ! [X531: d_term] : ( d_one = X531 ) ),
inference(flattening,[status(thm)],[f10]) ).
thf(f10,plain,
( ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
<=> ( ! [X0: subst > term > subst > $o] :
~ ! [X1: term > $o] :
~ ! [X2: term] :
( ( X0 @ id @ X2 @ id )
= ( X1 @ X2 ) )
=> ( ! [X3: term,X4: term > $o] :
( ( $true
= ( X4 @ X3 ) )
| ~ ! [X5: term,X6: term] :
( ( ( X4 @ X5 )
!= $true )
| ( $true
= ( X4 @ ( ap @ X5 @ X6 ) ) )
| ( ( X4 @ X6 )
!= $true ) )
| ~ ! [X7: term] :
( ( ( X4 @ X7 )
= $true )
| ( $true
!= ( var @ X7 ) ) )
| ~ ! [X8: term] :
( ( ( X4 @ ( lam @ X8 ) )
= $true )
| ~ ! [X9: term] :
( ( $true
!= ( X4 @ X9 ) )
| ( $true
= ( X4 @ ( sub @ X8 @ ( push @ X9 @ id ) ) ) ) ) ) )
=> ( ! [X10: term] :
( ( sub @ X10 @ id )
= X10 )
=> ( ! [X11: term,X12: subst > term > subst > $o,X13: term > $o] :
( ~ ! [X14: term] :
( ( X13 @ X14 )
= ( X12 @ id @ X14 @ id ) )
| ~ ! [X15: subst > term > term] :
( ~ ! [X16: term] :
( ( $true
!= ( X12 @ id @ X16 @ id ) )
| ( ( X12 @ id @ ( X15 @ id @ X16 ) @ id )
= $true ) )
| ~ ! [X17: term,X18: subst,X19: subst] :
( ( sub @ ( X15 @ X19 @ X17 ) @ X18 )
= ( X15 @ ( comp @ X19 @ X18 ) @ ( sub @ X17 @ X18 ) ) )
| ( $true
= ( X12 @ id @ ( lam @ ( X15 @ sh @ one ) ) @ id ) ) )
| ( ( X13 @ ( lam @ X11 ) )
= $true )
| ~ ! [X20: term] :
( ( ( X13 @ X20 )
!= $true )
| ( $true
= ( X13 @ ( sub @ X11 @ ( push @ X20 @ id ) ) ) ) ) )
=> ! [X21: subst > term > subst > $o,X22: term] :
( ~ ! [X23: term,X24: term] :
( ( ( X21 @ id @ X24 @ id )
!= $true )
| ( $true
= ( X21 @ id @ ( ap @ ( sub @ X23 @ id ) @ X24 ) @ id ) )
| ( $true
!= ( X21 @ id @ X23 @ id ) ) )
| ~ ! [X25: subst > term > term] :
( ~ ! [X26: term] :
( ( ( X21 @ id @ X26 @ id )
!= $true )
| ( ( X21 @ id @ ( X25 @ id @ X26 ) @ id )
= $true ) )
| ( ( X21 @ id @ ( lam @ ( X25 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X27: term,X28: subst,X29: subst] :
( ( X25 @ ( comp @ X28 @ X29 ) @ ( sub @ X27 @ X29 ) )
= ( sub @ ( X25 @ X28 @ X27 ) @ X29 ) ) )
| ( $true
= ( X21 @ id @ X22 @ id ) ) ) ) ) ) ) )
& ( ! [X30: term,X31: term] :
( ( X30 = X31 )
| ( ( lam @ X30 )
!= ( lam @ X31 ) ) )
<=> ( laminj = $true ) )
& ( ( hoasinduction_lem3 = $true )
<=> ! [X32: term,X33: subst > term > subst > $o] :
( ( $true
= ( X33 @ id @ ( lam @ X32 ) @ id ) )
| ~ ! [X34: term,X35: subst,X36: subst,X37: subst] :
( ( ( X33 @ X36 @ X34 @ ( comp @ X37 @ X35 ) )
= $true )
| ( ( X33 @ ( comp @ X36 @ X37 ) @ ( sub @ X34 @ X37 ) @ X35 )
!= $true ) )
| ~ ! [X38: subst,X39: subst,X40: subst,X41: term] :
( ( $true
!= ( X33 @ X39 @ X41 @ ( comp @ X40 @ X38 ) ) )
| ( $true
= ( X33 @ ( comp @ X39 @ X40 ) @ ( sub @ X41 @ X40 ) @ X38 ) ) )
| ~ ! [X42: subst > term > term] :
( ~ ! [X43: term] :
( ( ( X33 @ id @ ( X42 @ id @ X43 ) @ id )
= $true )
| ( $true
!= ( X33 @ id @ X43 @ id ) ) )
| ( ( X33 @ id @ ( lam @ ( X42 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X44: term,X45: subst,X46: subst] :
( ( X42 @ ( comp @ X46 @ X45 ) @ ( sub @ X44 @ X45 ) )
= ( sub @ ( X42 @ X46 @ X44 ) @ X45 ) ) )
| ~ ! [X47: term] :
( ( ( X33 @ id @ ( sub @ X32 @ ( push @ X47 @ id ) ) @ id )
= $true )
| ( $true
!= ( X33 @ id @ X47 @ id ) ) ) ) )
& ( ! [X48: term,X49: term,X50: term,X51: term] :
( ( ( ap @ X49 @ X48 )
!= ( ap @ X50 @ X51 ) )
| ( X48 = X51 ) )
<=> ( apinj2 = $true ) )
& ( ulamvarsh = $true )
& ( axclos = $true )
& ( hoasinduction_lem1v2 = $true )
& ( ! [X52: subst] :
( ( comp @ X52 @ id )
= X52 )
<=> ( axidr = $true ) )
& ( ( hoasinduction_lem2v2 = $true )
<=> ! [X53: term,X54: term > $o,X55: subst > term > subst > $o,X56: term] :
( ( ( X54 @ X53 )
!= $true )
| ~ ! [X57: subst,X58: term,X59: subst,X60: subst] :
( ( ( X55 @ ( comp @ X60 @ X57 ) @ ( sub @ X58 @ X57 ) @ X59 )
= $true )
| ( $true
!= ( X55 @ X60 @ X58 @ ( comp @ X57 @ X59 ) ) ) )
| ~ ! [X61: term,X62: term] :
( ( ( X55 @ id @ X62 @ id )
!= $true )
| ( ( X55 @ id @ ( ap @ ( sub @ X62 @ id ) @ X61 ) @ id )
= $true )
| ( $true
!= ( X55 @ id @ X61 @ id ) ) )
| ( ( X54 @ ( ap @ X53 @ X56 ) )
= $true )
| ( ( X54 @ X56 )
!= $true )
| ~ ! [X63: term] :
( ( X55 @ id @ X63 @ id )
= ( X54 @ X63 ) )
| ~ ! [X64: subst,X65: term,X66: subst,X67: subst] :
( ( ( X55 @ ( comp @ X66 @ X67 ) @ ( sub @ X65 @ X67 ) @ X64 )
!= $true )
| ( ( X55 @ X66 @ X65 @ ( comp @ X67 @ X64 ) )
= $true ) ) ) )
& ( ( ! [X68: term] :
( ( sub @ X68 @ id )
= X68 )
=> ( ! [X69: term,X70: term,X71: term,X72: term] :
( ( X69 = X71 )
| ( ( ap @ X69 @ X70 )
!= ( ap @ X71 @ X72 ) ) )
=> ! [X73: term,X74: term,X75: term,X76: term] :
( ( X73 = X74 )
| ( ( ap @ ( sub @ X74 @ id ) @ X76 )
!= ( ap @ ( sub @ X73 @ id ) @ X75 ) ) ) ) )
<=> ( hoasapinj1_lthm = $true ) )
& ( ( axvarcons = $true )
<=> ! [X77: subst,X78: term] :
( ( sub @ one @ ( push @ X78 @ X77 ) )
= X78 ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( pushprop_lem2v2 = $true )
& ( axassoc = $true )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ( ! [X79: subst] :
( ( comp @ id @ X79 )
= X79 )
& ! [X80: subst] :
( ( comp @ X80 @ id )
= X80 ) )
<=> ( substmonoid = $true ) )
& ( ( hoasinduction_lem3a_lthm = $true )
<=> ( ! [X81: term] :
( ( sub @ X81 @ id )
= X81 )
=> ( ! [X82: subst > term > subst > $o,X83: term] :
( ( ( X82 @ id @ ( lam @ ( sub @ X83 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X84: subst > term > term] :
( ~ ! [X85: term,X86: subst,X87: subst] :
( ( sub @ ( X84 @ X87 @ X85 ) @ X86 )
= ( X84 @ ( comp @ X87 @ X86 ) @ ( sub @ X85 @ X86 ) ) )
| ~ ! [X88: term] :
( ( ( X82 @ id @ ( X84 @ id @ X88 ) @ id )
= $true )
| ( $true
!= ( X82 @ id @ X88 @ id ) ) )
| ( $true
= ( X82 @ id @ ( lam @ ( X84 @ sh @ one ) ) @ id ) ) )
| ~ ! [X89: term] :
( ( ( X82 @ id @ X89 @ id )
!= $true )
| ( $true
= ( X82 @ id @ ( sub @ X83 @ ( push @ X89 @ id ) ) @ id ) ) ) )
=> ! [X90: subst > term > subst > $o,X91: term] :
( ( ( X90 @ id @ ( lam @ X91 ) @ id )
= $true )
| ~ ! [X92: subst > term > term] :
( ~ ! [X93: term] :
( ( $true
= ( X90 @ id @ ( X92 @ id @ X93 ) @ id ) )
| ( $true
!= ( X90 @ id @ X93 @ id ) ) )
| ~ ! [X94: term,X95: subst,X96: subst] :
( ( sub @ ( X92 @ X96 @ X94 ) @ X95 )
= ( X92 @ ( comp @ X96 @ X95 ) @ ( sub @ X94 @ X95 ) ) )
| ( $true
= ( X90 @ id @ ( lam @ ( X92 @ sh @ one ) ) @ id ) ) )
| ~ ! [X97: term] :
( ( $true
!= ( X90 @ id @ X97 @ id ) )
| ( $true
= ( X90 @ id @ ( sub @ X91 @ ( push @ X97 @ id ) ) @ id ) ) ) ) ) ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
<=> ( ! [X98: term] :
( ( sub @ X98 @ id )
= X98 )
=> ! [X99: term > $o,X100: subst > term > subst > $o,X101: term] :
( ~ ! [X102: term] :
( ( ( X99 @ X102 )
!= $true )
| ( ( X99 @ ( sub @ X101 @ ( push @ X102 @ id ) ) )
= $true ) )
| ~ ! [X103: subst > term > term] :
( ~ ! [X104: subst,X105: subst,X106: term] :
( ( X103 @ ( comp @ X105 @ X104 ) @ ( sub @ X106 @ X104 ) )
= ( sub @ ( X103 @ X105 @ X106 ) @ X104 ) )
| ~ ! [X107: term] :
( ( ( X100 @ id @ X107 @ id )
!= $true )
| ( $true
= ( X100 @ id @ ( X103 @ id @ X107 ) @ id ) ) )
| ( $true
= ( X100 @ id @ ( lam @ ( X103 @ sh @ one ) ) @ id ) ) )
| ~ ! [X108: subst,X109: term,X110: subst,X111: subst] :
( ( ( X100 @ ( comp @ X108 @ X110 ) @ ( sub @ X109 @ X110 ) @ X111 )
= $true )
| ( ( X100 @ X108 @ X109 @ ( comp @ X110 @ X111 ) )
!= $true ) )
| ~ ! [X112: term] :
( ( X100 @ id @ X112 @ id )
= ( X99 @ X112 ) )
| ( ( X99 @ ( lam @ X101 ) )
= $true )
| ~ ! [X113: subst,X114: subst,X115: term,X116: subst] :
( ( $true
!= ( X100 @ ( comp @ X114 @ X113 ) @ ( sub @ X115 @ X113 ) @ X116 ) )
| ( $true
= ( X100 @ X114 @ X115 @ ( comp @ X113 @ X116 ) ) ) ) ) ) )
& ( ( axshiftcons = $true )
<=> ! [X117: term,X118: subst] :
( ( comp @ sh @ ( push @ X117 @ X118 ) )
= X118 ) )
& ( ( pushprop_lem0 = $true )
<=> ! [X119: term > $o,X120: subst,X121: term] :
~ ! [X122: term > $o] :
~ ! [X123: term] :
( ( X122 @ X123 )
= ( X119 @ ( sub @ X123 @ ( push @ X121 @ X120 ) ) ) ) )
& ( lamnotap != $true )
& ( ! [X124: term] :
~ ! [X125: subst > term > term] :
~ ! [X126: term,X127: subst] :
( ( sub @ X124 @ ( push @ X126 @ X127 ) )
= ( X125 @ X127 @ X126 ) )
<=> ( hoasinduction_lem3v2_f_lthm = $true ) )
& ( axmap = $true )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( induction2_lthm = $true )
<=> ( ! [X128: term] :
( ( sub @ X128 @ id )
= X128 )
=> ( ! [X129: subst,X130: term > $o,X131: term] :
( ~ ! [X132: term] :
( ( ( X130 @ ( lam @ X132 ) )
= $true )
| ~ ! [X133: term] :
( ( $true
= ( X130 @ ( sub @ X132 @ ( push @ X133 @ id ) ) ) )
| ( ( X130 @ X133 )
!= $true ) ) )
| ~ ! [X134: term,X135: term] :
( ( ( X130 @ ( ap @ X134 @ X135 ) )
= $true )
| ( $true
!= ( X130 @ X135 ) )
| ( ( X130 @ X134 )
!= $true ) )
| ~ ! [X136: term] :
( ( $true
= ( X130 @ ( sub @ X136 @ X129 ) ) )
| ( ( var @ X136 )
!= $true ) )
| ( $true
= ( X130 @ ( sub @ X131 @ X129 ) ) ) )
=> ! [X137: term,X138: term > $o] :
( ~ ! [X139: term] :
( ( ( var @ X139 )
!= $true )
| ( ( X138 @ X139 )
= $true ) )
| ~ ! [X140: term,X141: term] :
( ( $true
!= ( X138 @ X141 ) )
| ( ( X138 @ ( ap @ X140 @ X141 ) )
= $true )
| ( ( X138 @ X140 )
!= $true ) )
| ~ ! [X142: term] :
( ~ ! [X143: term] :
( ( ( X138 @ X143 )
!= $true )
| ( ( X138 @ ( sub @ X142 @ ( push @ X143 @ id ) ) )
= $true ) )
| ( $true
= ( X138 @ ( lam @ X142 ) ) ) )
| ( $true
= ( X138 @ X137 ) ) ) ) ) )
& ( ! [X144: subst,X145: term > $o,X146: term] :
~ ! [X147: term > $o] :
~ ! [X148: term] :
( ( X145 @ ( sub @ X148 @ ( push @ X146 @ X144 ) ) )
= ( X147 @ X148 ) )
<=> ( pushprop_lem0_lthm = $true ) )
& ( induction2lem_gthm = $true )
& ( ( pushprop_lem1_lthm = $true )
<=> ( ! [X149: term,X150: subst] :
( ( sub @ one @ ( push @ X149 @ X150 ) )
= X149 )
=> ( ! [X151: subst,X152: term] :
( ( comp @ sh @ ( push @ X152 @ X151 ) )
= X151 )
=> ! [X153: term,X154: term > $o,X155: subst,X156: term,X157: term > $o] :
( ( $true
!= ( X154 @ X153 ) )
| ( ( X157 @ ( sub @ X153 @ ( push @ X156 @ X155 ) ) )
= $true ) ) ) ) )
& ( ( hoasinduction_lem3v2a = $true )
<=> ! [X158: term > $o,X159: subst > term > subst > $o,X160: term] :
( ~ ! [X161: term] :
( ( X158 @ X161 )
= ( X159 @ id @ X161 @ id ) )
| ~ ! [X162: subst > term > term] :
( ~ ! [X163: term] :
( ( $true
= ( X159 @ id @ ( X162 @ id @ X163 ) @ id ) )
| ( $true
!= ( X159 @ id @ X163 @ id ) ) )
| ( ( X159 @ id @ ( lam @ ( X162 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X164: subst,X165: term,X166: subst] :
( ( sub @ ( X162 @ X166 @ X165 ) @ X164 )
= ( X162 @ ( comp @ X166 @ X164 ) @ ( sub @ X165 @ X164 ) ) ) )
| ~ ! [X167: term] :
( ( ( X158 @ X167 )
!= $true )
| ( $true
= ( X158 @ ( sub @ X160 @ ( push @ X167 @ id ) ) ) ) )
| ( $true
= ( X158 @ ( lam @ X160 ) ) ) ) )
& ( ( hoasinduction_lthm = $true )
<=> ( ! [X168: term > $o,X169: term] :
( ( $true
= ( X168 @ X169 ) )
| ~ ! [X170: term] :
( ~ ! [X171: term] :
( ( $true
= ( X168 @ ( sub @ X170 @ ( push @ X171 @ id ) ) ) )
| ( ( X168 @ X171 )
!= $true ) )
| ( ( X168 @ ( lam @ X170 ) )
= $true ) )
| ~ ! [X172: term,X173: term] :
( ( $true
!= ( X168 @ X173 ) )
| ( ( X168 @ ( ap @ X173 @ X172 ) )
= $true )
| ( ( X168 @ X172 )
!= $true ) )
| ~ ! [X174: term] :
( ( ( var @ X174 )
!= $true )
| ( ( X168 @ X174 )
= $true ) ) )
=> ( ! [X175: term,X176: term,X177: subst > term > subst > $o] :
( ( $true
!= ( X177 @ id @ X176 @ id ) )
| ( ( X177 @ id @ ( ap @ X175 @ X176 ) @ id )
= $true )
| ~ ! [X178: subst,X179: subst,X180: term,X181: subst] :
( ( ( X177 @ X179 @ X180 @ ( comp @ X181 @ X178 ) )
!= $true )
| ( ( X177 @ ( comp @ X179 @ X181 ) @ ( sub @ X180 @ X181 ) @ X178 )
= $true ) )
| ( $true
!= ( X177 @ id @ X175 @ id ) )
| ~ ! [X182: subst,X183: subst,X184: term,X185: subst] :
( ( $true
= ( X177 @ X185 @ X184 @ ( comp @ X183 @ X182 ) ) )
| ( $true
!= ( X177 @ ( comp @ X185 @ X183 ) @ ( sub @ X184 @ X183 ) @ X182 ) ) )
| ~ ! [X186: term,X187: term] :
( ( $true
!= ( X177 @ id @ X187 @ id ) )
| ( $true
= ( X177 @ id @ ( ap @ ( sub @ X187 @ id ) @ X186 ) @ id ) )
| ( $true
!= ( X177 @ id @ X186 @ id ) ) ) )
=> ( ! [X188: term,X189: subst > term > subst > $o] :
( ~ ! [X190: subst,X191: term,X192: subst,X193: subst] :
( ( ( X189 @ X193 @ X191 @ ( comp @ X190 @ X192 ) )
!= $true )
| ( ( X189 @ ( comp @ X193 @ X190 ) @ ( sub @ X191 @ X190 ) @ X192 )
= $true ) )
| ~ ! [X194: subst,X195: subst,X196: term,X197: subst] :
( ( ( X189 @ ( comp @ X197 @ X195 ) @ ( sub @ X196 @ X195 ) @ X194 )
!= $true )
| ( ( X189 @ X197 @ X196 @ ( comp @ X195 @ X194 ) )
= $true ) )
| ~ ! [X198: term] :
( ( $true
!= ( X189 @ id @ X198 @ id ) )
| ( ( X189 @ id @ ( sub @ X188 @ ( push @ X198 @ id ) ) @ id )
= $true ) )
| ( ( X189 @ id @ ( lam @ X188 ) @ id )
= $true )
| ~ ! [X199: subst > term > term] :
( ~ ! [X200: term,X201: subst,X202: subst] :
( ( sub @ ( X199 @ X201 @ X200 ) @ X202 )
= ( X199 @ ( comp @ X201 @ X202 ) @ ( sub @ X200 @ X202 ) ) )
| ~ ! [X203: term] :
( ( ( X189 @ id @ X203 @ id )
!= $true )
| ( ( X189 @ id @ ( X199 @ id @ X203 ) @ id )
= $true ) )
| ( ( X189 @ id @ ( lam @ ( X199 @ sh @ one ) ) @ id )
= $true ) ) )
=> ! [X204: subst > term > subst > $o,X205: term] :
( ~ ! [X206: term,X207: term] :
( ( $true
= ( X204 @ id @ ( ap @ ( sub @ X207 @ id ) @ X206 ) @ id ) )
| ( $true
!= ( X204 @ id @ X206 @ id ) )
| ( $true
!= ( X204 @ id @ X207 @ id ) ) )
| ~ ! [X208: subst,X209: subst,X210: subst,X211: term] :
( ( ( X204 @ X210 @ X211 @ ( comp @ X208 @ X209 ) )
= $true )
| ( $true
!= ( X204 @ ( comp @ X210 @ X208 ) @ ( sub @ X211 @ X208 ) @ X209 ) ) )
| ~ ! [X212: subst,X213: subst,X214: term,X215: subst] :
( ( $true
!= ( X204 @ X213 @ X214 @ ( comp @ X212 @ X215 ) ) )
| ( ( X204 @ ( comp @ X213 @ X212 ) @ ( sub @ X214 @ X212 ) @ X215 )
= $true ) )
| ~ ! [X216: term] :
( ( ( X204 @ id @ X216 @ id )
= $true )
| ( $true
!= ( var @ ( sub @ X216 @ id ) ) ) )
| ~ ! [X217: subst > term > term] :
( ~ ! [X218: subst,X219: term,X220: subst] :
( ( sub @ ( X217 @ X220 @ X219 ) @ X218 )
= ( X217 @ ( comp @ X220 @ X218 ) @ ( sub @ X219 @ X218 ) ) )
| ( ( X204 @ id @ ( lam @ ( X217 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X221: term] :
( ( $true
!= ( X204 @ id @ X221 @ id ) )
| ( ( X204 @ id @ ( X217 @ id @ X221 ) @ id )
= $true ) ) )
| ( $true
= ( X204 @ id @ X205 @ id ) ) ) ) ) ) )
& ( hoaslaminj_gthm = $true )
& ( ! [X222: term,X223: subst > term > subst > $o] :
( ~ ! [X224: term] :
( ( ( X223 @ id @ X224 @ id )
!= $true )
| ( $true
= ( X223 @ id @ ( sub @ X222 @ ( push @ X224 @ id ) ) @ id ) ) )
| ( $true
= ( X223 @ id @ ( lam @ ( sub @ X222 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X225: term,X226: subst > term > term] :
( ~ ! [X227: subst,X228: term,X229: subst] :
( ( sub @ ( sub @ X225 @ ( push @ X228 @ X229 ) ) @ X227 )
= ( sub @ ( X226 @ X229 @ X228 ) @ X227 ) )
| ~ ! [X230: subst,X231: term,X232: subst] :
( ( sub @ X225 @ ( push @ ( sub @ X231 @ X232 ) @ ( comp @ X230 @ X232 ) ) )
= ( X226 @ ( comp @ X230 @ X232 ) @ ( sub @ X231 @ X232 ) ) )
| ~ ! [X233: term] :
( ( $true
!= ( X223 @ id @ X233 @ id ) )
| ( ( X223 @ id @ ( X226 @ id @ X233 ) @ id )
= $true ) )
| ( $true
= ( X223 @ id @ ( lam @ ( X226 @ sh @ one ) ) @ id ) ) ) )
<=> ( hoasinduction_lem3aaa = $true ) )
& ( hoasapnotvar = $true )
& ! [X234: d_term,X235: d_term] :
( ( ( d2term @ X234 )
= ( d2term @ X235 ) )
=> ( X234 = X235 ) )
& ( ( d2subst @ d_id )
= sh )
& ( hoaslamnotvar_gthm = $true )
& ( ( axvarid = $true )
<=> ! [X236: term] :
( ( sub @ X236 @ id )
= X236 ) )
& ( ( hoaslaminj_lthm = $true )
<=> ( ! [X237: subst,X238: term] :
( ( sub @ one @ ( push @ X238 @ X237 ) )
= X238 )
=> ( ! [X239: term,X240: subst] :
( ( comp @ sh @ ( push @ X239 @ X240 ) )
= X240 )
=> ( ! [X241: term,X242: term] :
( ( X241 = X242 )
| ( ( lam @ X241 )
!= ( lam @ X242 ) ) )
=> ! [X243: subst,X244: term,X245: subst > term > term,X246: subst > term > term] :
( ( ( lam @ ( X246 @ sh @ one ) )
!= ( lam @ ( X245 @ sh @ one ) ) )
| ~ ! [X247: term,X248: subst,X249: subst] :
( ( sub @ ( X246 @ X248 @ X247 ) @ X249 )
= ( X246 @ ( comp @ X248 @ X249 ) @ ( sub @ X247 @ X249 ) ) )
| ~ ! [X250: subst,X251: term,X252: subst] :
( ( X245 @ ( comp @ X250 @ X252 ) @ ( sub @ X251 @ X252 ) )
= ( sub @ ( X245 @ X250 @ X251 ) @ X252 ) )
| ( ( X246 @ X243 @ X244 )
= ( X245 @ X243 @ X244 ) ) ) ) ) ) )
& ( hoaslamnotvar = $true )
& ( ( ! [X253: term] :
( ( sub @ X253 @ id )
= X253 )
=> ! [X254: term] :
( ( sub @ X254 @ id )
= X254 ) )
<=> ( termmset_lthm = $true ) )
& ( substmonoid_gthm = $true )
& ( ( induction = $true )
<=> ! [X255: term,X256: term > $o] :
( ~ ! [X257: term] :
( ( $true
!= ( X256 @ X257 ) )
| ( ( X256 @ ( lam @ X257 ) )
= $true ) )
| ( ( X256 @ X255 )
= $true )
| ~ ! [X258: term,X259: term] :
( ( ( X256 @ X258 )
!= $true )
| ( $true
!= ( X256 @ X259 ) )
| ( ( X256 @ ( ap @ X259 @ X258 ) )
= $true ) )
| ~ ! [X260: term] :
( ( $true
= ( X256 @ X260 ) )
| ( ( var @ X260 )
!= $true ) ) ) )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( pushprop_lem2v2_lthm = $true )
& ( ( apinj1 = $true )
<=> ! [X261: term,X262: term,X263: term,X264: term] :
( ( X262 = X264 )
| ( ( ap @ X264 @ X263 )
!= ( ap @ X262 @ X261 ) ) ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( hoasinduction_lem2_gthm = $true )
& ( ( d2subst @ d_id )
= id )
& ! [X265: d_subst,X266: d_subst] :
( ( ( d2subst @ X266 )
= ( d2subst @ X265 ) )
=> ( X265 = X266 ) )
& ( ( axscons = $true )
<=> ! [X267: subst] :
( ( push @ ( sub @ one @ X267 ) @ ( comp @ sh @ X267 ) )
= X267 ) )
& ( pushprop_lthm = $true )
& ( ( induction2 = $true )
<=> ! [X268: term > $o,X269: term] :
( ~ ! [X270: term] :
( ~ ! [X271: term] :
( ( $true
!= ( X268 @ X271 ) )
| ( $true
= ( X268 @ ( sub @ X270 @ ( push @ X271 @ id ) ) ) ) )
| ( ( X268 @ ( lam @ X270 ) )
= $true ) )
| ~ ! [X272: term,X273: term] :
( ( $true
!= ( X268 @ X272 ) )
| ( ( X268 @ X273 )
!= $true )
| ( ( X268 @ ( ap @ X273 @ X272 ) )
= $true ) )
| ( ( X268 @ X269 )
= $true )
| ~ ! [X274: term] :
( ( ( var @ X274 )
!= $true )
| ( $true
= ( X268 @ X274 ) ) ) ) )
& ( ! [X275: term,X276: term,X277: term > $o,X278: subst,X279: term > $o] :
( ( ( X277 @ ( sub @ X276 @ ( push @ X275 @ X278 ) ) )
= $true )
| ( ( X279 @ X276 )
!= $true ) )
<=> ( pushprop_lem1 = $true ) )
& ( hoasinduction_lem1_gthm = $true )
& ( ( hoasinduction_lem3v2_f = $true )
<=> ! [X280: term] :
~ ! [X281: subst > term > term] :
~ ! [X282: term,X283: subst] :
( ( X281 @ X283 @ X282 )
= ( sub @ X280 @ ( push @ X282 @ X283 ) ) ) )
& ( hoasinduction_gthm = $true )
& ( ( ! [X284: term,X285: subst] :
( ( sub @ one @ ( push @ X284 @ X285 ) )
= X284 )
=> ! [X286: term,X287: subst,X288: term > $o,X289: term > $o] :
( ( ( X289 @ one )
= $true )
| ( $true
!= ( X288 @ X286 ) )
| ~ ! [X290: term] :
( ( X288 @ ( sub @ X290 @ ( push @ X286 @ X287 ) ) )
= ( X289 @ X290 ) ) ) )
<=> ( pushprop_lem1v2_lthm = $true ) )
& ( one
= ( d2term @ d_one ) )
& ! [X291: d_subst] : ( d_id = X291 )
& ( ! [X292: term,X293: subst > term > subst > $o] :
( ~ ! [X294: subst > term > term] :
( ~ ! [X295: subst,X296: term,X297: subst] :
( ( X294 @ ( comp @ X295 @ X297 ) @ ( sub @ X296 @ X297 ) )
= ( sub @ ( X294 @ X295 @ X296 ) @ X297 ) )
| ( $true
= ( X293 @ id @ ( lam @ ( X294 @ sh @ one ) ) @ id ) )
| ~ ! [X298: term] :
( ( $true
= ( X293 @ id @ ( X294 @ id @ X298 ) @ id ) )
| ( $true
!= ( X293 @ id @ X298 @ id ) ) ) )
| ~ ! [X299: subst,X300: subst,X301: term,X302: subst] :
( ( ( X293 @ X302 @ X301 @ ( comp @ X300 @ X299 ) )
!= $true )
| ( $true
= ( X293 @ ( comp @ X302 @ X300 ) @ ( sub @ X301 @ X300 ) @ X299 ) ) )
| ( ( X293 @ id @ X292 @ id )
= $true )
| ~ ! [X303: term] :
( ( ( X293 @ id @ X303 @ id )
= $true )
| ( $true
!= ( var @ ( sub @ X303 @ id ) ) ) )
| ~ ! [X304: term,X305: term] :
( ( $true
!= ( X293 @ id @ X305 @ id ) )
| ( $true
= ( X293 @ id @ ( ap @ ( sub @ X304 @ id ) @ X305 ) @ id ) )
| ( $true
!= ( X293 @ id @ X304 @ id ) ) )
| ~ ! [X306: term,X307: subst,X308: subst,X309: subst] :
( ( ( X293 @ X308 @ X306 @ ( comp @ X307 @ X309 ) )
= $true )
| ( $true
!= ( X293 @ ( comp @ X308 @ X307 ) @ ( sub @ X306 @ X307 ) @ X309 ) ) ) )
<=> ( hoasinduction = $true ) )
& ( pushprop = $true )
& ( ulamvar1 != $true )
& ( hoasapinj1_gthm = $true )
& ( hoasinduction_lem1v2_gthm = $true )
& ( hoaslamnotvar_lthm = $true )
& ( ( hoasinduction_lem3v2 = $true )
<=> ! [X310: term,X311: subst > term > subst > $o,X312: term > $o] :
( ~ ! [X313: term] :
( ( X312 @ X313 )
= ( X311 @ id @ X313 @ id ) )
| ~ ! [X314: term] :
( ( ( X312 @ X314 )
!= $true )
| ( ( X312 @ ( sub @ X310 @ ( push @ X314 @ id ) ) )
= $true ) )
| ( ( X312 @ ( lam @ X310 ) )
= $true )
| ~ ! [X315: subst,X316: subst,X317: subst,X318: term] :
( ( ( X311 @ ( comp @ X316 @ X317 ) @ ( sub @ X318 @ X317 ) @ X315 )
!= $true )
| ( $true
= ( X311 @ X316 @ X318 @ ( comp @ X317 @ X315 ) ) ) )
| ~ ! [X319: subst,X320: subst,X321: term,X322: subst] :
( ( ( X311 @ X322 @ X321 @ ( comp @ X319 @ X320 ) )
!= $true )
| ( ( X311 @ ( comp @ X322 @ X319 ) @ ( sub @ X321 @ X319 ) @ X320 )
= $true ) )
| ~ ! [X323: subst > term > term] :
( ~ ! [X324: term] :
( ( $true
!= ( X311 @ id @ X324 @ id ) )
| ( ( X311 @ id @ ( X323 @ id @ X324 ) @ id )
= $true ) )
| ( ( X311 @ id @ ( lam @ ( X323 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X325: term,X326: subst,X327: subst] :
( ( X323 @ ( comp @ X327 @ X326 ) @ ( sub @ X325 @ X326 ) )
= ( sub @ ( X323 @ X327 @ X325 ) @ X326 ) ) ) ) )
& ( pushprop_gthm = $true )
& ( apnotvar = $true )
& ( hoasinduction_lem2_lthm = $true )
& ( ( shinj = $true )
<=> ! [X328: term,X329: term] :
( ( X328 = X329 )
| ( ( sub @ X329 @ sh )
!= ( sub @ X328 @ sh ) ) ) )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ! [X330: term,X331: subst > term > subst > $o] :
( ~ ! [X332: subst > term > term] :
( ( $true
= ( X331 @ id @ ( lam @ ( X332 @ sh @ one ) ) @ id ) )
| ~ ! [X333: term] :
( ( ( X331 @ id @ ( X332 @ id @ X333 ) @ id )
= $true )
| ( ( X331 @ id @ X333 @ id )
!= $true ) )
| ~ ! [X334: subst,X335: subst,X336: term] :
( ( sub @ ( X332 @ X335 @ X336 ) @ X334 )
= ( X332 @ ( comp @ X335 @ X334 ) @ ( sub @ X336 @ X334 ) ) ) )
| ( ( X331 @ id @ X330 @ id )
= $true )
| ~ ! [X337: term,X338: term] :
( ( ( X331 @ id @ ( ap @ ( sub @ X337 @ id ) @ X338 ) @ id )
= $true )
| ( ( X331 @ id @ X337 @ id )
!= $true )
| ( ( X331 @ id @ X338 @ id )
!= $true ) ) )
<=> ( hoasinduction_no_psi_cond = $true ) )
& ( ! [X339: term] :
~ ! [X340: subst > term > term] :
( ( X340 @ sh @ one )
!= ( sub @ X339 @ ( push @ one @ sh ) ) )
<=> ( hoasinduction_lem3b_lthm = $true ) )
& ( hoasinduction_lem3_gthm = $true )
& ( hoasapnotvar_lthm = $true )
& ( ( hoaslamnotap = $true )
<=> ! [X341: subst > term > term,X342: term,X343: term] :
( ( ( ap @ ( sub @ X342 @ id ) @ X343 )
!= ( lam @ ( X341 @ sh @ one ) ) )
| ~ ! [X344: subst,X345: term,X346: subst] :
( ( sub @ ( X341 @ X346 @ X345 ) @ X344 )
= ( X341 @ ( comp @ X346 @ X344 ) @ ( sub @ X345 @ X344 ) ) ) ) )
& ( hoaslamnotap_lthm = $true )
& ( pushprop_lem0_gthm = $true )
& ( axabs = $true )
& ( axapp = $true )
& ( ( hoasinduction_lthm_3 = $true )
<=> ( ! [X347: subst > term > subst > $o] :
~ ! [X348: term > $o] :
~ ! [X349: term] :
( ( X347 @ id @ X349 @ id )
= ( X348 @ X349 ) )
=> ( ! [X350: term,X351: term > $o] :
( ~ ! [X352: term] :
( ( ( X351 @ X352 )
= $true )
| ( ( var @ X352 )
!= $true ) )
| ~ ! [X353: term,X354: term] :
( ( $true
= ( X351 @ ( ap @ X354 @ X353 ) ) )
| ( ( X351 @ X353 )
!= $true )
| ( $true
!= ( X351 @ X354 ) ) )
| ( $true
= ( X351 @ X350 ) )
| ~ ! [X355: term] :
( ( $true
= ( X351 @ ( lam @ X355 ) ) )
| ~ ! [X356: term] :
( ( ( X351 @ X356 )
!= $true )
| ( ( X351 @ ( sub @ X355 @ ( push @ X356 @ id ) ) )
= $true ) ) ) )
=> ( ! [X357: term] :
( ( sub @ X357 @ id )
= X357 )
=> ( ! [X358: subst > term > subst > $o,X359: term,X360: term > $o] :
( ~ ! [X361: term] :
( ( X360 @ X361 )
= ( X358 @ id @ X361 @ id ) )
| ~ ! [X362: subst > term > term] :
( ~ ! [X363: term] :
( ( ( X358 @ id @ X363 @ id )
!= $true )
| ( ( X358 @ id @ ( X362 @ id @ X363 ) @ id )
= $true ) )
| ~ ! [X364: subst,X365: subst,X366: term] :
( ( sub @ ( X362 @ X364 @ X366 ) @ X365 )
= ( X362 @ ( comp @ X364 @ X365 ) @ ( sub @ X366 @ X365 ) ) )
| ( $true
= ( X358 @ id @ ( lam @ ( X362 @ sh @ one ) ) @ id ) ) )
| ( $true
= ( X360 @ ( lam @ X359 ) ) )
| ~ ! [X367: term] :
( ( $true
= ( X360 @ ( sub @ X359 @ ( push @ X367 @ id ) ) ) )
| ( ( X360 @ X367 )
!= $true ) ) )
=> ! [X368: term,X369: subst > term > subst > $o] :
( ~ ! [X370: term,X371: subst,X372: subst,X373: subst] :
( ( $true
= ( X369 @ X373 @ X370 @ ( comp @ X372 @ X371 ) ) )
| ( $true
!= ( X369 @ ( comp @ X373 @ X372 ) @ ( sub @ X370 @ X372 ) @ X371 ) ) )
| ~ ! [X374: term,X375: term] :
( ( ( X369 @ id @ X375 @ id )
!= $true )
| ( $true
!= ( X369 @ id @ X374 @ id ) )
| ( ( X369 @ id @ ( ap @ ( sub @ X374 @ id ) @ X375 ) @ id )
= $true ) )
| ~ ! [X376: subst,X377: subst,X378: subst,X379: term] :
( ( ( X369 @ ( comp @ X378 @ X376 ) @ ( sub @ X379 @ X376 ) @ X377 )
= $true )
| ( ( X369 @ X378 @ X379 @ ( comp @ X376 @ X377 ) )
!= $true ) )
| ~ ! [X380: subst > term > term] :
( ~ ! [X381: term] :
( ( $true
!= ( X369 @ id @ X381 @ id ) )
| ( ( X369 @ id @ ( X380 @ id @ X381 ) @ id )
= $true ) )
| ~ ! [X382: subst,X383: term,X384: subst] :
( ( X380 @ ( comp @ X382 @ X384 ) @ ( sub @ X383 @ X384 ) )
= ( sub @ ( X380 @ X382 @ X383 ) @ X384 ) )
| ( $true
= ( X369 @ id @ ( lam @ ( X380 @ sh @ one ) ) @ id ) ) )
| ~ ! [X385: term] :
( ( $true
!= ( var @ ( sub @ X385 @ id ) ) )
| ( $true
= ( X369 @ id @ X385 @ id ) ) )
| ( $true
= ( X369 @ id @ X368 @ id ) ) ) ) ) ) ) )
& ( ( induction2lem = $true )
<=> ! [X386: term,X387: subst,X388: term > $o] :
( ~ ! [X389: term] :
( ( ( X388 @ ( sub @ X389 @ X387 ) )
= $true )
| ( $true
!= ( var @ X389 ) ) )
| ~ ! [X390: term,X391: term] :
( ( $true
!= ( X388 @ X391 ) )
| ( ( X388 @ X390 )
!= $true )
| ( ( X388 @ ( ap @ X391 @ X390 ) )
= $true ) )
| ( $true
= ( X388 @ ( sub @ X386 @ X387 ) ) )
| ~ ! [X392: term] :
( ( ( X388 @ ( lam @ X392 ) )
= $true )
| ~ ! [X393: term] :
( ( $true
!= ( X388 @ X393 ) )
| ( ( X388 @ ( sub @ X392 @ ( push @ X393 @ id ) ) )
= $true ) ) ) ) )
& ( ( termmset = $true )
<=> ! [X394: term] :
( ( sub @ X394 @ id )
= X394 ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( pushprop_lthm_orig = $true )
& ( ( substmonoid_lthm = $true )
<=> ( ! [X395: subst] :
( ( comp @ id @ X395 )
= X395 )
=> ( ! [X396: subst] :
( ( comp @ X396 @ id )
= X396 )
=> ( ! [X397: subst] :
( ( comp @ id @ X397 )
= X397 )
& ! [X398: subst] :
( ( comp @ X398 @ id )
= X398 ) ) ) ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( ! [X399: subst,X400: term > $o,X401: term > $o,X402: term] :
( ~ ! [X403: term] :
( ( X400 @ ( sub @ X403 @ ( push @ X402 @ X399 ) ) )
= ( X401 @ X403 ) )
| ( $true
= ( X401 @ one ) )
| ( $true
!= ( X400 @ X402 ) ) )
<=> ( pushprop_lem1v2 = $true ) )
& ( ( hoaslaminj = $true )
<=> ! [X404: subst,X405: subst > term > term,X406: term,X407: subst > term > term] :
( ~ ! [X408: term,X409: subst,X410: subst] :
( ( X407 @ ( comp @ X409 @ X410 ) @ ( sub @ X408 @ X410 ) )
= ( sub @ ( X407 @ X409 @ X408 ) @ X410 ) )
| ( ( X407 @ X404 @ X406 )
= ( X405 @ X404 @ X406 ) )
| ~ ! [X411: subst,X412: subst,X413: term] :
( ( X405 @ ( comp @ X412 @ X411 ) @ ( sub @ X413 @ X411 ) )
= ( sub @ ( X405 @ X412 @ X413 ) @ X411 ) )
| ( ( lam @ ( X407 @ sh @ one ) )
!= ( lam @ ( X405 @ sh @ one ) ) ) ) )
& ( axvarshift = $true )
& ( ! [X414: term,X415: subst > term > subst > $o] :
( ~ ! [X416: term] :
( ( ( X415 @ id @ ( sub @ X414 @ ( push @ X416 @ id ) ) @ id )
= $true )
| ( ( X415 @ id @ X416 @ id )
!= $true ) )
| ( ( X415 @ id @ ( lam @ ( sub @ X414 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X417: subst > term > term] :
( ~ ! [X418: subst,X419: term,X420: subst] :
( ( sub @ ( X417 @ X418 @ X419 ) @ X420 )
= ( X417 @ ( comp @ X418 @ X420 ) @ ( sub @ X419 @ X420 ) ) )
| ~ ! [X421: term] :
( ( ( X415 @ id @ ( X417 @ id @ X421 ) @ id )
= $true )
| ( $true
!= ( X415 @ id @ X421 @ id ) ) )
| ( ( X415 @ id @ ( lam @ ( X417 @ sh @ one ) ) @ id )
= $true ) ) )
<=> ( hoasinduction_lem3aa_lthm = $true ) )
& ( pushprop_lem2v2_gthm = $true )
& ( pushprop_lem3v2_lthm = $true )
& ( lamnotvar = $true )
& ( induction2_gthm = $true )
& ( pushprop_lem3v2 = $true )
& ! [X422: term] :
? [X423: d_term] :
( ( d2term @ X423 )
= X422 )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ( hoasinduction_lem3_lthm = $true )
<=> ( ! [X424: term] :
( ( sub @ X424 @ id )
= X424 )
=> ( ! [X425: subst > term > subst > $o,X426: term] :
( ~ ! [X427: subst > term > term] :
( ~ ! [X428: subst,X429: term,X430: subst] :
( ( X427 @ ( comp @ X430 @ X428 ) @ ( sub @ X429 @ X428 ) )
= ( sub @ ( X427 @ X430 @ X429 ) @ X428 ) )
| ( $true
= ( X425 @ id @ ( lam @ ( X427 @ sh @ one ) ) @ id ) )
| ~ ! [X431: term] :
( ( $true
!= ( X425 @ id @ X431 @ id ) )
| ( ( X425 @ id @ ( X427 @ id @ X431 ) @ id )
= $true ) ) )
| ( $true
= ( X425 @ id @ ( lam @ ( sub @ X426 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X432: term] :
( ( $true
= ( X425 @ id @ ( sub @ X426 @ ( push @ X432 @ id ) ) @ id ) )
| ( ( X425 @ id @ X432 @ id )
!= $true ) ) )
=> ! [X433: term,X434: subst > term > subst > $o] :
( ~ ! [X435: term] :
( ( $true
!= ( X434 @ id @ X435 @ id ) )
| ( ( X434 @ id @ ( sub @ X433 @ ( push @ X435 @ id ) ) @ id )
= $true ) )
| ( ( X434 @ id @ ( lam @ X433 ) @ id )
= $true )
| ~ ! [X436: subst,X437: term,X438: subst,X439: subst] :
( ( ( X434 @ X436 @ X437 @ ( comp @ X439 @ X438 ) )
!= $true )
| ( $true
= ( X434 @ ( comp @ X436 @ X439 ) @ ( sub @ X437 @ X439 ) @ X438 ) ) )
| ~ ! [X440: subst,X441: term,X442: subst,X443: subst] :
( ( ( X434 @ X442 @ X441 @ ( comp @ X440 @ X443 ) )
= $true )
| ( ( X434 @ ( comp @ X442 @ X440 ) @ ( sub @ X441 @ X440 ) @ X443 )
!= $true ) )
| ~ ! [X444: subst > term > term] :
( ( ( X434 @ id @ ( lam @ ( X444 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X445: term] :
( ( ( X434 @ id @ ( X444 @ id @ X445 ) @ id )
= $true )
| ( ( X434 @ id @ X445 @ id )
!= $true ) )
| ~ ! [X446: subst,X447: term,X448: subst] :
( ( X444 @ ( comp @ X448 @ X446 ) @ ( sub @ X447 @ X446 ) )
= ( sub @ ( X444 @ X448 @ X447 ) @ X446 ) ) ) ) ) ) )
& ( ! [X449: subst > term > subst > $o] :
~ ! [X450: term > $o] :
~ ! [X451: term] :
( ( X449 @ id @ X451 @ id )
= ( X450 @ X451 ) )
<=> ( hoasinduction_lem0_lthm = $true ) )
& ( pushprop_lem1_gthm = $true )
& ( hoasinduction_lem1 = $true )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( hoasapnotvar_gthm = $true )
& ( hoaslamnotap_gthm = $true )
& ( ( hoasinduction_lem2 = $true )
<=> ! [X452: term,X453: term,X454: subst > term > subst > $o] :
( ( ( X454 @ id @ X453 @ id )
!= $true )
| ~ ! [X455: subst,X456: subst,X457: term,X458: subst] :
( ( ( X454 @ X458 @ X457 @ ( comp @ X455 @ X456 ) )
= $true )
| ( $true
!= ( X454 @ ( comp @ X458 @ X455 ) @ ( sub @ X457 @ X455 ) @ X456 ) ) )
| ( ( X454 @ id @ ( ap @ X452 @ X453 ) @ id )
= $true )
| ~ ! [X459: subst,X460: term,X461: subst,X462: subst] :
( ( ( X454 @ X461 @ X460 @ ( comp @ X459 @ X462 ) )
!= $true )
| ( ( X454 @ ( comp @ X461 @ X459 ) @ ( sub @ X460 @ X459 ) @ X462 )
= $true ) )
| ( ( X454 @ id @ X452 @ id )
!= $true )
| ~ ! [X463: term,X464: term] :
( ( $true
!= ( X454 @ id @ X463 @ id ) )
| ( $true
= ( X454 @ id @ ( ap @ ( sub @ X463 @ id ) @ X464 ) @ id ) )
| ( ( X454 @ id @ X464 @ id )
!= $true ) ) ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
<=> ( ! [X465: term] :
~ ! [X466: subst > term > term] :
~ ! [X467: subst,X468: term] :
( ( sub @ X465 @ ( push @ X468 @ X467 ) )
= ( X466 @ X467 @ X468 ) )
=> ( ! [X469: term] :
( ( sub @ X469 @ id )
= X469 )
=> ! [X470: subst > term > subst > $o,X471: term,X472: term > $o] :
( ~ ! [X473: subst > term > term] :
( ( ( X470 @ id @ ( lam @ ( X473 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X474: term] :
( ( ( X470 @ id @ X474 @ id )
!= $true )
| ( ( X470 @ id @ ( X473 @ id @ X474 ) @ id )
= $true ) )
| ~ ! [X475: subst,X476: subst,X477: term] :
( ( X473 @ ( comp @ X476 @ X475 ) @ ( sub @ X477 @ X475 ) )
= ( sub @ ( X473 @ X476 @ X477 ) @ X475 ) ) )
| ~ ! [X478: term] :
( ( X470 @ id @ X478 @ id )
= ( X472 @ X478 ) )
| ( ( X472 @ ( lam @ X471 ) )
= $true )
| ~ ! [X479: term] :
( ( $true
!= ( X472 @ X479 ) )
| ( ( X472 @ ( sub @ X471 @ ( push @ X479 @ id ) ) )
= $true ) ) ) ) ) )
& ( ! [X480: term,X481: term,X482: term,X483: term] :
( ( ( ap @ ( sub @ X482 @ id ) @ X481 )
!= ( ap @ ( sub @ X480 @ id ) @ X483 ) )
| ( X481 = X483 ) )
<=> ( hoasapinj2 = $true ) )
& ! [X484: subst] :
? [X485: d_subst] :
( ( d2subst @ X485 )
= X484 )
& ( ( hoasapinj1 = $true )
<=> ! [X486: term,X487: term,X488: term,X489: term] :
( ( ( ap @ ( sub @ X489 @ id ) @ X486 )
!= ( ap @ ( sub @ X488 @ id ) @ X487 ) )
| ( X488 = X489 ) ) )
& ( ( hoasinduction_lem3a = $true )
<=> ! [X490: term,X491: subst > term > subst > $o] :
( ~ ! [X492: term] :
( ( ( X491 @ id @ ( sub @ X490 @ ( push @ X492 @ id ) ) @ id )
= $true )
| ( ( X491 @ id @ X492 @ id )
!= $true ) )
| ( $true
= ( X491 @ id @ ( lam @ X490 ) @ id ) )
| ~ ! [X493: subst > term > term] :
( ~ ! [X494: subst,X495: subst,X496: term] :
( ( X493 @ ( comp @ X494 @ X495 ) @ ( sub @ X496 @ X495 ) )
= ( sub @ ( X493 @ X494 @ X496 ) @ X495 ) )
| ( ( X491 @ id @ ( lam @ ( X493 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X497: term] :
( ( ( X491 @ id @ X497 @ id )
!= $true )
| ( ( X491 @ id @ ( X493 @ id @ X497 ) @ id )
= $true ) ) ) ) )
& ( ( hoasinduction_lem3aa = $true )
<=> ! [X498: subst > term > subst > $o,X499: term] :
( ( $true
= ( X498 @ id @ ( lam @ ( sub @ X499 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X500: term] :
( ( $true
= ( X498 @ id @ ( sub @ X499 @ ( push @ X500 @ id ) ) @ id ) )
| ( $true
!= ( X498 @ id @ X500 @ id ) ) )
| ~ ! [X501: subst > term > term] :
( ( $true
= ( X498 @ id @ ( lam @ ( X501 @ sh @ one ) ) @ id ) )
| ~ ! [X502: subst,X503: subst,X504: term] :
( ( X501 @ ( comp @ X502 @ X503 ) @ ( sub @ X504 @ X503 ) )
= ( sub @ ( X501 @ X502 @ X504 ) @ X503 ) )
| ~ ! [X505: term] :
( ( $true
!= ( X498 @ id @ X505 @ id ) )
| ( $true
= ( X498 @ id @ ( X501 @ id @ X505 ) @ id ) ) ) ) ) )
& ( ulamvarind = $true )
& ( ( ! [X506: term,X507: subst] :
( ( sub @ one @ ( push @ X506 @ X507 ) )
= X506 )
=> ( ! [X508: subst,X509: term] :
( ( comp @ sh @ ( push @ X509 @ X508 ) )
= X508 )
=> ( ! [X510: subst] :
( ( comp @ X510 @ id )
= X510 )
=> ( ! [X511: term,X512: term > $o] :
( ~ ! [X513: term] :
( ( $true
!= ( X512 @ X513 ) )
| ( ( X512 @ ( lam @ X513 ) )
= $true ) )
| ~ ! [X514: term] :
( ( ( var @ X514 )
!= $true )
| ( ( X512 @ X514 )
= $true ) )
| ( ( X512 @ X511 )
= $true )
| ~ ! [X515: term,X516: term] :
( ( ( X512 @ ( ap @ X516 @ X515 ) )
= $true )
| ( $true
!= ( X512 @ X516 ) )
| ( ( X512 @ X515 )
!= $true ) ) )
=> ! [X517: subst,X518: term > $o,X519: term] :
( ~ ! [X520: term] :
( ( ( X518 @ ( lam @ X520 ) )
= $true )
| ~ ! [X521: term] :
( ( $true
= ( X518 @ ( sub @ X520 @ ( push @ X521 @ id ) ) ) )
| ( $true
!= ( X518 @ X521 ) ) ) )
| ~ ! [X522: term,X523: term] :
( ( $true
= ( X518 @ ( ap @ X523 @ X522 ) ) )
| ( ( X518 @ X523 )
!= $true )
| ( ( X518 @ X522 )
!= $true ) )
| ( $true
= ( X518 @ ( sub @ X519 @ X517 ) ) )
| ~ ! [X524: term] :
( ( $true
= ( X518 @ ( sub @ X524 @ X517 ) ) )
| ( ( var @ X524 )
!= $true ) ) ) ) ) ) )
<=> ( induction2lem_lthm = $true ) )
& ( hoasinduction_lem1_lthm = $true )
& ( ! [X525: subst > term > subst > $o] :
~ ! [X526: term > $o] :
~ ! [X527: term] :
( ( X525 @ id @ X527 @ id )
= ( X526 @ X527 ) )
<=> ( hoasinduction_lem0 = $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 ) ) ) ) )
& ( ! [X528: subst] :
( ( comp @ id @ X528 )
= X528 )
<=> ( axidl = $true ) )
& ( termmset_gthm = $true )
& ( hoasapinj2_gthm = $true )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ! [X529: term] :
~ ! [X530: subst > term > term] :
( ( X530 @ sh @ one )
!= ( sub @ X529 @ ( push @ one @ sh ) ) )
<=> ( hoasinduction_lem3b = $true ) )
& ! [X531: d_term] : ( d_one = X531 )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( hoasapinj2_lthm = $true )
<=> ( ! [X532: term,X533: term,X534: term,X535: term] :
( ( X533 = X534 )
| ( ( ap @ X532 @ X534 )
!= ( ap @ X535 @ X533 ) ) )
=> ! [X536: term,X537: term,X538: term,X539: term] :
( ( ( ap @ ( sub @ X536 @ id ) @ X539 )
!= ( ap @ ( sub @ X537 @ id ) @ X538 ) )
| ( X538 = X539 ) ) ) )
& ( hoasinduction_lem3b_gthm = $true ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( ( hoasinduction_no_psi_cond_lthm = $true )
<=> ( ! [X0: subst > term > subst > $o] :
~ ! [X1: term > $o] :
~ ! [X2: term] :
( ( X0 @ id @ X2 @ id )
= ( X1 @ X2 ) )
=> ( ! [X3: term,X4: term > $o] :
( ( $true
= ( X4 @ X3 ) )
| ~ ! [X5: term,X6: term] :
( ( ( X4 @ X5 )
!= $true )
| ( $true
= ( X4 @ ( ap @ X5 @ X6 ) ) )
| ( ( X4 @ X6 )
!= $true ) )
| ~ ! [X7: term] :
( ( ( X4 @ X7 )
= $true )
| ( $true
!= ( var @ X7 ) ) )
| ~ ! [X8: term] :
( ( ( X4 @ ( lam @ X8 ) )
= $true )
| ~ ! [X9: term] :
( ( $true
!= ( X4 @ X9 ) )
| ( $true
= ( X4 @ ( sub @ X8 @ ( push @ X9 @ id ) ) ) ) ) ) )
=> ( ! [X10: term] :
( ( sub @ X10 @ id )
= X10 )
=> ( ! [X11: term,X12: subst > term > subst > $o,X13: term > $o] :
( ~ ! [X14: term] :
( ( X13 @ X14 )
= ( X12 @ id @ X14 @ id ) )
| ~ ! [X15: subst > term > term] :
( ~ ! [X16: term] :
( ( $true
!= ( X12 @ id @ X16 @ id ) )
| ( ( X12 @ id @ ( X15 @ id @ X16 ) @ id )
= $true ) )
| ~ ! [X17: term,X18: subst,X19: subst] :
( ( sub @ ( X15 @ X19 @ X17 ) @ X18 )
= ( X15 @ ( comp @ X19 @ X18 ) @ ( sub @ X17 @ X18 ) ) )
| ( $true
= ( X12 @ id @ ( lam @ ( X15 @ sh @ one ) ) @ id ) ) )
| ( ( X13 @ ( lam @ X11 ) )
= $true )
| ~ ! [X20: term] :
( ( ( X13 @ X20 )
!= $true )
| ( $true
= ( X13 @ ( sub @ X11 @ ( push @ X20 @ id ) ) ) ) ) )
=> ! [X21: subst > term > subst > $o,X22: term] :
( ~ ! [X23: term,X24: term] :
( ( ( X21 @ id @ X24 @ id )
!= $true )
| ( $true
= ( X21 @ id @ ( ap @ ( sub @ X23 @ id ) @ X24 ) @ id ) )
| ( $true
!= ( X21 @ id @ X23 @ id ) ) )
| ~ ! [X25: subst > term > term] :
( ~ ! [X26: term] :
( ( ( X21 @ id @ X26 @ id )
!= $true )
| ( ( X21 @ id @ ( X25 @ id @ X26 ) @ id )
= $true ) )
| ( ( X21 @ id @ ( lam @ ( X25 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X27: term,X28: subst,X29: subst] :
( ( X25 @ ( comp @ X28 @ X29 ) @ ( sub @ X27 @ X29 ) )
= ( sub @ ( X25 @ X28 @ X27 ) @ X29 ) ) )
| ( $true
= ( X21 @ id @ X22 @ id ) ) ) ) ) ) ) )
& ( ! [X30: term,X31: term] :
( ( X30 = X31 )
| ( ( lam @ X30 )
!= ( lam @ X31 ) ) )
<=> ( laminj = $true ) )
& ( ( hoasinduction_lem3 = $true )
<=> ! [X32: term,X33: subst > term > subst > $o] :
( ( $true
= ( X33 @ id @ ( lam @ X32 ) @ id ) )
| ~ ! [X34: term,X35: subst,X36: subst,X37: subst] :
( ( ( X33 @ X36 @ X34 @ ( comp @ X37 @ X35 ) )
= $true )
| ( ( X33 @ ( comp @ X36 @ X37 ) @ ( sub @ X34 @ X37 ) @ X35 )
!= $true ) )
| ~ ! [X38: subst,X39: subst,X40: subst,X41: term] :
( ( $true
!= ( X33 @ X39 @ X41 @ ( comp @ X40 @ X38 ) ) )
| ( $true
= ( X33 @ ( comp @ X39 @ X40 ) @ ( sub @ X41 @ X40 ) @ X38 ) ) )
| ~ ! [X42: subst > term > term] :
( ~ ! [X43: term] :
( ( ( X33 @ id @ ( X42 @ id @ X43 ) @ id )
= $true )
| ( $true
!= ( X33 @ id @ X43 @ id ) ) )
| ( ( X33 @ id @ ( lam @ ( X42 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X44: term,X45: subst,X46: subst] :
( ( X42 @ ( comp @ X46 @ X45 ) @ ( sub @ X44 @ X45 ) )
= ( sub @ ( X42 @ X46 @ X44 ) @ X45 ) ) )
| ~ ! [X47: term] :
( ( ( X33 @ id @ ( sub @ X32 @ ( push @ X47 @ id ) ) @ id )
= $true )
| ( $true
!= ( X33 @ id @ X47 @ id ) ) ) ) )
& ( ! [X48: term,X49: term,X50: term,X51: term] :
( ( ( ap @ X49 @ X48 )
!= ( ap @ X50 @ X51 ) )
| ( X48 = X51 ) )
<=> ( apinj2 = $true ) )
& ( ulamvarsh = $true )
& ( axclos = $true )
& ( hoasinduction_lem1v2 = $true )
& ( ! [X52: subst] :
( ( comp @ X52 @ id )
= X52 )
<=> ( axidr = $true ) )
& ( ( hoasinduction_lem2v2 = $true )
<=> ! [X53: term,X54: term > $o,X55: subst > term > subst > $o,X56: term] :
( ( ( X54 @ X53 )
!= $true )
| ~ ! [X57: subst,X58: term,X59: subst,X60: subst] :
( ( ( X55 @ ( comp @ X60 @ X57 ) @ ( sub @ X58 @ X57 ) @ X59 )
= $true )
| ( $true
!= ( X55 @ X60 @ X58 @ ( comp @ X57 @ X59 ) ) ) )
| ~ ! [X61: term,X62: term] :
( ( ( X55 @ id @ X62 @ id )
!= $true )
| ( ( X55 @ id @ ( ap @ ( sub @ X62 @ id ) @ X61 ) @ id )
= $true )
| ( $true
!= ( X55 @ id @ X61 @ id ) ) )
| ( ( X54 @ ( ap @ X53 @ X56 ) )
= $true )
| ( ( X54 @ X56 )
!= $true )
| ~ ! [X63: term] :
( ( X55 @ id @ X63 @ id )
= ( X54 @ X63 ) )
| ~ ! [X64: subst,X65: term,X66: subst,X67: subst] :
( ( ( X55 @ ( comp @ X66 @ X67 ) @ ( sub @ X65 @ X67 ) @ X64 )
!= $true )
| ( ( X55 @ X66 @ X65 @ ( comp @ X67 @ X64 ) )
= $true ) ) ) )
& ( ( ! [X68: term] :
( ( sub @ X68 @ id )
= X68 )
=> ( ! [X69: term,X70: term,X71: term,X72: term] :
( ( X69 = X71 )
| ( ( ap @ X69 @ X70 )
!= ( ap @ X71 @ X72 ) ) )
=> ! [X73: term,X74: term,X75: term,X76: term] :
( ( X73 = X74 )
| ( ( ap @ ( sub @ X74 @ id ) @ X76 )
!= ( ap @ ( sub @ X73 @ id ) @ X75 ) ) ) ) )
<=> ( hoasapinj1_lthm = $true ) )
& ( ( axvarcons = $true )
<=> ! [X77: subst,X78: term] :
( ( sub @ one @ ( push @ X78 @ X77 ) )
= X78 ) )
& ( hoasinduction_p_and_p_prime
= ( ^ [Y0: subst > term > subst > $o,Y1: term > $o] :
( !! @ term
@ ^ [Y2: term] :
( ( Y1 @ Y2 )
= ( Y0 @ id @ Y2 @ id ) ) ) ) )
& ( pushprop_lem2v2 = $true )
& ( axassoc = $true )
& ( ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
& ( ( ! [X82: subst] :
( ( comp @ id @ X82 )
= X82 )
& ! [X83: subst] :
( ( comp @ X83 @ id )
= X83 ) )
<=> ( substmonoid = $true ) )
& ( ( hoasinduction_lem3a_lthm = $true )
<=> ( ! [X84: term] :
( ( sub @ X84 @ id )
= X84 )
=> ( ! [X85: subst > term > subst > $o,X86: term] :
( ( ( X85 @ id @ ( lam @ ( sub @ X86 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X87: subst > term > term] :
( ~ ! [X88: term,X89: subst,X90: subst] :
( ( X87 @ ( comp @ X90 @ X89 ) @ ( sub @ X88 @ X89 ) )
= ( sub @ ( X87 @ X90 @ X88 ) @ X89 ) )
| ~ ! [X91: term] :
( ( $true
= ( X85 @ id @ ( X87 @ id @ X91 ) @ id ) )
| ( $true
!= ( X85 @ id @ X91 @ id ) ) )
| ( $true
= ( X85 @ id @ ( lam @ ( X87 @ sh @ one ) ) @ id ) ) )
| ~ ! [X92: term] :
( ( $true
!= ( X85 @ id @ X92 @ id ) )
| ( ( X85 @ id @ ( sub @ X86 @ ( push @ X92 @ id ) ) @ id )
= $true ) ) )
=> ! [X93: subst > term > subst > $o,X94: term] :
( ( $true
= ( X93 @ id @ ( lam @ X94 ) @ id ) )
| ~ ! [X95: subst > term > term] :
( ~ ! [X96: term] :
( ( $true
= ( X93 @ id @ ( X95 @ id @ X96 ) @ id ) )
| ( $true
!= ( X93 @ id @ X96 @ id ) ) )
| ~ ! [X97: term,X98: subst,X99: subst] :
( ( X95 @ ( comp @ X99 @ X98 ) @ ( sub @ X97 @ X98 ) )
= ( sub @ ( X95 @ X99 @ X97 ) @ X98 ) )
| ( ( X93 @ id @ ( lam @ ( X95 @ sh @ one ) ) @ id )
= $true ) )
| ~ ! [X100: term] :
( ( $true
!= ( X93 @ id @ X100 @ id ) )
| ( $true
= ( X93 @ id @ ( sub @ X94 @ ( push @ X100 @ id ) ) @ id ) ) ) ) ) ) )
& ( ( hoasinduction_lem3v2_lthm = $true )
<=> ( ! [X101: term] :
( ( sub @ X101 @ id )
= X101 )
=> ! [X102: term > $o,X103: subst > term > subst > $o,X104: term] :
( ~ ! [X105: term] :
( ( ( X102 @ X105 )
!= $true )
| ( ( X102 @ ( sub @ X104 @ ( push @ X105 @ id ) ) )
= $true ) )
| ~ ! [X106: subst > term > term] :
( ~ ! [X107: subst,X108: subst,X109: term] :
( ( X106 @ ( comp @ X108 @ X107 ) @ ( sub @ X109 @ X107 ) )
= ( sub @ ( X106 @ X108 @ X109 ) @ X107 ) )
| ~ ! [X110: term] :
( ( $true
!= ( X103 @ id @ X110 @ id ) )
| ( $true
= ( X103 @ id @ ( X106 @ id @ X110 ) @ id ) ) )
| ( ( X103 @ id @ ( lam @ ( X106 @ sh @ one ) ) @ id )
= $true ) )
| ~ ! [X111: subst,X112: term,X113: subst,X114: subst] :
( ( ( X103 @ ( comp @ X111 @ X113 ) @ ( sub @ X112 @ X113 ) @ X114 )
= $true )
| ( $true
!= ( X103 @ X111 @ X112 @ ( comp @ X113 @ X114 ) ) ) )
| ~ ! [X115: term] :
( ( X103 @ id @ X115 @ id )
= ( X102 @ X115 ) )
| ( ( X102 @ ( lam @ X104 ) )
= $true )
| ~ ! [X116: subst,X117: subst,X118: term,X119: subst] :
( ( ( X103 @ ( comp @ X117 @ X116 ) @ ( sub @ X118 @ X116 ) @ X119 )
!= $true )
| ( ( X103 @ X117 @ X118 @ ( comp @ X116 @ X119 ) )
= $true ) ) ) ) )
& ( ! [X120: term,X121: subst] :
( ( comp @ sh @ ( push @ X120 @ X121 ) )
= X121 )
<=> ( axshiftcons = $true ) )
& ( ( pushprop_lem0 = $true )
<=> ! [X122: term > $o,X123: subst,X124: term] :
~ ! [X125: term > $o] :
~ ! [X126: term] :
( ( X125 @ X126 )
= ( X122 @ ( sub @ X126 @ ( push @ X124 @ X123 ) ) ) ) )
& ( lamnotap != $true )
& ( ! [X127: term] :
~ ! [X128: subst > term > term] :
~ ! [X129: term,X130: subst] :
( ( sub @ X127 @ ( push @ X129 @ X130 ) )
= ( X128 @ X130 @ X129 ) )
<=> ( hoasinduction_lem3v2_f_lthm = $true ) )
& ( axmap = $true )
& ( hoasinduction_lem2v2_gthm = $true )
& ( ( induction2_lthm = $true )
<=> ( ! [X131: term] :
( ( sub @ X131 @ id )
= X131 )
=> ( ! [X132: subst,X133: term > $o,X134: term] :
( ~ ! [X135: term] :
( ( ( X133 @ ( lam @ X135 ) )
= $true )
| ~ ! [X136: term] :
( ( ( X133 @ ( sub @ X135 @ ( push @ X136 @ id ) ) )
= $true )
| ( ( X133 @ X136 )
!= $true ) ) )
| ~ ! [X137: term,X138: term] :
( ( ( X133 @ ( ap @ X137 @ X138 ) )
= $true )
| ( $true
!= ( X133 @ X138 ) )
| ( $true
!= ( X133 @ X137 ) ) )
| ~ ! [X139: term] :
( ( $true
= ( X133 @ ( sub @ X139 @ X132 ) ) )
| ( ( var @ X139 )
!= $true ) )
| ( ( X133 @ ( sub @ X134 @ X132 ) )
= $true ) )
=> ! [X140: term,X141: term > $o] :
( ~ ! [X142: term] :
( ( $true
!= ( var @ X142 ) )
| ( $true
= ( X141 @ X142 ) ) )
| ~ ! [X143: term,X144: term] :
( ( ( X141 @ X144 )
!= $true )
| ( ( X141 @ ( ap @ X143 @ X144 ) )
= $true )
| ( ( X141 @ X143 )
!= $true ) )
| ~ ! [X145: term] :
( ~ ! [X146: term] :
( ( ( X141 @ X146 )
!= $true )
| ( ( X141 @ ( sub @ X145 @ ( push @ X146 @ id ) ) )
= $true ) )
| ( ( X141 @ ( lam @ X145 ) )
= $true ) )
| ( $true
= ( X141 @ X140 ) ) ) ) ) )
& ( ( pushprop_lem0_lthm = $true )
<=> ! [X147: subst,X148: term > $o,X149: term] :
~ ! [X150: term > $o] :
~ ! [X151: term] :
( ( X148 @ ( sub @ X151 @ ( push @ X149 @ X147 ) ) )
= ( X150 @ X151 ) ) )
& ( induction2lem_gthm = $true )
& ( ( pushprop_lem1_lthm = $true )
<=> ( ! [X152: term,X153: subst] :
( ( sub @ one @ ( push @ X152 @ X153 ) )
= X152 )
=> ( ! [X154: subst,X155: term] :
( ( comp @ sh @ ( push @ X155 @ X154 ) )
= X154 )
=> ! [X156: term,X157: term > $o,X158: subst,X159: term,X160: term > $o] :
( ( $true
!= ( X157 @ X156 ) )
| ( $true
= ( X160 @ ( sub @ X156 @ ( push @ X159 @ X158 ) ) ) ) ) ) ) )
& ( ( hoasinduction_lem3v2a = $true )
<=> ! [X161: term > $o,X162: subst > term > subst > $o,X163: term] :
( ~ ! [X164: term] :
( ( X162 @ id @ X164 @ id )
= ( X161 @ X164 ) )
| ~ ! [X165: subst > term > term] :
( ~ ! [X166: term] :
( ( $true
= ( X162 @ id @ ( X165 @ id @ X166 ) @ id ) )
| ( ( X162 @ id @ X166 @ id )
!= $true ) )
| ( ( X162 @ id @ ( lam @ ( X165 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X167: subst,X168: term,X169: subst] :
( ( X165 @ ( comp @ X169 @ X167 ) @ ( sub @ X168 @ X167 ) )
= ( sub @ ( X165 @ X169 @ X168 ) @ X167 ) ) )
| ~ ! [X170: term] :
( ( ( X161 @ X170 )
!= $true )
| ( ( X161 @ ( sub @ X163 @ ( push @ X170 @ id ) ) )
= $true ) )
| ( $true
= ( X161 @ ( lam @ X163 ) ) ) ) )
& ( ( hoasinduction_lthm = $true )
<=> ( ! [X171: term > $o,X172: term] :
( ( ( X171 @ X172 )
= $true )
| ~ ! [X173: term] :
( ~ ! [X174: term] :
( ( $true
= ( X171 @ ( sub @ X173 @ ( push @ X174 @ id ) ) ) )
| ( ( X171 @ X174 )
!= $true ) )
| ( $true
= ( X171 @ ( lam @ X173 ) ) ) )
| ~ ! [X175: term,X176: term] :
( ( ( X171 @ X176 )
!= $true )
| ( ( X171 @ ( ap @ X176 @ X175 ) )
= $true )
| ( $true
!= ( X171 @ X175 ) ) )
| ~ ! [X177: term] :
( ( ( var @ X177 )
!= $true )
| ( ( X171 @ X177 )
= $true ) ) )
=> ( ! [X178: term,X179: term,X180: subst > term > subst > $o] :
( ( $true
!= ( X180 @ id @ X179 @ id ) )
| ( ( X180 @ id @ ( ap @ X178 @ X179 ) @ id )
= $true )
| ~ ! [X181: subst,X182: subst,X183: term,X184: subst] :
( ( ( X180 @ X182 @ X183 @ ( comp @ X184 @ X181 ) )
!= $true )
| ( $true
= ( X180 @ ( comp @ X182 @ X184 ) @ ( sub @ X183 @ X184 ) @ X181 ) ) )
| ( $true
!= ( X180 @ id @ X178 @ id ) )
| ~ ! [X185: subst,X186: subst,X187: term,X188: subst] :
( ( ( X180 @ X188 @ X187 @ ( comp @ X186 @ X185 ) )
= $true )
| ( $true
!= ( X180 @ ( comp @ X188 @ X186 ) @ ( sub @ X187 @ X186 ) @ X185 ) ) )
| ~ ! [X189: term,X190: term] :
( ( ( X180 @ id @ X190 @ id )
!= $true )
| ( $true
= ( X180 @ id @ ( ap @ ( sub @ X190 @ id ) @ X189 ) @ id ) )
| ( $true
!= ( X180 @ id @ X189 @ id ) ) ) )
=> ( ! [X191: term,X192: subst > term > subst > $o] :
( ~ ! [X193: subst,X194: term,X195: subst,X196: subst] :
( ( ( X192 @ X196 @ X194 @ ( comp @ X193 @ X195 ) )
!= $true )
| ( ( X192 @ ( comp @ X196 @ X193 ) @ ( sub @ X194 @ X193 ) @ X195 )
= $true ) )
| ~ ! [X197: subst,X198: subst,X199: term,X200: subst] :
( ( ( X192 @ ( comp @ X200 @ X198 ) @ ( sub @ X199 @ X198 ) @ X197 )
!= $true )
| ( $true
= ( X192 @ X200 @ X199 @ ( comp @ X198 @ X197 ) ) ) )
| ~ ! [X201: term] :
( ( $true
!= ( X192 @ id @ X201 @ id ) )
| ( $true
= ( X192 @ id @ ( sub @ X191 @ ( push @ X201 @ id ) ) @ id ) ) )
| ( ( X192 @ id @ ( lam @ X191 ) @ id )
= $true )
| ~ ! [X202: subst > term > term] :
( ~ ! [X203: term,X204: subst,X205: subst] :
( ( X202 @ ( comp @ X204 @ X205 ) @ ( sub @ X203 @ X205 ) )
= ( sub @ ( X202 @ X204 @ X203 ) @ X205 ) )
| ~ ! [X206: term] :
( ( ( X192 @ id @ X206 @ id )
!= $true )
| ( ( X192 @ id @ ( X202 @ id @ X206 ) @ id )
= $true ) )
| ( $true
= ( X192 @ id @ ( lam @ ( X202 @ sh @ one ) ) @ id ) ) ) )
=> ! [X207: subst > term > subst > $o,X208: term] :
( ~ ! [X209: term,X210: term] :
( ( ( X207 @ id @ ( ap @ ( sub @ X210 @ id ) @ X209 ) @ id )
= $true )
| ( ( X207 @ id @ X209 @ id )
!= $true )
| ( ( X207 @ id @ X210 @ id )
!= $true ) )
| ~ ! [X211: subst,X212: subst,X213: subst,X214: term] :
( ( ( X207 @ X213 @ X214 @ ( comp @ X211 @ X212 ) )
= $true )
| ( $true
!= ( X207 @ ( comp @ X213 @ X211 ) @ ( sub @ X214 @ X211 ) @ X212 ) ) )
| ~ ! [X215: subst,X216: subst,X217: term,X218: subst] :
( ( $true
!= ( X207 @ X216 @ X217 @ ( comp @ X215 @ X218 ) ) )
| ( ( X207 @ ( comp @ X216 @ X215 ) @ ( sub @ X217 @ X215 ) @ X218 )
= $true ) )
| ~ ! [X219: term] :
( ( ( X207 @ id @ X219 @ id )
= $true )
| ( $true
!= ( var @ ( sub @ X219 @ id ) ) ) )
| ~ ! [X220: subst > term > term] :
( ~ ! [X221: subst,X222: term,X223: subst] :
( ( sub @ ( X220 @ X223 @ X222 ) @ X221 )
= ( X220 @ ( comp @ X223 @ X221 ) @ ( sub @ X222 @ X221 ) ) )
| ( $true
= ( X207 @ id @ ( lam @ ( X220 @ sh @ one ) ) @ id ) )
| ~ ! [X224: term] :
( ( ( X207 @ id @ X224 @ id )
!= $true )
| ( ( X207 @ id @ ( X220 @ id @ X224 ) @ id )
= $true ) ) )
| ( $true
= ( X207 @ id @ X208 @ id ) ) ) ) ) ) )
& ( hoaslaminj_gthm = $true )
& ( ! [X225: term,X226: subst > term > subst > $o] :
( ~ ! [X227: term] :
( ( $true
!= ( X226 @ id @ X227 @ id ) )
| ( $true
= ( X226 @ id @ ( sub @ X225 @ ( push @ X227 @ id ) ) @ id ) ) )
| ( ( X226 @ id @ ( lam @ ( sub @ X225 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X228: term,X229: subst > term > term] :
( ~ ! [X230: subst,X231: term,X232: subst] :
( ( sub @ ( X229 @ X232 @ X231 ) @ X230 )
= ( sub @ ( sub @ X228 @ ( push @ X231 @ X232 ) ) @ X230 ) )
| ~ ! [X233: subst,X234: term,X235: subst] :
( ( sub @ X228 @ ( push @ ( sub @ X234 @ X235 ) @ ( comp @ X233 @ X235 ) ) )
= ( X229 @ ( comp @ X233 @ X235 ) @ ( sub @ X234 @ X235 ) ) )
| ~ ! [X236: term] :
( ( ( X226 @ id @ X236 @ id )
!= $true )
| ( ( X226 @ id @ ( X229 @ id @ X236 ) @ id )
= $true ) )
| ( $true
= ( X226 @ id @ ( lam @ ( X229 @ sh @ one ) ) @ id ) ) ) )
<=> ( hoasinduction_lem3aaa = $true ) )
& ( hoasapnotvar = $true )
& ! [X237: d_term,X238: d_term] :
( ( ( d2term @ X237 )
= ( d2term @ X238 ) )
=> ( X237 = X238 ) )
& ( ( d2subst @ d_id )
= sh )
& ( hoaslamnotvar_gthm = $true )
& ( ! [X239: term] :
( ( sub @ X239 @ id )
= X239 )
<=> ( axvarid = $true ) )
& ( ( hoaslaminj_lthm = $true )
<=> ( ! [X240: subst,X241: term] :
( ( sub @ one @ ( push @ X241 @ X240 ) )
= X241 )
=> ( ! [X242: term,X243: subst] :
( ( comp @ sh @ ( push @ X242 @ X243 ) )
= X243 )
=> ( ! [X244: term,X245: term] :
( ( ( lam @ X244 )
!= ( lam @ X245 ) )
| ( X244 = X245 ) )
=> ! [X246: subst,X247: term,X248: subst > term > term,X249: subst > term > term] :
( ( ( X249 @ X246 @ X247 )
= ( X248 @ X246 @ X247 ) )
| ~ ! [X250: term,X251: subst,X252: subst] :
( ( X249 @ ( comp @ X251 @ X252 ) @ ( sub @ X250 @ X252 ) )
= ( sub @ ( X249 @ X251 @ X250 ) @ X252 ) )
| ( ( lam @ ( X248 @ sh @ one ) )
!= ( lam @ ( X249 @ sh @ one ) ) )
| ~ ! [X253: subst,X254: term,X255: subst] :
( ( sub @ ( X248 @ X253 @ X254 ) @ X255 )
= ( X248 @ ( comp @ X253 @ X255 ) @ ( sub @ X254 @ X255 ) ) ) ) ) ) ) )
& ( hoaslamnotvar = $true )
& ( ( termmset_lthm = $true )
<=> ( ! [X256: term] :
( ( sub @ X256 @ id )
= X256 )
=> ! [X257: term] :
( ( sub @ X257 @ id )
= X257 ) ) )
& ( substmonoid_gthm = $true )
& ( ( induction = $true )
<=> ! [X258: term,X259: term > $o] :
( ~ ! [X260: term] :
( ( $true
!= ( X259 @ X260 ) )
| ( ( X259 @ ( lam @ X260 ) )
= $true ) )
| ( ( X259 @ X258 )
= $true )
| ~ ! [X261: term,X262: term] :
( ( ( X259 @ X261 )
!= $true )
| ( ( X259 @ X262 )
!= $true )
| ( ( X259 @ ( ap @ X262 @ X261 ) )
= $true ) )
| ~ ! [X263: term] :
( ( ( X259 @ X263 )
= $true )
| ( ( var @ X263 )
!= $true ) ) ) )
& ( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) )
& ( pushprop_lem2v2_lthm = $true )
& ( ! [X266: term,X267: term,X268: term,X269: term] :
( ( ( ap @ X267 @ X266 )
!= ( ap @ X269 @ X268 ) )
| ( X267 = X269 ) )
<=> ( apinj1 = $true ) )
& ( ( var @ ( d2term @ d_one ) )
!= $true )
& ( hoasinduction_lem2_gthm = $true )
& ( ( d2subst @ d_id )
= id )
& ! [X270: d_subst,X271: d_subst] :
( ( ( d2subst @ X271 )
= ( d2subst @ X270 ) )
=> ( X270 = X271 ) )
& ( ( axscons = $true )
<=> ! [X272: subst] :
( ( push @ ( sub @ one @ X272 ) @ ( comp @ sh @ X272 ) )
= X272 ) )
& ( pushprop_lthm = $true )
& ( ( induction2 = $true )
<=> ! [X273: term > $o,X274: term] :
( ~ ! [X275: term] :
( ~ ! [X276: term] :
( ( $true
!= ( X273 @ X276 ) )
| ( $true
= ( X273 @ ( sub @ X275 @ ( push @ X276 @ id ) ) ) ) )
| ( ( X273 @ ( lam @ X275 ) )
= $true ) )
| ~ ! [X277: term,X278: term] :
( ( ( X273 @ X277 )
!= $true )
| ( $true
!= ( X273 @ X278 ) )
| ( ( X273 @ ( ap @ X278 @ X277 ) )
= $true ) )
| ( ( X273 @ X274 )
= $true )
| ~ ! [X279: term] :
( ( $true
!= ( var @ X279 ) )
| ( ( X273 @ X279 )
= $true ) ) ) )
& ( ! [X280: term,X281: term,X282: term > $o,X283: subst,X284: term > $o] :
( ( $true
= ( X282 @ ( sub @ X281 @ ( push @ X280 @ X283 ) ) ) )
| ( ( X284 @ X281 )
!= $true ) )
<=> ( pushprop_lem1 = $true ) )
& ( hoasinduction_lem1_gthm = $true )
& ( ! [X285: term] :
~ ! [X286: subst > term > term] :
~ ! [X287: term,X288: subst] :
( ( X286 @ X288 @ X287 )
= ( sub @ X285 @ ( push @ X287 @ X288 ) ) )
<=> ( hoasinduction_lem3v2_f = $true ) )
& ( hoasinduction_gthm = $true )
& ( ( ! [X289: term,X290: subst] :
( ( sub @ one @ ( push @ X289 @ X290 ) )
= X289 )
=> ! [X291: term,X292: subst,X293: term > $o,X294: term > $o] :
( ( ( X294 @ one )
= $true )
| ( $true
!= ( X293 @ X291 ) )
| ~ ! [X295: term] :
( ( X294 @ X295 )
= ( X293 @ ( sub @ X295 @ ( push @ X291 @ X292 ) ) ) ) ) )
<=> ( pushprop_lem1v2_lthm = $true ) )
& ( one
= ( d2term @ d_one ) )
& ! [X296: d_subst] : ( d_id = X296 )
& ( ! [X297: term,X298: subst > term > subst > $o] :
( ~ ! [X299: subst > term > term] :
( ~ ! [X300: subst,X301: term,X302: subst] :
( ( X299 @ ( comp @ X300 @ X302 ) @ ( sub @ X301 @ X302 ) )
= ( sub @ ( X299 @ X300 @ X301 ) @ X302 ) )
| ( $true
= ( X298 @ id @ ( lam @ ( X299 @ sh @ one ) ) @ id ) )
| ~ ! [X303: term] :
( ( $true
= ( X298 @ id @ ( X299 @ id @ X303 ) @ id ) )
| ( ( X298 @ id @ X303 @ id )
!= $true ) ) )
| ~ ! [X304: subst,X305: subst,X306: term,X307: subst] :
( ( ( X298 @ X307 @ X306 @ ( comp @ X305 @ X304 ) )
!= $true )
| ( ( X298 @ ( comp @ X307 @ X305 ) @ ( sub @ X306 @ X305 ) @ X304 )
= $true ) )
| ( $true
= ( X298 @ id @ X297 @ id ) )
| ~ ! [X308: term] :
( ( $true
= ( X298 @ id @ X308 @ id ) )
| ( $true
!= ( var @ ( sub @ X308 @ id ) ) ) )
| ~ ! [X309: term,X310: term] :
( ( ( X298 @ id @ X310 @ id )
!= $true )
| ( ( X298 @ id @ ( ap @ ( sub @ X309 @ id ) @ X310 ) @ id )
= $true )
| ( $true
!= ( X298 @ id @ X309 @ id ) ) )
| ~ ! [X311: term,X312: subst,X313: subst,X314: subst] :
( ( $true
= ( X298 @ X313 @ X311 @ ( comp @ X312 @ X314 ) ) )
| ( ( X298 @ ( comp @ X313 @ X312 ) @ ( sub @ X311 @ X312 ) @ X314 )
!= $true ) ) )
<=> ( hoasinduction = $true ) )
& ( pushprop = $true )
& ( ulamvar1 != $true )
& ( hoasapinj1_gthm = $true )
& ( hoasinduction_lem1v2_gthm = $true )
& ( hoaslamnotvar_lthm = $true )
& ( ( hoasinduction_lem3v2 = $true )
<=> ! [X315: term,X316: subst > term > subst > $o,X317: term > $o] :
( ~ ! [X318: term] :
( ( X316 @ id @ X318 @ id )
= ( X317 @ X318 ) )
| ~ ! [X319: term] :
( ( ( X317 @ X319 )
!= $true )
| ( ( X317 @ ( sub @ X315 @ ( push @ X319 @ id ) ) )
= $true ) )
| ( ( X317 @ ( lam @ X315 ) )
= $true )
| ~ ! [X320: subst,X321: subst,X322: subst,X323: term] :
( ( ( X316 @ ( comp @ X321 @ X322 ) @ ( sub @ X323 @ X322 ) @ X320 )
!= $true )
| ( $true
= ( X316 @ X321 @ X323 @ ( comp @ X322 @ X320 ) ) ) )
| ~ ! [X324: subst,X325: subst,X326: term,X327: subst] :
( ( ( X316 @ X327 @ X326 @ ( comp @ X324 @ X325 ) )
!= $true )
| ( ( X316 @ ( comp @ X327 @ X324 ) @ ( sub @ X326 @ X324 ) @ X325 )
= $true ) )
| ~ ! [X328: subst > term > term] :
( ~ ! [X329: term] :
( ( ( X316 @ id @ X329 @ id )
!= $true )
| ( ( X316 @ id @ ( X328 @ id @ X329 ) @ id )
= $true ) )
| ( $true
= ( X316 @ id @ ( lam @ ( X328 @ sh @ one ) ) @ id ) )
| ~ ! [X330: term,X331: subst,X332: subst] :
( ( X328 @ ( comp @ X332 @ X331 ) @ ( sub @ X330 @ X331 ) )
= ( sub @ ( X328 @ X332 @ X330 ) @ X331 ) ) ) ) )
& ( pushprop_gthm = $true )
& ( apnotvar = $true )
& ( hoasinduction_lem2_lthm = $true )
& ( ( shinj = $true )
<=> ! [X333: term,X334: term] :
( ( X333 = X334 )
| ( ( sub @ X333 @ sh )
!= ( sub @ X334 @ sh ) ) ) )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ! [X335: term,X336: subst > term > subst > $o] :
( ~ ! [X337: subst > term > term] :
( ( ( X336 @ id @ ( lam @ ( X337 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X338: term] :
( ( $true
= ( X336 @ id @ ( X337 @ id @ X338 ) @ id ) )
| ( ( X336 @ id @ X338 @ id )
!= $true ) )
| ~ ! [X339: subst,X340: subst,X341: term] :
( ( X337 @ ( comp @ X340 @ X339 ) @ ( sub @ X341 @ X339 ) )
= ( sub @ ( X337 @ X340 @ X341 ) @ X339 ) ) )
| ( $true
= ( X336 @ id @ X335 @ id ) )
| ~ ! [X342: term,X343: term] :
( ( ( X336 @ id @ ( ap @ ( sub @ X342 @ id ) @ X343 ) @ id )
= $true )
| ( ( X336 @ id @ X342 @ id )
!= $true )
| ( ( X336 @ id @ X343 @ id )
!= $true ) ) )
<=> ( hoasinduction_no_psi_cond = $true ) )
& ( ! [X344: term] :
~ ! [X345: subst > term > term] :
( ( sub @ X344 @ ( push @ one @ sh ) )
!= ( X345 @ sh @ one ) )
<=> ( hoasinduction_lem3b_lthm = $true ) )
& ( hoasinduction_lem3_gthm = $true )
& ( hoasapnotvar_lthm = $true )
& ( ( hoaslamnotap = $true )
<=> ! [X346: subst > term > term,X347: term,X348: term] :
( ~ ! [X349: subst,X350: term,X351: subst] :
( ( X346 @ ( comp @ X351 @ X349 ) @ ( sub @ X350 @ X349 ) )
= ( sub @ ( X346 @ X351 @ X350 ) @ X349 ) )
| ( ( lam @ ( X346 @ sh @ one ) )
!= ( ap @ ( sub @ X347 @ id ) @ X348 ) ) ) )
& ( hoaslamnotap_lthm = $true )
& ( pushprop_lem0_gthm = $true )
& ( axabs = $true )
& ( axapp = $true )
& ( ( hoasinduction_lthm_3 = $true )
<=> ( ! [X352: subst > term > subst > $o] :
~ ! [X353: term > $o] :
~ ! [X354: term] :
( ( X352 @ id @ X354 @ id )
= ( X353 @ X354 ) )
=> ( ! [X355: term,X356: term > $o] :
( ~ ! [X357: term] :
( ( $true
= ( X356 @ X357 ) )
| ( $true
!= ( var @ X357 ) ) )
| ~ ! [X358: term,X359: term] :
( ( $true
= ( X356 @ ( ap @ X359 @ X358 ) ) )
| ( ( X356 @ X358 )
!= $true )
| ( ( X356 @ X359 )
!= $true ) )
| ( $true
= ( X356 @ X355 ) )
| ~ ! [X360: term] :
( ( ( X356 @ ( lam @ X360 ) )
= $true )
| ~ ! [X361: term] :
( ( $true
!= ( X356 @ X361 ) )
| ( $true
= ( X356 @ ( sub @ X360 @ ( push @ X361 @ id ) ) ) ) ) ) )
=> ( ! [X362: term] :
( ( sub @ X362 @ id )
= X362 )
=> ( ! [X363: subst > term > subst > $o,X364: term,X365: term > $o] :
( ~ ! [X366: term] :
( ( X363 @ id @ X366 @ id )
= ( X365 @ X366 ) )
| ~ ! [X367: subst > term > term] :
( ~ ! [X368: term] :
( ( ( X363 @ id @ X368 @ id )
!= $true )
| ( ( X363 @ id @ ( X367 @ id @ X368 ) @ id )
= $true ) )
| ~ ! [X369: subst,X370: subst,X371: term] :
( ( X367 @ ( comp @ X369 @ X370 ) @ ( sub @ X371 @ X370 ) )
= ( sub @ ( X367 @ X369 @ X371 ) @ X370 ) )
| ( ( X363 @ id @ ( lam @ ( X367 @ sh @ one ) ) @ id )
= $true ) )
| ( ( X365 @ ( lam @ X364 ) )
= $true )
| ~ ! [X372: term] :
( ( $true
= ( X365 @ ( sub @ X364 @ ( push @ X372 @ id ) ) ) )
| ( $true
!= ( X365 @ X372 ) ) ) )
=> ! [X373: term,X374: subst > term > subst > $o] :
( ~ ! [X375: term,X376: subst,X377: subst,X378: subst] :
( ( ( X374 @ X378 @ X375 @ ( comp @ X377 @ X376 ) )
= $true )
| ( ( X374 @ ( comp @ X378 @ X377 ) @ ( sub @ X375 @ X377 ) @ X376 )
!= $true ) )
| ~ ! [X379: term,X380: term] :
( ( ( X374 @ id @ X380 @ id )
!= $true )
| ( $true
!= ( X374 @ id @ X379 @ id ) )
| ( $true
= ( X374 @ id @ ( ap @ ( sub @ X379 @ id ) @ X380 ) @ id ) ) )
| ~ ! [X381: subst,X382: subst,X383: subst,X384: term] :
( ( ( X374 @ ( comp @ X383 @ X381 ) @ ( sub @ X384 @ X381 ) @ X382 )
= $true )
| ( $true
!= ( X374 @ X383 @ X384 @ ( comp @ X381 @ X382 ) ) ) )
| ~ ! [X385: subst > term > term] :
( ~ ! [X386: term] :
( ( ( X374 @ id @ X386 @ id )
!= $true )
| ( ( X374 @ id @ ( X385 @ id @ X386 ) @ id )
= $true ) )
| ~ ! [X387: subst,X388: term,X389: subst] :
( ( X385 @ ( comp @ X387 @ X389 ) @ ( sub @ X388 @ X389 ) )
= ( sub @ ( X385 @ X387 @ X388 ) @ X389 ) )
| ( $true
= ( X374 @ id @ ( lam @ ( X385 @ sh @ one ) ) @ id ) ) )
| ~ ! [X390: term] :
( ( ( var @ ( sub @ X390 @ id ) )
!= $true )
| ( ( X374 @ id @ X390 @ id )
= $true ) )
| ( ( X374 @ id @ X373 @ id )
= $true ) ) ) ) ) ) )
& ( ( induction2lem = $true )
<=> ! [X391: term,X392: subst,X393: term > $o] :
( ~ ! [X394: term] :
( ( $true
= ( X393 @ ( sub @ X394 @ X392 ) ) )
| ( $true
!= ( var @ X394 ) ) )
| ~ ! [X395: term,X396: term] :
( ( ( X393 @ X396 )
!= $true )
| ( ( X393 @ X395 )
!= $true )
| ( $true
= ( X393 @ ( ap @ X396 @ X395 ) ) ) )
| ( $true
= ( X393 @ ( sub @ X391 @ X392 ) ) )
| ~ ! [X397: term] :
( ( $true
= ( X393 @ ( lam @ X397 ) ) )
| ~ ! [X398: term] :
( ( $true
!= ( X393 @ X398 ) )
| ( $true
= ( X393 @ ( sub @ X397 @ ( push @ X398 @ id ) ) ) ) ) ) ) )
& ( ! [X399: term] :
( ( sub @ X399 @ id )
= X399 )
<=> ( termmset = $true ) )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& ( pushprop_lthm_orig = $true )
& ( ( ! [X400: subst] :
( ( comp @ id @ X400 )
= X400 )
=> ( ! [X401: subst] :
( ( comp @ X401 @ id )
= X401 )
=> ( ! [X402: subst] :
( ( comp @ id @ X402 )
= X402 )
& ! [X403: subst] :
( ( comp @ X403 @ id )
= X403 ) ) ) )
<=> ( substmonoid_lthm = $true ) )
& ( hoasinduction_lem3v2_gthm = $true )
& ( pushprop_lem1v2_gthm = $true )
& ( ! [X404: subst,X405: term > $o,X406: term > $o,X407: term] :
( ~ ! [X408: term] :
( ( X405 @ ( sub @ X408 @ ( push @ X407 @ X404 ) ) )
= ( X406 @ X408 ) )
| ( ( X406 @ one )
= $true )
| ( ( X405 @ X407 )
!= $true ) )
<=> ( pushprop_lem1v2 = $true ) )
& ( ( hoaslaminj = $true )
<=> ! [X409: subst,X410: subst > term > term,X411: term,X412: subst > term > term] :
( ( ( lam @ ( X412 @ sh @ one ) )
!= ( lam @ ( X410 @ sh @ one ) ) )
| ~ ! [X413: term,X414: subst,X415: subst] :
( ( sub @ ( X412 @ X414 @ X413 ) @ X415 )
= ( X412 @ ( comp @ X414 @ X415 ) @ ( sub @ X413 @ X415 ) ) )
| ( ( X410 @ X409 @ X411 )
= ( X412 @ X409 @ X411 ) )
| ~ ! [X416: subst,X417: subst,X418: term] :
( ( sub @ ( X410 @ X417 @ X418 ) @ X416 )
= ( X410 @ ( comp @ X417 @ X416 ) @ ( sub @ X418 @ X416 ) ) ) ) )
& ( axvarshift = $true )
& ( ! [X419: term,X420: subst > term > subst > $o] :
( ~ ! [X421: term] :
( ( ( X420 @ id @ ( sub @ X419 @ ( push @ X421 @ id ) ) @ id )
= $true )
| ( $true
!= ( X420 @ id @ X421 @ id ) ) )
| ( $true
= ( X420 @ id @ ( lam @ ( sub @ X419 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X422: subst > term > term] :
( ~ ! [X423: subst,X424: term,X425: subst] :
( ( X422 @ ( comp @ X423 @ X425 ) @ ( sub @ X424 @ X425 ) )
= ( sub @ ( X422 @ X423 @ X424 ) @ X425 ) )
| ~ ! [X426: term] :
( ( ( X420 @ id @ ( X422 @ id @ X426 ) @ id )
= $true )
| ( ( X420 @ id @ X426 @ id )
!= $true ) )
| ( ( X420 @ id @ ( lam @ ( X422 @ sh @ one ) ) @ id )
= $true ) ) )
<=> ( hoasinduction_lem3aa_lthm = $true ) )
& ( pushprop_lem2v2_gthm = $true )
& ( pushprop_lem3v2_lthm = $true )
& ( lamnotvar = $true )
& ( induction2_gthm = $true )
& ( pushprop_lem3v2 = $true )
& ! [X427: term] :
? [X428: d_term] :
( ( d2term @ X428 )
= X427 )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( ( hoasinduction_lem3_lthm = $true )
<=> ( ! [X429: term] :
( ( sub @ X429 @ id )
= X429 )
=> ( ! [X430: subst > term > subst > $o,X431: term] :
( ~ ! [X432: subst > term > term] :
( ~ ! [X433: subst,X434: term,X435: subst] :
( ( sub @ ( X432 @ X435 @ X434 ) @ X433 )
= ( X432 @ ( comp @ X435 @ X433 ) @ ( sub @ X434 @ X433 ) ) )
| ( ( X430 @ id @ ( lam @ ( X432 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X436: term] :
( ( ( X430 @ id @ X436 @ id )
!= $true )
| ( $true
= ( X430 @ id @ ( X432 @ id @ X436 ) @ id ) ) ) )
| ( ( X430 @ id @ ( lam @ ( sub @ X431 @ ( push @ one @ sh ) ) ) @ id )
= $true )
| ~ ! [X437: term] :
( ( $true
= ( X430 @ id @ ( sub @ X431 @ ( push @ X437 @ id ) ) @ id ) )
| ( $true
!= ( X430 @ id @ X437 @ id ) ) ) )
=> ! [X438: term,X439: subst > term > subst > $o] :
( ~ ! [X440: term] :
( ( ( X439 @ id @ X440 @ id )
!= $true )
| ( ( X439 @ id @ ( sub @ X438 @ ( push @ X440 @ id ) ) @ id )
= $true ) )
| ( $true
= ( X439 @ id @ ( lam @ X438 ) @ id ) )
| ~ ! [X441: subst,X442: term,X443: subst,X444: subst] :
( ( $true
!= ( X439 @ X441 @ X442 @ ( comp @ X444 @ X443 ) ) )
| ( ( X439 @ ( comp @ X441 @ X444 ) @ ( sub @ X442 @ X444 ) @ X443 )
= $true ) )
| ~ ! [X445: subst,X446: term,X447: subst,X448: subst] :
( ( $true
= ( X439 @ X447 @ X446 @ ( comp @ X445 @ X448 ) ) )
| ( ( X439 @ ( comp @ X447 @ X445 ) @ ( sub @ X446 @ X445 ) @ X448 )
!= $true ) )
| ~ ! [X449: subst > term > term] :
( ( ( X439 @ id @ ( lam @ ( X449 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X450: term] :
( ( ( X439 @ id @ ( X449 @ id @ X450 ) @ id )
= $true )
| ( ( X439 @ id @ X450 @ id )
!= $true ) )
| ~ ! [X451: subst,X452: term,X453: subst] :
( ( X449 @ ( comp @ X453 @ X451 ) @ ( sub @ X452 @ X451 ) )
= ( sub @ ( X449 @ X453 @ X452 ) @ X451 ) ) ) ) ) ) )
& ( ( hoasinduction_lem0_lthm = $true )
<=> ! [X454: subst > term > subst > $o] :
~ ! [X455: term > $o] :
~ ! [X456: term] :
( ( X454 @ id @ X456 @ id )
= ( X455 @ X456 ) ) )
& ( pushprop_lem1_gthm = $true )
& ( hoasinduction_lem1 = $true )
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( hoasapnotvar_gthm = $true )
& ( hoaslamnotap_gthm = $true )
& ( ( hoasinduction_lem2 = $true )
<=> ! [X457: term,X458: term,X459: subst > term > subst > $o] :
( ( ( X459 @ id @ X458 @ id )
!= $true )
| ~ ! [X460: subst,X461: subst,X462: term,X463: subst] :
( ( ( X459 @ X463 @ X462 @ ( comp @ X460 @ X461 ) )
= $true )
| ( ( X459 @ ( comp @ X463 @ X460 ) @ ( sub @ X462 @ X460 ) @ X461 )
!= $true ) )
| ( $true
= ( X459 @ id @ ( ap @ X457 @ X458 ) @ id ) )
| ~ ! [X464: subst,X465: term,X466: subst,X467: subst] :
( ( $true
!= ( X459 @ X466 @ X465 @ ( comp @ X464 @ X467 ) ) )
| ( $true
= ( X459 @ ( comp @ X466 @ X464 ) @ ( sub @ X465 @ X464 ) @ X467 ) ) )
| ( ( X459 @ id @ X457 @ id )
!= $true )
| ~ ! [X468: term,X469: term] :
( ( $true
!= ( X459 @ id @ X468 @ id ) )
| ( ( X459 @ id @ ( ap @ ( sub @ X468 @ id ) @ X469 ) @ id )
= $true )
| ( $true
!= ( X459 @ id @ X469 @ id ) ) ) ) )
& ( ( hoasinduction_lem3v2a_lthm = $true )
<=> ( ! [X470: term] :
~ ! [X471: subst > term > term] :
~ ! [X472: subst,X473: term] :
( ( X471 @ X472 @ X473 )
= ( sub @ X470 @ ( push @ X473 @ X472 ) ) )
=> ( ! [X474: term] :
( ( sub @ X474 @ id )
= X474 )
=> ! [X475: subst > term > subst > $o,X476: term,X477: term > $o] :
( ~ ! [X478: subst > term > term] :
( ( ( X475 @ id @ ( lam @ ( X478 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X479: term] :
( ( $true
!= ( X475 @ id @ X479 @ id ) )
| ( $true
= ( X475 @ id @ ( X478 @ id @ X479 ) @ id ) ) )
| ~ ! [X480: subst,X481: subst,X482: term] :
( ( X478 @ ( comp @ X481 @ X480 ) @ ( sub @ X482 @ X480 ) )
= ( sub @ ( X478 @ X481 @ X482 ) @ X480 ) ) )
| ~ ! [X483: term] :
( ( X475 @ id @ X483 @ id )
= ( X477 @ X483 ) )
| ( ( X477 @ ( lam @ X476 ) )
= $true )
| ~ ! [X484: term] :
( ( $true
!= ( X477 @ X484 ) )
| ( $true
= ( X477 @ ( sub @ X476 @ ( push @ X484 @ id ) ) ) ) ) ) ) ) )
& ( ( hoasapinj2 = $true )
<=> ! [X485: term,X486: term,X487: term,X488: term] :
( ( ( ap @ ( sub @ X487 @ id ) @ X486 )
!= ( ap @ ( sub @ X485 @ id ) @ X488 ) )
| ( X486 = X488 ) ) )
& ! [X489: subst] :
? [X490: d_subst] :
( ( d2subst @ X490 )
= X489 )
& ( ( hoasapinj1 = $true )
<=> ! [X491: term,X492: term,X493: term,X494: term] :
( ( ( ap @ ( sub @ X493 @ id ) @ X492 )
!= ( ap @ ( sub @ X494 @ id ) @ X491 ) )
| ( X493 = X494 ) ) )
& ( ( hoasinduction_lem3a = $true )
<=> ! [X495: term,X496: subst > term > subst > $o] :
( ~ ! [X497: term] :
( ( ( X496 @ id @ ( sub @ X495 @ ( push @ X497 @ id ) ) @ id )
= $true )
| ( ( X496 @ id @ X497 @ id )
!= $true ) )
| ( $true
= ( X496 @ id @ ( lam @ X495 ) @ id ) )
| ~ ! [X498: subst > term > term] :
( ~ ! [X499: subst,X500: subst,X501: term] :
( ( sub @ ( X498 @ X499 @ X501 ) @ X500 )
= ( X498 @ ( comp @ X499 @ X500 ) @ ( sub @ X501 @ X500 ) ) )
| ( ( X496 @ id @ ( lam @ ( X498 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X502: term] :
( ( ( X496 @ id @ X502 @ id )
!= $true )
| ( $true
= ( X496 @ id @ ( X498 @ id @ X502 ) @ id ) ) ) ) ) )
& ( ( hoasinduction_lem3aa = $true )
<=> ! [X503: subst > term > subst > $o,X504: term] :
( ( $true
= ( X503 @ id @ ( lam @ ( sub @ X504 @ ( push @ one @ sh ) ) ) @ id ) )
| ~ ! [X505: term] :
( ( ( X503 @ id @ ( sub @ X504 @ ( push @ X505 @ id ) ) @ id )
= $true )
| ( ( X503 @ id @ X505 @ id )
!= $true ) )
| ~ ! [X506: subst > term > term] :
( ( ( X503 @ id @ ( lam @ ( X506 @ sh @ one ) ) @ id )
= $true )
| ~ ! [X507: subst,X508: subst,X509: term] :
( ( X506 @ ( comp @ X507 @ X508 ) @ ( sub @ X509 @ X508 ) )
= ( sub @ ( X506 @ X507 @ X509 ) @ X508 ) )
| ~ ! [X510: term] :
( ( $true
!= ( X503 @ id @ X510 @ id ) )
| ( $true
= ( X503 @ id @ ( X506 @ id @ X510 ) @ id ) ) ) ) ) )
& ( ulamvarind = $true )
& ( ( ! [X511: term,X512: subst] :
( ( sub @ one @ ( push @ X511 @ X512 ) )
= X511 )
=> ( ! [X513: subst,X514: term] :
( ( comp @ sh @ ( push @ X514 @ X513 ) )
= X513 )
=> ( ! [X515: subst] :
( ( comp @ X515 @ id )
= X515 )
=> ( ! [X516: term,X517: term > $o] :
( ~ ! [X518: term] :
( ( $true
!= ( X517 @ X518 ) )
| ( ( X517 @ ( lam @ X518 ) )
= $true ) )
| ~ ! [X519: term] :
( ( $true
!= ( var @ X519 ) )
| ( $true
= ( X517 @ X519 ) ) )
| ( $true
= ( X517 @ X516 ) )
| ~ ! [X520: term,X521: term] :
( ( ( X517 @ ( ap @ X521 @ X520 ) )
= $true )
| ( $true
!= ( X517 @ X521 ) )
| ( ( X517 @ X520 )
!= $true ) ) )
=> ! [X522: subst,X523: term > $o,X524: term] :
( ~ ! [X525: term] :
( ( ( X523 @ ( lam @ X525 ) )
= $true )
| ~ ! [X526: term] :
( ( ( X523 @ ( sub @ X525 @ ( push @ X526 @ id ) ) )
= $true )
| ( $true
!= ( X523 @ X526 ) ) ) )
| ~ ! [X527: term,X528: term] :
( ( ( X523 @ ( ap @ X528 @ X527 ) )
= $true )
| ( ( X523 @ X528 )
!= $true )
| ( ( X523 @ X527 )
!= $true ) )
| ( $true
= ( X523 @ ( sub @ X524 @ X522 ) ) )
| ~ ! [X529: term] :
( ( ( X523 @ ( sub @ X529 @ X522 ) )
= $true )
| ( ( var @ X529 )
!= $true ) ) ) ) ) ) )
<=> ( induction2lem_lthm = $true ) )
& ( hoasinduction_lem1_lthm = $true )
& ( ! [X530: subst > term > subst > $o] :
~ ! [X531: term > $o] :
~ ! [X532: term] :
( ( X530 @ id @ X532 @ id )
= ( X531 @ X532 ) )
<=> ( hoasinduction_lem0 = $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 ) ) ) ) )
& ( ! [X538: subst] :
( ( comp @ id @ X538 )
= X538 )
<=> ( axidl = $true ) )
& ( termmset_gthm = $true )
& ( hoasapinj2_gthm = $true )
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ! [X539: term] :
~ ! [X540: subst > term > term] :
( ( X540 @ sh @ one )
!= ( sub @ X539 @ ( push @ one @ sh ) ) )
<=> ( hoasinduction_lem3b = $true ) )
& ! [X541: d_term] : ( d_one = X541 )
& ( hoasinduction_lem3a_gthm = $true )
& ( ( ! [X542: term,X543: term,X544: term,X545: term] :
( ( ( ap @ X542 @ X544 )
!= ( ap @ X545 @ X543 ) )
| ( X543 = X544 ) )
=> ! [X546: term,X547: term,X548: term,X549: term] :
( ( ( ap @ ( sub @ X546 @ id ) @ X549 )
!= ( ap @ ( sub @ X547 @ id ) @ X548 ) )
| ( X548 = X549 ) ) )
<=> ( hoasapinj2_lthm = $true ) )
& ( hoasinduction_lem3b_gthm = $true ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( hoasinduction_no_psi_cond_lthm
<=> ( ! [X0: subst > term > subst > $o] :
~ ! [X1: term > $o] :
~ ! [X2: term] :
( ( X0 @ id @ X2 @ id )
= ( X1 @ X2 ) )
=> ( ! [X3: term,X4: term > $o] :
( ( X4 @ X3 )
| ~ ! [X5: term,X6: term] :
( ~ ( X4 @ X5 )
| ( X4 @ ( ap @ X5 @ X6 ) )
| ~ ( X4 @ X6 ) )
| ~ ! [X7: term] :
( ( X4 @ X7 )
| ~ ( var @ X7 ) )
| ~ ! [X8: term] :
( ( X4 @ ( lam @ X8 ) )
| ~ ! [X9: term] :
( ~ ( X4 @ X9 )
| ( X4 @ ( sub @ X8 @ ( push @ X9 @ id ) ) ) ) ) )
=> ( ! [X10: term] :
( ( sub @ X10 @ id )
= X10 )
=> ( ! [X11: term,X12: subst > term > subst > $o,X13: term > $o] :
( ~ ! [X14: term] :
( ( X13 @ X14 )
= ( X12 @ id @ X14 @ id ) )
| ~ ! [X15: subst > term > term] :
( ~ ! [X16: term] :
( ~ ( X12 @ id @ X16 @ id )
| ( X12 @ id @ ( X15 @ id @ X16 ) @ id ) )
| ~ ! [X17: term,X18: subst,X19: subst] :
( ( sub @ ( X15 @ X19 @ X17 ) @ X18 )
= ( X15 @ ( comp @ X19 @ X18 ) @ ( sub @ X17 @ X18 ) ) )
| ( X12 @ id @ ( lam @ ( X15 @ sh @ one ) ) @ id ) )
| ( X13 @ ( lam @ X11 ) )
| ~ ! [X20: term] :
( ~ ( X13 @ X20 )
| ( X13 @ ( sub @ X11 @ ( push @ X20 @ id ) ) ) ) )
=> ! [X21: subst > term > subst > $o,X22: term] :
( ~ ! [X23: term,X24: term] :
( ~ ( X21 @ id @ X24 @ id )
| ( X21 @ id @ ( ap @ ( sub @ X23 @ id ) @ X24 ) @ id )
| ~ ( X21 @ id @ X23 @ id ) )
| ~ ! [X25: subst > term > term] :
( ~ ! [X26: term] :
( ~ ( X21 @ id @ X26 @ id )
| ( X21 @ id @ ( X25 @ id @ X26 ) @ id ) )
| ( X21 @ id @ ( lam @ ( X25 @ sh @ one ) ) @ id )
| ~ ! [X27: term,X28: subst,X29: subst] :
( ( X25 @ ( comp @ X28 @ X29 ) @ ( sub @ X27 @ X29 ) )
= ( sub @ ( X25 @ X28 @ X27 ) @ X29 ) ) )
| ( X21 @ id @ X22 @ id ) ) ) ) ) ) )
& ( ! [X30: term,X31: term] :
( ( ( lam @ X30 )
!= ( lam @ X31 ) )
| ( X30 = X31 ) )
<=> laminj )
& ( hoasinduction_lem3
<=> ! [X32: term,X33: subst > term > subst > $o] :
( ( X33 @ id @ ( lam @ X32 ) @ id )
| ~ ! [X34: term,X35: subst,X36: subst,X37: subst] :
( ( X33 @ X36 @ X34 @ ( comp @ X37 @ X35 ) )
| ~ ( X33 @ ( comp @ X36 @ X37 ) @ ( sub @ X34 @ X37 ) @ X35 ) )
| ~ ! [X38: subst,X39: subst,X40: subst,X41: term] :
( ~ ( X33 @ X39 @ X41 @ ( comp @ X40 @ X38 ) )
| ( X33 @ ( comp @ X39 @ X40 ) @ ( sub @ X41 @ X40 ) @ X38 ) )
| ~ ! [X42: subst > term > term] :
( ~ ! [X43: term] :
( ( X33 @ id @ ( X42 @ id @ X43 ) @ id )
| ~ ( X33 @ id @ X43 @ id ) )
| ( X33 @ id @ ( lam @ ( X42 @ sh @ one ) ) @ id )
| ~ ! [X44: term,X45: subst,X46: subst] :
( ( X42 @ ( comp @ X46 @ X45 ) @ ( sub @ X44 @ X45 ) )
= ( sub @ ( X42 @ X46 @ X44 ) @ X45 ) ) )
| ~ ! [X47: term] :
( ( X33 @ id @ ( sub @ X32 @ ( push @ X47 @ id ) ) @ id )
| ~ ( X33 @ id @ X47 @ id ) ) ) )
& ( apinj2
<=> ! [X48: term,X49: term,X50: term,X51: term] :
( ( X48 = X51 )
| ( ( ap @ X49 @ X48 )
!= ( ap @ X50 @ X51 ) ) ) )
& ulamvarsh
& axclos
& hoasinduction_lem1v2
& ( axidr
<=> ! [X52: subst] :
( ( comp @ X52 @ id )
= X52 ) )
& ( hoasinduction_lem2v2
<=> ! [X53: term,X54: term > $o,X55: subst > term > subst > $o,X56: term] :
( ~ ( X54 @ X53 )
| ~ ! [X57: subst,X58: term,X59: subst,X60: subst] :
( ( X55 @ ( comp @ X60 @ X57 ) @ ( sub @ X58 @ X57 ) @ X59 )
| ~ ( X55 @ X60 @ X58 @ ( comp @ X57 @ X59 ) ) )
| ~ ! [X61: term,X62: term] :
( ~ ( X55 @ id @ X62 @ id )
| ( X55 @ id @ ( ap @ ( sub @ X62 @ id ) @ X61 ) @ id )
| ~ ( X55 @ id @ X61 @ id ) )
| ( X54 @ ( ap @ X53 @ X56 ) )
| ~ ( X54 @ X56 )
| ~ ! [X63: term] :
( ( X55 @ id @ X63 @ id )
= ( X54 @ X63 ) )
| ~ ! [X64: subst,X65: term,X66: subst,X67: subst] :
( ~ ( X55 @ ( comp @ X66 @ X67 ) @ ( sub @ X65 @ X67 ) @ X64 )
| ( X55 @ X66 @ X65 @ ( comp @ X67 @ X64 ) ) ) ) )
& ( hoasapinj1_lthm
<=> ( ! [X68: term] :
( ( sub @ X68 @ id )
= X68 )
=> ( ! [X69: term,X70: term,X71: term,X72: term] :
( ( ( ap @ X69 @ X70 )
!= ( ap @ X71 @ X72 ) )
| ( X69 = X71 ) )
=> ! [X73: term,X74: term,X75: term,X76: term] :
( ( ( ap @ ( sub @ X74 @ id ) @ X76 )
!= ( ap @ ( sub @ X73 @ id ) @ X75 ) )
| ( X73 = X74 ) ) ) ) )
& ( ! [X77: subst,X78: term] :
( ( sub @ one @ ( push @ X78 @ X77 ) )
= X78 )
<=> axvarcons )
& ( ( ^ [X79: subst > term > subst > $o,X80: term > $o] :
! [X81: term] :
( ( X80 @ X81 )
= ( X79 @ id @ X81 @ id ) ) )
= hoasinduction_p_and_p_prime )
& pushprop_lem2v2
& axassoc
& ~ ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
& ( ( ! [X82: subst] :
( ( comp @ id @ X82 )
= X82 )
& ! [X83: subst] :
( ( comp @ X83 @ id )
= X83 ) )
<=> substmonoid )
& ( hoasinduction_lem3a_lthm
<=> ( ! [X84: term] :
( ( sub @ X84 @ id )
= X84 )
=> ( ! [X85: subst > term > subst > $o,X86: term] :
( ( X85 @ id @ ( lam @ ( sub @ X86 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X87: subst > term > term] :
( ~ ! [X88: term,X89: subst,X90: subst] :
( ( X87 @ ( comp @ X90 @ X89 ) @ ( sub @ X88 @ X89 ) )
= ( sub @ ( X87 @ X90 @ X88 ) @ X89 ) )
| ~ ! [X91: term] :
( ( X85 @ id @ ( X87 @ id @ X91 ) @ id )
| ~ ( X85 @ id @ X91 @ id ) )
| ( X85 @ id @ ( lam @ ( X87 @ sh @ one ) ) @ id ) )
| ~ ! [X92: term] :
( ~ ( X85 @ id @ X92 @ id )
| ( X85 @ id @ ( sub @ X86 @ ( push @ X92 @ id ) ) @ id ) ) )
=> ! [X93: subst > term > subst > $o,X94: term] :
( ( X93 @ id @ ( lam @ X94 ) @ id )
| ~ ! [X95: subst > term > term] :
( ~ ! [X96: term] :
( ( X93 @ id @ ( X95 @ id @ X96 ) @ id )
| ~ ( X93 @ id @ X96 @ id ) )
| ~ ! [X97: term,X98: subst,X99: subst] :
( ( X95 @ ( comp @ X99 @ X98 ) @ ( sub @ X97 @ X98 ) )
= ( sub @ ( X95 @ X99 @ X97 ) @ X98 ) )
| ( X93 @ id @ ( lam @ ( X95 @ sh @ one ) ) @ id ) )
| ~ ! [X100: term] :
( ~ ( X93 @ id @ X100 @ id )
| ( X93 @ id @ ( sub @ X94 @ ( push @ X100 @ id ) ) @ id ) ) ) ) ) )
& ( hoasinduction_lem3v2_lthm
<=> ( ! [X101: term] :
( ( sub @ X101 @ id )
= X101 )
=> ! [X102: term > $o,X103: subst > term > subst > $o,X104: term] :
( ~ ! [X105: term] :
( ~ ( X102 @ X105 )
| ( X102 @ ( sub @ X104 @ ( push @ X105 @ id ) ) ) )
| ~ ! [X106: subst > term > term] :
( ~ ! [X107: subst,X108: subst,X109: term] :
( ( X106 @ ( comp @ X108 @ X107 ) @ ( sub @ X109 @ X107 ) )
= ( sub @ ( X106 @ X108 @ X109 ) @ X107 ) )
| ~ ! [X110: term] :
( ~ ( X103 @ id @ X110 @ id )
| ( X103 @ id @ ( X106 @ id @ X110 ) @ id ) )
| ( X103 @ id @ ( lam @ ( X106 @ sh @ one ) ) @ id ) )
| ~ ! [X111: subst,X112: term,X113: subst,X114: subst] :
( ( X103 @ ( comp @ X111 @ X113 ) @ ( sub @ X112 @ X113 ) @ X114 )
| ~ ( X103 @ X111 @ X112 @ ( comp @ X113 @ X114 ) ) )
| ~ ! [X115: term] :
( ( X103 @ id @ X115 @ id )
= ( X102 @ X115 ) )
| ( X102 @ ( lam @ X104 ) )
| ~ ! [X116: subst,X117: subst,X118: term,X119: subst] :
( ~ ( X103 @ ( comp @ X117 @ X116 ) @ ( sub @ X118 @ X116 ) @ X119 )
| ( X103 @ X117 @ X118 @ ( comp @ X116 @ X119 ) ) ) ) ) )
& ( ! [X120: term,X121: subst] :
( ( comp @ sh @ ( push @ X120 @ X121 ) )
= X121 )
<=> axshiftcons )
& ( pushprop_lem0
<=> ! [X122: term > $o,X123: subst,X124: term] :
~ ! [X125: term > $o] :
~ ! [X126: term] :
( ( X125 @ X126 )
= ( X122 @ ( sub @ X126 @ ( push @ X124 @ X123 ) ) ) ) )
& ~ lamnotap
& ( ! [X127: term] :
~ ! [X128: subst > term > term] :
~ ! [X129: term,X130: subst] :
( ( sub @ X127 @ ( push @ X129 @ X130 ) )
= ( X128 @ X130 @ X129 ) )
<=> hoasinduction_lem3v2_f_lthm )
& axmap
& hoasinduction_lem2v2_gthm
& ( induction2_lthm
<=> ( ! [X131: term] :
( ( sub @ X131 @ id )
= X131 )
=> ( ! [X132: subst,X133: term > $o,X134: term] :
( ~ ! [X135: term] :
( ( X133 @ ( lam @ X135 ) )
| ~ ! [X136: term] :
( ( X133 @ ( sub @ X135 @ ( push @ X136 @ id ) ) )
| ~ ( X133 @ X136 ) ) )
| ~ ! [X137: term,X138: term] :
( ( X133 @ ( ap @ X137 @ X138 ) )
| ~ ( X133 @ X138 )
| ~ ( X133 @ X137 ) )
| ~ ! [X139: term] :
( ( X133 @ ( sub @ X139 @ X132 ) )
| ~ ( var @ X139 ) )
| ( X133 @ ( sub @ X134 @ X132 ) ) )
=> ! [X140: term,X141: term > $o] :
( ~ ! [X142: term] :
( ~ ( var @ X142 )
| ( X141 @ X142 ) )
| ~ ! [X143: term,X144: term] :
( ~ ( X141 @ X144 )
| ( X141 @ ( ap @ X143 @ X144 ) )
| ~ ( X141 @ X143 ) )
| ~ ! [X145: term] :
( ~ ! [X146: term] :
( ~ ( X141 @ X146 )
| ( X141 @ ( sub @ X145 @ ( push @ X146 @ id ) ) ) )
| ( X141 @ ( lam @ X145 ) ) )
| ( X141 @ X140 ) ) ) ) )
& ( pushprop_lem0_lthm
<=> ! [X147: subst,X148: term > $o,X149: term] :
~ ! [X150: term > $o] :
~ ! [X151: term] :
( ( X148 @ ( sub @ X151 @ ( push @ X149 @ X147 ) ) )
= ( X150 @ X151 ) ) )
& induction2lem_gthm
& ( pushprop_lem1_lthm
<=> ( ! [X152: term,X153: subst] :
( ( sub @ one @ ( push @ X152 @ X153 ) )
= X152 )
=> ( ! [X154: subst,X155: term] :
( ( comp @ sh @ ( push @ X155 @ X154 ) )
= X154 )
=> ! [X156: term,X157: term > $o,X158: subst,X159: term,X160: term > $o] :
( ~ ( X157 @ X156 )
| ( X160 @ ( sub @ X156 @ ( push @ X159 @ X158 ) ) ) ) ) ) )
& ( hoasinduction_lem3v2a
<=> ! [X161: term > $o,X162: subst > term > subst > $o,X163: term] :
( ~ ! [X164: term] :
( ( X162 @ id @ X164 @ id )
= ( X161 @ X164 ) )
| ~ ! [X165: subst > term > term] :
( ~ ! [X166: term] :
( ( X162 @ id @ ( X165 @ id @ X166 ) @ id )
| ~ ( X162 @ id @ X166 @ id ) )
| ( X162 @ id @ ( lam @ ( X165 @ sh @ one ) ) @ id )
| ~ ! [X167: subst,X168: term,X169: subst] :
( ( X165 @ ( comp @ X169 @ X167 ) @ ( sub @ X168 @ X167 ) )
= ( sub @ ( X165 @ X169 @ X168 ) @ X167 ) ) )
| ~ ! [X170: term] :
( ~ ( X161 @ X170 )
| ( X161 @ ( sub @ X163 @ ( push @ X170 @ id ) ) ) )
| ( X161 @ ( lam @ X163 ) ) ) )
& ( hoasinduction_lthm
<=> ( ! [X171: term > $o,X172: term] :
( ( X171 @ X172 )
| ~ ! [X173: term] :
( ~ ! [X174: term] :
( ( X171 @ ( sub @ X173 @ ( push @ X174 @ id ) ) )
| ~ ( X171 @ X174 ) )
| ( X171 @ ( lam @ X173 ) ) )
| ~ ! [X175: term,X176: term] :
( ~ ( X171 @ X176 )
| ( X171 @ ( ap @ X176 @ X175 ) )
| ~ ( X171 @ X175 ) )
| ~ ! [X177: term] :
( ~ ( var @ X177 )
| ( X171 @ X177 ) ) )
=> ( ! [X178: term,X179: term,X180: subst > term > subst > $o] :
( ~ ( X180 @ id @ X179 @ id )
| ( X180 @ id @ ( ap @ X178 @ X179 ) @ id )
| ~ ! [X181: subst,X182: subst,X183: term,X184: subst] :
( ~ ( X180 @ X182 @ X183 @ ( comp @ X184 @ X181 ) )
| ( X180 @ ( comp @ X182 @ X184 ) @ ( sub @ X183 @ X184 ) @ X181 ) )
| ~ ( X180 @ id @ X178 @ id )
| ~ ! [X185: subst,X186: subst,X187: term,X188: subst] :
( ( X180 @ X188 @ X187 @ ( comp @ X186 @ X185 ) )
| ~ ( X180 @ ( comp @ X188 @ X186 ) @ ( sub @ X187 @ X186 ) @ X185 ) )
| ~ ! [X189: term,X190: term] :
( ~ ( X180 @ id @ X190 @ id )
| ( X180 @ id @ ( ap @ ( sub @ X190 @ id ) @ X189 ) @ id )
| ~ ( X180 @ id @ X189 @ id ) ) )
=> ( ! [X191: term,X192: subst > term > subst > $o] :
( ~ ! [X193: subst,X194: term,X195: subst,X196: subst] :
( ~ ( X192 @ X196 @ X194 @ ( comp @ X193 @ X195 ) )
| ( X192 @ ( comp @ X196 @ X193 ) @ ( sub @ X194 @ X193 ) @ X195 ) )
| ~ ! [X197: subst,X198: subst,X199: term,X200: subst] :
( ~ ( X192 @ ( comp @ X200 @ X198 ) @ ( sub @ X199 @ X198 ) @ X197 )
| ( X192 @ X200 @ X199 @ ( comp @ X198 @ X197 ) ) )
| ~ ! [X201: term] :
( ~ ( X192 @ id @ X201 @ id )
| ( X192 @ id @ ( sub @ X191 @ ( push @ X201 @ id ) ) @ id ) )
| ( X192 @ id @ ( lam @ X191 ) @ id )
| ~ ! [X202: subst > term > term] :
( ~ ! [X203: term,X204: subst,X205: subst] :
( ( X202 @ ( comp @ X204 @ X205 ) @ ( sub @ X203 @ X205 ) )
= ( sub @ ( X202 @ X204 @ X203 ) @ X205 ) )
| ~ ! [X206: term] :
( ~ ( X192 @ id @ X206 @ id )
| ( X192 @ id @ ( X202 @ id @ X206 ) @ id ) )
| ( X192 @ id @ ( lam @ ( X202 @ sh @ one ) ) @ id ) ) )
=> ! [X207: subst > term > subst > $o,X208: term] :
( ~ ! [X209: term,X210: term] :
( ( X207 @ id @ ( ap @ ( sub @ X210 @ id ) @ X209 ) @ id )
| ~ ( X207 @ id @ X209 @ id )
| ~ ( X207 @ id @ X210 @ id ) )
| ~ ! [X211: subst,X212: subst,X213: subst,X214: term] :
( ( X207 @ X213 @ X214 @ ( comp @ X211 @ X212 ) )
| ~ ( X207 @ ( comp @ X213 @ X211 ) @ ( sub @ X214 @ X211 ) @ X212 ) )
| ~ ! [X215: subst,X216: subst,X217: term,X218: subst] :
( ~ ( X207 @ X216 @ X217 @ ( comp @ X215 @ X218 ) )
| ( X207 @ ( comp @ X216 @ X215 ) @ ( sub @ X217 @ X215 ) @ X218 ) )
| ~ ! [X219: term] :
( ( X207 @ id @ X219 @ id )
| ~ ( var @ ( sub @ X219 @ id ) ) )
| ~ ! [X220: subst > term > term] :
( ~ ! [X221: subst,X222: term,X223: subst] :
( ( sub @ ( X220 @ X223 @ X222 ) @ X221 )
= ( X220 @ ( comp @ X223 @ X221 ) @ ( sub @ X222 @ X221 ) ) )
| ( X207 @ id @ ( lam @ ( X220 @ sh @ one ) ) @ id )
| ~ ! [X224: term] :
( ~ ( X207 @ id @ X224 @ id )
| ( X207 @ id @ ( X220 @ id @ X224 ) @ id ) ) )
| ( X207 @ id @ X208 @ id ) ) ) ) ) )
& hoaslaminj_gthm
& ( ! [X225: term,X226: subst > term > subst > $o] :
( ~ ! [X227: term] :
( ~ ( X226 @ id @ X227 @ id )
| ( X226 @ id @ ( sub @ X225 @ ( push @ X227 @ id ) ) @ id ) )
| ( X226 @ id @ ( lam @ ( sub @ X225 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X228: term,X229: subst > term > term] :
( ~ ! [X230: subst,X231: term,X232: subst] :
( ( sub @ ( X229 @ X232 @ X231 ) @ X230 )
= ( sub @ ( sub @ X228 @ ( push @ X231 @ X232 ) ) @ X230 ) )
| ~ ! [X233: subst,X234: term,X235: subst] :
( ( sub @ X228 @ ( push @ ( sub @ X234 @ X235 ) @ ( comp @ X233 @ X235 ) ) )
= ( X229 @ ( comp @ X233 @ X235 ) @ ( sub @ X234 @ X235 ) ) )
| ~ ! [X236: term] :
( ~ ( X226 @ id @ X236 @ id )
| ( X226 @ id @ ( X229 @ id @ X236 ) @ id ) )
| ( X226 @ id @ ( lam @ ( X229 @ sh @ one ) ) @ id ) ) )
<=> hoasinduction_lem3aaa )
& hoasapnotvar
& ! [X237: d_term,X238: d_term] :
( ( ( d2term @ X237 )
= ( d2term @ X238 ) )
=> ( X237 = X238 ) )
& ( ( d2subst @ d_id )
= sh )
& hoaslamnotvar_gthm
& ( ! [X239: term] :
( ( sub @ X239 @ id )
= X239 )
<=> axvarid )
& ( hoaslaminj_lthm
<=> ( ! [X240: subst,X241: term] :
( ( sub @ one @ ( push @ X241 @ X240 ) )
= X241 )
=> ( ! [X242: term,X243: subst] :
( ( comp @ sh @ ( push @ X242 @ X243 ) )
= X243 )
=> ( ! [X244: term,X245: term] :
( ( ( lam @ X244 )
!= ( lam @ X245 ) )
| ( X244 = X245 ) )
=> ! [X246: subst,X247: term,X248: subst > term > term,X249: subst > term > term] :
( ( ( X249 @ X246 @ X247 )
= ( X248 @ X246 @ X247 ) )
| ~ ! [X250: term,X251: subst,X252: subst] :
( ( X249 @ ( comp @ X251 @ X252 ) @ ( sub @ X250 @ X252 ) )
= ( sub @ ( X249 @ X251 @ X250 ) @ X252 ) )
| ( ( lam @ ( X248 @ sh @ one ) )
!= ( lam @ ( X249 @ sh @ one ) ) )
| ~ ! [X253: subst,X254: term,X255: subst] :
( ( sub @ ( X248 @ X253 @ X254 ) @ X255 )
= ( X248 @ ( comp @ X253 @ X255 ) @ ( sub @ X254 @ X255 ) ) ) ) ) ) ) )
& hoaslamnotvar
& ( termmset_lthm
<=> ( ! [X256: term] :
( ( sub @ X256 @ id )
= X256 )
=> ! [X257: term] :
( ( sub @ X257 @ id )
= X257 ) ) )
& substmonoid_gthm
& ( induction
<=> ! [X258: term,X259: term > $o] :
( ~ ! [X260: term] :
( ~ ( X259 @ X260 )
| ( X259 @ ( lam @ X260 ) ) )
| ( X259 @ X258 )
| ~ ! [X261: term,X262: term] :
( ~ ( X259 @ X261 )
| ~ ( X259 @ X262 )
| ( X259 @ ( ap @ X262 @ X261 ) ) )
| ~ ! [X263: term] :
( ( X259 @ X263 )
| ~ ( var @ X263 ) ) ) )
& ( hoaslam
= ( ^ [X264: subst,X265: subst > term > term] : ( d2term @ d_one ) ) )
& pushprop_lem2v2_lthm
& ( ! [X266: term,X267: term,X268: term,X269: term] :
( ( ( ap @ X267 @ X266 )
!= ( ap @ X269 @ X268 ) )
| ( X267 = X269 ) )
<=> apinj1 )
& ~ ( var @ ( d2term @ d_one ) )
& hoasinduction_lem2_gthm
& ( ( d2subst @ d_id )
= id )
& ! [X270: d_subst,X271: d_subst] :
( ( ( d2subst @ X271 )
= ( d2subst @ X270 ) )
=> ( X270 = X271 ) )
& ( axscons
<=> ! [X272: subst] :
( ( push @ ( sub @ one @ X272 ) @ ( comp @ sh @ X272 ) )
= X272 ) )
& pushprop_lthm
& ( induction2
<=> ! [X273: term > $o,X274: term] :
( ~ ! [X275: term] :
( ~ ! [X276: term] :
( ~ ( X273 @ X276 )
| ( X273 @ ( sub @ X275 @ ( push @ X276 @ id ) ) ) )
| ( X273 @ ( lam @ X275 ) ) )
| ~ ! [X277: term,X278: term] :
( ~ ( X273 @ X277 )
| ~ ( X273 @ X278 )
| ( X273 @ ( ap @ X278 @ X277 ) ) )
| ( X273 @ X274 )
| ~ ! [X279: term] :
( ~ ( var @ X279 )
| ( X273 @ X279 ) ) ) )
& ( ! [X280: term,X281: term,X282: term > $o,X283: subst,X284: term > $o] :
( ( X282 @ ( sub @ X281 @ ( push @ X280 @ X283 ) ) )
| ~ ( X284 @ X281 ) )
<=> pushprop_lem1 )
& hoasinduction_lem1_gthm
& ( ! [X285: term] :
~ ! [X286: subst > term > term] :
~ ! [X287: term,X288: subst] :
( ( X286 @ X288 @ X287 )
= ( sub @ X285 @ ( push @ X287 @ X288 ) ) )
<=> hoasinduction_lem3v2_f )
& hoasinduction_gthm
& ( ( ! [X289: term,X290: subst] :
( ( sub @ one @ ( push @ X289 @ X290 ) )
= X289 )
=> ! [X291: term,X292: subst,X293: term > $o,X294: term > $o] :
( ( X294 @ one )
| ~ ( X293 @ X291 )
| ~ ! [X295: term] :
( ( X294 @ X295 )
= ( X293 @ ( sub @ X295 @ ( push @ X291 @ X292 ) ) ) ) ) )
<=> pushprop_lem1v2_lthm )
& ( one
= ( d2term @ d_one ) )
& ! [X296: d_subst] : ( d_id = X296 )
& ( ! [X297: term,X298: subst > term > subst > $o] :
( ~ ! [X299: subst > term > term] :
( ~ ! [X300: subst,X301: term,X302: subst] :
( ( X299 @ ( comp @ X300 @ X302 ) @ ( sub @ X301 @ X302 ) )
= ( sub @ ( X299 @ X300 @ X301 ) @ X302 ) )
| ( X298 @ id @ ( lam @ ( X299 @ sh @ one ) ) @ id )
| ~ ! [X303: term] :
( ( X298 @ id @ ( X299 @ id @ X303 ) @ id )
| ~ ( X298 @ id @ X303 @ id ) ) )
| ~ ! [X304: subst,X305: subst,X306: term,X307: subst] :
( ~ ( X298 @ X307 @ X306 @ ( comp @ X305 @ X304 ) )
| ( X298 @ ( comp @ X307 @ X305 ) @ ( sub @ X306 @ X305 ) @ X304 ) )
| ( X298 @ id @ X297 @ id )
| ~ ! [X308: term] :
( ( X298 @ id @ X308 @ id )
| ~ ( var @ ( sub @ X308 @ id ) ) )
| ~ ! [X309: term,X310: term] :
( ~ ( X298 @ id @ X310 @ id )
| ( X298 @ id @ ( ap @ ( sub @ X309 @ id ) @ X310 ) @ id )
| ~ ( X298 @ id @ X309 @ id ) )
| ~ ! [X311: term,X312: subst,X313: subst,X314: subst] :
( ( X298 @ X313 @ X311 @ ( comp @ X312 @ X314 ) )
| ~ ( X298 @ ( comp @ X313 @ X312 ) @ ( sub @ X311 @ X312 ) @ X314 ) ) )
<=> hoasinduction )
& pushprop
& ~ ulamvar1
& hoasapinj1_gthm
& hoasinduction_lem1v2_gthm
& hoaslamnotvar_lthm
& ( hoasinduction_lem3v2
<=> ! [X315: term,X316: subst > term > subst > $o,X317: term > $o] :
( ~ ! [X318: term] :
( ( X316 @ id @ X318 @ id )
= ( X317 @ X318 ) )
| ~ ! [X319: term] :
( ~ ( X317 @ X319 )
| ( X317 @ ( sub @ X315 @ ( push @ X319 @ id ) ) ) )
| ( X317 @ ( lam @ X315 ) )
| ~ ! [X320: subst,X321: subst,X322: subst,X323: term] :
( ~ ( X316 @ ( comp @ X321 @ X322 ) @ ( sub @ X323 @ X322 ) @ X320 )
| ( X316 @ X321 @ X323 @ ( comp @ X322 @ X320 ) ) )
| ~ ! [X324: subst,X325: subst,X326: term,X327: subst] :
( ~ ( X316 @ X327 @ X326 @ ( comp @ X324 @ X325 ) )
| ( X316 @ ( comp @ X327 @ X324 ) @ ( sub @ X326 @ X324 ) @ X325 ) )
| ~ ! [X328: subst > term > term] :
( ~ ! [X329: term] :
( ~ ( X316 @ id @ X329 @ id )
| ( X316 @ id @ ( X328 @ id @ X329 ) @ id ) )
| ( X316 @ id @ ( lam @ ( X328 @ sh @ one ) ) @ id )
| ~ ! [X330: term,X331: subst,X332: subst] :
( ( X328 @ ( comp @ X332 @ X331 ) @ ( sub @ X330 @ X331 ) )
= ( sub @ ( X328 @ X332 @ X330 ) @ X331 ) ) ) ) )
& pushprop_gthm
& apnotvar
& hoasinduction_lem2_lthm
& ( shinj
<=> ! [X333: term,X334: term] :
( ( X333 = X334 )
| ( ( sub @ X333 @ sh )
!= ( sub @ X334 @ sh ) ) ) )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ! [X335: term,X336: subst > term > subst > $o] :
( ~ ! [X337: subst > term > term] :
( ( X336 @ id @ ( lam @ ( X337 @ sh @ one ) ) @ id )
| ~ ! [X338: term] :
( ( X336 @ id @ ( X337 @ id @ X338 ) @ id )
| ~ ( X336 @ id @ X338 @ id ) )
| ~ ! [X339: subst,X340: subst,X341: term] :
( ( X337 @ ( comp @ X340 @ X339 ) @ ( sub @ X341 @ X339 ) )
= ( sub @ ( X337 @ X340 @ X341 ) @ X339 ) ) )
| ( X336 @ id @ X335 @ id )
| ~ ! [X342: term,X343: term] :
( ( X336 @ id @ ( ap @ ( sub @ X342 @ id ) @ X343 ) @ id )
| ~ ( X336 @ id @ X342 @ id )
| ~ ( X336 @ id @ X343 @ id ) ) )
<=> hoasinduction_no_psi_cond )
& ( ! [X344: term] :
~ ! [X345: subst > term > term] :
( ( sub @ X344 @ ( push @ one @ sh ) )
!= ( X345 @ sh @ one ) )
<=> hoasinduction_lem3b_lthm )
& hoasinduction_lem3_gthm
& hoasapnotvar_lthm
& ( hoaslamnotap
<=> ! [X346: subst > term > term,X347: term,X348: term] :
( ~ ! [X349: subst,X350: term,X351: subst] :
( ( X346 @ ( comp @ X351 @ X349 ) @ ( sub @ X350 @ X349 ) )
= ( sub @ ( X346 @ X351 @ X350 ) @ X349 ) )
| ( ( lam @ ( X346 @ sh @ one ) )
!= ( ap @ ( sub @ X347 @ id ) @ X348 ) ) ) )
& hoaslamnotap_lthm
& pushprop_lem0_gthm
& axabs
& axapp
& ( hoasinduction_lthm_3
<=> ( ! [X352: subst > term > subst > $o] :
~ ! [X353: term > $o] :
~ ! [X354: term] :
( ( X352 @ id @ X354 @ id )
= ( X353 @ X354 ) )
=> ( ! [X355: term,X356: term > $o] :
( ~ ! [X357: term] :
( ( X356 @ X357 )
| ~ ( var @ X357 ) )
| ~ ! [X358: term,X359: term] :
( ( X356 @ ( ap @ X359 @ X358 ) )
| ~ ( X356 @ X358 )
| ~ ( X356 @ X359 ) )
| ( X356 @ X355 )
| ~ ! [X360: term] :
( ( X356 @ ( lam @ X360 ) )
| ~ ! [X361: term] :
( ~ ( X356 @ X361 )
| ( X356 @ ( sub @ X360 @ ( push @ X361 @ id ) ) ) ) ) )
=> ( ! [X362: term] :
( ( sub @ X362 @ id )
= X362 )
=> ( ! [X363: subst > term > subst > $o,X364: term,X365: term > $o] :
( ~ ! [X366: term] :
( ( X363 @ id @ X366 @ id )
= ( X365 @ X366 ) )
| ~ ! [X367: subst > term > term] :
( ~ ! [X368: term] :
( ~ ( X363 @ id @ X368 @ id )
| ( X363 @ id @ ( X367 @ id @ X368 ) @ id ) )
| ~ ! [X369: subst,X370: subst,X371: term] :
( ( X367 @ ( comp @ X369 @ X370 ) @ ( sub @ X371 @ X370 ) )
= ( sub @ ( X367 @ X369 @ X371 ) @ X370 ) )
| ( X363 @ id @ ( lam @ ( X367 @ sh @ one ) ) @ id ) )
| ( X365 @ ( lam @ X364 ) )
| ~ ! [X372: term] :
( ( X365 @ ( sub @ X364 @ ( push @ X372 @ id ) ) )
| ~ ( X365 @ X372 ) ) )
=> ! [X373: term,X374: subst > term > subst > $o] :
( ~ ! [X375: term,X376: subst,X377: subst,X378: subst] :
( ( X374 @ X378 @ X375 @ ( comp @ X377 @ X376 ) )
| ~ ( X374 @ ( comp @ X378 @ X377 ) @ ( sub @ X375 @ X377 ) @ X376 ) )
| ~ ! [X379: term,X380: term] :
( ~ ( X374 @ id @ X380 @ id )
| ~ ( X374 @ id @ X379 @ id )
| ( X374 @ id @ ( ap @ ( sub @ X379 @ id ) @ X380 ) @ id ) )
| ~ ! [X381: subst,X382: subst,X383: subst,X384: term] :
( ( X374 @ ( comp @ X383 @ X381 ) @ ( sub @ X384 @ X381 ) @ X382 )
| ~ ( X374 @ X383 @ X384 @ ( comp @ X381 @ X382 ) ) )
| ~ ! [X385: subst > term > term] :
( ~ ! [X386: term] :
( ~ ( X374 @ id @ X386 @ id )
| ( X374 @ id @ ( X385 @ id @ X386 ) @ id ) )
| ~ ! [X387: subst,X388: term,X389: subst] :
( ( X385 @ ( comp @ X387 @ X389 ) @ ( sub @ X388 @ X389 ) )
= ( sub @ ( X385 @ X387 @ X388 ) @ X389 ) )
| ( X374 @ id @ ( lam @ ( X385 @ sh @ one ) ) @ id ) )
| ~ ! [X390: term] :
( ~ ( var @ ( sub @ X390 @ id ) )
| ( X374 @ id @ X390 @ id ) )
| ( X374 @ id @ X373 @ id ) ) ) ) ) ) )
& ( induction2lem
<=> ! [X391: term,X392: subst,X393: term > $o] :
( ~ ! [X394: term] :
( ( X393 @ ( sub @ X394 @ X392 ) )
| ~ ( var @ X394 ) )
| ~ ! [X395: term,X396: term] :
( ~ ( X393 @ X396 )
| ~ ( X393 @ X395 )
| ( X393 @ ( ap @ X396 @ X395 ) ) )
| ( X393 @ ( sub @ X391 @ X392 ) )
| ~ ! [X397: term] :
( ( X393 @ ( lam @ X397 ) )
| ~ ! [X398: term] :
( ~ ( X393 @ X398 )
| ( X393 @ ( sub @ X397 @ ( push @ X398 @ id ) ) ) ) ) ) )
& ( ! [X399: term] :
( ( sub @ X399 @ id )
= X399 )
<=> termmset )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& pushprop_lthm_orig
& ( ( ! [X400: subst] :
( ( comp @ id @ X400 )
= X400 )
=> ( ! [X401: subst] :
( ( comp @ X401 @ id )
= X401 )
=> ( ! [X402: subst] :
( ( comp @ id @ X402 )
= X402 )
& ! [X403: subst] :
( ( comp @ X403 @ id )
= X403 ) ) ) )
<=> substmonoid_lthm )
& hoasinduction_lem3v2_gthm
& pushprop_lem1v2_gthm
& ( ! [X404: subst,X405: term > $o,X406: term > $o,X407: term] :
( ~ ! [X408: term] :
( ( X405 @ ( sub @ X408 @ ( push @ X407 @ X404 ) ) )
= ( X406 @ X408 ) )
| ( X406 @ one )
| ~ ( X405 @ X407 ) )
<=> pushprop_lem1v2 )
& ( hoaslaminj
<=> ! [X409: subst,X410: subst > term > term,X411: term,X412: subst > term > term] :
( ( ( lam @ ( X412 @ sh @ one ) )
!= ( lam @ ( X410 @ sh @ one ) ) )
| ~ ! [X413: term,X414: subst,X415: subst] :
( ( sub @ ( X412 @ X414 @ X413 ) @ X415 )
= ( X412 @ ( comp @ X414 @ X415 ) @ ( sub @ X413 @ X415 ) ) )
| ( ( X410 @ X409 @ X411 )
= ( X412 @ X409 @ X411 ) )
| ~ ! [X416: subst,X417: subst,X418: term] :
( ( sub @ ( X410 @ X417 @ X418 ) @ X416 )
= ( X410 @ ( comp @ X417 @ X416 ) @ ( sub @ X418 @ X416 ) ) ) ) )
& axvarshift
& ( ! [X419: term,X420: subst > term > subst > $o] :
( ~ ! [X421: term] :
( ( X420 @ id @ ( sub @ X419 @ ( push @ X421 @ id ) ) @ id )
| ~ ( X420 @ id @ X421 @ id ) )
| ( X420 @ id @ ( lam @ ( sub @ X419 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X422: subst > term > term] :
( ~ ! [X423: subst,X424: term,X425: subst] :
( ( X422 @ ( comp @ X423 @ X425 ) @ ( sub @ X424 @ X425 ) )
= ( sub @ ( X422 @ X423 @ X424 ) @ X425 ) )
| ~ ! [X426: term] :
( ( X420 @ id @ ( X422 @ id @ X426 ) @ id )
| ~ ( X420 @ id @ X426 @ id ) )
| ( X420 @ id @ ( lam @ ( X422 @ sh @ one ) ) @ id ) ) )
<=> hoasinduction_lem3aa_lthm )
& pushprop_lem2v2_gthm
& pushprop_lem3v2_lthm
& lamnotvar
& induction2_gthm
& pushprop_lem3v2
& ! [X427: term] :
? [X428: d_term] :
( ( d2term @ X428 )
= X427 )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( hoasinduction_lem3_lthm
<=> ( ! [X429: term] :
( ( sub @ X429 @ id )
= X429 )
=> ( ! [X430: subst > term > subst > $o,X431: term] :
( ~ ! [X432: subst > term > term] :
( ~ ! [X433: subst,X434: term,X435: subst] :
( ( sub @ ( X432 @ X435 @ X434 ) @ X433 )
= ( X432 @ ( comp @ X435 @ X433 ) @ ( sub @ X434 @ X433 ) ) )
| ( X430 @ id @ ( lam @ ( X432 @ sh @ one ) ) @ id )
| ~ ! [X436: term] :
( ~ ( X430 @ id @ X436 @ id )
| ( X430 @ id @ ( X432 @ id @ X436 ) @ id ) ) )
| ( X430 @ id @ ( lam @ ( sub @ X431 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X437: term] :
( ( X430 @ id @ ( sub @ X431 @ ( push @ X437 @ id ) ) @ id )
| ~ ( X430 @ id @ X437 @ id ) ) )
=> ! [X438: term,X439: subst > term > subst > $o] :
( ~ ! [X440: term] :
( ~ ( X439 @ id @ X440 @ id )
| ( X439 @ id @ ( sub @ X438 @ ( push @ X440 @ id ) ) @ id ) )
| ( X439 @ id @ ( lam @ X438 ) @ id )
| ~ ! [X441: subst,X442: term,X443: subst,X444: subst] :
( ~ ( X439 @ X441 @ X442 @ ( comp @ X444 @ X443 ) )
| ( X439 @ ( comp @ X441 @ X444 ) @ ( sub @ X442 @ X444 ) @ X443 ) )
| ~ ! [X445: subst,X446: term,X447: subst,X448: subst] :
( ( X439 @ X447 @ X446 @ ( comp @ X445 @ X448 ) )
| ~ ( X439 @ ( comp @ X447 @ X445 ) @ ( sub @ X446 @ X445 ) @ X448 ) )
| ~ ! [X449: subst > term > term] :
( ( X439 @ id @ ( lam @ ( X449 @ sh @ one ) ) @ id )
| ~ ! [X450: term] :
( ( X439 @ id @ ( X449 @ id @ X450 ) @ id )
| ~ ( X439 @ id @ X450 @ id ) )
| ~ ! [X451: subst,X452: term,X453: subst] :
( ( X449 @ ( comp @ X453 @ X451 ) @ ( sub @ X452 @ X451 ) )
= ( sub @ ( X449 @ X453 @ X452 ) @ X451 ) ) ) ) ) ) )
& ( hoasinduction_lem0_lthm
<=> ! [X454: subst > term > subst > $o] :
~ ! [X455: term > $o] :
~ ! [X456: term] :
( ( X454 @ id @ X456 @ id )
= ( X455 @ X456 ) ) )
& pushprop_lem1_gthm
& hoasinduction_lem1
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& hoasapnotvar_gthm
& hoaslamnotap_gthm
& ( hoasinduction_lem2
<=> ! [X457: term,X458: term,X459: subst > term > subst > $o] :
( ~ ( X459 @ id @ X458 @ id )
| ~ ! [X460: subst,X461: subst,X462: term,X463: subst] :
( ( X459 @ X463 @ X462 @ ( comp @ X460 @ X461 ) )
| ~ ( X459 @ ( comp @ X463 @ X460 ) @ ( sub @ X462 @ X460 ) @ X461 ) )
| ( X459 @ id @ ( ap @ X457 @ X458 ) @ id )
| ~ ! [X464: subst,X465: term,X466: subst,X467: subst] :
( ~ ( X459 @ X466 @ X465 @ ( comp @ X464 @ X467 ) )
| ( X459 @ ( comp @ X466 @ X464 ) @ ( sub @ X465 @ X464 ) @ X467 ) )
| ~ ( X459 @ id @ X457 @ id )
| ~ ! [X468: term,X469: term] :
( ~ ( X459 @ id @ X468 @ id )
| ( X459 @ id @ ( ap @ ( sub @ X468 @ id ) @ X469 ) @ id )
| ~ ( X459 @ id @ X469 @ id ) ) ) )
& ( hoasinduction_lem3v2a_lthm
<=> ( ! [X470: term] :
~ ! [X471: subst > term > term] :
~ ! [X472: subst,X473: term] :
( ( X471 @ X472 @ X473 )
= ( sub @ X470 @ ( push @ X473 @ X472 ) ) )
=> ( ! [X474: term] :
( ( sub @ X474 @ id )
= X474 )
=> ! [X475: subst > term > subst > $o,X476: term,X477: term > $o] :
( ~ ! [X478: subst > term > term] :
( ( X475 @ id @ ( lam @ ( X478 @ sh @ one ) ) @ id )
| ~ ! [X479: term] :
( ~ ( X475 @ id @ X479 @ id )
| ( X475 @ id @ ( X478 @ id @ X479 ) @ id ) )
| ~ ! [X480: subst,X481: subst,X482: term] :
( ( X478 @ ( comp @ X481 @ X480 ) @ ( sub @ X482 @ X480 ) )
= ( sub @ ( X478 @ X481 @ X482 ) @ X480 ) ) )
| ~ ! [X483: term] :
( ( X475 @ id @ X483 @ id )
= ( X477 @ X483 ) )
| ( X477 @ ( lam @ X476 ) )
| ~ ! [X484: term] :
( ~ ( X477 @ X484 )
| ( X477 @ ( sub @ X476 @ ( push @ X484 @ id ) ) ) ) ) ) ) )
& ( hoasapinj2
<=> ! [X485: term,X486: term,X487: term,X488: term] :
( ( ( ap @ ( sub @ X487 @ id ) @ X486 )
!= ( ap @ ( sub @ X485 @ id ) @ X488 ) )
| ( X486 = X488 ) ) )
& ! [X489: subst] :
? [X490: d_subst] :
( ( d2subst @ X490 )
= X489 )
& ( hoasapinj1
<=> ! [X491: term,X492: term,X493: term,X494: term] :
( ( ( ap @ ( sub @ X493 @ id ) @ X492 )
!= ( ap @ ( sub @ X494 @ id ) @ X491 ) )
| ( X493 = X494 ) ) )
& ( hoasinduction_lem3a
<=> ! [X495: term,X496: subst > term > subst > $o] :
( ~ ! [X497: term] :
( ( X496 @ id @ ( sub @ X495 @ ( push @ X497 @ id ) ) @ id )
| ~ ( X496 @ id @ X497 @ id ) )
| ( X496 @ id @ ( lam @ X495 ) @ id )
| ~ ! [X498: subst > term > term] :
( ~ ! [X499: subst,X500: subst,X501: term] :
( ( sub @ ( X498 @ X499 @ X501 ) @ X500 )
= ( X498 @ ( comp @ X499 @ X500 ) @ ( sub @ X501 @ X500 ) ) )
| ( X496 @ id @ ( lam @ ( X498 @ sh @ one ) ) @ id )
| ~ ! [X502: term] :
( ~ ( X496 @ id @ X502 @ id )
| ( X496 @ id @ ( X498 @ id @ X502 ) @ id ) ) ) ) )
& ( hoasinduction_lem3aa
<=> ! [X503: subst > term > subst > $o,X504: term] :
( ( X503 @ id @ ( lam @ ( sub @ X504 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X505: term] :
( ( X503 @ id @ ( sub @ X504 @ ( push @ X505 @ id ) ) @ id )
| ~ ( X503 @ id @ X505 @ id ) )
| ~ ! [X506: subst > term > term] :
( ( X503 @ id @ ( lam @ ( X506 @ sh @ one ) ) @ id )
| ~ ! [X507: subst,X508: subst,X509: term] :
( ( X506 @ ( comp @ X507 @ X508 ) @ ( sub @ X509 @ X508 ) )
= ( sub @ ( X506 @ X507 @ X509 ) @ X508 ) )
| ~ ! [X510: term] :
( ~ ( X503 @ id @ X510 @ id )
| ( X503 @ id @ ( X506 @ id @ X510 ) @ id ) ) ) ) )
& ulamvarind
& ( ( ! [X511: term,X512: subst] :
( ( sub @ one @ ( push @ X511 @ X512 ) )
= X511 )
=> ( ! [X513: subst,X514: term] :
( ( comp @ sh @ ( push @ X514 @ X513 ) )
= X513 )
=> ( ! [X515: subst] :
( ( comp @ X515 @ id )
= X515 )
=> ( ! [X516: term,X517: term > $o] :
( ~ ! [X518: term] :
( ~ ( X517 @ X518 )
| ( X517 @ ( lam @ X518 ) ) )
| ~ ! [X519: term] :
( ~ ( var @ X519 )
| ( X517 @ X519 ) )
| ( X517 @ X516 )
| ~ ! [X520: term,X521: term] :
( ( X517 @ ( ap @ X521 @ X520 ) )
| ~ ( X517 @ X521 )
| ~ ( X517 @ X520 ) ) )
=> ! [X522: subst,X523: term > $o,X524: term] :
( ~ ! [X525: term] :
( ( X523 @ ( lam @ X525 ) )
| ~ ! [X526: term] :
( ( X523 @ ( sub @ X525 @ ( push @ X526 @ id ) ) )
| ~ ( X523 @ X526 ) ) )
| ~ ! [X527: term,X528: term] :
( ( X523 @ ( ap @ X528 @ X527 ) )
| ~ ( X523 @ X528 )
| ~ ( X523 @ X527 ) )
| ( X523 @ ( sub @ X524 @ X522 ) )
| ~ ! [X529: term] :
( ( X523 @ ( sub @ X529 @ X522 ) )
| ~ ( var @ X529 ) ) ) ) ) ) )
<=> induction2lem_lthm )
& hoasinduction_lem1_lthm
& ( ! [X530: subst > term > subst > $o] :
~ ! [X531: term > $o] :
~ ! [X532: term] :
( ( X530 @ id @ X532 @ id )
= ( X531 @ X532 ) )
<=> hoasinduction_lem0 )
& ( ( ^ [X533: term,X534: subst,X535: term > $o,X536: term > $o] :
! [X537: term] :
( ( X535 @ ( sub @ X537 @ ( push @ X533 @ X534 ) ) )
= ( X536 @ X537 ) ) )
= pushprop_p_and_p_prime )
& ( ! [X538: subst] :
( ( comp @ id @ X538 )
= X538 )
<=> axidl )
& termmset_gthm
& hoasapinj2_gthm
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ! [X539: term] :
~ ! [X540: subst > term > term] :
( ( X540 @ sh @ one )
!= ( sub @ X539 @ ( push @ one @ sh ) ) )
<=> hoasinduction_lem3b )
& ! [X541: d_term] : ( d_one = X541 )
& hoasinduction_lem3a_gthm
& ( ( ! [X542: term,X543: term,X544: term,X545: term] :
( ( ( ap @ X542 @ X544 )
!= ( ap @ X545 @ X543 ) )
| ( X543 = X544 ) )
=> ! [X546: term,X547: term,X548: term,X549: term] :
( ( ( ap @ ( sub @ X546 @ id ) @ X549 )
!= ( ap @ ( sub @ X547 @ id ) @ X548 ) )
| ( X548 = X549 ) ) )
<=> hoasapinj2_lthm )
& hoasinduction_lem3b_gthm ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ( d2subst @ d_id )
= ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& ( hoasinduction_no_psi_cond_lthm
<=> ( ! [X10: subst > term > subst > $o] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
=> ( ! [X22: term,X10: term > $o] :
( ( X10 @ X22 )
| ~ ! [X13: term,X15: term] :
( ~ ( X10 @ X13 )
| ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X15 ) )
| ~ ! [X13: term] :
( ( X10 @ X13 )
| ~ ( var @ X13 ) )
| ~ ! [X13: term] :
( ( X10 @ ( lam @ X13 ) )
| ~ ! [X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) ) ) ) )
=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X29: term,X10: subst > term > subst > $o,X11: term > $o] :
( ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ~ ! [X13: term,X25: subst,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) )
| ( X11 @ ( lam @ X29 ) )
| ~ ! [X15: term] :
( ~ ( X11 @ X15 )
| ( X11 @ ( sub @ X29 @ ( push @ X15 @ id ) ) ) ) )
=> ! [X10: subst > term > subst > $o,X30: term] :
( ~ ! [X13: term,X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term,X14: subst,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) )
| ( X10 @ id @ X30 @ id ) ) ) ) ) ) )
& ( ! [X13: term,X15: term] :
( ( ( lam @ X13 )
!= ( lam @ X15 ) )
| ( X13 = X15 ) )
<=> laminj )
& ( hoasinduction_lem3
<=> ! [X27: term,X10: subst > term > subst > $o] :
( ( X10 @ id @ ( lam @ X27 ) @ id )
| ~ ! [X13: term,X25: subst,X14: subst,X26: subst] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X25: subst,X14: subst,X26: subst,X13: term] :
( ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term,X25: subst,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) )
| ~ ! [X15: term] :
( ( X10 @ id @ ( sub @ X27 @ ( push @ X15 @ id ) ) @ id )
| ~ ( X10 @ id @ X15 @ id ) ) ) )
& ( apinj2
<=> ! [X20: term,X15: term,X13: term,X19: term] :
( ( X19 = X20 )
| ( ( ap @ X13 @ X19 )
!= ( ap @ X15 @ X20 ) ) ) )
& ulamvarsh
& axclos
& hoasinduction_lem1v2
& ( axidr
<=> ! [X14: subst] :
( ( comp @ X14 @ id )
= X14 ) )
& ( hoasinduction_lem2v2
<=> ! [X44: term,X11: term > $o,X10: subst > term > subst > $o,X45: term] :
( ~ ( X11 @ X44 )
| ~ ! [X26: subst,X13: term,X25: subst,X14: subst] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X15: term,X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ( X11 @ ( ap @ X44 @ X45 ) )
| ~ ( X11 @ X45 )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ~ ! [X25: subst,X13: term,X14: subst,X26: subst] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) ) ) )
& ( hoasapinj1_lthm
<=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X15: term,X20: term,X13: term,X19: term] :
( ( ( ap @ X13 @ X19 )
!= ( ap @ X15 @ X20 ) )
| ( X13 = X15 ) )
=> ! [X15: term,X13: term,X20: term,X19: term] :
( ( ( ap @ ( sub @ X13 @ id ) @ X19 )
!= ( ap @ ( sub @ X15 @ id ) @ X20 ) )
| ( X13 = X15 ) ) ) ) )
& ( ! [X14: subst,X13: term] :
( ( sub @ one @ ( push @ X13 @ X14 ) )
= X13 )
<=> axvarcons )
& ( ( ^ [X10: subst > term > subst > $o,X11: term > $o] :
! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) ) )
= hoasinduction_p_and_p_prime )
& pushprop_lem2v2
& axassoc
& ~ ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
& ( ( ! [X14: subst] :
( ( comp @ id @ X14 )
= X14 )
& ! [X14: subst] :
( ( comp @ X14 @ id )
= X14 ) )
<=> substmonoid )
& ( hoasinduction_lem3a_lthm
<=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X10: subst > term > subst > $o,X42: term] :
( ( X10 @ id @ ( lam @ ( sub @ X42 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term,X25: subst,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) )
| ~ ! [X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( sub @ X42 @ ( push @ X15 @ id ) ) @ 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 ) )
| ~ ! [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 ) )
| ~ ! [X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( sub @ X43 @ ( push @ X15 @ id ) ) @ id ) ) ) ) ) )
& ( hoasinduction_lem3v2_lthm
<=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ! [X11: term > $o,X10: subst > term > subst > $o,X48: term] :
( ~ ! [X15: term] :
( ~ ( X11 @ X15 )
| ( X11 @ ( sub @ X48 @ ( push @ X15 @ id ) ) ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X25: subst,X14: subst,X13: term] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) )
| ~ ! [X14: subst,X13: term,X26: subst,X25: subst] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ( X11 @ ( lam @ X48 ) )
| ~ ! [X26: subst,X14: subst,X13: term,X25: subst] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) ) ) ) )
& ( ! [X13: term,X14: subst] :
( ( comp @ sh @ ( push @ X13 @ X14 ) )
= X14 )
<=> axshiftcons )
& ( pushprop_lem0
<=> ! [X10: term > $o,X14: subst,X13: term] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ ( sub @ X12 @ ( push @ X13 @ X14 ) ) ) ) )
& ~ lamnotap
& ( ! [X15: term] :
~ ! [X18: subst > term > term] :
~ ! [X13: term,X14: subst] :
( ( sub @ X15 @ ( push @ X13 @ X14 ) )
= ( X18 @ X14 @ X13 ) )
<=> hoasinduction_lem3v2_f_lthm )
& axmap
& hoasinduction_lem2v2_gthm
& ( induction2_lthm
<=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X17: subst,X10: term > $o,X16: term] :
( ~ ! [X13: term] :
( ( X10 @ ( lam @ X13 ) )
| ~ ! [X15: term] :
( ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) )
| ~ ( X10 @ X15 ) ) )
| ~ ! [X13: term,X15: term] :
( ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X15 )
| ~ ( X10 @ X13 ) )
| ~ ! [X15: term] :
( ( X10 @ ( sub @ X15 @ X17 ) )
| ~ ( var @ X15 ) )
| ( X10 @ ( sub @ X16 @ X17 ) ) )
=> ! [X22: term,X10: term > $o] :
( ~ ! [X13: term] :
( ~ ( var @ X13 )
| ( X10 @ X13 ) )
| ~ ! [X13: term,X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X13 ) )
| ~ ! [X13: term] :
( ~ ! [X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) ) )
| ( X10 @ ( lam @ X13 ) ) )
| ( X10 @ X22 ) ) ) ) )
& ( pushprop_lem0_lthm
<=> ! [X14: subst,X10: term > $o,X13: term] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ ( sub @ X12 @ ( push @ X13 @ X14 ) ) ) ) )
& induction2lem_gthm
& ( pushprop_lem1_lthm
<=> ( ! [X13: term,X14: subst] :
( ( sub @ one @ ( push @ X13 @ X14 ) )
= X13 )
=> ( ! [X14: subst,X13: term] :
( ( comp @ sh @ ( push @ X13 @ X14 ) )
= X14 )
=> ! [X13: term,X10: term > $o,X14: subst,X15: term,X26: term > $o] :
( ~ ( X10 @ X13 )
| ( X26 @ ( sub @ X13 @ ( push @ X15 @ X14 ) ) ) ) ) ) )
& ( hoasinduction_lem3v2a
<=> ! [X11: term > $o,X10: subst > term > subst > $o,X29: term] :
( ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X25: subst,X13: term,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) )
| ~ ! [X15: term] :
( ~ ( X11 @ X15 )
| ( X11 @ ( sub @ X29 @ ( push @ X15 @ id ) ) ) )
| ( X11 @ ( lam @ X29 ) ) ) )
& ( hoasinduction_lthm
<=> ( ! [X10: term > $o,X22: term] :
( ( X10 @ X22 )
| ~ ! [X13: term] :
( ~ ! [X15: term] :
( ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) )
| ~ ( X10 @ X15 ) )
| ( X10 @ ( lam @ X13 ) ) )
| ~ ! [X15: term,X13: term] :
( ~ ( X10 @ X13 )
| ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X15 ) )
| ~ ! [X13: term] :
( ~ ( var @ X13 )
| ( X10 @ X13 ) ) )
=> ( ! [X23: term,X24: term,X10: subst > term > subst > $o] :
( ~ ( X10 @ id @ X24 @ id )
| ( X10 @ id @ ( ap @ X23 @ X24 ) @ id )
| ~ ! [X25: subst,X14: subst,X13: term,X26: subst] :
( ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ( X10 @ id @ X23 @ id )
| ~ ! [X25: subst,X26: subst,X13: term,X14: subst] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X15: term,X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X15 @ id ) ) )
=> ( ! [X27: term,X10: subst > term > subst > $o] :
( ~ ! [X26: subst,X13: term,X25: subst,X14: subst] :
( ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X25: subst,X26: subst,X13: term,X14: subst] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( sub @ X27 @ ( push @ X15 @ id ) ) @ id ) )
| ( X10 @ id @ ( lam @ X27 ) @ id )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term,X14: subst,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) ) )
=> ! [X10: subst > term > subst > $o,X28: term] :
( ~ ! [X15: term,X13: term] :
( ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X15 @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ~ ! [X26: subst,X25: subst,X14: subst,X13: term] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X26: subst,X14: subst,X13: term,X25: subst] :
( ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X13: term] :
( ( X10 @ id @ X13 @ id )
| ~ ( var @ ( sub @ X13 @ id ) ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X25: subst,X13: term,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) ) )
| ( X10 @ id @ X28 @ id ) ) ) ) ) )
& hoaslaminj_gthm
& ( ! [X34: term,X10: subst > term > subst > $o] :
( ~ ! [X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( sub @ X34 @ ( push @ X15 @ id ) ) @ id ) )
| ( X10 @ id @ ( lam @ ( sub @ X34 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X35: term,X18: subst > term > term] :
( ~ ! [X38: subst,X37: term,X36: subst] :
( ( sub @ ( X18 @ X36 @ X37 ) @ X38 )
= ( sub @ ( sub @ X35 @ ( push @ X37 @ X36 ) ) @ X38 ) )
| ~ ! [X39: subst,X40: term,X41: subst] :
( ( X18 @ ( comp @ X39 @ X41 ) @ ( sub @ X40 @ X41 ) )
= ( sub @ X35 @ ( push @ ( sub @ X40 @ X41 ) @ ( comp @ X39 @ X41 ) ) ) )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) ) )
<=> hoasinduction_lem3aaa )
& hoasapnotvar
& ! [X2: d_term,X3: d_term] :
( ( ( d2term @ X2 )
= ( d2term @ X3 ) )
=> ( X2 = X3 ) )
& ( ( d2subst @ d_id )
= sh )
& hoaslamnotvar_gthm
& ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
<=> axvarid )
& ( hoaslaminj_lthm
<=> ( ! [X14: subst,X13: term] :
( ( sub @ one @ ( push @ X13 @ X14 ) )
= X13 )
=> ( ! [X13: term,X14: subst] :
( ( comp @ sh @ ( push @ X13 @ X14 ) )
= X14 )
=> ( ! [X13: term,X15: term] :
( ( ( lam @ X13 )
!= ( lam @ X15 ) )
| ( X13 = X15 ) )
=> ! [X32: subst,X33: term,X18: subst > term > term,X31: subst > term > term] :
( ( ( X18 @ X32 @ X33 )
= ( X31 @ X32 @ X33 ) )
| ~ ! [X13: term,X14: subst,X25: subst] :
( ( sub @ ( X31 @ X14 @ X13 ) @ X25 )
= ( X31 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( ( lam @ ( X18 @ sh @ one ) )
!= ( lam @ ( X31 @ sh @ one ) ) )
| ~ ! [X14: subst,X13: term,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) ) ) ) ) )
& hoaslamnotvar
& ( termmset_lthm
<=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ! [X13: term] :
( ( sub @ X13 @ id )
= X13 ) ) )
& substmonoid_gthm
& ( induction
<=> ! [X21: term,X10: term > $o] :
( ~ ! [X13: term] :
( ~ ( X10 @ X13 )
| ( X10 @ ( lam @ X13 ) ) )
| ( X10 @ X21 )
| ~ ! [X15: term,X13: term] :
( ~ ( X10 @ X15 )
| ~ ( X10 @ X13 )
| ( X10 @ ( ap @ X13 @ X15 ) ) )
| ~ ! [X13: term] :
( ( X10 @ X13 )
| ~ ( var @ X13 ) ) ) )
& ( hoaslam
= ( ^ [X8: subst,X9: subst > term > term] : ( d2term @ d_one ) ) )
& pushprop_lem2v2_lthm
& ( ! [X20: term,X15: term,X19: term,X13: term] :
( ( ( ap @ X13 @ X19 )
!= ( ap @ X15 @ X20 ) )
| ( X13 = X15 ) )
<=> apinj1 )
& ~ ( var @ ( d2term @ d_one ) )
& hoasinduction_lem2_gthm
& ( ( d2subst @ d_id )
= id )
& ! [X6: d_subst,X7: d_subst] :
( ( ( d2subst @ X6 )
= ( d2subst @ X7 ) )
=> ( X6 = X7 ) )
& ( axscons
<=> ! [X14: subst] :
( ( push @ ( sub @ one @ X14 ) @ ( comp @ sh @ X14 ) )
= X14 ) )
& pushprop_lthm
& ( induction2
<=> ! [X10: term > $o,X22: term] :
( ~ ! [X13: term] :
( ~ ! [X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) ) )
| ( X10 @ ( lam @ X13 ) ) )
| ~ ! [X15: term,X13: term] :
( ~ ( X10 @ X15 )
| ~ ( X10 @ X13 )
| ( X10 @ ( ap @ X13 @ X15 ) ) )
| ( X10 @ X22 )
| ~ ! [X13: term] :
( ~ ( var @ X13 )
| ( X10 @ X13 ) ) ) )
& ( ! [X15: term,X13: term,X26: term > $o,X14: subst,X10: term > $o] :
( ( X26 @ ( sub @ X13 @ ( push @ X15 @ X14 ) ) )
| ~ ( X10 @ X13 ) )
<=> pushprop_lem1 )
& hoasinduction_lem1_gthm
& ( ! [X15: term] :
~ ! [X18: subst > term > term] :
~ ! [X13: term,X14: subst] :
( ( sub @ X15 @ ( push @ X13 @ X14 ) )
= ( X18 @ X14 @ X13 ) )
<=> hoasinduction_lem3v2_f )
& hoasinduction_gthm
& ( ( ! [X13: term,X14: subst] :
( ( sub @ one @ ( push @ X13 @ X14 ) )
= X13 )
=> ! [X13: term,X14: subst,X10: term > $o,X11: term > $o] :
( ( X11 @ one )
| ~ ( X10 @ X13 )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ ( sub @ X12 @ ( push @ X13 @ X14 ) ) ) ) ) )
<=> pushprop_lem1v2_lthm )
& ( one
= ( d2term @ d_one ) )
& ! [X5: d_subst] : ( d_id = X5 )
& ( ! [X28: term,X10: subst > term > subst > $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 @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) ) )
| ~ ! [X25: subst,X26: subst,X13: term,X14: subst] :
( ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ( X10 @ id @ X28 @ id )
| ~ ! [X13: term] :
( ( X10 @ id @ X13 @ id )
| ~ ( var @ ( sub @ X13 @ id ) ) )
| ~ ! [X13: term,X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ~ ! [X13: term,X26: subst,X14: subst,X25: subst] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) ) )
<=> hoasinduction )
& pushprop
& ~ ulamvar1
& hoasapinj1_gthm
& hoasinduction_lem1v2_gthm
& hoaslamnotvar_lthm
& ( hoasinduction_lem3v2
<=> ! [X48: term,X10: subst > term > subst > $o,X11: term > $o] :
( ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ~ ! [X15: term] :
( ~ ( X11 @ X15 )
| ( X11 @ ( sub @ X48 @ ( push @ X15 @ id ) ) ) )
| ( X11 @ ( lam @ X48 ) )
| ~ ! [X25: subst,X14: subst,X26: subst,X13: term] :
( ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X26: subst,X25: subst,X13: term,X14: subst] :
( ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ( 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 ) ) ) ) ) )
& pushprop_gthm
& apnotvar
& hoasinduction_lem2_lthm
& ( shinj
<=> ! [X15: term,X13: term] :
( ( X13 = X15 )
| ( ( sub @ X13 @ sh )
!= ( sub @ X15 @ sh ) ) ) )
& ( ( d2term @ d_one )
= ( lam @ ( d2term @ d_one ) ) )
& ( ! [X30: term,X10: subst > term > subst > $o] :
( ~ ! [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 @ X30 @ id )
| ~ ! [X13: term,X15: term] :
( ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X13 @ id )
| ~ ( X10 @ id @ X15 @ id ) ) )
<=> hoasinduction_no_psi_cond )
& ( ! [X15: term] :
~ ! [X18: subst > term > term] :
( ( X18 @ sh @ one )
!= ( sub @ X15 @ ( push @ one @ sh ) ) )
<=> hoasinduction_lem3b_lthm )
& hoasinduction_lem3_gthm
& hoasapnotvar_lthm
& ( hoaslamnotap
<=> ! [X18: subst > term > term,X46: term,X47: term] :
( ~ ! [X25: subst,X13: term,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( ( lam @ ( X18 @ sh @ one ) )
!= ( ap @ ( sub @ X46 @ id ) @ X47 ) ) ) )
& hoaslamnotap_lthm
& pushprop_lem0_gthm
& axabs
& axapp
& ( hoasinduction_lthm_3
<=> ( ! [X10: subst > term > subst > $o] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
=> ( ! [X22: term,X10: term > $o] :
( ~ ! [X13: term] :
( ( X10 @ X13 )
| ~ ( var @ X13 ) )
| ~ ! [X15: term,X13: term] :
( ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X15 )
| ~ ( X10 @ X13 ) )
| ( X10 @ X22 )
| ~ ! [X13: term] :
( ( X10 @ ( lam @ X13 ) )
| ~ ! [X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) ) ) ) )
=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X10: subst > term > subst > $o,X29: term,X11: term > $o] :
( ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ~ ! [X14: subst,X25: subst,X13: term] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) )
| ( X11 @ ( lam @ X29 ) )
| ~ ! [X15: term] :
( ( X11 @ ( sub @ X29 @ ( push @ X15 @ id ) ) )
| ~ ( X11 @ X15 ) ) )
=> ! [X28: term,X10: subst > term > subst > $o] :
( ~ ! [X13: term,X25: subst,X26: subst,X14: subst] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X13: term,X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id ) )
| ~ ! [X26: subst,X25: subst,X14: subst,X13: term] :
( ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 )
| ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) ) )
| ~ ! [X18: subst > term > term] :
( ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ~ ! [X14: subst,X13: term,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) )
| ~ ! [X13: term] :
( ~ ( var @ ( sub @ X13 @ id ) )
| ( X10 @ id @ X13 @ id ) )
| ( X10 @ id @ X28 @ id ) ) ) ) ) ) )
& ( induction2lem
<=> ! [X16: term,X17: subst,X10: term > $o] :
( ~ ! [X15: term] :
( ( X10 @ ( sub @ X15 @ X17 ) )
| ~ ( var @ X15 ) )
| ~ ! [X15: term,X13: term] :
( ~ ( X10 @ X13 )
| ~ ( X10 @ X15 )
| ( X10 @ ( ap @ X13 @ X15 ) ) )
| ( X10 @ ( sub @ X16 @ X17 ) )
| ~ ! [X13: term] :
( ( X10 @ ( lam @ X13 ) )
| ~ ! [X15: term] :
( ~ ( X10 @ X15 )
| ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) ) ) ) ) )
& ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
<=> termmset )
& ( ( d2term @ d_one )
= ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) )
& pushprop_lthm_orig
& ( ( ! [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 )
& hoasinduction_lem3v2_gthm
& pushprop_lem1v2_gthm
& ( ! [X14: subst,X10: term > $o,X11: term > $o,X13: term] :
( ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ ( sub @ X12 @ ( push @ X13 @ X14 ) ) ) )
| ( X11 @ one )
| ~ ( X10 @ X13 ) )
<=> pushprop_lem1v2 )
& ( hoaslaminj
<=> ! [X32: subst,X31: subst > term > term,X33: term,X18: subst > term > term] :
( ( ( lam @ ( X18 @ sh @ one ) )
!= ( lam @ ( X31 @ sh @ one ) ) )
| ~ ! [X13: term,X14: subst,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( ( X18 @ X32 @ X33 )
= ( X31 @ X32 @ X33 ) )
| ~ ! [X25: subst,X14: subst,X13: term] :
( ( sub @ ( X31 @ X14 @ X13 ) @ X25 )
= ( X31 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) ) )
& axvarshift
& ( ! [X42: term,X10: subst > term > subst > $o] :
( ~ ! [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,X13: term,X25: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ~ ! [X13: term] :
( ( X10 @ id @ ( X18 @ id @ X13 ) @ id )
| ~ ( X10 @ id @ X13 @ id ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id ) ) )
<=> hoasinduction_lem3aa_lthm )
& pushprop_lem2v2_gthm
& pushprop_lem3v2_lthm
& lamnotvar
& induction2_gthm
& pushprop_lem3v2
& ! [X0: term] :
? [X1: d_term] :
( ( d2term @ X1 )
= X0 )
& ( ( d2subst @ d_id )
= ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) )
& ( hoasinduction_lem3_lthm
<=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ( ! [X10: subst > term > subst > $o,X42: term] :
( ~ ! [X18: subst > term > term] :
( ~ ! [X25: subst,X13: term,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) ) )
| ( X10 @ id @ ( lam @ ( sub @ X42 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [X15: term] :
( ( X10 @ id @ ( sub @ X42 @ ( push @ X15 @ id ) ) @ id )
| ~ ( X10 @ id @ X15 @ id ) ) )
=> ! [X27: term,X10: subst > term > subst > $o] :
( ~ ! [X15: term] :
( ~ ( X10 @ id @ X15 @ id )
| ( X10 @ id @ ( sub @ X27 @ ( push @ X15 @ id ) ) @ id ) )
| ( X10 @ id @ ( lam @ X27 ) @ id )
| ~ ! [X14: subst,X13: term,X25: subst,X26: subst] :
( ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [X26: subst,X13: term,X14: subst,X25: subst] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ! [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,X13: term,X14: subst] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) ) ) ) ) )
& ( hoasinduction_lem0_lthm
<=> ! [X10: subst > term > subst > $o] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) ) )
& pushprop_lem1_gthm
& hoasinduction_lem1
& ( ( d2term @ d_one )
= ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) )
& hoasapnotvar_gthm
& hoaslamnotap_gthm
& ( hoasinduction_lem2
<=> ! [X23: term,X24: term,X10: subst > term > subst > $o] :
( ~ ( X10 @ id @ X24 @ id )
| ~ ! [X26: subst,X25: subst,X13: term,X14: subst] :
( ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ~ ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ( X10 @ id @ ( ap @ X23 @ X24 ) @ id )
| ~ ! [X26: subst,X13: term,X14: subst,X25: subst] :
( ~ ( X10 @ X14 @ X13 @ ( comp @ X26 @ X25 ) )
| ( X10 @ ( comp @ X14 @ X26 ) @ ( sub @ X13 @ X26 ) @ X25 ) )
| ~ ( X10 @ id @ X23 @ id )
| ~ ! [X13: term,X15: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( ap @ ( sub @ X13 @ id ) @ X15 ) @ id )
| ~ ( X10 @ id @ X15 @ id ) ) ) )
& ( hoasinduction_lem3v2a_lthm
<=> ( ! [X15: term] :
~ ! [X18: subst > term > term] :
~ ! [X14: subst,X13: term] :
( ( sub @ X15 @ ( push @ X13 @ X14 ) )
= ( X18 @ X14 @ X13 ) )
=> ( ! [X13: term] :
( ( sub @ X13 @ id )
= X13 )
=> ! [X10: subst > term > subst > $o,X29: term,X11: term > $o] :
( ~ ! [X18: subst > term > term] :
( ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
| ~ ! [X25: subst,X14: subst,X13: term] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) ) )
| ~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
| ( X11 @ ( lam @ X29 ) )
| ~ ! [X15: term] :
( ~ ( X11 @ X15 )
| ( X11 @ ( sub @ X29 @ ( push @ X15 @ id ) ) ) ) ) ) ) )
& ( hoasapinj2
<=> ! [X13: term,X20: term,X15: term,X19: term] :
( ( ( ap @ ( sub @ X13 @ id ) @ X19 )
!= ( ap @ ( sub @ X15 @ id ) @ X20 ) )
| ( X19 = X20 ) ) )
& ! [X4: subst] :
? [X5: d_subst] :
( ( d2subst @ X5 )
= X4 )
& ( hoasapinj1
<=> ! [X19: term,X20: term,X15: term,X13: term] :
( ( ( ap @ ( sub @ X13 @ id ) @ X19 )
!= ( ap @ ( sub @ X15 @ id ) @ X20 ) )
| ( X13 = X15 ) ) )
& ( hoasinduction_lem3a
<=> ! [X43: term,X10: subst > term > subst > $o] :
( ~ ! [X15: term] :
( ( X10 @ id @ ( sub @ X43 @ ( push @ X15 @ id ) ) @ id )
| ~ ( X10 @ id @ X15 @ id ) )
| ( X10 @ id @ ( lam @ X43 ) @ id )
| ~ ! [X18: subst > term > term] :
( ~ ! [X14: subst,X25: subst,X13: term] :
( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) ) )
| ( X10 @ id @ ( lam @ ( X18 @ sh @ one ) ) @ id )
| ~ ! [X13: term] :
( ~ ( X10 @ id @ X13 @ id )
| ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) ) ) ) )
& ( hoasinduction_lem3aa
<=> ! [X10: subst > term > subst > $o,X42: term] :
( ( X10 @ id @ ( lam @ ( sub @ X42 @ ( push @ one @ sh ) ) ) @ id )
| ~ ! [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 )
| ~ ! [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 ) ) ) ) )
& ulamvarind
& ( ( ! [X13: term,X14: subst] :
( ( sub @ one @ ( push @ X13 @ X14 ) )
= X13 )
=> ( ! [X14: subst,X13: term] :
( ( comp @ sh @ ( push @ X13 @ X14 ) )
= X14 )
=> ( ! [X14: subst] :
( ( comp @ X14 @ id )
= X14 )
=> ( ! [X21: term,X10: term > $o] :
( ~ ! [X13: term] :
( ~ ( X10 @ X13 )
| ( X10 @ ( lam @ X13 ) ) )
| ~ ! [X13: term] :
( ~ ( var @ X13 )
| ( X10 @ X13 ) )
| ( X10 @ X21 )
| ~ ! [X15: term,X13: term] :
( ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X13 )
| ~ ( X10 @ X15 ) ) )
=> ! [X17: subst,X10: term > $o,X16: term] :
( ~ ! [X13: term] :
( ( X10 @ ( lam @ X13 ) )
| ~ ! [X15: term] :
( ( X10 @ ( sub @ X13 @ ( push @ X15 @ id ) ) )
| ~ ( X10 @ X15 ) ) )
| ~ ! [X15: term,X13: term] :
( ( X10 @ ( ap @ X13 @ X15 ) )
| ~ ( X10 @ X13 )
| ~ ( X10 @ X15 ) )
| ( X10 @ ( sub @ X16 @ X17 ) )
| ~ ! [X15: term] :
( ( X10 @ ( sub @ X15 @ X17 ) )
| ~ ( var @ X15 ) ) ) ) ) ) )
<=> induction2lem_lthm )
& hoasinduction_lem1_lthm
& ( ! [X10: subst > term > subst > $o] :
~ ! [X11: term > $o] :
~ ! [X12: term] :
( ( X11 @ X12 )
= ( X10 @ id @ X12 @ id ) )
<=> hoasinduction_lem0 )
& ( ( ^ [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] :
( ( comp @ id @ X14 )
= X14 )
<=> axidl )
& termmset_gthm
& hoasapinj2_gthm
& ( ( d2term @ d_one )
= ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) )
& ( ! [X15: term] :
~ ! [X18: subst > term > term] :
( ( X18 @ sh @ one )
!= ( sub @ X15 @ ( push @ one @ sh ) ) )
<=> hoasinduction_lem3b )
& ! [X1: d_term] : ( d_one = X1 )
& hoasinduction_lem3a_gthm
& ( ( ! [X13: term,X20: term,X19: term,X15: term] :
( ( ( ap @ X13 @ X19 )
!= ( ap @ X15 @ X20 ) )
| ( X19 = X20 ) )
=> ! [X15: term,X13: term,X19: term,X20: term] :
( ( ( ap @ ( sub @ X13 @ id ) @ X19 )
!= ( ap @ ( sub @ X15 @ id ) @ X20 ) )
| ( X19 = X20 ) ) )
<=> hoasapinj2_lthm )
& hoasinduction_lem3b_gthm ),
file('/export/starexec/sandbox2/tmp/tmp.xoR6yAHn1s/DTF2THF_17021.p',alg444_1) ).
thf(f1412,plain,
! [X97: term] :
( ( d2term @ ( sK563 @ X97 ) )
= X97 ),
inference(cnf_transformation,[status(thm)],[f749]) ).
thf(f3463,plain,
( ( ( sK322 @ ( d2subst @ d_id ) @ ( lam @ ( sub @ sK321 @ ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ) @ ( d2subst @ d_id ) )
!= $true )
| spl654_371 ),
inference(avatar_component_clause,[status(thm)],[f3462]) ).
thf(f3462,definition,
( spl654_371
<=> ( ( sK322 @ ( d2subst @ d_id ) @ ( lam @ ( sub @ sK321 @ ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ) @ ( d2subst @ d_id ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl654_371])],[avatar_definition]) ).
thf(f14981,plain,
( spl654_294
| ~ spl654_488 ),
inference(avatar_contradiction_clause,[status(thm)],[f14980]) ).
thf(f14980,plain,
( $false
| spl654_294
| ~ spl654_488 ),
inference(subsumption_resolution,[status(thm)],[f14979,f3127]) ).
thf(f3127,plain,
( ( $true
!= ( sP44 @ sK322 ) )
| spl654_294 ),
inference(avatar_component_clause,[status(thm)],[f3126]) ).
thf(f3126,definition,
( spl654_294
<=> ( $true
= ( sP44 @ sK322 ) ) ),
introduced(definition,[new_symbols(naming,[spl654_294])],[avatar_definition]) ).
thf(f14979,plain,
( ( $true
= ( sP44 @ sK322 ) )
| ~ spl654_488 ),
inference(trivial_inequality_removal,[status(thm)],[f14923]) ).
thf(f14923,plain,
( ( $true
= ( sP44 @ sK322 ) )
| ( $true != $true )
| ~ spl654_488 ),
inference(superposition,[status(thm)],[f8836,f14864]) ).
thf(f14864,plain,
! [X0: subst > term > subst > $o] :
( ( ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true )
| ( ( sP44 @ X0 )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f14863,f11205]) ).
thf(f11205,plain,
! [X0: subst > term > subst > $o,X8: subst,X6: term,X7: subst] :
( ( ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ X7 )
= $true )
| ( ( X0 @ X8 @ X6 @ ( d2subst @ d_id ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f11204]) ).
thf(f11204,plain,
! [X0: subst > term > subst > $o,X8: subst,X6: term,X7: subst] :
( ( $true != $true )
| ( ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ X7 )
= $true )
| ( ( X0 @ X8 @ X6 @ ( d2subst @ d_id ) )
!= $true ) ),
inference(backward_demodulation,[status(thm)],[f9346,f11203]) ).
thf(f11203,plain,
! [X0: subst > term > subst > $o] :
( $true
= ( sP67 @ X0 ) ),
inference(subsumption_resolution,[status(thm)],[f11202,f7764]) ).
thf(f7764,plain,
! [X0: subst > term > subst > $o] :
( ( ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true )
| ( $true
= ( sP67 @ X0 ) ) ),
inference(forward_demodulation,[status(thm)],[f7763,f3855]) ).
thf(f3855,plain,
! [X262: subst] :
( ( d2subst @ d_id )
= X262 ),
inference(forward_demodulation,[status(thm)],[f1286,f1499]) ).
thf(f1499,plain,
! [X18: d_subst] : ( d_id = X18 ),
inference(cnf_transformation,[status(thm)],[f749]) ).
thf(f1286,plain,
! [X262: subst] :
( ( d2subst @ ( sK644 @ X262 ) )
= X262 ),
inference(cnf_transformation,[status(thm)],[f749]) ).
thf(f7763,plain,
! [X0: subst > term > subst > $o] :
( ( ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( comp @ ( sK245 @ X0 ) @ ( sK247 @ X0 ) ) )
= $true )
| ( $true
= ( sP67 @ X0 ) ) ),
inference(forward_demodulation,[status(thm)],[f7762,f3865]) ).
thf(f7762,plain,
! [X0: subst > term > subst > $o] :
( ( $true
= ( sP67 @ X0 ) )
| ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( sK246 @ X0 ) @ ( comp @ ( sK245 @ X0 ) @ ( sK247 @ X0 ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f970,f3855]) ).
thf(f970,plain,
! [X0: subst > term > subst > $o] :
( ( ( X0 @ ( sK248 @ X0 ) @ ( sK246 @ X0 ) @ ( comp @ ( sK245 @ X0 ) @ ( sK247 @ X0 ) ) )
= $true )
| ( $true
= ( sP67 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f331]) ).
thf(f331,plain,
! [X0: subst > term > subst > $o] :
( ( ( $true
= ( sP67 @ X0 ) )
| ( ( ( X0 @ ( sK248 @ X0 ) @ ( sK246 @ X0 ) @ ( comp @ ( sK245 @ X0 ) @ ( sK247 @ X0 ) ) )
= $true )
& ( $true
!= ( X0 @ ( comp @ ( sK248 @ X0 ) @ ( sK245 @ X0 ) ) @ ( sub @ ( sK246 @ X0 ) @ ( sK245 @ X0 ) ) @ ( sK247 @ X0 ) ) ) ) )
& ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( $true
!= ( X0 @ X8 @ X6 @ ( comp @ X5 @ X7 ) ) )
| ( ( X0 @ ( comp @ X8 @ X5 ) @ ( sub @ X6 @ X5 ) @ X7 )
= $true ) )
| ( $true
!= ( sP67 @ X0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK245,sK246,sK247,sK248])],[f329,f330]) ).
thf(f330,plain,
! [X0: subst > term > subst > $o] :
( ? [X1: subst,X2: term,X3: subst,X4: subst] :
( ( ( X0 @ X4 @ X2 @ ( comp @ X1 @ X3 ) )
= $true )
& ( $true
!= ( X0 @ ( comp @ X4 @ X1 ) @ ( sub @ X2 @ X1 ) @ X3 ) ) )
=> ( ( ( X0 @ ( sK248 @ X0 ) @ ( sK246 @ X0 ) @ ( comp @ ( sK245 @ X0 ) @ ( sK247 @ X0 ) ) )
= $true )
& ( $true
!= ( X0 @ ( comp @ ( sK248 @ X0 ) @ ( sK245 @ X0 ) ) @ ( sub @ ( sK246 @ X0 ) @ ( sK245 @ X0 ) ) @ ( sK247 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f329,plain,
! [X0: subst > term > subst > $o] :
( ( ( $true
= ( sP67 @ X0 ) )
| ? [X1: subst,X2: term,X3: subst,X4: subst] :
( ( ( X0 @ X4 @ X2 @ ( comp @ X1 @ X3 ) )
= $true )
& ( $true
!= ( X0 @ ( comp @ X4 @ X1 ) @ ( sub @ X2 @ X1 ) @ X3 ) ) ) )
& ( ! [X5: subst,X6: term,X7: subst,X8: subst] :
( ( $true
!= ( X0 @ X8 @ X6 @ ( comp @ X5 @ X7 ) ) )
| ( ( X0 @ ( comp @ X8 @ X5 ) @ ( sub @ X6 @ X5 ) @ X7 )
= $true ) )
| ( $true
!= ( sP67 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f328]) ).
thf(f328,plain,
! [X189: subst > term > subst > $o] :
( ( ( $true
= ( sP67 @ X189 ) )
| ? [X190: subst,X191: term,X192: subst,X193: subst] :
( ( ( X189 @ X193 @ X191 @ ( comp @ X190 @ X192 ) )
= $true )
& ( ( X189 @ ( comp @ X193 @ X190 ) @ ( sub @ X191 @ X190 ) @ X192 )
!= $true ) ) )
& ( ! [X190: subst,X191: term,X192: subst,X193: subst] :
( ( ( X189 @ X193 @ X191 @ ( comp @ X190 @ X192 ) )
!= $true )
| ( ( X189 @ ( comp @ X193 @ X190 ) @ ( sub @ X191 @ X190 ) @ X192 )
= $true ) )
| ( $true
!= ( sP67 @ X189 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f83]) ).
thf(f11202,plain,
! [X0: subst > term > subst > $o] :
( ( $true
= ( sP67 @ X0 ) )
| ( ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true ) ),
inference(forward_demodulation,[status(thm)],[f11201,f3855]) ).
thf(f11201,plain,
! [X0: subst > term > subst > $o] :
( ( ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( sK247 @ X0 ) )
!= $true )
| ( $true
= ( sP67 @ X0 ) ) ),
inference(forward_demodulation,[status(thm)],[f11200,f3865]) ).
thf(f11200,plain,
! [X0: subst > term > subst > $o] :
( ( $true
= ( sP67 @ X0 ) )
| ( $true
!= ( X0 @ ( d2subst @ d_id ) @ ( sub @ ( sK246 @ X0 ) @ ( sK245 @ X0 ) ) @ ( sK247 @ X0 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f969,f3855]) ).
thf(f969,plain,
! [X0: subst > term > subst > $o] :
( ( $true
!= ( X0 @ ( comp @ ( sK248 @ X0 ) @ ( sK245 @ X0 ) ) @ ( sub @ ( sK246 @ X0 ) @ ( sK245 @ X0 ) ) @ ( sK247 @ X0 ) ) )
| ( $true
= ( sP67 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f331]) ).
thf(f9346,plain,
! [X0: subst > term > subst > $o,X8: subst,X6: term,X7: subst] :
( ( ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ X7 )
= $true )
| ( ( X0 @ X8 @ X6 @ ( d2subst @ d_id ) )
!= $true )
| ( $true
!= ( sP67 @ X0 ) ) ),
inference(forward_demodulation,[status(thm)],[f9345,f3855]) ).
thf(f9345,plain,
! [X0: subst > term > subst > $o,X8: subst,X6: term,X7: subst,X5: subst] :
( ( $true
!= ( sP67 @ X0 ) )
| ( ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ X7 )
= $true )
| ( $true
!= ( X0 @ X8 @ X6 @ ( comp @ X5 @ X7 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f9344,f3865]) ).
thf(f9344,plain,
! [X0: subst > term > subst > $o,X8: subst,X6: term,X7: subst,X5: subst] :
( ( $true
!= ( sP67 @ X0 ) )
| ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( sub @ X6 @ X5 ) @ X7 ) )
| ( $true
!= ( X0 @ X8 @ X6 @ ( comp @ X5 @ X7 ) ) ) ),
inference(forward_demodulation,[status(thm)],[f968,f3855]) ).
thf(f968,plain,
! [X0: subst > term > subst > $o,X8: subst,X6: term,X7: subst,X5: subst] :
( ( ( X0 @ ( comp @ X8 @ X5 ) @ ( sub @ X6 @ X5 ) @ X7 )
= $true )
| ( $true
!= ( X0 @ X8 @ X6 @ ( comp @ X5 @ X7 ) ) )
| ( $true
!= ( sP67 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f331]) ).
thf(f14863,plain,
! [X2: subst > term > term,X0: subst > term > subst > $o] :
( ( ( X0 @ ( d2subst @ d_id ) @ ( lam @ ( X2 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) ) @ ( d2subst @ d_id ) )
= $true )
| ( ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true )
| ( ( sP44 @ X0 )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f14862,f3865]) ).
thf(f14862,plain,
! [X2: subst > term > term,X0: subst > term > subst > $o] :
( ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( sK324 @ X2 @ X0 ) @ ( d2subst @ d_id ) ) )
| ( ( X0 @ ( d2subst @ d_id ) @ ( lam @ ( X2 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) ) @ ( d2subst @ d_id ) )
= $true )
| ( ( sP44 @ X0 )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f14861,f3869]) ).
thf(f3869,plain,
! [X0: term,X1: term] : ( X0 = X1 ),
inference(superposition,[status(thm)],[f3865,f3865]) ).
thf(f14861,plain,
! [X2: subst > term > term,X0: subst > term > subst > $o,X1: term] :
( ( ( sP44 @ X0 )
= $true )
| ( ( X0 @ ( d2subst @ d_id ) @ ( lam @ ( X2 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) ) @ ( d2subst @ d_id ) )
= $true )
| ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( sK324 @ X2 @ X0 ) @ ( d2subst @ d_id ) ) )
| ( ( sub @ X1 @ ( push @ ( sub @ ( sK329 @ X2 @ X1 ) @ ( sK330 @ X2 @ X1 ) ) @ ( comp @ ( sK328 @ X2 @ X1 ) @ ( sK330 @ X2 @ X1 ) ) ) )
!= ( X2 @ ( comp @ ( sK328 @ X2 @ X1 ) @ ( sK330 @ X2 @ X1 ) ) @ ( sub @ ( sK329 @ X2 @ X1 ) @ ( sK330 @ X2 @ X1 ) ) ) ) ),
inference(subsumption_resolution,[status(thm)],[f1649,f3869]) ).
thf(f1649,plain,
! [X2: subst > term > term,X0: subst > term > subst > $o,X1: term] :
( ( ( sub @ ( X2 @ ( sK327 @ X2 @ X1 ) @ ( sK326 @ X2 @ X1 ) ) @ ( sK325 @ X2 @ X1 ) )
!= ( sub @ ( sub @ X1 @ ( push @ ( sK326 @ X2 @ X1 ) @ ( sK327 @ X2 @ X1 ) ) ) @ ( sK325 @ X2 @ X1 ) ) )
| ( ( sP44 @ X0 )
= $true )
| ( ( X0 @ ( d2subst @ d_id ) @ ( lam @ ( X2 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) ) ) @ ( d2subst @ d_id ) )
= $true )
| ( ( sub @ X1 @ ( push @ ( sub @ ( sK329 @ X2 @ X1 ) @ ( sK330 @ X2 @ X1 ) ) @ ( comp @ ( sK328 @ X2 @ X1 ) @ ( sK330 @ X2 @ X1 ) ) ) )
!= ( X2 @ ( comp @ ( sK328 @ X2 @ X1 ) @ ( sK330 @ X2 @ X1 ) ) @ ( sub @ ( sK329 @ X2 @ X1 ) @ ( sK330 @ X2 @ X1 ) ) ) )
| ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( sK324 @ X2 @ X0 ) @ ( d2subst @ d_id ) ) ) ),
inference(definition_unfolding,[status(thm)],[f1074,f1388,f1388,f1388,f1344,f1494,f1388]) ).
thf(f1494,plain,
( one
= ( d2term @ d_one ) ),
inference(cnf_transformation,[status(thm)],[f749]) ).
thf(f1344,plain,
( ( d2subst @ d_id )
= sh ),
inference(cnf_transformation,[status(thm)],[f749]) ).
thf(f1388,plain,
( ( d2subst @ d_id )
= id ),
inference(cnf_transformation,[status(thm)],[f749]) ).
thf(f1074,plain,
! [X2: subst > term > term,X0: subst > term > subst > $o,X1: term] :
( ( ( sP44 @ X0 )
= $true )
| ( ( X0 @ id @ ( sK324 @ X2 @ X0 ) @ id )
= $true )
| ( ( sub @ ( X2 @ ( sK327 @ X2 @ X1 ) @ ( sK326 @ X2 @ X1 ) ) @ ( sK325 @ X2 @ X1 ) )
!= ( sub @ ( sub @ X1 @ ( push @ ( sK326 @ X2 @ X1 ) @ ( sK327 @ X2 @ X1 ) ) ) @ ( sK325 @ X2 @ X1 ) ) )
| ( $true
= ( X0 @ id @ ( lam @ ( X2 @ sh @ one ) ) @ id ) )
| ( ( sub @ X1 @ ( push @ ( sub @ ( sK329 @ X2 @ X1 ) @ ( sK330 @ X2 @ X1 ) ) @ ( comp @ ( sK328 @ X2 @ X1 ) @ ( sK330 @ X2 @ X1 ) ) ) )
!= ( X2 @ ( comp @ ( sK328 @ X2 @ X1 ) @ ( sK330 @ X2 @ X1 ) ) @ ( sub @ ( sK329 @ X2 @ X1 ) @ ( sK330 @ X2 @ X1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f441]) ).
thf(f441,plain,
! [X0: subst > term > subst > $o] :
( ( ( ( sP44 @ X0 )
= $true )
| ! [X1: term,X2: subst > term > term] :
( ( ( ( X0 @ id @ ( X2 @ id @ ( sK324 @ X2 @ X0 ) ) @ id )
!= $true )
& ( ( X0 @ id @ ( sK324 @ X2 @ X0 ) @ id )
= $true ) )
| ( ( sub @ ( X2 @ ( sK327 @ X2 @ X1 ) @ ( sK326 @ X2 @ X1 ) ) @ ( sK325 @ X2 @ X1 ) )
!= ( sub @ ( sub @ X1 @ ( push @ ( sK326 @ X2 @ X1 ) @ ( sK327 @ X2 @ X1 ) ) ) @ ( sK325 @ X2 @ X1 ) ) )
| ( $true
= ( X0 @ id @ ( lam @ ( X2 @ sh @ one ) ) @ id ) )
| ( ( sub @ X1 @ ( push @ ( sub @ ( sK329 @ X2 @ X1 ) @ ( sK330 @ X2 @ X1 ) ) @ ( comp @ ( sK328 @ X2 @ X1 ) @ ( sK330 @ X2 @ X1 ) ) ) )
!= ( X2 @ ( comp @ ( sK328 @ X2 @ X1 ) @ ( sK330 @ X2 @ X1 ) ) @ ( sub @ ( sK329 @ X2 @ X1 ) @ ( sK330 @ X2 @ X1 ) ) ) ) ) )
& ( ( ! [X12: term] :
( ( $true
= ( X0 @ id @ ( sK332 @ X0 @ id @ X12 ) @ id ) )
| ( $true
!= ( X0 @ id @ X12 @ id ) ) )
& ! [X13: subst,X14: term,X15: subst] :
( ( sub @ ( sub @ ( sK331 @ X0 ) @ ( push @ X14 @ X15 ) ) @ X13 )
= ( sub @ ( sK332 @ X0 @ X15 @ X14 ) @ X13 ) )
& ( ( X0 @ id @ ( lam @ ( sK332 @ X0 @ sh @ one ) ) @ id )
!= $true )
& ! [X16: subst,X17: term,X18: subst] :
( ( sK332 @ X0 @ ( comp @ X16 @ X18 ) @ ( sub @ X17 @ X18 ) )
= ( sub @ ( sK331 @ X0 ) @ ( push @ ( sub @ X17 @ X18 ) @ ( comp @ X16 @ X18 ) ) ) ) )
| ( ( sP44 @ X0 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK324,sK325,sK326,sK327,sK328,sK329,sK330,sK331,sK332])],[f436,f440,f439,f438,f437]) ).
thf(f437,plain,
! [X0: subst > term > subst > $o,X2: subst > term > term] :
( ? [X3: term] :
( ( ( X0 @ id @ ( X2 @ id @ X3 ) @ id )
!= $true )
& ( ( X0 @ id @ X3 @ id )
= $true ) )
=> ( ( ( X0 @ id @ ( X2 @ id @ ( sK324 @ X2 @ X0 ) ) @ id )
!= $true )
& ( ( X0 @ id @ ( sK324 @ X2 @ X0 ) @ id )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f438,plain,
! [X1: term,X2: subst > term > term] :
( ? [X4: subst,X5: term,X6: subst] :
( ( sub @ ( sub @ X1 @ ( push @ X5 @ X6 ) ) @ X4 )
!= ( sub @ ( X2 @ X6 @ X5 ) @ X4 ) )
=> ( ( sub @ ( X2 @ ( sK327 @ X2 @ X1 ) @ ( sK326 @ X2 @ X1 ) ) @ ( sK325 @ X2 @ X1 ) )
!= ( sub @ ( sub @ X1 @ ( push @ ( sK326 @ X2 @ X1 ) @ ( sK327 @ X2 @ X1 ) ) ) @ ( sK325 @ X2 @ X1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f439,plain,
! [X1: term,X2: subst > term > term] :
( ? [X7: subst,X8: term,X9: subst] :
( ( sub @ X1 @ ( push @ ( sub @ X8 @ X9 ) @ ( comp @ X7 @ X9 ) ) )
!= ( X2 @ ( comp @ X7 @ X9 ) @ ( sub @ X8 @ X9 ) ) )
=> ( ( sub @ X1 @ ( push @ ( sub @ ( sK329 @ X2 @ X1 ) @ ( sK330 @ X2 @ X1 ) ) @ ( comp @ ( sK328 @ X2 @ X1 ) @ ( sK330 @ X2 @ X1 ) ) ) )
!= ( X2 @ ( comp @ ( sK328 @ X2 @ X1 ) @ ( sK330 @ X2 @ X1 ) ) @ ( sub @ ( sK329 @ X2 @ X1 ) @ ( sK330 @ X2 @ X1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f440,plain,
! [X0: subst > term > subst > $o] :
( ? [X10: term,X11: subst > term > term] :
( ! [X12: term] :
( ( ( X0 @ id @ ( X11 @ id @ X12 ) @ id )
= $true )
| ( $true
!= ( X0 @ id @ X12 @ id ) ) )
& ! [X13: subst,X14: term,X15: subst] :
( ( sub @ ( X11 @ X15 @ X14 ) @ X13 )
= ( sub @ ( sub @ X10 @ ( push @ X14 @ X15 ) ) @ X13 ) )
& ( ( X0 @ id @ ( lam @ ( X11 @ sh @ one ) ) @ id )
!= $true )
& ! [X16: subst,X17: term,X18: subst] :
( ( sub @ X10 @ ( push @ ( sub @ X17 @ X18 ) @ ( comp @ X16 @ X18 ) ) )
= ( X11 @ ( comp @ X16 @ X18 ) @ ( sub @ X17 @ X18 ) ) ) )
=> ( ! [X12: term] :
( ( $true
= ( X0 @ id @ ( sK332 @ X0 @ id @ X12 ) @ id ) )
| ( $true
!= ( X0 @ id @ X12 @ id ) ) )
& ! [X15: subst,X14: term,X13: subst] :
( ( sub @ ( sub @ ( sK331 @ X0 ) @ ( push @ X14 @ X15 ) ) @ X13 )
= ( sub @ ( sK332 @ X0 @ X15 @ X14 ) @ X13 ) )
& ( ( X0 @ id @ ( lam @ ( sK332 @ X0 @ sh @ one ) ) @ id )
!= $true )
& ! [X18: subst,X17: term,X16: subst] :
( ( sK332 @ X0 @ ( comp @ X16 @ X18 ) @ ( sub @ X17 @ X18 ) )
= ( sub @ ( sK331 @ X0 ) @ ( push @ ( sub @ X17 @ X18 ) @ ( comp @ X16 @ X18 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f436,plain,
! [X0: subst > term > subst > $o] :
( ( ( ( sP44 @ X0 )
= $true )
| ! [X1: term,X2: subst > term > term] :
( ? [X3: term] :
( ( ( X0 @ id @ ( X2 @ id @ X3 ) @ id )
!= $true )
& ( ( X0 @ id @ X3 @ id )
= $true ) )
| ? [X4: subst,X5: term,X6: subst] :
( ( sub @ ( sub @ X1 @ ( push @ X5 @ X6 ) ) @ X4 )
!= ( sub @ ( X2 @ X6 @ X5 ) @ X4 ) )
| ( $true
= ( X0 @ id @ ( lam @ ( X2 @ sh @ one ) ) @ id ) )
| ? [X7: subst,X8: term,X9: subst] :
( ( sub @ X1 @ ( push @ ( sub @ X8 @ X9 ) @ ( comp @ X7 @ X9 ) ) )
!= ( X2 @ ( comp @ X7 @ X9 ) @ ( sub @ X8 @ X9 ) ) ) ) )
& ( ? [X10: term,X11: subst > term > term] :
( ! [X12: term] :
( ( ( X0 @ id @ ( X11 @ id @ X12 ) @ id )
= $true )
| ( $true
!= ( X0 @ id @ X12 @ id ) ) )
& ! [X13: subst,X14: term,X15: subst] :
( ( sub @ ( X11 @ X15 @ X14 ) @ X13 )
= ( sub @ ( sub @ X10 @ ( push @ X14 @ X15 ) ) @ X13 ) )
& ( ( X0 @ id @ ( lam @ ( X11 @ sh @ one ) ) @ id )
!= $true )
& ! [X16: subst,X17: term,X18: subst] :
( ( sub @ X10 @ ( push @ ( sub @ X17 @ X18 ) @ ( comp @ X16 @ X18 ) ) )
= ( X11 @ ( comp @ X16 @ X18 ) @ ( sub @ X17 @ X18 ) ) ) )
| ( ( sP44 @ X0 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f435]) ).
thf(f435,plain,
! [X223: subst > term > subst > $o] :
( ( ( ( sP44 @ X223 )
= $true )
| ! [X225: term,X226: subst > term > term] :
( ? [X233: term] :
( ( ( X223 @ id @ ( X226 @ id @ X233 ) @ id )
!= $true )
& ( $true
= ( X223 @ id @ X233 @ id ) ) )
| ? [X227: subst,X228: term,X229: subst] :
( ( sub @ ( sub @ X225 @ ( push @ X228 @ X229 ) ) @ X227 )
!= ( sub @ ( X226 @ X229 @ X228 ) @ X227 ) )
| ( $true
= ( X223 @ id @ ( lam @ ( X226 @ sh @ one ) ) @ id ) )
| ? [X230: subst,X231: term,X232: subst] :
( ( sub @ X225 @ ( push @ ( sub @ X231 @ X232 ) @ ( comp @ X230 @ X232 ) ) )
!= ( X226 @ ( comp @ X230 @ X232 ) @ ( sub @ X231 @ X232 ) ) ) ) )
& ( ? [X225: term,X226: subst > term > term] :
( ! [X233: term] :
( ( ( X223 @ id @ ( X226 @ id @ X233 ) @ id )
= $true )
| ( $true
!= ( X223 @ id @ X233 @ id ) ) )
& ! [X227: subst,X228: term,X229: subst] :
( ( sub @ ( sub @ X225 @ ( push @ X228 @ X229 ) ) @ X227 )
= ( sub @ ( X226 @ X229 @ X228 ) @ X227 ) )
& ( $true
!= ( X223 @ id @ ( lam @ ( X226 @ sh @ one ) ) @ id ) )
& ! [X230: subst,X231: term,X232: subst] :
( ( sub @ X225 @ ( push @ ( sub @ X231 @ X232 ) @ ( comp @ X230 @ X232 ) ) )
= ( X226 @ ( comp @ X230 @ X232 ) @ ( sub @ X231 @ X232 ) ) ) )
| ( ( sP44 @ X223 )
!= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f60]) ).
thf(f8836,plain,
( ! [X2: term] :
( ( sK322 @ ( d2subst @ d_id ) @ X2 @ ( d2subst @ d_id ) )
!= $true )
| ~ spl654_488 ),
inference(avatar_component_clause,[status(thm)],[f8835]) ).
thf(f8835,definition,
( spl654_488
<=> ! [X2: term] :
( ( sK322 @ ( d2subst @ d_id ) @ X2 @ ( d2subst @ d_id ) )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl654_488])],[avatar_definition]) ).
thf(f14490,plain,
( spl654_344
| ~ spl654_521 ),
inference(avatar_split_clause,[status(thm)],[f14442,f11472,f3345]) ).
thf(f3345,definition,
( spl654_344
<=> ! [X1: subst > term > subst > $o] :
( ( $true
= ( sP111 @ X1 ) )
| ( ( sP112 @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl654_344])],[avatar_definition]) ).
thf(f11472,definition,
( spl654_521
<=> ! [X0: subst > term > subst > $o] :
( ( ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true )
| ( ( sP112 @ X0 )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl654_521])],[avatar_definition]) ).
thf(f14442,plain,
( ! [X0: subst > term > subst > $o] :
( ( $true
= ( sP111 @ X0 ) )
| ( ( sP112 @ X0 )
= $true ) )
| ~ spl654_521 ),
inference(trivial_inequality_removal,[status(thm)],[f14417]) ).
thf(f14417,plain,
( ! [X0: subst > term > subst > $o] :
( ( $true != $true )
| ( ( sP112 @ X0 )
= $true )
| ( $true
= ( sP111 @ X0 ) ) )
| ~ spl654_521 ),
inference(superposition,[status(thm)],[f8545,f11473]) ).
thf(f11473,plain,
( ! [X0: subst > term > subst > $o] :
( ( ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true )
| ( ( sP112 @ X0 )
= $true ) )
| ~ spl654_521 ),
inference(avatar_component_clause,[status(thm)],[f11472]) ).
thf(f8545,plain,
! [X0: subst > term > subst > $o] :
( ( ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
!= $true )
| ( $true
= ( sP111 @ X0 ) ) ),
inference(forward_demodulation,[status(thm)],[f1855,f3865]) ).
thf(f1855,plain,
! [X0: subst > term > subst > $o] :
( ( $true
= ( sP111 @ X0 ) )
| ( ( X0 @ ( d2subst @ d_id ) @ ( lam @ ( sub @ ( sK647 @ X0 ) @ ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ) @ ( d2subst @ d_id ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f1525,f1388,f1494,f1344,f1388]) ).
thf(f1525,plain,
! [X0: subst > term > subst > $o] :
( ( $true
= ( sP111 @ X0 ) )
| ( $true
!= ( X0 @ id @ ( lam @ ( sub @ ( sK647 @ X0 ) @ ( push @ one @ sh ) ) ) @ id ) ) ),
inference(cnf_transformation,[status(thm)],[f759]) ).
thf(f759,plain,
! [X0: subst > term > subst > $o] :
( ( ( $true
= ( sP111 @ X0 ) )
| ( ( $true
!= ( X0 @ id @ ( lam @ ( sub @ ( sK647 @ X0 ) @ ( push @ one @ sh ) ) ) @ id ) )
& ! [X2: term] :
( ( ( X0 @ id @ X2 @ id )
!= $true )
| ( $true
= ( X0 @ id @ ( sub @ ( sK647 @ X0 ) @ ( push @ X2 @ id ) ) @ id ) ) ) ) )
& ( ! [X3: term] :
( ( $true
= ( X0 @ id @ ( lam @ ( sub @ X3 @ ( push @ one @ sh ) ) ) @ id ) )
| ( ( $true
= ( X0 @ id @ ( sK648 @ X3 @ X0 ) @ id ) )
& ( ( X0 @ id @ ( sub @ X3 @ ( push @ ( sK648 @ X3 @ X0 ) @ id ) ) @ id )
!= $true ) ) )
| ( $true
!= ( sP111 @ X0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK647,sK648])],[f756,f758,f757]) ).
thf(f757,plain,
! [X0: subst > term > subst > $o] :
( ? [X1: term] :
( ( ( X0 @ id @ ( lam @ ( sub @ X1 @ ( push @ one @ sh ) ) ) @ id )
!= $true )
& ! [X2: term] :
( ( ( X0 @ id @ X2 @ id )
!= $true )
| ( ( X0 @ id @ ( sub @ X1 @ ( push @ X2 @ id ) ) @ id )
= $true ) ) )
=> ( ( $true
!= ( X0 @ id @ ( lam @ ( sub @ ( sK647 @ X0 ) @ ( push @ one @ sh ) ) ) @ id ) )
& ! [X2: term] :
( ( ( X0 @ id @ X2 @ id )
!= $true )
| ( $true
= ( X0 @ id @ ( sub @ ( sK647 @ X0 ) @ ( push @ X2 @ id ) ) @ id ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f758,plain,
! [X0: subst > term > subst > $o,X3: term] :
( ? [X4: term] :
( ( ( X0 @ id @ X4 @ id )
= $true )
& ( ( X0 @ id @ ( sub @ X3 @ ( push @ X4 @ id ) ) @ id )
!= $true ) )
=> ( ( $true
= ( X0 @ id @ ( sK648 @ X3 @ X0 ) @ id ) )
& ( ( X0 @ id @ ( sub @ X3 @ ( push @ ( sK648 @ X3 @ X0 ) @ id ) ) @ id )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f756,plain,
! [X0: subst > term > subst > $o] :
( ( ( $true
= ( sP111 @ X0 ) )
| ? [X1: term] :
( ( ( X0 @ id @ ( lam @ ( sub @ X1 @ ( push @ one @ sh ) ) ) @ id )
!= $true )
& ! [X2: term] :
( ( ( X0 @ id @ X2 @ id )
!= $true )
| ( ( X0 @ id @ ( sub @ X1 @ ( push @ X2 @ id ) ) @ id )
= $true ) ) ) )
& ( ! [X3: term] :
( ( $true
= ( X0 @ id @ ( lam @ ( sub @ X3 @ ( push @ one @ sh ) ) ) @ id ) )
| ? [X4: term] :
( ( ( X0 @ id @ X4 @ id )
= $true )
& ( ( X0 @ id @ ( sub @ X3 @ ( push @ X4 @ id ) ) @ id )
!= $true ) ) )
| ( $true
!= ( sP111 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f755]) ).
thf(f755,plain,
! [X0: subst > term > subst > $o] :
( ( ( $true
= ( sP111 @ X0 ) )
| ? [X7: term] :
( ( $true
!= ( X0 @ id @ ( lam @ ( sub @ X7 @ ( push @ one @ sh ) ) ) @ id ) )
& ! [X8: term] :
( ( $true
!= ( X0 @ id @ X8 @ id ) )
| ( $true
= ( X0 @ id @ ( sub @ X7 @ ( push @ X8 @ id ) ) @ id ) ) ) ) )
& ( ! [X7: term] :
( ( $true
= ( X0 @ id @ ( lam @ ( sub @ X7 @ ( push @ one @ sh ) ) ) @ id ) )
| ? [X8: term] :
( ( $true
= ( X0 @ id @ X8 @ id ) )
& ( $true
!= ( X0 @ id @ ( sub @ X7 @ ( push @ X8 @ id ) ) @ id ) ) ) )
| ( $true
!= ( sP111 @ X0 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f128]) ).
thf(f128,plain,
! [X0: subst > term > subst > $o] :
( ( $true
= ( sP111 @ X0 ) )
<=> ! [X7: term] :
( ( $true
= ( X0 @ id @ ( lam @ ( sub @ X7 @ ( push @ one @ sh ) ) ) @ id ) )
| ? [X8: term] :
( ( $true
= ( X0 @ id @ X8 @ id ) )
& ( $true
!= ( X0 @ id @ ( sub @ X7 @ ( push @ X8 @ id ) ) @ id ) ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f14373,plain,
~ spl654_520,
inference(avatar_contradiction_clause,[status(thm)],[f14372]) ).
thf(f14372,plain,
( $false
| ~ spl654_520 ),
inference(subsumption_resolution,[status(thm)],[f14371,f11470]) ).
thf(f11470,plain,
( ! [X1: subst > term > term] :
( ( sP110 @ X1 )
!= $true )
| ~ spl654_520 ),
inference(avatar_component_clause,[status(thm)],[f11469]) ).
thf(f11469,definition,
( spl654_520
<=> ! [X1: subst > term > term] :
( ( sP110 @ X1 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl654_520])],[avatar_definition]) ).
thf(f14371,plain,
! [X0: subst > term > term] :
( $true
= ( sP110 @ X0 ) ),
inference(subsumption_resolution,[status(thm)],[f14370,f3869]) ).
thf(f14370,plain,
! [X0: subst > term > term,X1: term] :
( ( ( sub @ ( X0 @ ( sK651 @ X1 @ X0 ) @ ( sK650 @ X1 @ X0 ) ) @ ( sK649 @ X1 @ X0 ) )
!= ( sub @ ( sub @ X1 @ ( push @ ( sK650 @ X1 @ X0 ) @ ( sK651 @ X1 @ X0 ) ) ) @ ( sK649 @ X1 @ X0 ) ) )
| ( $true
= ( sP110 @ X0 ) ) ),
inference(subsumption_resolution,[status(thm)],[f1528,f3869]) ).
thf(f1528,plain,
! [X0: subst > term > term,X1: term] :
( ( ( sub @ X1 @ ( push @ ( sub @ ( sK650 @ X1 @ X0 ) @ ( sK649 @ X1 @ X0 ) ) @ ( comp @ ( sK651 @ X1 @ X0 ) @ ( sK649 @ X1 @ X0 ) ) ) )
!= ( X0 @ ( comp @ ( sK651 @ X1 @ X0 ) @ ( sK649 @ X1 @ X0 ) ) @ ( sub @ ( sK650 @ X1 @ X0 ) @ ( sK649 @ X1 @ X0 ) ) ) )
| ( $true
= ( sP110 @ X0 ) )
| ( ( sub @ ( X0 @ ( sK651 @ X1 @ X0 ) @ ( sK650 @ X1 @ X0 ) ) @ ( sK649 @ X1 @ X0 ) )
!= ( sub @ ( sub @ X1 @ ( push @ ( sK650 @ X1 @ X0 ) @ ( sK651 @ X1 @ X0 ) ) ) @ ( sK649 @ X1 @ X0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f764]) ).
thf(f764,plain,
! [X0: subst > term > term] :
( ( ( $true
= ( sP110 @ X0 ) )
| ! [X1: term] :
( ( ( sub @ X1 @ ( push @ ( sub @ ( sK650 @ X1 @ X0 ) @ ( sK649 @ X1 @ X0 ) ) @ ( comp @ ( sK651 @ X1 @ X0 ) @ ( sK649 @ X1 @ X0 ) ) ) )
!= ( X0 @ ( comp @ ( sK651 @ X1 @ X0 ) @ ( sK649 @ X1 @ X0 ) ) @ ( sub @ ( sK650 @ X1 @ X0 ) @ ( sK649 @ X1 @ X0 ) ) ) )
| ( ( sub @ ( X0 @ ( sK651 @ X1 @ X0 ) @ ( sK650 @ X1 @ X0 ) ) @ ( sK649 @ X1 @ X0 ) )
!= ( sub @ ( sub @ X1 @ ( push @ ( sK650 @ X1 @ X0 ) @ ( sK651 @ X1 @ X0 ) ) ) @ ( sK649 @ X1 @ X0 ) ) ) ) )
& ( ! [X6: subst,X7: term,X8: subst] :
( ( ( sub @ ( sK652 @ X0 ) @ ( push @ ( sub @ X7 @ X6 ) @ ( comp @ X8 @ X6 ) ) )
= ( X0 @ ( comp @ X8 @ X6 ) @ ( sub @ X7 @ X6 ) ) )
& ( ( sub @ ( sub @ ( sK652 @ X0 ) @ ( push @ X7 @ X8 ) ) @ X6 )
= ( sub @ ( X0 @ X8 @ X7 ) @ X6 ) ) )
| ( $true
!= ( sP110 @ X0 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK649,sK650,sK651,sK652])],[f761,f763,f762]) ).
thf(f762,plain,
! [X0: subst > term > term,X1: term] :
( ? [X2: subst,X3: term,X4: subst] :
( ( ( sub @ X1 @ ( push @ ( sub @ X3 @ X2 ) @ ( comp @ X4 @ X2 ) ) )
!= ( X0 @ ( comp @ X4 @ X2 ) @ ( sub @ X3 @ X2 ) ) )
| ( ( sub @ ( sub @ X1 @ ( push @ X3 @ X4 ) ) @ X2 )
!= ( sub @ ( X0 @ X4 @ X3 ) @ X2 ) ) )
=> ( ( ( sub @ X1 @ ( push @ ( sub @ ( sK650 @ X1 @ X0 ) @ ( sK649 @ X1 @ X0 ) ) @ ( comp @ ( sK651 @ X1 @ X0 ) @ ( sK649 @ X1 @ X0 ) ) ) )
!= ( X0 @ ( comp @ ( sK651 @ X1 @ X0 ) @ ( sK649 @ X1 @ X0 ) ) @ ( sub @ ( sK650 @ X1 @ X0 ) @ ( sK649 @ X1 @ X0 ) ) ) )
| ( ( sub @ ( X0 @ ( sK651 @ X1 @ X0 ) @ ( sK650 @ X1 @ X0 ) ) @ ( sK649 @ X1 @ X0 ) )
!= ( sub @ ( sub @ X1 @ ( push @ ( sK650 @ X1 @ X0 ) @ ( sK651 @ X1 @ X0 ) ) ) @ ( sK649 @ X1 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f763,plain,
! [X0: subst > term > term] :
( ? [X5: term] :
! [X6: subst,X7: term,X8: subst] :
( ( ( sub @ X5 @ ( push @ ( sub @ X7 @ X6 ) @ ( comp @ X8 @ X6 ) ) )
= ( X0 @ ( comp @ X8 @ X6 ) @ ( sub @ X7 @ X6 ) ) )
& ( ( sub @ ( sub @ X5 @ ( push @ X7 @ X8 ) ) @ X6 )
= ( sub @ ( X0 @ X8 @ X7 ) @ X6 ) ) )
=> ! [X8: subst,X7: term,X6: subst] :
( ( ( sub @ ( sK652 @ X0 ) @ ( push @ ( sub @ X7 @ X6 ) @ ( comp @ X8 @ X6 ) ) )
= ( X0 @ ( comp @ X8 @ X6 ) @ ( sub @ X7 @ X6 ) ) )
& ( ( sub @ ( sub @ ( sK652 @ X0 ) @ ( push @ X7 @ X8 ) ) @ X6 )
= ( sub @ ( X0 @ X8 @ X7 ) @ X6 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f761,plain,
! [X0: subst > term > term] :
( ( ( $true
= ( sP110 @ X0 ) )
| ! [X1: term] :
? [X2: subst,X3: term,X4: subst] :
( ( ( sub @ X1 @ ( push @ ( sub @ X3 @ X2 ) @ ( comp @ X4 @ X2 ) ) )
!= ( X0 @ ( comp @ X4 @ X2 ) @ ( sub @ X3 @ X2 ) ) )
| ( ( sub @ ( sub @ X1 @ ( push @ X3 @ X4 ) ) @ X2 )
!= ( sub @ ( X0 @ X4 @ X3 ) @ X2 ) ) ) )
& ( ? [X5: term] :
! [X6: subst,X7: term,X8: subst] :
( ( ( sub @ X5 @ ( push @ ( sub @ X7 @ X6 ) @ ( comp @ X8 @ X6 ) ) )
= ( X0 @ ( comp @ X8 @ X6 ) @ ( sub @ X7 @ X6 ) ) )
& ( ( sub @ ( sub @ X5 @ ( push @ X7 @ X8 ) ) @ X6 )
= ( sub @ ( X0 @ X8 @ X7 ) @ X6 ) ) )
| ( $true
!= ( sP110 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f760]) ).
thf(f760,plain,
! [X1: subst > term > term] :
( ( ( ( sP110 @ X1 )
= $true )
| ! [X2: term] :
? [X3: subst,X4: term,X5: subst] :
( ( ( sub @ X2 @ ( push @ ( sub @ X4 @ X3 ) @ ( comp @ X5 @ X3 ) ) )
!= ( X1 @ ( comp @ X5 @ X3 ) @ ( sub @ X4 @ X3 ) ) )
| ( ( sub @ ( sub @ X2 @ ( push @ X4 @ X5 ) ) @ X3 )
!= ( sub @ ( X1 @ X5 @ X4 ) @ X3 ) ) ) )
& ( ? [X2: term] :
! [X3: subst,X4: term,X5: subst] :
( ( ( sub @ X2 @ ( push @ ( sub @ X4 @ X3 ) @ ( comp @ X5 @ X3 ) ) )
= ( X1 @ ( comp @ X5 @ X3 ) @ ( sub @ X4 @ X3 ) ) )
& ( ( sub @ ( sub @ X2 @ ( push @ X4 @ X5 ) ) @ X3 )
= ( sub @ ( X1 @ X5 @ X4 ) @ X3 ) ) )
| ( ( sP110 @ X1 )
!= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f127]) ).
thf(f127,plain,
! [X1: subst > term > term] :
( ( ( sP110 @ X1 )
= $true )
<=> ? [X2: term] :
! [X3: subst,X4: term,X5: subst] :
( ( ( sub @ X2 @ ( push @ ( sub @ X4 @ X3 ) @ ( comp @ X5 @ X3 ) ) )
= ( X1 @ ( comp @ X5 @ X3 ) @ ( sub @ X4 @ X3 ) ) )
& ( ( sub @ ( sub @ X2 @ ( push @ X4 @ X5 ) ) @ X3 )
= ( sub @ ( X1 @ X5 @ X4 ) @ X3 ) ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f11474,plain,
( spl654_520
| spl654_521 ),
inference(avatar_split_clause,[status(thm)],[f11467,f11472,f11469]) ).
thf(f11467,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ( ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true )
| ( ( sP110 @ X1 )
!= $true )
| ( ( sP112 @ X0 )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f1859,f11205]) ).
thf(f1859,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ( ( sP112 @ X0 )
= $true )
| ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( sK645 @ X1 @ X0 ) @ ( d2subst @ d_id ) ) )
| ( ( X0 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
= $true )
| ( ( sP110 @ X1 )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f1852]) ).
thf(f1852,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ( ( sP112 @ X0 )
= $true )
| ( $true
= ( X0 @ ( d2subst @ d_id )
@ ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one )
@ ( d2subst @ d_id )
@ ^ [Y0: subst,Y1: term] : ( X1 @ Y0 @ Y1 ) )
@ ( d2subst @ d_id ) ) )
| ( ( sP110 @ X1 )
!= $true )
| ( $true
= ( X0 @ ( d2subst @ d_id ) @ ( sK645 @ X1 @ X0 ) @ ( d2subst @ d_id ) ) ) ),
inference(definition_unfolding,[status(thm)],[f1520,f1388,f1388,f1388,f1420,f1388,f1388]) ).
thf(f1420,plain,
( hoaslam
= ( ^ [Y0: subst,Y1: subst > term > term] : ( d2term @ d_one ) ) ),
inference(cnf_transformation,[status(thm)],[f749]) ).
thf(f1520,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ( ( sP112 @ X0 )
= $true )
| ( $true
= ( X0 @ id @ ( sK645 @ X1 @ X0 ) @ id ) )
| ( ( sP110 @ X1 )
!= $true )
| ( ( X0 @ id
@ ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( X1 @ Y0 @ Y1 ) )
@ id )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f754]) ).
thf(f754,plain,
! [X0: subst > term > subst > $o] :
( ( ( ( sP112 @ X0 )
= $true )
| ! [X1: subst > term > term] :
( ( ( ( X0 @ id @ ( X1 @ id @ ( sK645 @ X1 @ X0 ) ) @ id )
!= $true )
& ( $true
= ( X0 @ id @ ( sK645 @ X1 @ X0 ) @ id ) ) )
| ( ( sP110 @ X1 )
!= $true )
| ( ( X0 @ id
@ ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( X1 @ Y0 @ Y1 ) )
@ id )
= $true ) ) )
& ( ( ! [X4: term] :
( ( ( X0 @ id @ ( sK646 @ X0 @ id @ X4 ) @ id )
= $true )
| ( ( X0 @ id @ X4 @ id )
!= $true ) )
& ( $true
= ( sP110 @ ( sK646 @ X0 ) ) )
& ( ( X0 @ id
@ ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( sK646 @ X0 @ Y0 @ Y1 ) )
@ id )
!= $true ) )
| ( ( sP112 @ X0 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK645,sK646])],[f751,f753,f752]) ).
thf(f752,plain,
! [X0: subst > term > subst > $o,X1: subst > term > term] :
( ? [X2: term] :
( ( ( X0 @ id @ ( X1 @ id @ X2 ) @ id )
!= $true )
& ( ( X0 @ id @ X2 @ id )
= $true ) )
=> ( ( ( X0 @ id @ ( X1 @ id @ ( sK645 @ X1 @ X0 ) ) @ id )
!= $true )
& ( $true
= ( X0 @ id @ ( sK645 @ X1 @ X0 ) @ id ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f753,plain,
! [X0: subst > term > subst > $o] :
( ? [X3: subst > term > term] :
( ! [X4: term] :
( ( $true
= ( X0 @ id @ ( X3 @ id @ X4 ) @ id ) )
| ( ( X0 @ id @ X4 @ id )
!= $true ) )
& ( $true
= ( sP110 @ X3 ) )
& ( $true
!= ( X0 @ id
@ ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( X3 @ Y0 @ Y1 ) )
@ id ) ) )
=> ( ! [X4: term] :
( ( ( X0 @ id @ ( sK646 @ X0 @ id @ X4 ) @ id )
= $true )
| ( ( X0 @ id @ X4 @ id )
!= $true ) )
& ( $true
= ( sP110 @ ( sK646 @ X0 ) ) )
& ( ( X0 @ id
@ ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( sK646 @ X0 @ Y0 @ Y1 ) )
@ id )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f751,plain,
! [X0: subst > term > subst > $o] :
( ( ( ( sP112 @ X0 )
= $true )
| ! [X1: subst > term > term] :
( ? [X2: term] :
( ( ( X0 @ id @ ( X1 @ id @ X2 ) @ id )
!= $true )
& ( ( X0 @ id @ X2 @ id )
= $true ) )
| ( ( sP110 @ X1 )
!= $true )
| ( ( X0 @ id
@ ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( X1 @ Y0 @ Y1 ) )
@ id )
= $true ) ) )
& ( ? [X3: subst > term > term] :
( ! [X4: term] :
( ( $true
= ( X0 @ id @ ( X3 @ id @ X4 ) @ id ) )
| ( ( X0 @ id @ X4 @ id )
!= $true ) )
& ( $true
= ( sP110 @ X3 ) )
& ( $true
!= ( X0 @ id
@ ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( X3 @ Y0 @ Y1 ) )
@ id ) ) )
| ( ( sP112 @ X0 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f750]) ).
thf(f750,plain,
! [X0: subst > term > subst > $o] :
( ( ( ( sP112 @ X0 )
= $true )
| ! [X1: subst > term > term] :
( ? [X6: term] :
( ( ( X0 @ id @ ( X1 @ id @ X6 ) @ id )
!= $true )
& ( ( X0 @ id @ X6 @ id )
= $true ) )
| ( ( sP110 @ X1 )
!= $true )
| ( ( X0 @ id
@ ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( X1 @ Y0 @ Y1 ) )
@ id )
= $true ) ) )
& ( ? [X1: subst > term > term] :
( ! [X6: term] :
( ( ( X0 @ id @ ( X1 @ id @ X6 ) @ id )
= $true )
| ( ( X0 @ id @ X6 @ id )
!= $true ) )
& ( ( sP110 @ X1 )
= $true )
& ( ( X0 @ id
@ ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( X1 @ Y0 @ Y1 ) )
@ id )
!= $true ) )
| ( ( sP112 @ X0 )
!= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f129]) ).
thf(f129,plain,
! [X0: subst > term > subst > $o] :
( ( ( sP112 @ X0 )
= $true )
<=> ? [X1: subst > term > term] :
( ! [X6: term] :
( ( ( X0 @ id @ ( X1 @ id @ X6 ) @ id )
= $true )
| ( ( X0 @ id @ X6 @ id )
!= $true ) )
& ( ( sP110 @ X1 )
= $true )
& ( ( X0 @ id
@ ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( X1 @ Y0 @ Y1 ) )
@ id )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f8846,plain,
( spl654_242
| spl654_250
| ~ spl654_344 ),
inference(avatar_contradiction_clause,[status(thm)],[f8845]) ).
thf(f8845,plain,
( $false
| spl654_242
| spl654_250
| ~ spl654_344 ),
inference(subsumption_resolution,[status(thm)],[f8844,f2933]) ).
thf(f2933,plain,
( ( ( sP112 @ sK653 )
!= $true )
| spl654_250 ),
inference(avatar_component_clause,[status(thm)],[f2932]) ).
thf(f2932,definition,
( spl654_250
<=> ( ( sP112 @ sK653 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl654_250])],[avatar_definition]) ).
thf(f8844,plain,
( ( ( sP112 @ sK653 )
= $true )
| spl654_242
| ~ spl654_344 ),
inference(trivial_inequality_removal,[status(thm)],[f8843]) ).
thf(f8843,plain,
( ( $true != $true )
| ( ( sP112 @ sK653 )
= $true )
| spl654_242
| ~ spl654_344 ),
inference(superposition,[status(thm)],[f2902,f3346]) ).
thf(f3346,plain,
( ! [X1: subst > term > subst > $o] :
( ( $true
= ( sP111 @ X1 ) )
| ( ( sP112 @ X1 )
= $true ) )
| ~ spl654_344 ),
inference(avatar_component_clause,[status(thm)],[f3345]) ).
thf(f2902,plain,
( ( $true
!= ( sP111 @ sK653 ) )
| spl654_242 ),
inference(avatar_component_clause,[status(thm)],[f2901]) ).
thf(f2901,definition,
( spl654_242
<=> ( $true
= ( sP111 @ sK653 ) ) ),
introduced(definition,[new_symbols(naming,[spl654_242])],[avatar_definition]) ).
thf(f8837,plain,
( spl654_487
| spl654_488
| ~ spl654_74 ),
inference(avatar_split_clause,[status(thm)],[f7236,f2200,f8835,f8832]) ).
thf(f2200,definition,
( spl654_74
<=> ! [X2: term] :
( ( ( sK322 @ ( d2subst @ d_id ) @ X2 @ ( d2subst @ d_id ) )
!= $true )
| ( ( sK322 @ ( d2subst @ d_id ) @ ( sub @ sK321 @ ( push @ X2 @ ( d2subst @ d_id ) ) ) @ ( d2subst @ d_id ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl654_74])],[avatar_definition]) ).
thf(f7236,plain,
( ! [X2: term] :
( ( ( sK322 @ ( d2subst @ d_id ) @ X2 @ ( d2subst @ d_id ) )
!= $true )
| ( $true
= ( sK322 @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) )
| ~ spl654_74 ),
inference(forward_demodulation,[status(thm)],[f2201,f3865]) ).
thf(f2201,plain,
( ! [X2: term] :
( ( ( sK322 @ ( d2subst @ d_id ) @ ( sub @ sK321 @ ( push @ X2 @ ( d2subst @ d_id ) ) ) @ ( d2subst @ d_id ) )
= $true )
| ( ( sK322 @ ( d2subst @ d_id ) @ X2 @ ( d2subst @ d_id ) )
!= $true ) )
| ~ spl654_74 ),
inference(avatar_component_clause,[status(thm)],[f2200]) ).
thf(f3464,plain,
( spl654_73
| ~ spl654_371 ),
inference(avatar_split_clause,[status(thm)],[f1645,f3462,f2197]) ).
thf(f2197,definition,
( spl654_73
<=> ( $true = sP45 ) ),
introduced(definition,[new_symbols(naming,[spl654_73])],[avatar_definition]) ).
thf(f1645,plain,
( ( $true = sP45 )
| ( ( sK322 @ ( d2subst @ d_id ) @ ( lam @ ( sub @ sK321 @ ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) ) @ ( d2subst @ d_id ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f1067,f1388,f1494,f1344,f1388]) ).
thf(f1067,plain,
( ( $true = sP45 )
| ( ( sK322 @ id @ ( lam @ ( sub @ sK321 @ ( push @ one @ sh ) ) ) @ id )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f434]) ).
thf(f434,plain,
( ( ( $true = sP45 )
| ( ( $true
!= ( sP44 @ sK322 ) )
& ! [X2: term] :
( ( ( sK322 @ id @ X2 @ id )
!= $true )
| ( $true
= ( sK322 @ id @ ( sub @ sK321 @ ( push @ X2 @ id ) ) @ id ) ) )
& ( ( sK322 @ id @ ( lam @ ( sub @ sK321 @ ( push @ one @ sh ) ) ) @ id )
!= $true ) ) )
& ( ! [X3: term,X4: subst > term > subst > $o] :
( ( $true
= ( sP44 @ X4 ) )
| ( ( $true
= ( X4 @ id @ ( sK323 @ X4 @ X3 ) @ id ) )
& ( ( X4 @ id @ ( sub @ X3 @ ( push @ ( sK323 @ X4 @ X3 ) @ id ) ) @ id )
!= $true ) )
| ( ( X4 @ id @ ( lam @ ( sub @ X3 @ ( push @ one @ sh ) ) ) @ id )
= $true ) )
| ( $true != sP45 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK321,sK322,sK323])],[f431,f433,f432]) ).
thf(f432,plain,
( ? [X0: term,X1: subst > term > subst > $o] :
( ( $true
!= ( sP44 @ X1 ) )
& ! [X2: term] :
( ( $true
!= ( X1 @ id @ X2 @ id ) )
| ( $true
= ( X1 @ id @ ( sub @ X0 @ ( push @ X2 @ id ) ) @ id ) ) )
& ( ( X1 @ id @ ( lam @ ( sub @ X0 @ ( push @ one @ sh ) ) ) @ id )
!= $true ) )
=> ( ( $true
!= ( sP44 @ sK322 ) )
& ! [X2: term] :
( ( ( sK322 @ id @ X2 @ id )
!= $true )
| ( $true
= ( sK322 @ id @ ( sub @ sK321 @ ( push @ X2 @ id ) ) @ id ) ) )
& ( ( sK322 @ id @ ( lam @ ( sub @ sK321 @ ( push @ one @ sh ) ) ) @ id )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f433,plain,
! [X3: term,X4: subst > term > subst > $o] :
( ? [X5: term] :
( ( ( X4 @ id @ X5 @ id )
= $true )
& ( ( X4 @ id @ ( sub @ X3 @ ( push @ X5 @ id ) ) @ id )
!= $true ) )
=> ( ( $true
= ( X4 @ id @ ( sK323 @ X4 @ X3 ) @ id ) )
& ( ( X4 @ id @ ( sub @ X3 @ ( push @ ( sK323 @ X4 @ X3 ) @ id ) ) @ id )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f431,plain,
( ( ( $true = sP45 )
| ? [X0: term,X1: subst > term > subst > $o] :
( ( $true
!= ( sP44 @ X1 ) )
& ! [X2: term] :
( ( $true
!= ( X1 @ id @ X2 @ id ) )
| ( $true
= ( X1 @ id @ ( sub @ X0 @ ( push @ X2 @ id ) ) @ id ) ) )
& ( ( X1 @ id @ ( lam @ ( sub @ X0 @ ( push @ one @ sh ) ) ) @ id )
!= $true ) ) )
& ( ! [X3: term,X4: subst > term > subst > $o] :
( ( $true
= ( sP44 @ X4 ) )
| ? [X5: term] :
( ( ( X4 @ id @ X5 @ id )
= $true )
& ( ( X4 @ id @ ( sub @ X3 @ ( push @ X5 @ id ) ) @ id )
!= $true ) )
| ( ( X4 @ id @ ( lam @ ( sub @ X3 @ ( push @ one @ sh ) ) ) @ id )
= $true ) )
| ( $true != sP45 ) ) ),
inference(rectify,[status(thm)],[f430]) ).
thf(f430,plain,
( ( ( $true = sP45 )
| ? [X222: term,X223: subst > term > subst > $o] :
( ( ( sP44 @ X223 )
!= $true )
& ! [X224: term] :
( ( ( X223 @ id @ X224 @ id )
!= $true )
| ( $true
= ( X223 @ id @ ( sub @ X222 @ ( push @ X224 @ id ) ) @ id ) ) )
& ( $true
!= ( X223 @ id @ ( lam @ ( sub @ X222 @ ( push @ one @ sh ) ) ) @ id ) ) ) )
& ( ! [X222: term,X223: subst > term > subst > $o] :
( ( ( sP44 @ X223 )
= $true )
| ? [X224: term] :
( ( ( X223 @ id @ X224 @ id )
= $true )
& ( $true
!= ( X223 @ id @ ( sub @ X222 @ ( push @ X224 @ id ) ) @ id ) ) )
| ( $true
= ( X223 @ id @ ( lam @ ( sub @ X222 @ ( push @ one @ sh ) ) ) @ id ) ) )
| ( $true != sP45 ) ) ),
inference(nnf_transformation,[status(thm)],[f61]) ).
thf(f3268,plain,
( spl654_241
| ~ spl654_73 ),
inference(avatar_split_clause,[status(thm)],[f1422,f2197,f2898]) ).
thf(f2898,definition,
( spl654_241
<=> ( hoasinduction_lem3aaa = $true ) ),
introduced(definition,[new_symbols(naming,[spl654_241])],[avatar_definition]) ).
thf(f1422,plain,
( ( hoasinduction_lem3aaa = $true )
| ( $true != sP45 ) ),
inference(cnf_transformation,[status(thm)],[f749]) ).
thf(f3128,plain,
( ~ spl654_294
| spl654_73 ),
inference(avatar_split_clause,[status(thm)],[f1069,f2197,f3126]) ).
thf(f1069,plain,
( ( $true
!= ( sP44 @ sK322 ) )
| ( $true = sP45 ) ),
inference(cnf_transformation,[status(thm)],[f434]) ).
thf(f2934,plain,
( ~ spl654_250
| ~ spl654_241 ),
inference(avatar_split_clause,[status(thm)],[f1531,f2898,f2932]) ).
thf(f1531,plain,
( ( ( sP112 @ sK653 )
!= $true )
| ( hoasinduction_lem3aaa != $true ) ),
inference(cnf_transformation,[status(thm)],[f768]) ).
thf(f768,plain,
( ( ( hoasinduction_lem3aaa != $true )
| ( ( ( sP112 @ sK653 )
!= $true )
& ( $true
!= ( sP111 @ sK653 ) ) ) )
& ( ( hoasinduction_lem3aaa = $true )
| ! [X1: subst > term > subst > $o] :
( ( ( sP112 @ X1 )
= $true )
| ( $true
= ( sP111 @ X1 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK653])],[f766,f767]) ).
thf(f767,plain,
( ? [X0: subst > term > subst > $o] :
( ( ( sP112 @ X0 )
!= $true )
& ( $true
!= ( sP111 @ X0 ) ) )
=> ( ( ( sP112 @ sK653 )
!= $true )
& ( $true
!= ( sP111 @ sK653 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f766,plain,
( ( ( hoasinduction_lem3aaa != $true )
| ? [X0: subst > term > subst > $o] :
( ( ( sP112 @ X0 )
!= $true )
& ( $true
!= ( sP111 @ X0 ) ) ) )
& ( ( hoasinduction_lem3aaa = $true )
| ! [X1: subst > term > subst > $o] :
( ( ( sP112 @ X1 )
= $true )
| ( $true
= ( sP111 @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f765]) ).
thf(f765,plain,
( ( ( hoasinduction_lem3aaa != $true )
| ? [X0: subst > term > subst > $o] :
( ( ( sP112 @ X0 )
!= $true )
& ( $true
!= ( sP111 @ X0 ) ) ) )
& ( ( hoasinduction_lem3aaa = $true )
| ! [X0: subst > term > subst > $o] :
( ( ( sP112 @ X0 )
= $true )
| ( $true
= ( sP111 @ X0 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f130]) ).
thf(f130,plain,
( ! [X0: subst > term > subst > $o] :
( ( ( sP112 @ X0 )
= $true )
| ( $true
= ( sP111 @ X0 ) ) )
<~> ( hoasinduction_lem3aaa = $true ) ),
inference(definition_folding,[status(thm)],[f15,f129,f128,f127]) ).
thf(f15,plain,
( ! [X0: subst > term > subst > $o] :
( ? [X1: subst > term > term] :
( ! [X6: term] :
( ( ( X0 @ id @ ( X1 @ id @ X6 ) @ id )
= $true )
| ( ( X0 @ id @ X6 @ id )
!= $true ) )
& ? [X2: term] :
! [X3: subst,X4: term,X5: subst] :
( ( ( sub @ X2 @ ( push @ ( sub @ X4 @ X3 ) @ ( comp @ X5 @ X3 ) ) )
= ( X1 @ ( comp @ X5 @ X3 ) @ ( sub @ X4 @ X3 ) ) )
& ( ( sub @ ( sub @ X2 @ ( push @ X4 @ X5 ) ) @ X3 )
= ( sub @ ( X1 @ X5 @ X4 ) @ X3 ) ) )
& ( ( X0 @ id
@ ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( X1 @ Y0 @ Y1 ) )
@ id )
!= $true ) )
| ! [X7: term] :
( ( $true
= ( X0 @ id @ ( lam @ ( sub @ X7 @ ( push @ one @ sh ) ) ) @ id ) )
| ? [X8: term] :
( ( $true
= ( X0 @ id @ X8 @ id ) )
& ( $true
!= ( X0 @ id @ ( sub @ X7 @ ( push @ X8 @ id ) ) @ id ) ) ) ) )
<~> ( hoasinduction_lem3aaa = $true ) ),
inference(flattening,[status(thm)],[f14]) ).
thf(f14,plain,
( ( hoasinduction_lem3aaa = $true )
<~> ! [X0: subst > term > subst > $o] :
( ! [X7: term] :
( ( $true
= ( X0 @ id @ ( lam @ ( sub @ X7 @ ( push @ one @ sh ) ) ) @ id ) )
| ? [X8: term] :
( ( $true
= ( X0 @ id @ X8 @ id ) )
& ( $true
!= ( X0 @ id @ ( sub @ X7 @ ( push @ X8 @ id ) ) @ id ) ) ) )
| ? [X1: subst > term > term] :
( ( ( X0 @ id
@ ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( X1 @ Y0 @ Y1 ) )
@ id )
!= $true )
& ! [X6: term] :
( ( ( X0 @ id @ ( X1 @ id @ X6 ) @ id )
= $true )
| ( ( X0 @ id @ X6 @ id )
!= $true ) )
& ? [X2: term] :
! [X3: subst,X4: term,X5: subst] :
( ( ( sub @ X2 @ ( push @ ( sub @ X4 @ X3 ) @ ( comp @ X5 @ X3 ) ) )
= ( X1 @ ( comp @ X5 @ X3 ) @ ( sub @ X4 @ X3 ) ) )
& ( ( sub @ ( sub @ X2 @ ( push @ X4 @ X5 ) ) @ X3 )
= ( sub @ ( X1 @ X5 @ X4 ) @ X3 ) ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ( ( hoasinduction_lem3aaa = $true )
<=> ! [X0: subst > term > subst > $o] :
( ! [X1: subst > term > term] :
( ? [X2: term] :
! [X3: subst,X4: term,X5: subst] :
( ( ( sub @ X2 @ ( push @ ( sub @ X4 @ X3 ) @ ( comp @ X5 @ X3 ) ) )
= ( X1 @ ( comp @ X5 @ X3 ) @ ( sub @ X4 @ X3 ) ) )
& ( ( sub @ ( sub @ X2 @ ( push @ X4 @ X5 ) ) @ X3 )
= ( sub @ ( X1 @ X5 @ X4 ) @ X3 ) ) )
=> ( ! [X6: term] :
( ( ( X0 @ id @ X6 @ id )
= $true )
=> ( ( X0 @ id @ ( X1 @ id @ X6 ) @ id )
= $true ) )
=> ( ( X0 @ id
@ ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( X1 @ Y0 @ Y1 ) )
@ id )
= $true ) ) )
=> ! [X7: term] :
( ! [X8: term] :
( ( $true
= ( X0 @ id @ X8 @ id ) )
=> ( $true
= ( X0 @ id @ ( sub @ X7 @ ( push @ X8 @ id ) ) @ id ) ) )
=> ( $true
= ( X0 @ id @ ( lam @ ( sub @ X7 @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,plain,
~ ( ! [X0: subst > term > subst > $o] :
( ! [X1: subst > term > term] :
( ? [X2: term] :
! [X3: subst,X4: term,X5: subst] :
( ( ( sub @ X2 @ ( push @ ( sub @ X4 @ X3 ) @ ( comp @ X5 @ X3 ) ) )
= ( X1 @ ( comp @ X5 @ X3 ) @ ( sub @ X4 @ X3 ) ) )
& ( ( sub @ ( sub @ X2 @ ( push @ X4 @ X5 ) ) @ X3 )
= ( sub @ ( X1 @ X5 @ X4 ) @ X3 ) ) )
=> ( ! [X6: term] :
( ( ( X0 @ id @ X6 @ id )
= $true )
=> ( ( X0 @ id @ ( X1 @ id @ X6 ) @ id )
= $true ) )
=> ( ( X0 @ id
@ ( hoaslam @ id
@ ^ [Y0: subst,Y1: term] : ( X1 @ Y0 @ Y1 ) )
@ id )
= $true ) ) )
=> ! [X9: term] :
( ! [X10: term] :
( ( ( X0 @ id @ X10 @ id )
= $true )
=> ( ( X0 @ id @ ( sub @ X9 @ ( push @ X10 @ id ) ) @ id )
= $true ) )
=> ( $true
= ( X0 @ id @ ( lam @ ( sub @ X9 @ ( push @ one @ sh ) ) ) @ id ) ) ) )
<=> ( hoasinduction_lem3aaa = $true ) ),
inference(fool_elimination,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: subst > term > subst > $o] :
( ( ! [X1: subst > term > term] :
( ? [X2: term] :
! [X3: subst,X4: term,X5: subst] :
( ( ( sub @ X2 @ ( push @ ( sub @ X4 @ X3 ) @ ( comp @ X5 @ X3 ) ) )
= ( X1 @ ( comp @ X5 @ X3 ) @ ( sub @ X4 @ X3 ) ) )
& ( ( sub @ ( sub @ X2 @ ( push @ X4 @ X5 ) ) @ X3 )
= ( sub @ ( X1 @ X5 @ X4 ) @ X3 ) ) )
=> ( ! [X6: term] :
( ( X0 @ id @ X6 @ id )
=> ( X0 @ id @ ( X1 @ id @ X6 ) @ id ) )
=> ( X0 @ id
@ ( hoaslam @ id
@ ^ [X7: subst,X8: term] : ( X1 @ X7 @ X8 ) )
@ id ) ) )
=> ! [X9: term] :
( ! [X10: term] :
( ( X0 @ id @ X10 @ id )
=> ( X0 @ id @ ( sub @ X9 @ ( push @ X10 @ id ) ) @ id ) )
=> ( X0 @ id @ ( lam @ ( sub @ X9 @ ( push @ one @ sh ) ) ) @ id ) ) )
= hoasinduction_lem3aaa ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,negated_conjecture,
~ ! [X10: subst > term > subst > $o] :
( ( ! [X18: subst > term > term] :
( ? [X19: term] :
! [X25: subst,X13: term,X14: subst] :
( ( ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) )
= ( sub @ X19 @ ( push @ ( sub @ X13 @ X25 ) @ ( comp @ X14 @ X25 ) ) ) )
& ( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( sub @ ( sub @ X19 @ ( push @ X13 @ X14 ) ) @ X25 ) ) )
=> ( ! [X13: term] :
( ( X10 @ id @ X13 @ id )
=> ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
=> ( X10 @ id
@ ( hoaslam @ id
@ ^ [X14: subst,X13: term] : ( X18 @ X14 @ X13 ) )
@ id ) ) )
=> ! [X13: term] :
( ! [X15: term] :
( ( X10 @ id @ X15 @ id )
=> ( X10 @ id @ ( sub @ X13 @ ( push @ X15 @ id ) ) @ id ) )
=> ( X10 @ id @ ( lam @ ( sub @ X13 @ ( push @ one @ sh ) ) ) @ id ) ) )
= hoasinduction_lem3aaa ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f2,conjecture,
! [X10: subst > term > subst > $o] :
( ( ! [X18: subst > term > term] :
( ? [X19: term] :
! [X25: subst,X13: term,X14: subst] :
( ( ( X18 @ ( comp @ X14 @ X25 ) @ ( sub @ X13 @ X25 ) )
= ( sub @ X19 @ ( push @ ( sub @ X13 @ X25 ) @ ( comp @ X14 @ X25 ) ) ) )
& ( ( sub @ ( X18 @ X14 @ X13 ) @ X25 )
= ( sub @ ( sub @ X19 @ ( push @ X13 @ X14 ) ) @ X25 ) ) )
=> ( ! [X13: term] :
( ( X10 @ id @ X13 @ id )
=> ( X10 @ id @ ( X18 @ id @ X13 ) @ id ) )
=> ( X10 @ id
@ ( hoaslam @ id
@ ^ [X14: subst,X13: term] : ( X18 @ X14 @ X13 ) )
@ id ) ) )
=> ! [X13: term] :
( ! [X15: term] :
( ( X10 @ id @ X15 @ id )
=> ( X10 @ id @ ( sub @ X13 @ ( push @ X15 @ id ) ) @ id ) )
=> ( X10 @ id @ ( lam @ ( sub @ X13 @ ( push @ one @ sh ) ) ) @ id ) ) )
= hoasinduction_lem3aaa ),
file('/export/starexec/sandbox2/tmp/tmp.xoR6yAHn1s/DTF2THF_17021.p',hoasinduction_lem3aaa) ).
thf(f2903,plain,
( ~ spl654_241
| ~ spl654_242 ),
inference(avatar_split_clause,[status(thm)],[f1530,f2901,f2898]) ).
thf(f1530,plain,
( ( hoasinduction_lem3aaa != $true )
| ( $true
!= ( sP111 @ sK653 ) ) ),
inference(cnf_transformation,[status(thm)],[f768]) ).
thf(f2202,plain,
( spl654_73
| spl654_74 ),
inference(avatar_split_clause,[status(thm)],[f1644,f2200,f2197]) ).
thf(f1644,plain,
! [X2: term] :
( ( ( sK322 @ ( d2subst @ d_id ) @ X2 @ ( d2subst @ d_id ) )
!= $true )
| ( $true = sP45 )
| ( ( sK322 @ ( d2subst @ d_id ) @ ( sub @ sK321 @ ( push @ X2 @ ( d2subst @ d_id ) ) ) @ ( d2subst @ d_id ) )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f1068,f1388,f1388,f1388,f1388,f1388]) ).
thf(f1068,plain,
! [X2: term] :
( ( $true = sP45 )
| ( ( sK322 @ id @ X2 @ id )
!= $true )
| ( $true
= ( sK322 @ id @ ( sub @ sK321 @ ( push @ X2 @ id ) ) @ id ) ) ),
inference(cnf_transformation,[status(thm)],[f434]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.13/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.33 % Computer : n001.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue May 5 09:11:03 EDT 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.33 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.30/0.45 thf(spec,logic,$$dhol).
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 % File : SWX153_1 : TPTP v9.3.0. Released v9.3.0.
% 0.30/0.45 % Domain : Software Verification
% 0.30/0.45 % Problem : Benchmark: ALG444^1, Active target: hoasinduction_lem3aaa
% 0.30/0.45 % Version : Especial.
% 0.30/0.45 % English :
% 0.30/0.45
% 0.30/0.45 % Refs : [Kon26] Kondylidou (2026), Email to Geoff Sutcliffe
% 0.30/0.45 % Source : [Kon26]
% 0.30/0.45 % Names : ALG444^1__005__axclos.verify [Kon26]
% 0.30/0.45
% 0.30/0.45 % Status : Theorem
% 0.30/0.45 % Rating : ? v9.3.0
% 0.30/0.45 % Syntax : Number of formulae : 132 ( 1 unt; 130 typ; 0 def)
% 0.30/0.45 % Number of atoms : 256 ( 130 equ; 0 cnn)
% 0.30/0.45 % Maximal formula atoms : 248 ( 128 avg)
% 0.30/0.45 % Number of connectives : 2633 ( 333 ~; 306 |; 130 &;1764 @)
% 0.30/0.45 % ( 56 <=>; 44 =>; 0 <=; 0 <~>)
% 0.30/0.45 % Maximal formula depth : 151 ( 76 avg)
% 0.30/0.45 % Number of types : 5 ( 4 usr)
% 0.30/0.45 % Number of type conns : 227 ( 227 >; 0 *; 0 +; 0 <<)
% 0.30/0.45 % Number of symbols : 127 ( 126 usr; 113 con; 0-4 aty)
% 0.30/0.45 % Number of variables : 561 ( 10 ^; 548 !; 3 ?; 561 :)
% 0.30/0.45 % SPC : TH0_THM_EQU_NAR
% 0.30/0.45
% 0.30/0.45 % Comments :
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 thf(term_type,type,
% 0.30/0.45 term: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(subst_type,type,
% 0.30/0.45 subst: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(one_decl,type,
% 0.30/0.45 one: term ).
% 0.30/0.45
% 0.30/0.45 thf(ap_decl,type,
% 0.30/0.45 ap: term > term > term ).
% 0.30/0.45
% 0.30/0.45 thf(lam_decl,type,
% 0.30/0.45 lam: term > term ).
% 0.30/0.45
% 0.30/0.45 thf(sub_decl,type,
% 0.30/0.45 sub: term > subst > term ).
% 0.30/0.45
% 0.30/0.45 thf(id_decl,type,
% 0.30/0.45 id: subst ).
% 0.30/0.45
% 0.30/0.45 thf(sh_decl,type,
% 0.30/0.45 sh: subst ).
% 0.30/0.45
% 0.30/0.45 thf(push_decl,type,
% 0.30/0.45 push: term > subst > subst ).
% 0.30/0.45
% 0.30/0.45 thf(comp_decl,type,
% 0.30/0.45 comp: subst > subst > subst ).
% 0.30/0.45
% 0.30/0.45 thf(var_decl,type,
% 0.30/0.45 var: term > $o ).
% 0.30/0.45
% 0.30/0.45 thf(pushprop_lem1v2_decl,type,
% 0.30/0.45 pushprop_lem1v2: $o ).
% 0.30/0.45
% 0.30/0.45 thf(pushprop_lem1_gthm_decl,type,
% 0.30/0.45 pushprop_lem1_gthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(axmap_decl,type,
% 0.30/0.45 axmap: $o ).
% 0.30/0.45
% 0.30/0.45 thf(pushprop_lem0_gthm_decl,type,
% 0.30/0.45 pushprop_lem0_gthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(shinj_decl,type,
% 0.30/0.45 shinj: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasinduction_lem1v2_decl,type,
% 0.30/0.45 hoasinduction_lem1v2: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasinduction_lem1v2_gthm_decl,type,
% 0.30/0.45 hoasinduction_lem1v2_gthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasap_decl,type,
% 0.30/0.45 hoasap: subst > term > subst > term > term ).
% 0.30/0.45
% 0.30/0.45 thf(induction2lem_decl,type,
% 0.30/0.45 induction2lem: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasinduction_lem3v2_f_decl,type,
% 0.30/0.45 hoasinduction_lem3v2_f: $o ).
% 0.30/0.45
% 0.30/0.45 thf(axvarshift_decl,type,
% 0.30/0.45 axvarshift: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasapinj2_decl,type,
% 0.30/0.45 hoasapinj2: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasapnotvar_gthm_decl,type,
% 0.30/0.45 hoasapnotvar_gthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasapinj1_decl,type,
% 0.30/0.45 hoasapinj1: $o ).
% 0.30/0.45
% 0.30/0.45 thf(ulamvar1_decl,type,
% 0.30/0.45 ulamvar1: $o ).
% 0.30/0.45
% 0.30/0.45 thf(induction2lem_lthm_decl,type,
% 0.30/0.45 induction2lem_lthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasinduction_lem3v2_gthm_decl,type,
% 0.30/0.45 hoasinduction_lem3v2_gthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(apnotvar_decl,type,
% 0.30/0.45 apnotvar: $o ).
% 0.30/0.45
% 0.30/0.45 thf(pushprop_lthm_orig_decl,type,
% 0.30/0.45 pushprop_lthm_orig: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasinduction_lem3v2_f_lthm_decl,type,
% 0.30/0.45 hoasinduction_lem3v2_f_lthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasinduction_lthm_decl,type,
% 0.30/0.45 hoasinduction_lthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasinduction_no_psi_cond_lthm_decl,type,
% 0.30/0.45 hoasinduction_no_psi_cond_lthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoaslaminj_decl,type,
% 0.30/0.45 hoaslaminj: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasinduction_lem3aaa_decl,type,
% 0.30/0.45 hoasinduction_lem3aaa: $o ).
% 0.30/0.45
% 0.30/0.45 thf(induction2lem_gthm_decl,type,
% 0.30/0.45 induction2lem_gthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasinduction_lem3aa_lthm_decl,type,
% 0.30/0.45 hoasinduction_lem3aa_lthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasinduction_lem3_decl,type,
% 0.30/0.45 hoasinduction_lem3: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasinduction_lem2_decl,type,
% 0.30/0.45 hoasinduction_lem2: $o ).
% 0.30/0.45
% 0.30/0.45 thf(termmset_lthm_decl,type,
% 0.30/0.45 termmset_lthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasinduction_lem1_decl,type,
% 0.30/0.45 hoasinduction_lem1: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoaslamnotap_lthm_decl,type,
% 0.30/0.45 hoaslamnotap_lthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(pushprop_lem1v2_lthm_decl,type,
% 0.30/0.45 pushprop_lem1v2_lthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasapnotvar_decl,type,
% 0.30/0.45 hoasapnotvar: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasinduction_lem0_decl,type,
% 0.30/0.45 hoasinduction_lem0: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasinduction_decl,type,
% 0.30/0.45 hoasinduction: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasinduction_gthm_decl,type,
% 0.30/0.45 hoasinduction_gthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(axapp_decl,type,
% 0.30/0.45 axapp: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoaslamnotvar_lthm_decl,type,
% 0.30/0.45 hoaslamnotvar_lthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(pushprop_lem3v2_lthm_decl,type,
% 0.30/0.45 pushprop_lem3v2_lthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasinduction_lem3b_lthm_decl,type,
% 0.30/0.45 hoasinduction_lem3b_lthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(ulamvarind_decl,type,
% 0.30/0.45 ulamvarind: $o ).
% 0.30/0.45
% 0.30/0.45 thf(induction_decl,type,
% 0.30/0.45 induction: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasinduction_lem3a_lthm_decl,type,
% 0.30/0.45 hoasinduction_lem3a_lthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(termmset_gthm_decl,type,
% 0.30/0.45 termmset_gthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasinduction_lem3aa_decl,type,
% 0.30/0.45 hoasinduction_lem3aa: $o ).
% 0.30/0.45
% 0.30/0.45 thf(pushprop_lem1v2_gthm_decl,type,
% 0.30/0.45 pushprop_lem1v2_gthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoaslamnotap_gthm_decl,type,
% 0.30/0.45 hoaslamnotap_gthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoaslamnotvar_gthm_decl,type,
% 0.30/0.45 hoaslamnotvar_gthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasinduction_lem3b_gthm_decl,type,
% 0.30/0.45 hoasinduction_lem3b_gthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(pushprop_lem2v2_decl,type,
% 0.30/0.45 pushprop_lem2v2: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasinduction_lem3a_gthm_decl,type,
% 0.30/0.45 hoasinduction_lem3a_gthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(axclos_decl,type,
% 0.30/0.45 axclos: $o ).
% 0.30/0.45
% 0.30/0.45 thf(axassoc_decl,type,
% 0.30/0.45 axassoc: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasinduction_lem2v2_decl,type,
% 0.30/0.45 hoasinduction_lem2v2: $o ).
% 0.30/0.45
% 0.30/0.45 thf(pushprop_lthm_decl,type,
% 0.30/0.45 pushprop_lthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(apinj2_decl,type,
% 0.30/0.45 apinj2: $o ).
% 0.30/0.45
% 0.30/0.45 thf(apinj1_decl,type,
% 0.30/0.45 apinj1: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasapinj2_lthm_decl,type,
% 0.30/0.45 hoasapinj2_lthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasinduction_lem3v2a_decl,type,
% 0.30/0.45 hoasinduction_lem3v2a: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasapinj1_lthm_decl,type,
% 0.30/0.45 hoasapinj1_lthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoaslaminj_lthm_decl,type,
% 0.30/0.45 hoaslaminj_lthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(axvarcons_decl,type,
% 0.30/0.45 axvarcons: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoaslam_decl,type,
% 0.30/0.45 hoaslam: subst > ( subst > term > term ) > term ).
% 0.30/0.45
% 0.30/0.45 thf(axscons_decl,type,
% 0.30/0.45 axscons: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasinduction_lem2v2_gthm_decl,type,
% 0.30/0.45 hoasinduction_lem2v2_gthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(axidr_decl,type,
% 0.30/0.45 axidr: $o ).
% 0.30/0.45
% 0.30/0.45 thf(pushprop_lem1_decl,type,
% 0.30/0.45 pushprop_lem1: $o ).
% 0.30/0.45
% 0.30/0.45 thf(laminj_decl,type,
% 0.30/0.45 laminj: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasinduction_lem3_lthm_decl,type,
% 0.30/0.45 hoasinduction_lem3_lthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(pushprop_lem0_decl,type,
% 0.30/0.45 pushprop_lem0: $o ).
% 0.30/0.45
% 0.30/0.45 thf(pushprop_gthm_decl,type,
% 0.30/0.45 pushprop_gthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(axabs_decl,type,
% 0.30/0.45 axabs: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasinduction_lem3v2a_lthm_decl,type,
% 0.30/0.45 hoasinduction_lem3v2a_lthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasinduction_lem2_lthm_decl,type,
% 0.30/0.45 hoasinduction_lem2_lthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasapinj2_gthm_decl,type,
% 0.30/0.45 hoasapinj2_gthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasinduction_p_and_p_prime_decl,type,
% 0.30/0.45 hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasinduction_lem1_lthm_decl,type,
% 0.30/0.45 hoasinduction_lem1_lthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(lamnotap_decl,type,
% 0.30/0.45 lamnotap: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasapinj1_gthm_decl,type,
% 0.30/0.45 hoasapinj1_gthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoaslamnotvar_decl,type,
% 0.30/0.45 hoaslamnotvar: $o ).
% 0.30/0.45
% 0.30/0.45 thf(axidl_decl,type,
% 0.30/0.45 axidl: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoaslaminj_gthm_decl,type,
% 0.30/0.45 hoaslaminj_gthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(induction2_lthm_decl,type,
% 0.30/0.45 induction2_lthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasinduction_lem0_lthm_decl,type,
% 0.30/0.45 hoasinduction_lem0_lthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(substmonoid_lthm_decl,type,
% 0.30/0.45 substmonoid_lthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(pushprop_decl,type,
% 0.30/0.45 pushprop: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasinduction_lem3_gthm_decl,type,
% 0.30/0.45 hoasinduction_lem3_gthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasinduction_lem2_gthm_decl,type,
% 0.30/0.45 hoasinduction_lem2_gthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasinduction_lem3b_decl,type,
% 0.30/0.45 hoasinduction_lem3b: $o ).
% 0.30/0.45
% 0.30/0.45 thf(substmonoid_decl,type,
% 0.30/0.45 substmonoid: $o ).
% 0.30/0.45
% 0.30/0.45 thf(lamnotvar_decl,type,
% 0.30/0.45 lamnotvar: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasinduction_lem3a_decl,type,
% 0.30/0.45 hoasinduction_lem3a: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasinduction_lem1_gthm_decl,type,
% 0.30/0.45 hoasinduction_lem1_gthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasinduction_no_psi_cond_decl,type,
% 0.30/0.45 hoasinduction_no_psi_cond: $o ).
% 0.30/0.45
% 0.30/0.45 thf(induction2_gthm_decl,type,
% 0.30/0.45 induction2_gthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(pushprop_lem2v2_lthm_decl,type,
% 0.30/0.45 pushprop_lem2v2_lthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasvar_decl,type,
% 0.30/0.45 hoasvar: subst > term > subst > $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoaslamnotap_decl,type,
% 0.30/0.45 hoaslamnotap: $o ).
% 0.30/0.45
% 0.30/0.45 thf(substmonoid_gthm_decl,type,
% 0.30/0.45 substmonoid_gthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(ulamvarsh_decl,type,
% 0.30/0.45 ulamvarsh: $o ).
% 0.30/0.45
% 0.30/0.45 thf(induction2_decl,type,
% 0.30/0.45 induction2: $o ).
% 0.30/0.45
% 0.30/0.45 thf(pushprop_lem3v2_decl,type,
% 0.30/0.45 pushprop_lem3v2: $o ).
% 0.30/0.45
% 0.30/0.45 thf(pushprop_lem2v2_gthm_decl,type,
% 0.30/0.45 pushprop_lem2v2_gthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(pushprop_lem1_lthm_decl,type,
% 0.30/0.45 pushprop_lem1_lthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasinduction_lem3v2_decl,type,
% 0.30/0.45 hoasinduction_lem3v2: $o ).
% 0.30/0.45
% 0.30/0.45 thf(axshiftcons_decl,type,
% 0.30/0.45 axshiftcons: $o ).
% 0.30/0.45
% 0.30/0.45 thf(termmset_decl,type,
% 0.30/0.45 termmset: $o ).
% 0.30/0.45
% 0.30/0.45 thf(pushprop_lem0_lthm_decl,type,
% 0.30/0.45 pushprop_lem0_lthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasapnotvar_lthm_decl,type,
% 0.30/0.45 hoasapnotvar_lthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasinduction_lem3v2_lthm_decl,type,
% 0.30/0.45 hoasinduction_lem3v2_lthm: $o ).
% 0.30/0.45
% 0.30/0.45 thf(pushprop_p_and_p_prime_decl,type,
% 0.30/0.45 pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
% 0.30/0.45
% 0.30/0.45 thf(axvarid_decl,type,
% 0.30/0.45 axvarid: $o ).
% 0.30/0.45
% 0.30/0.45 thf(hoasinduction_lthm_3_decl,type,
% 0.30/0.45 hoasinduction_lthm_3: $o ).
% 0.30/0.45
% 0.30/0.45 %----Types of the domains
% 0.30/0.45 thf(d_term_type,type,
% 0.30/0.45 d_term: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(d_subst_type,type,
% 0.30/0.45 d_subst: $tType ).
% 0.30/0.45
% 0.30/0.45 %----Types of the promotion functions
% 0.30/0.45 thf(d2term_decl,type,
% 0.30/0.45 d2term: d_term > term ).
% 0.30/0.45
% 0.30/0.45 thf(d2subst_decl,type,
% 0.30/0.45 d2subst: d_subst > subst ).
% 0.30/0.45
% 0.30/0.45 %----Types of the domain elements
% 0.30/0.45 thf(d_one_decl,type,
% 0.30/0.45 d_one: d_term ).
% 0.30/0.45
% 0.30/0.45 thf(d_id_decl,type,
% 0.30/0.45 d_id: d_subst ).
% 0.30/0.45
% 0.30/0.45 thf(alg444_1,axiom,
% 0.30/0.45 ( ! [T: term] :
% 0.30/0.45 ? [DT: d_term] :
% 0.30/0.45 ( T
% 0.30/0.45 = ( d2term @ DT ) )
% 0.30/0.45 & ! [DT: d_term] : ( DT = d_one )
% 0.30/0.45 & ! [DT1: d_term,DT2: d_term] :
% 0.30/0.45 ( ( ( d2term @ DT1 )
% 0.30/0.45 = ( d2term @ DT2 ) )
% 0.30/0.45 => ( DT1 = DT2 ) )
% 0.30/0.45 & ! [S: subst] :
% 0.30/0.45 ? [DS: d_subst] :
% 0.30/0.45 ( S
% 0.30/0.45 = ( d2subst @ DS ) )
% 0.30/0.45 & ! [DS: d_subst] : ( DS = d_id )
% 0.30/0.45 & ! [DS1: d_subst,DS2: d_subst] :
% 0.30/0.45 ( ( ( d2subst @ DS1 )
% 0.30/0.45 = ( d2subst @ DS2 ) )
% 0.30/0.45 => ( DS1 = DS2 ) )
% 0.30/0.45 & ( one
% 0.30/0.45 = ( d2term @ d_one ) )
% 0.30/0.45 & ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
% 0.30/0.45 = ( d2term @ d_one ) )
% 0.30/0.45 & ( ( lam @ ( d2term @ d_one ) )
% 0.30/0.45 = ( d2term @ d_one ) )
% 0.30/0.45 & ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 0.30/0.45 = ( d2term @ d_one ) )
% 0.30/0.45 & ( id
% 0.30/0.45 = ( d2subst @ d_id ) )
% 0.30/0.45 & ( sh
% 0.30/0.45 = ( d2subst @ d_id ) )
% 0.30/0.45 & ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 0.30/0.45 = ( d2subst @ d_id ) )
% 0.30/0.45 & ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
% 0.30/0.45 = ( d2subst @ d_id ) )
% 0.30/0.45 & ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
% 0.30/0.45 = ( d2term @ d_one ) )
% 0.30/0.45 & ( hoaslam
% 0.30/0.45 = ( ^ [Bound_variable_4913: subst,Bound_variable_4915: subst > term > term] : ( d2term @ d_one ) ) )
% 0.30/0.45 & ( hoasinduction_p_and_p_prime
% 0.30/0.45 = ( ^ [P: subst > term > subst > $o,Q: term > $o] :
% 0.30/0.45 ! [X: term] :
% 0.30/0.45 ( ( Q @ X )
% 0.30/0.45 = ( P @ id @ X @ id ) ) ) )
% 0.30/0.45 & ( pushprop_p_and_p_prime
% 0.30/0.45 = ( ^ [A: term,M: subst,P: term > $o,Q: term > $o] :
% 0.30/0.45 ! [X: term] :
% 0.30/0.45 ( ( Q @ X )
% 0.30/0.45 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) )
% 0.30/0.45 & ~ ( var @ ( d2term @ d_one ) )
% 0.30/0.45 & ( pushprop_lem1v2
% 0.30/0.45 <=> ! [P: term > $o,Q: term > $o,A: term,M: subst] :
% 0.30/0.45 ( ~ ( P @ A )
% 0.30/0.45 | ~ ! [X: term] :
% 0.30/0.45 ( ( Q @ X )
% 0.30/0.45 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) )
% 0.30/0.45 | ( Q @ one ) ) )
% 0.30/0.45 & pushprop_lem1_gthm
% 0.30/0.45 & axmap
% 0.30/0.45 & pushprop_lem0_gthm
% 0.30/0.45 & ( shinj
% 0.30/0.45 <=> ! [A: term,B: term] :
% 0.30/0.45 ( ( ( sub @ A @ sh )
% 0.30/0.45 != ( sub @ B @ sh ) )
% 0.30/0.45 | ( A = B ) ) )
% 0.30/0.45 & hoasinduction_lem1v2
% 0.30/0.45 & hoasinduction_lem1v2_gthm
% 0.30/0.45 & ( induction2lem
% 0.30/0.45 <=> ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 0.30/0.45 ( ~ ! [A: term,B: term] :
% 0.30/0.45 ( ~ ( P @ A )
% 0.30/0.45 | ~ ( P @ B )
% 0.30/0.45 | ( P @ ( ap @ A @ B ) ) )
% 0.30/0.45 | ~ ! [A: term] :
% 0.30/0.45 ( ~ ! [B: term] :
% 0.30/0.45 ( ~ ( P @ B )
% 0.30/0.45 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.30/0.45 | ( P @ ( lam @ A ) ) )
% 0.30/0.45 | ~ ! [B: term] :
% 0.30/0.45 ( ~ ( var @ B )
% 0.30/0.45 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 0.30/0.45 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) ) )
% 0.30/0.45 & ( hoasinduction_lem3v2_f
% 0.30/0.45 <=> ! [B: term] :
% 0.30/0.45 ~ ! [F: subst > term > term] :
% 0.30/0.45 ~ ! [A: term,M: subst] :
% 0.30/0.45 ( ( sub @ B @ ( push @ A @ M ) )
% 0.30/0.45 = ( F @ M @ A ) ) )
% 0.30/0.45 & axvarshift
% 0.30/0.45 & ( hoasapinj2
% 0.30/0.45 <=> ! [A: term,B: term,C: term,D: term] :
% 0.30/0.45 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 0.30/0.45 != ( ap @ ( sub @ B @ id ) @ D ) )
% 0.30/0.45 | ( C = D ) ) )
% 0.30/0.45 & hoasapnotvar_gthm
% 0.30/0.45 & ( hoasapinj1
% 0.30/0.45 <=> ! [A: term,B: term,C: term,D: term] :
% 0.30/0.45 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 0.30/0.45 != ( ap @ ( sub @ B @ id ) @ D ) )
% 0.30/0.45 | ( A = B ) ) )
% 0.30/0.45 & ~ ulamvar1
% 0.30/0.45 & ( induction2lem_lthm
% 0.30/0.45 <=> ( ! [A: term,M: subst] :
% 0.30/0.45 ( A
% 0.30/0.45 = ( sub @ one @ ( push @ A @ M ) ) )
% 0.30/0.45 => ( ! [A: term,M: subst] :
% 0.30/0.45 ( M
% 0.30/0.45 = ( comp @ sh @ ( push @ A @ M ) ) )
% 0.30/0.45 => ( ! [M: subst] :
% 0.30/0.45 ( M
% 0.30/0.45 = ( comp @ M @ id ) )
% 0.30/0.45 => ( ! [P: term > $o,Bound_variable_2140: term] :
% 0.30/0.45 ( ~ ! [A: term] :
% 0.30/0.45 ( ~ ( var @ A )
% 0.30/0.45 | ( P @ A ) )
% 0.30/0.45 | ~ ! [A: term,B: term] :
% 0.30/0.45 ( ~ ( P @ A )
% 0.30/0.45 | ~ ( P @ B )
% 0.30/0.45 | ( P @ ( ap @ A @ B ) ) )
% 0.30/0.45 | ~ ! [A: term] :
% 0.30/0.45 ( ~ ( P @ A )
% 0.30/0.45 | ( P @ ( lam @ A ) ) )
% 0.30/0.45 | ( P @ Bound_variable_2140 ) )
% 0.30/0.45 => ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 0.30/0.45 ( ~ ! [A: term,B: term] :
% 0.30/0.45 ( ~ ( P @ A )
% 0.30/0.45 | ~ ( P @ B )
% 0.30/0.45 | ( P @ ( ap @ A @ B ) ) )
% 0.30/0.45 | ~ ! [A: term] :
% 0.30/0.45 ( ~ ! [B: term] :
% 0.30/0.45 ( ~ ( P @ B )
% 0.30/0.45 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.30/0.45 | ( P @ ( lam @ A ) ) )
% 0.30/0.45 | ~ ! [B: term] :
% 0.30/0.45 ( ~ ( var @ B )
% 0.30/0.45 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 0.30/0.45 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) ) ) ) ) ) )
% 0.30/0.45 & hoasinduction_lem3v2_gthm
% 0.30/0.45 & apnotvar
% 0.30/0.45 & pushprop_lthm_orig
% 0.30/0.45 & ( hoasinduction_lem3v2_f_lthm
% 0.30/0.45 <=> ! [B: term] :
% 0.30/0.45 ~ ! [F: subst > term > term] :
% 0.30/0.45 ~ ! [A: term,M: subst] :
% 0.30/0.45 ( ( sub @ B @ ( push @ A @ M ) )
% 0.30/0.45 = ( F @ M @ A ) ) )
% 0.30/0.45 & ( hoasinduction_lthm
% 0.30/0.45 <=> ( ! [P: term > $o,Bound_variable_2367: term] :
% 0.30/0.45 ( ~ ! [A: term] :
% 0.30/0.45 ( ~ ( var @ A )
% 0.30/0.45 | ( P @ A ) )
% 0.30/0.45 | ~ ! [A: term,B: term] :
% 0.30/0.45 ( ~ ( P @ A )
% 0.30/0.45 | ~ ( P @ B )
% 0.30/0.45 | ( P @ ( ap @ A @ B ) ) )
% 0.30/0.45 | ~ ! [A: term] :
% 0.30/0.45 ( ~ ! [B: term] :
% 0.30/0.45 ( ~ ( P @ B )
% 0.30/0.45 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.30/0.45 | ( P @ ( lam @ A ) ) )
% 0.30/0.45 | ( P @ Bound_variable_2367 ) )
% 0.30/0.45 => ( ! [P: subst > term > subst > $o,Bound_variable_2999: term,Bound_variable_3001: term] :
% 0.30/0.45 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.45 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.30/0.45 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.30/0.45 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.45 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.30/0.45 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.30/0.45 | ~ ! [A: term,B: term] :
% 0.30/0.45 ( ~ ( P @ id @ A @ id )
% 0.30/0.45 | ~ ( P @ id @ B @ id )
% 0.30/0.45 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.30/0.45 | ~ ( P @ id @ Bound_variable_2999 @ id )
% 0.30/0.45 | ~ ( P @ id @ Bound_variable_3001 @ id )
% 0.30/0.45 | ( P @ id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) )
% 0.30/0.45 => ( ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 0.30/0.45 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.45 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.30/0.45 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.30/0.45 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.45 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.30/0.45 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.30/0.45 | ~ ! [F: subst > term > term] :
% 0.30/0.45 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.45 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.45 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.45 | ~ ! [A: term] :
% 0.30/0.45 ( ~ ( P @ id @ A @ id )
% 0.30/0.45 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.45 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.45 | ~ ! [B: term] :
% 0.30/0.45 ( ~ ( P @ id @ B @ id )
% 0.30/0.45 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 0.30/0.45 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) )
% 0.30/0.45 => ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 0.30/0.45 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.45 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.30/0.45 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.30/0.45 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.45 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.30/0.45 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.30/0.45 | ~ ! [A: term] :
% 0.30/0.45 ( ~ ( var @ ( sub @ A @ id ) )
% 0.30/0.45 | ( P @ id @ A @ id ) )
% 0.30/0.45 | ~ ! [A: term,B: term] :
% 0.30/0.45 ( ~ ( P @ id @ A @ id )
% 0.30/0.45 | ~ ( P @ id @ B @ id )
% 0.30/0.45 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.30/0.45 | ~ ! [F: subst > term > term] :
% 0.30/0.45 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.45 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.45 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.45 | ~ ! [A: term] :
% 0.30/0.45 ( ~ ( P @ id @ A @ id )
% 0.30/0.45 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.45 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.45 | ( P @ id @ Bound_variable_3283 @ id ) ) ) ) ) )
% 0.30/0.45 & ( hoasinduction_no_psi_cond_lthm
% 0.30/0.45 <=> ( ! [P: subst > term > subst > $o] :
% 0.30/0.45 ~ ! [Q: term > $o] :
% 0.30/0.45 ~ ! [X: term] :
% 0.30/0.45 ( ( Q @ X )
% 0.30/0.45 = ( P @ id @ X @ id ) )
% 0.30/0.45 => ( ! [P: term > $o,Bound_variable_2367: term] :
% 0.30/0.45 ( ~ ! [A: term] :
% 0.30/0.45 ( ~ ( var @ A )
% 0.30/0.45 | ( P @ A ) )
% 0.30/0.45 | ~ ! [A: term,B: term] :
% 0.30/0.45 ( ~ ( P @ A )
% 0.30/0.45 | ~ ( P @ B )
% 0.30/0.45 | ( P @ ( ap @ A @ B ) ) )
% 0.30/0.45 | ~ ! [A: term] :
% 0.30/0.45 ( ~ ! [B: term] :
% 0.30/0.45 ( ~ ( P @ B )
% 0.30/0.45 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.30/0.45 | ( P @ ( lam @ A ) ) )
% 0.30/0.45 | ( P @ Bound_variable_2367 ) )
% 0.30/0.45 => ( ! [A: term] :
% 0.30/0.45 ( A
% 0.30/0.45 = ( sub @ A @ id ) )
% 0.30/0.45 => ( ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 0.30/0.45 ( ~ ! [F: subst > term > term] :
% 0.30/0.45 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.45 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.45 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.45 | ~ ! [A: term] :
% 0.30/0.45 ( ~ ( P @ id @ A @ id )
% 0.30/0.45 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.45 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.45 | ~ ! [X: term] :
% 0.30/0.45 ( ( Q @ X )
% 0.30/0.45 = ( P @ id @ X @ id ) )
% 0.30/0.45 | ~ ! [B: term] :
% 0.30/0.45 ( ~ ( Q @ B )
% 0.30/0.45 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 0.30/0.45 | ( Q @ ( lam @ Bound_variable_2931 ) ) )
% 0.30/0.45 => ! [P: subst > term > subst > $o,Bound_variable_3295: term] :
% 0.30/0.45 ( ~ ! [A: term,B: term] :
% 0.30/0.45 ( ~ ( P @ id @ A @ id )
% 0.30/0.45 | ~ ( P @ id @ B @ id )
% 0.30/0.45 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.30/0.45 | ~ ! [F: subst > term > term] :
% 0.30/0.45 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.45 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.45 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.45 | ~ ! [A: term] :
% 0.30/0.45 ( ~ ( P @ id @ A @ id )
% 0.30/0.45 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.45 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.45 | ( P @ id @ Bound_variable_3295 @ id ) ) ) ) ) ) )
% 0.30/0.45 & ( hoaslaminj
% 0.30/0.45 <=> ! [F: subst > term > term,Bound_variable_2547: subst > term > term,Bound_variable_2549: subst,Bound_variable_2551: term] :
% 0.30/0.45 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.45 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.45 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.45 | ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.45 ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N )
% 0.30/0.45 = ( Bound_variable_2547 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.45 | ( ( lam @ ( F @ sh @ one ) )
% 0.30/0.45 != ( lam @ ( Bound_variable_2547 @ sh @ one ) ) )
% 0.30/0.45 | ( ( F @ Bound_variable_2549 @ Bound_variable_2551 )
% 0.30/0.45 = ( Bound_variable_2547 @ Bound_variable_2549 @ Bound_variable_2551 ) ) ) )
% 0.30/0.45 & ( hoasinduction_lem3aaa
% 0.30/0.45 <=> ! [P: subst > term > subst > $o,Bound_variable_3171: term] :
% 0.30/0.45 ( ~ ! [F: subst > term > term,Bound_variable_3149: term] :
% 0.30/0.45 ( ~ ! [A: term] :
% 0.30/0.45 ( ~ ( P @ id @ A @ id )
% 0.30/0.45 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.45 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id )
% 0.30/0.45 | ~ ! [Bound_variable_3072: subst,Bound_variable_3074: term,Bound_variable_3076: subst] :
% 0.30/0.45 ( ( sub @ ( F @ Bound_variable_3072 @ Bound_variable_3074 ) @ Bound_variable_3076 )
% 0.30/0.45 = ( sub @ ( sub @ Bound_variable_3149 @ ( push @ Bound_variable_3074 @ Bound_variable_3072 ) ) @ Bound_variable_3076 ) )
% 0.30/0.45 | ~ ! [Bound_variable_3090: subst,Bound_variable_3092: term,Bound_variable_3094: subst] :
% 0.30/0.45 ( ( F @ ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) @ ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) )
% 0.30/0.45 = ( sub @ Bound_variable_3149 @ ( push @ ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) @ ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) ) ) ) )
% 0.30/0.45 | ~ ! [B: term] :
% 0.30/0.45 ( ~ ( P @ id @ B @ id )
% 0.30/0.45 | ( P @ id @ ( sub @ Bound_variable_3171 @ ( push @ B @ id ) ) @ id ) )
% 0.30/0.45 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3171 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 0.30/0.45 & induction2lem_gthm
% 0.30/0.45 & ( hoasinduction_lem3aa_lthm
% 0.30/0.45 <=> ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 0.30/0.45 ( ~ ! [F: subst > term > term] :
% 0.30/0.45 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.45 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.45 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.45 | ~ ! [A: term] :
% 0.30/0.45 ( ~ ( P @ id @ A @ id )
% 0.30/0.45 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.45 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.45 | ~ ! [B: term] :
% 0.30/0.45 ( ~ ( P @ id @ B @ id )
% 0.30/0.45 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 0.30/0.45 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 0.30/0.45 & ( hoasinduction_lem3
% 0.30/0.45 <=> ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 0.30/0.45 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.45 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.30/0.45 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.30/0.45 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.45 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.30/0.45 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.30/0.45 | ~ ! [F: subst > term > term] :
% 0.30/0.45 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.45 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.45 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.45 | ~ ! [A: term] :
% 0.30/0.45 ( ~ ( P @ id @ A @ id )
% 0.30/0.45 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.45 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.45 | ~ ! [B: term] :
% 0.30/0.45 ( ~ ( P @ id @ B @ id )
% 0.30/0.45 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 0.30/0.45 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) ) )
% 0.30/0.45 & ( hoasinduction_lem2
% 0.30/0.45 <=> ! [P: subst > term > subst > $o,Bound_variable_2999: term,Bound_variable_3001: term] :
% 0.30/0.45 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.45 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.30/0.45 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.30/0.45 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.45 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.30/0.45 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.30/0.45 | ~ ! [A: term,B: term] :
% 0.30/0.45 ( ~ ( P @ id @ A @ id )
% 0.30/0.45 | ~ ( P @ id @ B @ id )
% 0.30/0.45 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.30/0.45 | ~ ( P @ id @ Bound_variable_2999 @ id )
% 0.30/0.45 | ~ ( P @ id @ Bound_variable_3001 @ id )
% 0.30/0.45 | ( P @ id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) ) )
% 0.30/0.45 & ( termmset_lthm
% 0.30/0.45 <=> ( ! [A: term] :
% 0.30/0.45 ( A
% 0.30/0.45 = ( sub @ A @ id ) )
% 0.30/0.45 => ! [A: term] :
% 0.30/0.45 ( A
% 0.30/0.45 = ( sub @ A @ id ) ) ) )
% 0.30/0.45 & hoasinduction_lem1
% 0.30/0.45 & hoaslamnotap_lthm
% 0.30/0.45 & ( pushprop_lem1v2_lthm
% 0.30/0.45 <=> ( ! [A: term,M: subst] :
% 0.30/0.45 ( A
% 0.30/0.45 = ( sub @ one @ ( push @ A @ M ) ) )
% 0.30/0.45 => ! [P: term > $o,Q: term > $o,A: term,M: subst] :
% 0.30/0.45 ( ~ ( P @ A )
% 0.30/0.45 | ~ ! [X: term] :
% 0.30/0.45 ( ( Q @ X )
% 0.30/0.45 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) )
% 0.30/0.45 | ( Q @ one ) ) ) )
% 0.30/0.45 & hoasapnotvar
% 0.30/0.45 & ( hoasinduction_lem0
% 0.30/0.45 <=> ! [P: subst > term > subst > $o] :
% 0.30/0.45 ~ ! [Q: term > $o] :
% 0.30/0.45 ~ ! [X: term] :
% 0.30/0.45 ( ( Q @ X )
% 0.30/0.45 = ( P @ id @ X @ id ) ) )
% 0.30/0.45 & ( hoasinduction
% 0.30/0.45 <=> ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 0.30/0.45 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.45 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.30/0.45 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.30/0.45 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.45 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.30/0.45 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.30/0.45 | ~ ! [A: term] :
% 0.30/0.45 ( ~ ( var @ ( sub @ A @ id ) )
% 0.30/0.45 | ( P @ id @ A @ id ) )
% 0.30/0.45 | ~ ! [A: term,B: term] :
% 0.30/0.45 ( ~ ( P @ id @ A @ id )
% 0.30/0.45 | ~ ( P @ id @ B @ id )
% 0.30/0.45 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.30/0.45 | ~ ! [F: subst > term > term] :
% 0.30/0.45 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.45 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.45 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.45 | ~ ! [A: term] :
% 0.30/0.45 ( ~ ( P @ id @ A @ id )
% 0.30/0.45 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.45 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.45 | ( P @ id @ Bound_variable_3283 @ id ) ) )
% 0.30/0.45 & hoasinduction_gthm
% 0.30/0.45 & axapp
% 0.30/0.45 & hoaslamnotvar_lthm
% 0.30/0.45 & pushprop_lem3v2_lthm
% 0.30/0.45 & ( hoasinduction_lem3b_lthm
% 0.30/0.45 <=> ! [B: term] :
% 0.30/0.45 ~ ! [F: subst > term > term] :
% 0.30/0.45 ( ( F @ sh @ one )
% 0.30/0.45 != ( sub @ B @ ( push @ one @ sh ) ) ) )
% 0.30/0.45 & ulamvarind
% 0.30/0.45 & ( induction
% 0.30/0.45 <=> ! [P: term > $o,Bound_variable_2140: term] :
% 0.30/0.45 ( ~ ! [A: term] :
% 0.30/0.45 ( ~ ( var @ A )
% 0.30/0.45 | ( P @ A ) )
% 0.30/0.45 | ~ ! [A: term,B: term] :
% 0.30/0.45 ( ~ ( P @ A )
% 0.30/0.45 | ~ ( P @ B )
% 0.30/0.45 | ( P @ ( ap @ A @ B ) ) )
% 0.30/0.45 | ~ ! [A: term] :
% 0.30/0.45 ( ~ ( P @ A )
% 0.30/0.45 | ( P @ ( lam @ A ) ) )
% 0.30/0.45 | ( P @ Bound_variable_2140 ) ) )
% 0.30/0.45 & ( hoasinduction_lem3a_lthm
% 0.30/0.45 <=> ( ! [A: term] :
% 0.30/0.45 ( A
% 0.30/0.45 = ( sub @ A @ id ) )
% 0.30/0.45 => ( ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 0.30/0.45 ( ~ ! [F: subst > term > term] :
% 0.30/0.45 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.45 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.45 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.45 | ~ ! [A: term] :
% 0.30/0.45 ( ~ ( P @ id @ A @ id )
% 0.30/0.45 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.45 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.45 | ~ ! [B: term] :
% 0.30/0.45 ( ~ ( P @ id @ B @ id )
% 0.30/0.45 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 0.30/0.45 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) )
% 0.30/0.45 => ! [P: subst > term > subst > $o,Bound_variable_3232: term] :
% 0.30/0.45 ( ~ ! [F: subst > term > term] :
% 0.30/0.45 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.45 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.45 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.45 | ~ ! [A: term] :
% 0.30/0.45 ( ~ ( P @ id @ A @ id )
% 0.30/0.45 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.45 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.45 | ~ ! [B: term] :
% 0.30/0.45 ( ~ ( P @ id @ B @ id )
% 0.30/0.45 | ( P @ id @ ( sub @ Bound_variable_3232 @ ( push @ B @ id ) ) @ id ) )
% 0.30/0.45 | ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) ) ) ) )
% 0.30/0.45 & termmset_gthm
% 0.30/0.45 & ( hoasinduction_lem3aa
% 0.30/0.45 <=> ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 0.30/0.45 ( ~ ! [F: subst > term > term] :
% 0.30/0.45 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.45 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.45 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.45 | ~ ! [A: term] :
% 0.30/0.45 ( ~ ( P @ id @ A @ id )
% 0.30/0.45 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.45 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.45 | ~ ! [B: term] :
% 0.30/0.45 ( ~ ( P @ id @ B @ id )
% 0.30/0.45 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 0.30/0.45 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 0.30/0.45 & pushprop_lem1v2_gthm
% 0.30/0.45 & hoaslamnotap_gthm
% 0.30/0.45 & hoaslamnotvar_gthm
% 0.30/0.45 & hoasinduction_lem3b_gthm
% 0.30/0.45 & pushprop_lem2v2
% 0.30/0.45 & hoasinduction_lem3a_gthm
% 0.30/0.45 & axclos
% 0.30/0.45 & axassoc
% 0.30/0.45 & ( hoasinduction_lem2v2
% 0.30/0.45 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2820: term,Bound_variable_2822: term] :
% 0.30/0.45 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.45 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.30/0.45 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.30/0.45 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.45 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.30/0.45 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.30/0.45 | ~ ! [A: term,B: term] :
% 0.30/0.45 ( ~ ( P @ id @ A @ id )
% 0.30/0.45 | ~ ( P @ id @ B @ id )
% 0.30/0.45 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.30/0.45 | ~ ! [X: term] :
% 0.30/0.45 ( ( Q @ X )
% 0.30/0.45 = ( P @ id @ X @ id ) )
% 0.30/0.45 | ~ ( Q @ Bound_variable_2820 )
% 0.30/0.45 | ~ ( Q @ Bound_variable_2822 )
% 0.30/0.45 | ( Q @ ( ap @ Bound_variable_2820 @ Bound_variable_2822 ) ) ) )
% 0.30/0.45 & pushprop_lthm
% 0.30/0.45 & ( apinj2
% 0.30/0.45 <=> ! [A: term,B: term,C: term,D: term] :
% 0.30/0.45 ( ( ( ap @ A @ C )
% 0.30/0.45 != ( ap @ B @ D ) )
% 0.30/0.45 | ( C = D ) ) )
% 0.30/0.45 & ( apinj1
% 0.30/0.45 <=> ! [A: term,B: term,C: term,D: term] :
% 0.30/0.45 ( ( ( ap @ A @ C )
% 0.30/0.45 != ( ap @ B @ D ) )
% 0.30/0.45 | ( A = B ) ) )
% 0.30/0.45 & ( hoasapinj2_lthm
% 0.30/0.45 <=> ( ! [A: term,B: term,C: term,D: term] :
% 0.30/0.45 ( ( ( ap @ A @ C )
% 0.30/0.46 != ( ap @ B @ D ) )
% 0.30/0.46 | ( C = D ) )
% 0.30/0.46 => ! [A: term,B: term,C: term,D: term] :
% 0.30/0.46 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 0.30/0.46 != ( ap @ ( sub @ B @ id ) @ D ) )
% 0.30/0.46 | ( C = D ) ) ) )
% 0.30/0.46 & ( hoasinduction_lem3v2a
% 0.30/0.46 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 0.30/0.46 ( ~ ! [F: subst > term > term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.46 | ~ ! [X: term] :
% 0.30/0.46 ( ( Q @ X )
% 0.30/0.46 = ( P @ id @ X @ id ) )
% 0.30/0.46 | ~ ! [B: term] :
% 0.30/0.46 ( ~ ( Q @ B )
% 0.30/0.46 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 0.30/0.46 | ( Q @ ( lam @ Bound_variable_2931 ) ) ) )
% 0.30/0.46 & ( hoasapinj1_lthm
% 0.30/0.46 <=> ( ! [A: term] :
% 0.30/0.46 ( A
% 0.30/0.46 = ( sub @ A @ id ) )
% 0.30/0.46 => ( ! [A: term,B: term,C: term,D: term] :
% 0.30/0.46 ( ( ( ap @ A @ C )
% 0.30/0.46 != ( ap @ B @ D ) )
% 0.30/0.46 | ( A = B ) )
% 0.30/0.46 => ! [A: term,B: term,C: term,D: term] :
% 0.30/0.46 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 0.30/0.46 != ( ap @ ( sub @ B @ id ) @ D ) )
% 0.30/0.46 | ( A = B ) ) ) ) )
% 0.30/0.46 & ( hoaslaminj_lthm
% 0.30/0.46 <=> ( ! [A: term,M: subst] :
% 0.30/0.46 ( A
% 0.30/0.46 = ( sub @ one @ ( push @ A @ M ) ) )
% 0.30/0.46 => ( ! [A: term,M: subst] :
% 0.30/0.46 ( M
% 0.30/0.46 = ( comp @ sh @ ( push @ A @ M ) ) )
% 0.30/0.46 => ( ! [A: term,B: term] :
% 0.30/0.46 ( ( ( lam @ A )
% 0.30/0.46 != ( lam @ B ) )
% 0.30/0.46 | ( A = B ) )
% 0.30/0.46 => ! [F: subst > term > term,Bound_variable_2547: subst > term > term,Bound_variable_2549: subst,Bound_variable_2551: term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.46 | ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N )
% 0.30/0.46 = ( Bound_variable_2547 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.46 | ( ( lam @ ( F @ sh @ one ) )
% 0.30/0.46 != ( lam @ ( Bound_variable_2547 @ sh @ one ) ) )
% 0.30/0.46 | ( ( F @ Bound_variable_2549 @ Bound_variable_2551 )
% 0.30/0.46 = ( Bound_variable_2547 @ Bound_variable_2549 @ Bound_variable_2551 ) ) ) ) ) ) )
% 0.30/0.46 & ( axvarcons
% 0.30/0.46 <=> ! [A: term,M: subst] :
% 0.30/0.46 ( A
% 0.30/0.46 = ( sub @ one @ ( push @ A @ M ) ) ) )
% 0.30/0.46 & ( axscons
% 0.30/0.46 <=> ! [M: subst] :
% 0.30/0.46 ( M
% 0.30/0.46 = ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) ) ) )
% 0.30/0.46 & hoasinduction_lem2v2_gthm
% 0.30/0.46 & ( axidr
% 0.30/0.46 <=> ! [M: subst] :
% 0.30/0.46 ( M
% 0.30/0.46 = ( comp @ M @ id ) ) )
% 0.30/0.46 & ( pushprop_lem1
% 0.30/0.46 <=> ! [P: term > $o,K: term > $o,A: term,M: subst,B: term] :
% 0.30/0.46 ( ~ ( P @ A )
% 0.30/0.46 | ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) )
% 0.30/0.46 & ( laminj
% 0.30/0.46 <=> ! [A: term,B: term] :
% 0.30/0.46 ( ( ( lam @ A )
% 0.30/0.46 != ( lam @ B ) )
% 0.30/0.46 | ( A = B ) ) )
% 0.30/0.46 & ( hoasinduction_lem3_lthm
% 0.30/0.46 <=> ( ! [A: term] :
% 0.30/0.46 ( A
% 0.30/0.46 = ( sub @ A @ id ) )
% 0.30/0.46 => ( ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 0.30/0.46 ( ~ ! [F: subst > term > term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.46 | ~ ! [B: term] :
% 0.30/0.46 ( ~ ( P @ id @ B @ id )
% 0.30/0.46 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) )
% 0.30/0.46 => ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.46 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.30/0.46 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.30/0.46 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.46 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.30/0.46 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.30/0.46 | ~ ! [F: subst > term > term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.46 | ~ ! [B: term] :
% 0.30/0.46 ( ~ ( P @ id @ B @ id )
% 0.30/0.46 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) ) ) ) )
% 0.30/0.46 & ( pushprop_lem0
% 0.30/0.46 <=> ! [P: term > $o,A: term,M: subst] :
% 0.30/0.46 ~ ! [Q: term > $o] :
% 0.30/0.46 ~ ! [X: term] :
% 0.30/0.46 ( ( Q @ X )
% 0.30/0.46 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) )
% 0.30/0.46 & pushprop_gthm
% 0.30/0.46 & axabs
% 0.30/0.46 & ( hoasinduction_lem3v2a_lthm
% 0.30/0.46 <=> ( ! [B: term] :
% 0.30/0.46 ~ ! [F: subst > term > term] :
% 0.30/0.46 ~ ! [A: term,M: subst] :
% 0.30/0.46 ( ( sub @ B @ ( push @ A @ M ) )
% 0.30/0.46 = ( F @ M @ A ) )
% 0.30/0.46 => ( ! [A: term] :
% 0.30/0.46 ( A
% 0.30/0.46 = ( sub @ A @ id ) )
% 0.30/0.46 => ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 0.30/0.46 ( ~ ! [F: subst > term > term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.46 | ~ ! [X: term] :
% 0.30/0.46 ( ( Q @ X )
% 0.30/0.46 = ( P @ id @ X @ id ) )
% 0.30/0.46 | ~ ! [B: term] :
% 0.30/0.46 ( ~ ( Q @ B )
% 0.30/0.46 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 0.30/0.46 | ( Q @ ( lam @ Bound_variable_2931 ) ) ) ) ) )
% 0.30/0.46 & hoasinduction_lem2_lthm
% 0.30/0.46 & hoasapinj2_gthm
% 0.30/0.46 & hoasinduction_lem1_lthm
% 0.30/0.46 & ~ lamnotap
% 0.30/0.46 & hoasapinj1_gthm
% 0.30/0.46 & hoaslamnotvar
% 0.30/0.46 & ( axidl
% 0.30/0.46 <=> ! [M: subst] :
% 0.30/0.46 ( M
% 0.30/0.46 = ( comp @ id @ M ) ) )
% 0.30/0.46 & hoaslaminj_gthm
% 0.30/0.46 & ( induction2_lthm
% 0.30/0.46 <=> ( ! [A: term] :
% 0.30/0.46 ( A
% 0.30/0.46 = ( sub @ A @ id ) )
% 0.30/0.46 => ( ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 0.30/0.46 ( ~ ! [A: term,B: term] :
% 0.30/0.46 ( ~ ( P @ A )
% 0.30/0.46 | ~ ( P @ B )
% 0.30/0.46 | ( P @ ( ap @ A @ B ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ! [B: term] :
% 0.30/0.46 ( ~ ( P @ B )
% 0.30/0.46 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.30/0.46 | ( P @ ( lam @ A ) ) )
% 0.30/0.46 | ~ ! [B: term] :
% 0.30/0.46 ( ~ ( var @ B )
% 0.30/0.46 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 0.30/0.46 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) )
% 0.30/0.46 => ! [P: term > $o,Bound_variable_2367: term] :
% 0.30/0.46 ( ~ ! [A: term] :
% 0.30/0.46 ( ~ ( var @ A )
% 0.30/0.46 | ( P @ A ) )
% 0.30/0.46 | ~ ! [A: term,B: term] :
% 0.30/0.46 ( ~ ( P @ A )
% 0.30/0.46 | ~ ( P @ B )
% 0.30/0.46 | ( P @ ( ap @ A @ B ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ! [B: term] :
% 0.30/0.46 ( ~ ( P @ B )
% 0.30/0.46 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.30/0.46 | ( P @ ( lam @ A ) ) )
% 0.30/0.46 | ( P @ Bound_variable_2367 ) ) ) ) )
% 0.30/0.46 & ( hoasinduction_lem0_lthm
% 0.30/0.46 <=> ! [P: subst > term > subst > $o] :
% 0.30/0.46 ~ ! [Q: term > $o] :
% 0.30/0.46 ~ ! [X: term] :
% 0.30/0.46 ( ( Q @ X )
% 0.30/0.46 = ( P @ id @ X @ id ) ) )
% 0.30/0.46 & ( substmonoid_lthm
% 0.30/0.46 <=> ( ! [M: subst] :
% 0.30/0.46 ( M
% 0.30/0.46 = ( comp @ id @ M ) )
% 0.30/0.46 => ( ! [M: subst] :
% 0.30/0.46 ( M
% 0.30/0.46 = ( comp @ M @ id ) )
% 0.30/0.46 => ( ! [M: subst] :
% 0.30/0.46 ( M
% 0.30/0.46 = ( comp @ id @ M ) )
% 0.30/0.46 & ! [M: subst] :
% 0.30/0.46 ( M
% 0.30/0.46 = ( comp @ M @ id ) ) ) ) ) )
% 0.30/0.46 & pushprop
% 0.30/0.46 & hoasinduction_lem3_gthm
% 0.30/0.46 & hoasinduction_lem2_gthm
% 0.30/0.46 & ( hoasinduction_lem3b
% 0.30/0.46 <=> ! [B: term] :
% 0.30/0.46 ~ ! [F: subst > term > term] :
% 0.30/0.46 ( ( F @ sh @ one )
% 0.30/0.46 != ( sub @ B @ ( push @ one @ sh ) ) ) )
% 0.30/0.46 & ( substmonoid
% 0.30/0.46 <=> ( ! [M: subst] :
% 0.30/0.46 ( M
% 0.30/0.46 = ( comp @ id @ M ) )
% 0.30/0.46 & ! [M: subst] :
% 0.30/0.46 ( M
% 0.30/0.46 = ( comp @ M @ id ) ) ) )
% 0.30/0.46 & lamnotvar
% 0.30/0.46 & ( hoasinduction_lem3a
% 0.30/0.46 <=> ! [P: subst > term > subst > $o,Bound_variable_3232: term] :
% 0.30/0.46 ( ~ ! [F: subst > term > term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.46 | ~ ! [B: term] :
% 0.30/0.46 ( ~ ( P @ id @ B @ id )
% 0.30/0.46 | ( P @ id @ ( sub @ Bound_variable_3232 @ ( push @ B @ id ) ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) ) )
% 0.30/0.46 & hoasinduction_lem1_gthm
% 0.30/0.46 & ( hoasinduction_no_psi_cond
% 0.30/0.46 <=> ! [P: subst > term > subst > $o,Bound_variable_3295: term] :
% 0.30/0.46 ( ~ ! [A: term,B: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ~ ( P @ id @ B @ id )
% 0.30/0.46 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.30/0.46 | ~ ! [F: subst > term > term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.46 | ( P @ id @ Bound_variable_3295 @ id ) ) )
% 0.30/0.46 & induction2_gthm
% 0.30/0.46 & pushprop_lem2v2_lthm
% 0.30/0.46 & ~ ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 0.30/0.46 & ( hoaslamnotap
% 0.30/0.46 <=> ! [F: subst > term > term,Bound_variable_2603: term,Bound_variable_2605: term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.46 | ( ( lam @ ( F @ sh @ one ) )
% 0.30/0.46 != ( ap @ ( sub @ Bound_variable_2603 @ id ) @ Bound_variable_2605 ) ) ) )
% 0.30/0.46 & substmonoid_gthm
% 0.30/0.46 & ulamvarsh
% 0.30/0.46 & ( induction2
% 0.30/0.46 <=> ! [P: term > $o,Bound_variable_2367: term] :
% 0.30/0.46 ( ~ ! [A: term] :
% 0.30/0.46 ( ~ ( var @ A )
% 0.30/0.46 | ( P @ A ) )
% 0.30/0.46 | ~ ! [A: term,B: term] :
% 0.30/0.46 ( ~ ( P @ A )
% 0.30/0.46 | ~ ( P @ B )
% 0.30/0.46 | ( P @ ( ap @ A @ B ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ! [B: term] :
% 0.30/0.46 ( ~ ( P @ B )
% 0.30/0.46 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.30/0.46 | ( P @ ( lam @ A ) ) )
% 0.30/0.46 | ( P @ Bound_variable_2367 ) ) )
% 0.30/0.46 & pushprop_lem3v2
% 0.30/0.46 & pushprop_lem2v2_gthm
% 0.30/0.46 & ( pushprop_lem1_lthm
% 0.30/0.46 <=> ( ! [A: term,M: subst] :
% 0.30/0.46 ( A
% 0.30/0.46 = ( sub @ one @ ( push @ A @ M ) ) )
% 0.30/0.46 => ( ! [A: term,M: subst] :
% 0.30/0.46 ( M
% 0.30/0.46 = ( comp @ sh @ ( push @ A @ M ) ) )
% 0.30/0.46 => ! [P: term > $o,K: term > $o,A: term,M: subst,B: term] :
% 0.30/0.46 ( ~ ( P @ A )
% 0.30/0.46 | ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) ) ) )
% 0.30/0.46 & ( hoasinduction_lem3v2
% 0.30/0.46 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2910: term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.46 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.30/0.46 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.30/0.46 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.46 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.30/0.46 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.30/0.46 | ~ ! [F: subst > term > term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.46 | ~ ! [X: term] :
% 0.30/0.46 ( ( Q @ X )
% 0.30/0.46 = ( P @ id @ X @ id ) )
% 0.30/0.46 | ~ ! [B: term] :
% 0.30/0.46 ( ~ ( Q @ B )
% 0.30/0.46 | ( Q @ ( sub @ Bound_variable_2910 @ ( push @ B @ id ) ) ) )
% 0.30/0.46 | ( Q @ ( lam @ Bound_variable_2910 ) ) ) )
% 0.30/0.46 & ( axshiftcons
% 0.30/0.46 <=> ! [A: term,M: subst] :
% 0.30/0.46 ( M
% 0.30/0.46 = ( comp @ sh @ ( push @ A @ M ) ) ) )
% 0.30/0.46 & ( termmset
% 0.30/0.46 <=> ! [A: term] :
% 0.30/0.46 ( A
% 0.30/0.46 = ( sub @ A @ id ) ) )
% 0.30/0.46 & ( pushprop_lem0_lthm
% 0.30/0.46 <=> ! [P: term > $o,A: term,M: subst] :
% 0.30/0.46 ~ ! [Q: term > $o] :
% 0.30/0.46 ~ ! [X: term] :
% 0.30/0.46 ( ( Q @ X )
% 0.30/0.46 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) )
% 0.30/0.46 & hoasapnotvar_lthm
% 0.30/0.46 & ( hoasinduction_lem3v2_lthm
% 0.30/0.46 <=> ( ! [A: term] :
% 0.30/0.46 ( A
% 0.30/0.46 = ( sub @ A @ id ) )
% 0.30/0.46 => ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2910: term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.46 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.30/0.46 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.30/0.46 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.46 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.30/0.46 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.30/0.46 | ~ ! [F: subst > term > term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.46 | ~ ! [X: term] :
% 0.30/0.46 ( ( Q @ X )
% 0.30/0.46 = ( P @ id @ X @ id ) )
% 0.30/0.46 | ~ ! [B: term] :
% 0.30/0.46 ( ~ ( Q @ B )
% 0.30/0.46 | ( Q @ ( sub @ Bound_variable_2910 @ ( push @ B @ id ) ) ) )
% 0.30/0.46 | ( Q @ ( lam @ Bound_variable_2910 ) ) ) ) )
% 0.30/0.46 & ( axvarid
% 0.30/0.46 <=> ! [A: term] :
% 0.30/0.46 ( A
% 0.30/0.46 = ( sub @ A @ id ) ) )
% 0.30/0.46 & ( hoasinduction_lthm_3
% 0.30/0.46 <=> ( ! [P: subst > term > subst > $o] :
% 0.30/0.46 ~ ! [Q: term > $o] :
% 0.30/0.46 ~ ! [X: term] :
% 0.30/0.46 ( ( Q @ X )
% 0.30/0.46 = ( P @ id @ X @ id ) )
% 0.30/0.46 => ( ! [P: term > $o,Bound_variable_2367: term] :
% 0.30/0.46 ( ~ ! [A: term] :
% 0.30/0.46 ( ~ ( var @ A )
% 0.30/0.46 | ( P @ A ) )
% 0.30/0.46 | ~ ! [A: term,B: term] :
% 0.30/0.46 ( ~ ( P @ A )
% 0.30/0.46 | ~ ( P @ B )
% 0.30/0.46 | ( P @ ( ap @ A @ B ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ! [B: term] :
% 0.30/0.46 ( ~ ( P @ B )
% 0.30/0.46 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 0.30/0.46 | ( P @ ( lam @ A ) ) )
% 0.30/0.46 | ( P @ Bound_variable_2367 ) )
% 0.30/0.46 => ( ! [A: term] :
% 0.30/0.46 ( A
% 0.30/0.46 = ( sub @ A @ id ) )
% 0.30/0.46 => ( ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 0.30/0.46 ( ~ ! [F: subst > term > term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.46 | ~ ! [X: term] :
% 0.30/0.46 ( ( Q @ X )
% 0.30/0.46 = ( P @ id @ X @ id ) )
% 0.30/0.46 | ~ ! [B: term] :
% 0.30/0.46 ( ~ ( Q @ B )
% 0.30/0.46 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 0.30/0.46 | ( Q @ ( lam @ Bound_variable_2931 ) ) )
% 0.30/0.46 => ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.46 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 0.30/0.46 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 0.30/0.46 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 0.30/0.46 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 0.30/0.46 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ( var @ ( sub @ A @ id ) )
% 0.30/0.46 | ( P @ id @ A @ id ) )
% 0.30/0.46 | ~ ! [A: term,B: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ~ ( P @ id @ B @ id )
% 0.30/0.46 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 0.30/0.46 | ~ ! [F: subst > term > term] :
% 0.30/0.46 ( ~ ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 0.30/0.46 | ~ ! [A: term] :
% 0.30/0.46 ( ~ ( P @ id @ A @ id )
% 0.30/0.46 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.46 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 0.30/0.46 | ( P @ id @ Bound_variable_3283 @ id ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(hoasinduction_lem3aaa,conjecture,
% 0.30/0.46 ( hoasinduction_lem3aaa
% 0.30/0.46 = ( ! [P: subst > term > subst > $o] :
% 0.30/0.46 ( ! [F: subst > term > term] :
% 0.30/0.46 ( ? [C: term] :
% 0.30/0.46 ! [M: subst,A: term,N: subst] :
% 0.30/0.46 ( ( ( sub @ ( F @ M @ A ) @ N )
% 0.30/0.46 = ( sub @ ( sub @ C @ ( push @ A @ M ) ) @ N ) )
% 0.30/0.46 & ( ( sub @ C @ ( push @ ( sub @ A @ N ) @ ( comp @ M @ N ) ) )
% 0.30/0.46 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) )
% 0.30/0.46 => ( ! [A: term] :
% 0.30/0.46 ( ( P @ id @ A @ id )
% 0.30/0.46 => ( P @ id @ ( F @ id @ A ) @ id ) )
% 0.30/0.46 => ( P @ id
% 0.30/0.46 @ ( hoaslam @ id
% 0.30/0.46 @ ^ [M: subst,A: term] : ( F @ M @ A ) )
% 0.30/0.46 @ id ) ) )
% 0.30/0.46 => ! [A: term] :
% 0.30/0.46 ( ! [B: term] :
% 0.30/0.46 ( ( P @ id @ B @ id )
% 0.30/0.46 => ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
% 0.30/0.46 => ( P @ id @ ( lam @ ( sub @ A @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 2.35/1.46 ---- Embedded in THF ---
% 2.35/1.46 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.35/1.46 %%% Generated on Tue May 05 09:11:04 EDT 2026
% 2.35/1.46 %%% using '$$dhol' embedding, version 1.3.0.
% 2.35/1.46 %%% Logic specification used:
% 2.35/1.46 %%% thf(spec, logic, $$dhol).
% 2.35/1.46
% 2.35/1.46 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.xoR6yAHn1s/DTF2DTF17021.p
% See solution above
% 2.35/1.47 ------------------------
% 2.55/1.50 ---- Cleaned THF ---
% 2.55/1.50 thf(term_type,type,
% 2.55/1.50 term: $tType ).
% 2.55/1.50
% 2.55/1.50 thf(subst_type,type,
% 2.55/1.50 subst: $tType ).
% 2.55/1.50
% 2.55/1.50 thf(one_decl,type,
% 2.55/1.50 one: term ).
% 2.55/1.50
% 2.55/1.50 thf(ap_decl,type,
% 2.55/1.50 ap: term > term > term ).
% 2.55/1.50
% 2.55/1.50 thf(lam_decl,type,
% 2.55/1.50 lam: term > term ).
% 2.55/1.50
% 2.55/1.50 thf(sub_decl,type,
% 2.55/1.50 sub: term > subst > term ).
% 2.55/1.50
% 2.55/1.50 thf(id_decl,type,
% 2.55/1.50 id: subst ).
% 2.55/1.50
% 2.55/1.50 thf(sh_decl,type,
% 2.55/1.50 sh: subst ).
% 2.55/1.50
% 2.55/1.50 thf(push_decl,type,
% 2.55/1.50 push: term > subst > subst ).
% 2.55/1.50
% 2.55/1.50 thf(comp_decl,type,
% 2.55/1.50 comp: subst > subst > subst ).
% 2.55/1.50
% 2.55/1.50 thf(var_decl,type,
% 2.55/1.50 var: term > $o ).
% 2.55/1.50
% 2.55/1.50 thf(pushprop_lem1v2_decl,type,
% 2.55/1.50 pushprop_lem1v2: $o ).
% 2.55/1.50
% 2.55/1.50 thf(pushprop_lem1_gthm_decl,type,
% 2.55/1.50 pushprop_lem1_gthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(axmap_decl,type,
% 2.55/1.50 axmap: $o ).
% 2.55/1.50
% 2.55/1.50 thf(pushprop_lem0_gthm_decl,type,
% 2.55/1.50 pushprop_lem0_gthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(shinj_decl,type,
% 2.55/1.50 shinj: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasinduction_lem1v2_decl,type,
% 2.55/1.50 hoasinduction_lem1v2: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasinduction_lem1v2_gthm_decl,type,
% 2.55/1.50 hoasinduction_lem1v2_gthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasap_decl,type,
% 2.55/1.50 hoasap: subst > term > subst > term > term ).
% 2.55/1.50
% 2.55/1.50 thf(induction2lem_decl,type,
% 2.55/1.50 induction2lem: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasinduction_lem3v2_f_decl,type,
% 2.55/1.50 hoasinduction_lem3v2_f: $o ).
% 2.55/1.50
% 2.55/1.50 thf(axvarshift_decl,type,
% 2.55/1.50 axvarshift: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasapinj2_decl,type,
% 2.55/1.50 hoasapinj2: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasapnotvar_gthm_decl,type,
% 2.55/1.50 hoasapnotvar_gthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasapinj1_decl,type,
% 2.55/1.50 hoasapinj1: $o ).
% 2.55/1.50
% 2.55/1.50 thf(ulamvar1_decl,type,
% 2.55/1.50 ulamvar1: $o ).
% 2.55/1.50
% 2.55/1.50 thf(induction2lem_lthm_decl,type,
% 2.55/1.50 induction2lem_lthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasinduction_lem3v2_gthm_decl,type,
% 2.55/1.50 hoasinduction_lem3v2_gthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(apnotvar_decl,type,
% 2.55/1.50 apnotvar: $o ).
% 2.55/1.50
% 2.55/1.50 thf(pushprop_lthm_orig_decl,type,
% 2.55/1.50 pushprop_lthm_orig: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasinduction_lem3v2_f_lthm_decl,type,
% 2.55/1.50 hoasinduction_lem3v2_f_lthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasinduction_lthm_decl,type,
% 2.55/1.50 hoasinduction_lthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasinduction_no_psi_cond_lthm_decl,type,
% 2.55/1.50 hoasinduction_no_psi_cond_lthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoaslaminj_decl,type,
% 2.55/1.50 hoaslaminj: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasinduction_lem3aaa_decl,type,
% 2.55/1.50 hoasinduction_lem3aaa: $o ).
% 2.55/1.50
% 2.55/1.50 thf(induction2lem_gthm_decl,type,
% 2.55/1.50 induction2lem_gthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasinduction_lem3aa_lthm_decl,type,
% 2.55/1.50 hoasinduction_lem3aa_lthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasinduction_lem3_decl,type,
% 2.55/1.50 hoasinduction_lem3: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasinduction_lem2_decl,type,
% 2.55/1.50 hoasinduction_lem2: $o ).
% 2.55/1.50
% 2.55/1.50 thf(termmset_lthm_decl,type,
% 2.55/1.50 termmset_lthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasinduction_lem1_decl,type,
% 2.55/1.50 hoasinduction_lem1: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoaslamnotap_lthm_decl,type,
% 2.55/1.50 hoaslamnotap_lthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(pushprop_lem1v2_lthm_decl,type,
% 2.55/1.50 pushprop_lem1v2_lthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasapnotvar_decl,type,
% 2.55/1.50 hoasapnotvar: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasinduction_lem0_decl,type,
% 2.55/1.50 hoasinduction_lem0: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasinduction_decl,type,
% 2.55/1.50 hoasinduction: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasinduction_gthm_decl,type,
% 2.55/1.50 hoasinduction_gthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(axapp_decl,type,
% 2.55/1.50 axapp: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoaslamnotvar_lthm_decl,type,
% 2.55/1.50 hoaslamnotvar_lthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(pushprop_lem3v2_lthm_decl,type,
% 2.55/1.50 pushprop_lem3v2_lthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasinduction_lem3b_lthm_decl,type,
% 2.55/1.50 hoasinduction_lem3b_lthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(ulamvarind_decl,type,
% 2.55/1.50 ulamvarind: $o ).
% 2.55/1.50
% 2.55/1.50 thf(induction_decl,type,
% 2.55/1.50 induction: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasinduction_lem3a_lthm_decl,type,
% 2.55/1.50 hoasinduction_lem3a_lthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(termmset_gthm_decl,type,
% 2.55/1.50 termmset_gthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasinduction_lem3aa_decl,type,
% 2.55/1.50 hoasinduction_lem3aa: $o ).
% 2.55/1.50
% 2.55/1.50 thf(pushprop_lem1v2_gthm_decl,type,
% 2.55/1.50 pushprop_lem1v2_gthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoaslamnotap_gthm_decl,type,
% 2.55/1.50 hoaslamnotap_gthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoaslamnotvar_gthm_decl,type,
% 2.55/1.50 hoaslamnotvar_gthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasinduction_lem3b_gthm_decl,type,
% 2.55/1.50 hoasinduction_lem3b_gthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(pushprop_lem2v2_decl,type,
% 2.55/1.50 pushprop_lem2v2: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasinduction_lem3a_gthm_decl,type,
% 2.55/1.50 hoasinduction_lem3a_gthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(axclos_decl,type,
% 2.55/1.50 axclos: $o ).
% 2.55/1.50
% 2.55/1.50 thf(axassoc_decl,type,
% 2.55/1.50 axassoc: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasinduction_lem2v2_decl,type,
% 2.55/1.50 hoasinduction_lem2v2: $o ).
% 2.55/1.50
% 2.55/1.50 thf(pushprop_lthm_decl,type,
% 2.55/1.50 pushprop_lthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(apinj2_decl,type,
% 2.55/1.50 apinj2: $o ).
% 2.55/1.50
% 2.55/1.50 thf(apinj1_decl,type,
% 2.55/1.50 apinj1: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasapinj2_lthm_decl,type,
% 2.55/1.50 hoasapinj2_lthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasinduction_lem3v2a_decl,type,
% 2.55/1.50 hoasinduction_lem3v2a: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasapinj1_lthm_decl,type,
% 2.55/1.50 hoasapinj1_lthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoaslaminj_lthm_decl,type,
% 2.55/1.50 hoaslaminj_lthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(axvarcons_decl,type,
% 2.55/1.50 axvarcons: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoaslam_decl,type,
% 2.55/1.50 hoaslam: subst > ( subst > term > term ) > term ).
% 2.55/1.50
% 2.55/1.50 thf(axscons_decl,type,
% 2.55/1.50 axscons: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasinduction_lem2v2_gthm_decl,type,
% 2.55/1.50 hoasinduction_lem2v2_gthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(axidr_decl,type,
% 2.55/1.50 axidr: $o ).
% 2.55/1.50
% 2.55/1.50 thf(pushprop_lem1_decl,type,
% 2.55/1.50 pushprop_lem1: $o ).
% 2.55/1.50
% 2.55/1.50 thf(laminj_decl,type,
% 2.55/1.50 laminj: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasinduction_lem3_lthm_decl,type,
% 2.55/1.50 hoasinduction_lem3_lthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(pushprop_lem0_decl,type,
% 2.55/1.50 pushprop_lem0: $o ).
% 2.55/1.50
% 2.55/1.50 thf(pushprop_gthm_decl,type,
% 2.55/1.50 pushprop_gthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(axabs_decl,type,
% 2.55/1.50 axabs: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasinduction_lem3v2a_lthm_decl,type,
% 2.55/1.50 hoasinduction_lem3v2a_lthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasinduction_lem2_lthm_decl,type,
% 2.55/1.50 hoasinduction_lem2_lthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasapinj2_gthm_decl,type,
% 2.55/1.50 hoasapinj2_gthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasinduction_p_and_p_prime_decl,type,
% 2.55/1.50 hoasinduction_p_and_p_prime: ( subst > term > subst > $o ) > ( term > $o ) > $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasinduction_lem1_lthm_decl,type,
% 2.55/1.50 hoasinduction_lem1_lthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(lamnotap_decl,type,
% 2.55/1.50 lamnotap: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasapinj1_gthm_decl,type,
% 2.55/1.50 hoasapinj1_gthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoaslamnotvar_decl,type,
% 2.55/1.50 hoaslamnotvar: $o ).
% 2.55/1.50
% 2.55/1.50 thf(axidl_decl,type,
% 2.55/1.50 axidl: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoaslaminj_gthm_decl,type,
% 2.55/1.50 hoaslaminj_gthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(induction2_lthm_decl,type,
% 2.55/1.50 induction2_lthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasinduction_lem0_lthm_decl,type,
% 2.55/1.50 hoasinduction_lem0_lthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(substmonoid_lthm_decl,type,
% 2.55/1.50 substmonoid_lthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(pushprop_decl,type,
% 2.55/1.50 pushprop: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasinduction_lem3_gthm_decl,type,
% 2.55/1.50 hoasinduction_lem3_gthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasinduction_lem2_gthm_decl,type,
% 2.55/1.50 hoasinduction_lem2_gthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasinduction_lem3b_decl,type,
% 2.55/1.50 hoasinduction_lem3b: $o ).
% 2.55/1.50
% 2.55/1.50 thf(substmonoid_decl,type,
% 2.55/1.50 substmonoid: $o ).
% 2.55/1.50
% 2.55/1.50 thf(lamnotvar_decl,type,
% 2.55/1.50 lamnotvar: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasinduction_lem3a_decl,type,
% 2.55/1.50 hoasinduction_lem3a: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasinduction_lem1_gthm_decl,type,
% 2.55/1.50 hoasinduction_lem1_gthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasinduction_no_psi_cond_decl,type,
% 2.55/1.50 hoasinduction_no_psi_cond: $o ).
% 2.55/1.50
% 2.55/1.50 thf(induction2_gthm_decl,type,
% 2.55/1.50 induction2_gthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(pushprop_lem2v2_lthm_decl,type,
% 2.55/1.50 pushprop_lem2v2_lthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasvar_decl,type,
% 2.55/1.50 hoasvar: subst > term > subst > $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoaslamnotap_decl,type,
% 2.55/1.50 hoaslamnotap: $o ).
% 2.55/1.50
% 2.55/1.50 thf(substmonoid_gthm_decl,type,
% 2.55/1.50 substmonoid_gthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(ulamvarsh_decl,type,
% 2.55/1.50 ulamvarsh: $o ).
% 2.55/1.50
% 2.55/1.50 thf(induction2_decl,type,
% 2.55/1.50 induction2: $o ).
% 2.55/1.50
% 2.55/1.50 thf(pushprop_lem3v2_decl,type,
% 2.55/1.50 pushprop_lem3v2: $o ).
% 2.55/1.50
% 2.55/1.50 thf(pushprop_lem2v2_gthm_decl,type,
% 2.55/1.50 pushprop_lem2v2_gthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(pushprop_lem1_lthm_decl,type,
% 2.55/1.50 pushprop_lem1_lthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasinduction_lem3v2_decl,type,
% 2.55/1.50 hoasinduction_lem3v2: $o ).
% 2.55/1.50
% 2.55/1.50 thf(axshiftcons_decl,type,
% 2.55/1.50 axshiftcons: $o ).
% 2.55/1.50
% 2.55/1.50 thf(termmset_decl,type,
% 2.55/1.50 termmset: $o ).
% 2.55/1.50
% 2.55/1.50 thf(pushprop_lem0_lthm_decl,type,
% 2.55/1.50 pushprop_lem0_lthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasapnotvar_lthm_decl,type,
% 2.55/1.50 hoasapnotvar_lthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasinduction_lem3v2_lthm_decl,type,
% 2.55/1.50 hoasinduction_lem3v2_lthm: $o ).
% 2.55/1.50
% 2.55/1.50 thf(pushprop_p_and_p_prime_decl,type,
% 2.55/1.50 pushprop_p_and_p_prime: term > subst > ( term > $o ) > ( term > $o ) > $o ).
% 2.55/1.50
% 2.55/1.50 thf(axvarid_decl,type,
% 2.55/1.50 axvarid: $o ).
% 2.55/1.50
% 2.55/1.50 thf(hoasinduction_lthm_3_decl,type,
% 2.55/1.50 hoasinduction_lthm_3: $o ).
% 2.55/1.50
% 2.55/1.50 thf(d_term_type,type,
% 2.55/1.50 d_term: $tType ).
% 2.55/1.50
% 2.55/1.50 thf(d_subst_type,type,
% 2.55/1.50 d_subst: $tType ).
% 2.55/1.50
% 2.55/1.50 thf(d2term_decl,type,
% 2.55/1.50 d2term: d_term > term ).
% 2.55/1.50
% 2.55/1.50 thf(d2subst_decl,type,
% 2.55/1.50 d2subst: d_subst > subst ).
% 2.55/1.50
% 2.55/1.50 thf(d_one_decl,type,
% 2.55/1.50 d_one: d_term ).
% 2.55/1.50
% 2.55/1.50 thf(d_id_decl,type,
% 2.55/1.50 d_id: d_subst ).
% 2.55/1.50
% 2.55/1.50 thf(alg444_1,axiom,
% 2.55/1.50 ( ! [T: term] :
% 2.55/1.50 ? [DT: d_term] :
% 2.55/1.50 ( T
% 2.55/1.50 = ( d2term @ DT ) )
% 2.55/1.50 & ! [DT: d_term] : ( DT = d_one )
% 2.55/1.50 & ! [DT1: d_term,DT2: d_term] :
% 2.55/1.50 ( ( ( d2term @ DT1 )
% 2.55/1.50 = ( d2term @ DT2 ) )
% 2.55/1.50 => ( DT1 = DT2 ) )
% 2.55/1.50 & ! [S: subst] :
% 2.55/1.50 ? [DS: d_subst] :
% 2.55/1.50 ( S
% 2.55/1.50 = ( d2subst @ DS ) )
% 2.55/1.50 & ! [DS: d_subst] : ( DS = d_id )
% 2.55/1.50 & ! [DS1: d_subst,DS2: d_subst] :
% 2.55/1.50 ( ( ( d2subst @ DS1 )
% 2.55/1.50 = ( d2subst @ DS2 ) )
% 2.55/1.50 => ( DS1 = DS2 ) )
% 2.55/1.50 & ( one
% 2.55/1.50 = ( d2term @ d_one ) )
% 2.55/1.50 & ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) )
% 2.55/1.50 = ( d2term @ d_one ) )
% 2.55/1.50 & ( ( lam @ ( d2term @ d_one ) )
% 2.55/1.50 = ( d2term @ d_one ) )
% 2.55/1.50 & ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 2.55/1.50 = ( d2term @ d_one ) )
% 2.55/1.50 & ( id
% 2.55/1.50 = ( d2subst @ d_id ) )
% 2.55/1.50 & ( sh
% 2.55/1.50 = ( d2subst @ d_id ) )
% 2.55/1.50 & ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 2.55/1.50 = ( d2subst @ d_id ) )
% 2.55/1.50 & ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) )
% 2.55/1.50 = ( d2subst @ d_id ) )
% 2.55/1.50 & ( ( hoasap @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ ( d2term @ d_one ) )
% 2.55/1.50 = ( d2term @ d_one ) )
% 2.55/1.50 & ( hoaslam
% 2.55/1.50 = ( ^ [Bound_variable_4913: subst,Bound_variable_4915: subst > term > term] : ( d2term @ d_one ) ) )
% 2.55/1.50 & ( hoasinduction_p_and_p_prime
% 2.55/1.50 = ( ^ [P: subst > term > subst > $o,Q: term > $o] :
% 2.55/1.50 ! [X: term] :
% 2.55/1.50 ( ( Q @ X )
% 2.55/1.50 = ( P @ id @ X @ id ) ) ) )
% 2.55/1.50 & ( pushprop_p_and_p_prime
% 2.55/1.50 = ( ^ [A: term,M: subst,P: term > $o,Q: term > $o] :
% 2.55/1.50 ! [X: term] :
% 2.55/1.50 ( ( Q @ X )
% 2.55/1.50 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) )
% 2.55/1.50 & ~ ( var @ ( d2term @ d_one ) )
% 2.55/1.50 & ( pushprop_lem1v2
% 2.55/1.50 <=> ! [P: term > $o,Q: term > $o,A: term,M: subst] :
% 2.55/1.50 ( ~ ( P @ A )
% 2.55/1.50 | ~ ! [X: term] :
% 2.55/1.50 ( ( Q @ X )
% 2.55/1.50 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) )
% 2.55/1.50 | ( Q @ one ) ) )
% 2.55/1.50 & pushprop_lem1_gthm
% 2.55/1.50 & axmap
% 2.55/1.50 & pushprop_lem0_gthm
% 2.55/1.50 & ( shinj
% 2.55/1.50 <=> ! [A: term,B: term] :
% 2.55/1.50 ( ( ( sub @ A @ sh )
% 2.55/1.50 != ( sub @ B @ sh ) )
% 2.55/1.50 | ( A = B ) ) )
% 2.55/1.50 & hoasinduction_lem1v2
% 2.55/1.50 & hoasinduction_lem1v2_gthm
% 2.55/1.50 & ( induction2lem
% 2.55/1.50 <=> ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 2.55/1.50 ( ~ ! [A: term,B: term] :
% 2.55/1.50 ( ~ ( P @ A )
% 2.55/1.50 | ~ ( P @ B )
% 2.55/1.50 | ( P @ ( ap @ A @ B ) ) )
% 2.55/1.50 | ~ ! [A: term] :
% 2.55/1.50 ( ~ ! [B: term] :
% 2.55/1.50 ( ~ ( P @ B )
% 2.55/1.50 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.55/1.50 | ( P @ ( lam @ A ) ) )
% 2.55/1.50 | ~ ! [B: term] :
% 2.55/1.50 ( ~ ( var @ B )
% 2.55/1.50 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 2.55/1.50 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) ) )
% 2.55/1.50 & ( hoasinduction_lem3v2_f
% 2.55/1.50 <=> ! [B: term] :
% 2.55/1.50 ~ ! [F: subst > term > term] :
% 2.55/1.50 ~ ! [A: term,M: subst] :
% 2.55/1.50 ( ( sub @ B @ ( push @ A @ M ) )
% 2.55/1.50 = ( F @ M @ A ) ) )
% 2.55/1.50 & axvarshift
% 2.55/1.50 & ( hoasapinj2
% 2.55/1.50 <=> ! [A: term,B: term,C: term,D: term] :
% 2.55/1.50 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 2.55/1.50 != ( ap @ ( sub @ B @ id ) @ D ) )
% 2.55/1.50 | ( C = D ) ) )
% 2.55/1.50 & hoasapnotvar_gthm
% 2.55/1.50 & ( hoasapinj1
% 2.55/1.50 <=> ! [A: term,B: term,C: term,D: term] :
% 2.55/1.50 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 2.55/1.50 != ( ap @ ( sub @ B @ id ) @ D ) )
% 2.55/1.50 | ( A = B ) ) )
% 2.55/1.50 & ~ ulamvar1
% 2.55/1.50 & ( induction2lem_lthm
% 2.55/1.50 <=> ( ! [A: term,M: subst] :
% 2.55/1.50 ( A
% 2.55/1.50 = ( sub @ one @ ( push @ A @ M ) ) )
% 2.55/1.50 => ( ! [A: term,M: subst] :
% 2.55/1.50 ( M
% 2.55/1.50 = ( comp @ sh @ ( push @ A @ M ) ) )
% 2.55/1.50 => ( ! [M: subst] :
% 2.55/1.50 ( M
% 2.55/1.50 = ( comp @ M @ id ) )
% 2.55/1.50 => ( ! [P: term > $o,Bound_variable_2140: term] :
% 2.55/1.50 ( ~ ! [A: term] :
% 2.55/1.50 ( ~ ( var @ A )
% 2.55/1.50 | ( P @ A ) )
% 2.55/1.50 | ~ ! [A: term,B: term] :
% 2.55/1.50 ( ~ ( P @ A )
% 2.55/1.50 | ~ ( P @ B )
% 2.55/1.50 | ( P @ ( ap @ A @ B ) ) )
% 2.55/1.50 | ~ ! [A: term] :
% 2.55/1.50 ( ~ ( P @ A )
% 2.55/1.50 | ( P @ ( lam @ A ) ) )
% 2.55/1.50 | ( P @ Bound_variable_2140 ) )
% 2.55/1.50 => ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 2.55/1.50 ( ~ ! [A: term,B: term] :
% 2.55/1.50 ( ~ ( P @ A )
% 2.55/1.50 | ~ ( P @ B )
% 2.55/1.50 | ( P @ ( ap @ A @ B ) ) )
% 2.55/1.50 | ~ ! [A: term] :
% 2.55/1.50 ( ~ ! [B: term] :
% 2.55/1.50 ( ~ ( P @ B )
% 2.55/1.50 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.55/1.50 | ( P @ ( lam @ A ) ) )
% 2.55/1.50 | ~ ! [B: term] :
% 2.55/1.50 ( ~ ( var @ B )
% 2.55/1.50 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 2.55/1.50 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) ) ) ) ) ) )
% 2.55/1.50 & hoasinduction_lem3v2_gthm
% 2.55/1.50 & apnotvar
% 2.55/1.50 & pushprop_lthm_orig
% 2.55/1.50 & ( hoasinduction_lem3v2_f_lthm
% 2.55/1.50 <=> ! [B: term] :
% 2.55/1.50 ~ ! [F: subst > term > term] :
% 2.55/1.50 ~ ! [A: term,M: subst] :
% 2.55/1.50 ( ( sub @ B @ ( push @ A @ M ) )
% 2.55/1.50 = ( F @ M @ A ) ) )
% 2.55/1.50 & ( hoasinduction_lthm
% 2.55/1.50 <=> ( ! [P: term > $o,Bound_variable_2367: term] :
% 2.55/1.50 ( ~ ! [A: term] :
% 2.55/1.50 ( ~ ( var @ A )
% 2.55/1.50 | ( P @ A ) )
% 2.55/1.50 | ~ ! [A: term,B: term] :
% 2.55/1.50 ( ~ ( P @ A )
% 2.55/1.50 | ~ ( P @ B )
% 2.55/1.50 | ( P @ ( ap @ A @ B ) ) )
% 2.55/1.50 | ~ ! [A: term] :
% 2.55/1.50 ( ~ ! [B: term] :
% 2.55/1.50 ( ~ ( P @ B )
% 2.55/1.50 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.55/1.50 | ( P @ ( lam @ A ) ) )
% 2.55/1.50 | ( P @ Bound_variable_2367 ) )
% 2.55/1.50 => ( ! [P: subst > term > subst > $o,Bound_variable_2999: term,Bound_variable_3001: term] :
% 2.55/1.50 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.55/1.50 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.55/1.50 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.55/1.50 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.55/1.50 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.55/1.50 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.55/1.50 | ~ ! [A: term,B: term] :
% 2.55/1.50 ( ~ ( P @ id @ A @ id )
% 2.55/1.50 | ~ ( P @ id @ B @ id )
% 2.55/1.50 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.55/1.50 | ~ ( P @ id @ Bound_variable_2999 @ id )
% 2.55/1.50 | ~ ( P @ id @ Bound_variable_3001 @ id )
% 2.55/1.50 | ( P @ id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) )
% 2.55/1.50 => ( ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 2.55/1.50 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.55/1.50 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.55/1.50 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.55/1.50 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.55/1.50 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.55/1.50 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.55/1.50 | ~ ! [F: subst > term > term] :
% 2.55/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.55/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.55/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.55/1.50 | ~ ! [A: term] :
% 2.55/1.50 ( ~ ( P @ id @ A @ id )
% 2.55/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.55/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.55/1.50 | ~ ! [B: term] :
% 2.55/1.50 ( ~ ( P @ id @ B @ id )
% 2.55/1.50 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 2.55/1.50 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) )
% 2.55/1.50 => ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 2.55/1.50 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.55/1.50 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.55/1.50 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.55/1.50 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.55/1.50 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.55/1.50 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.55/1.50 | ~ ! [A: term] :
% 2.55/1.50 ( ~ ( var @ ( sub @ A @ id ) )
% 2.55/1.50 | ( P @ id @ A @ id ) )
% 2.55/1.50 | ~ ! [A: term,B: term] :
% 2.55/1.50 ( ~ ( P @ id @ A @ id )
% 2.55/1.50 | ~ ( P @ id @ B @ id )
% 2.55/1.50 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.55/1.50 | ~ ! [F: subst > term > term] :
% 2.55/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.55/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.55/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.55/1.50 | ~ ! [A: term] :
% 2.55/1.50 ( ~ ( P @ id @ A @ id )
% 2.55/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.55/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.55/1.50 | ( P @ id @ Bound_variable_3283 @ id ) ) ) ) ) )
% 2.55/1.50 & ( hoasinduction_no_psi_cond_lthm
% 2.55/1.50 <=> ( ! [P: subst > term > subst > $o] :
% 2.55/1.50 ~ ! [Q: term > $o] :
% 2.55/1.50 ~ ! [X: term] :
% 2.55/1.50 ( ( Q @ X )
% 2.55/1.50 = ( P @ id @ X @ id ) )
% 2.55/1.50 => ( ! [P: term > $o,Bound_variable_2367: term] :
% 2.55/1.50 ( ~ ! [A: term] :
% 2.55/1.50 ( ~ ( var @ A )
% 2.55/1.50 | ( P @ A ) )
% 2.55/1.50 | ~ ! [A: term,B: term] :
% 2.55/1.50 ( ~ ( P @ A )
% 2.55/1.50 | ~ ( P @ B )
% 2.55/1.50 | ( P @ ( ap @ A @ B ) ) )
% 2.55/1.50 | ~ ! [A: term] :
% 2.55/1.50 ( ~ ! [B: term] :
% 2.55/1.50 ( ~ ( P @ B )
% 2.55/1.50 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.55/1.50 | ( P @ ( lam @ A ) ) )
% 2.55/1.50 | ( P @ Bound_variable_2367 ) )
% 2.55/1.50 => ( ! [A: term] :
% 2.55/1.50 ( A
% 2.55/1.50 = ( sub @ A @ id ) )
% 2.55/1.50 => ( ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 2.55/1.50 ( ~ ! [F: subst > term > term] :
% 2.55/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.55/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.55/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.55/1.50 | ~ ! [A: term] :
% 2.55/1.50 ( ~ ( P @ id @ A @ id )
% 2.55/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.55/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.55/1.50 | ~ ! [X: term] :
% 2.55/1.50 ( ( Q @ X )
% 2.55/1.50 = ( P @ id @ X @ id ) )
% 2.55/1.50 | ~ ! [B: term] :
% 2.55/1.50 ( ~ ( Q @ B )
% 2.55/1.50 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 2.55/1.50 | ( Q @ ( lam @ Bound_variable_2931 ) ) )
% 2.55/1.50 => ! [P: subst > term > subst > $o,Bound_variable_3295: term] :
% 2.55/1.50 ( ~ ! [A: term,B: term] :
% 2.55/1.50 ( ~ ( P @ id @ A @ id )
% 2.55/1.50 | ~ ( P @ id @ B @ id )
% 2.55/1.50 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.55/1.50 | ~ ! [F: subst > term > term] :
% 2.55/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.55/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.55/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.55/1.50 | ~ ! [A: term] :
% 2.55/1.50 ( ~ ( P @ id @ A @ id )
% 2.55/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.55/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.55/1.50 | ( P @ id @ Bound_variable_3295 @ id ) ) ) ) ) ) )
% 2.55/1.50 & ( hoaslaminj
% 2.55/1.50 <=> ! [F: subst > term > term,Bound_variable_2547: subst > term > term,Bound_variable_2549: subst,Bound_variable_2551: term] :
% 2.55/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.55/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.55/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.55/1.50 | ~ ! [M: subst,A: term,N: subst] :
% 2.55/1.50 ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N )
% 2.55/1.50 = ( Bound_variable_2547 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.55/1.50 | ( ( lam @ ( F @ sh @ one ) )
% 2.55/1.50 != ( lam @ ( Bound_variable_2547 @ sh @ one ) ) )
% 2.55/1.50 | ( ( F @ Bound_variable_2549 @ Bound_variable_2551 )
% 2.55/1.50 = ( Bound_variable_2547 @ Bound_variable_2549 @ Bound_variable_2551 ) ) ) )
% 2.55/1.50 & ( hoasinduction_lem3aaa
% 2.55/1.50 <=> ! [P: subst > term > subst > $o,Bound_variable_3171: term] :
% 2.55/1.50 ( ~ ! [F: subst > term > term,Bound_variable_3149: term] :
% 2.55/1.50 ( ~ ! [A: term] :
% 2.55/1.50 ( ~ ( P @ id @ A @ id )
% 2.55/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.55/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id )
% 2.55/1.50 | ~ ! [Bound_variable_3072: subst,Bound_variable_3074: term,Bound_variable_3076: subst] :
% 2.55/1.50 ( ( sub @ ( F @ Bound_variable_3072 @ Bound_variable_3074 ) @ Bound_variable_3076 )
% 2.55/1.50 = ( sub @ ( sub @ Bound_variable_3149 @ ( push @ Bound_variable_3074 @ Bound_variable_3072 ) ) @ Bound_variable_3076 ) )
% 2.55/1.50 | ~ ! [Bound_variable_3090: subst,Bound_variable_3092: term,Bound_variable_3094: subst] :
% 2.55/1.50 ( ( F @ ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) @ ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) )
% 2.55/1.50 = ( sub @ Bound_variable_3149 @ ( push @ ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) @ ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) ) ) ) )
% 2.55/1.50 | ~ ! [B: term] :
% 2.55/1.50 ( ~ ( P @ id @ B @ id )
% 2.55/1.50 | ( P @ id @ ( sub @ Bound_variable_3171 @ ( push @ B @ id ) ) @ id ) )
% 2.55/1.50 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3171 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 2.55/1.50 & induction2lem_gthm
% 2.55/1.50 & ( hoasinduction_lem3aa_lthm
% 2.55/1.50 <=> ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 2.55/1.50 ( ~ ! [F: subst > term > term] :
% 2.55/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.55/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.55/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.55/1.50 | ~ ! [A: term] :
% 2.55/1.50 ( ~ ( P @ id @ A @ id )
% 2.55/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.55/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.55/1.50 | ~ ! [B: term] :
% 2.55/1.50 ( ~ ( P @ id @ B @ id )
% 2.55/1.50 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 2.55/1.50 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 2.55/1.50 & ( hoasinduction_lem3
% 2.55/1.50 <=> ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 2.55/1.50 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.55/1.50 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.55/1.50 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.55/1.50 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.55/1.50 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.55/1.50 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.55/1.50 | ~ ! [F: subst > term > term] :
% 2.55/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.55/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.55/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.55/1.50 | ~ ! [A: term] :
% 2.55/1.50 ( ~ ( P @ id @ A @ id )
% 2.55/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.55/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.55/1.50 | ~ ! [B: term] :
% 2.55/1.50 ( ~ ( P @ id @ B @ id )
% 2.55/1.50 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 2.55/1.50 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) ) )
% 2.55/1.50 & ( hoasinduction_lem2
% 2.55/1.50 <=> ! [P: subst > term > subst > $o,Bound_variable_2999: term,Bound_variable_3001: term] :
% 2.55/1.50 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.55/1.50 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.55/1.50 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.55/1.50 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.55/1.50 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.55/1.50 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.55/1.50 | ~ ! [A: term,B: term] :
% 2.55/1.50 ( ~ ( P @ id @ A @ id )
% 2.55/1.50 | ~ ( P @ id @ B @ id )
% 2.55/1.50 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.55/1.50 | ~ ( P @ id @ Bound_variable_2999 @ id )
% 2.55/1.50 | ~ ( P @ id @ Bound_variable_3001 @ id )
% 2.55/1.50 | ( P @ id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) ) )
% 2.55/1.50 & ( termmset_lthm
% 2.55/1.50 <=> ( ! [A: term] :
% 2.55/1.50 ( A
% 2.55/1.50 = ( sub @ A @ id ) )
% 2.55/1.50 => ! [A: term] :
% 2.55/1.50 ( A
% 2.55/1.50 = ( sub @ A @ id ) ) ) )
% 2.55/1.50 & hoasinduction_lem1
% 2.55/1.50 & hoaslamnotap_lthm
% 2.55/1.50 & ( pushprop_lem1v2_lthm
% 2.55/1.50 <=> ( ! [A: term,M: subst] :
% 2.55/1.50 ( A
% 2.55/1.50 = ( sub @ one @ ( push @ A @ M ) ) )
% 2.55/1.50 => ! [P: term > $o,Q: term > $o,A: term,M: subst] :
% 2.55/1.50 ( ~ ( P @ A )
% 2.55/1.50 | ~ ! [X: term] :
% 2.55/1.50 ( ( Q @ X )
% 2.55/1.50 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) )
% 2.55/1.50 | ( Q @ one ) ) ) )
% 2.55/1.50 & hoasapnotvar
% 2.55/1.50 & ( hoasinduction_lem0
% 2.55/1.50 <=> ! [P: subst > term > subst > $o] :
% 2.55/1.50 ~ ! [Q: term > $o] :
% 2.55/1.50 ~ ! [X: term] :
% 2.55/1.50 ( ( Q @ X )
% 2.55/1.50 = ( P @ id @ X @ id ) ) )
% 2.55/1.50 & ( hoasinduction
% 2.55/1.50 <=> ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 2.55/1.50 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.55/1.50 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.55/1.50 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.55/1.50 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.55/1.50 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.55/1.50 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.55/1.50 | ~ ! [A: term] :
% 2.55/1.50 ( ~ ( var @ ( sub @ A @ id ) )
% 2.55/1.50 | ( P @ id @ A @ id ) )
% 2.55/1.50 | ~ ! [A: term,B: term] :
% 2.55/1.50 ( ~ ( P @ id @ A @ id )
% 2.55/1.50 | ~ ( P @ id @ B @ id )
% 2.55/1.50 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.55/1.50 | ~ ! [F: subst > term > term] :
% 2.55/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.55/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.55/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.55/1.50 | ~ ! [A: term] :
% 2.55/1.50 ( ~ ( P @ id @ A @ id )
% 2.55/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.55/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.55/1.50 | ( P @ id @ Bound_variable_3283 @ id ) ) )
% 2.55/1.50 & hoasinduction_gthm
% 2.55/1.50 & axapp
% 2.55/1.50 & hoaslamnotvar_lthm
% 2.55/1.50 & pushprop_lem3v2_lthm
% 2.55/1.50 & ( hoasinduction_lem3b_lthm
% 2.55/1.50 <=> ! [B: term] :
% 2.55/1.50 ~ ! [F: subst > term > term] :
% 2.55/1.50 ( ( F @ sh @ one )
% 2.55/1.50 != ( sub @ B @ ( push @ one @ sh ) ) ) )
% 2.55/1.50 & ulamvarind
% 2.55/1.50 & ( induction
% 2.55/1.50 <=> ! [P: term > $o,Bound_variable_2140: term] :
% 2.55/1.50 ( ~ ! [A: term] :
% 2.55/1.50 ( ~ ( var @ A )
% 2.55/1.50 | ( P @ A ) )
% 2.55/1.50 | ~ ! [A: term,B: term] :
% 2.55/1.50 ( ~ ( P @ A )
% 2.55/1.50 | ~ ( P @ B )
% 2.55/1.50 | ( P @ ( ap @ A @ B ) ) )
% 2.55/1.50 | ~ ! [A: term] :
% 2.55/1.50 ( ~ ( P @ A )
% 2.55/1.50 | ( P @ ( lam @ A ) ) )
% 2.55/1.50 | ( P @ Bound_variable_2140 ) ) )
% 2.55/1.50 & ( hoasinduction_lem3a_lthm
% 2.55/1.50 <=> ( ! [A: term] :
% 2.55/1.50 ( A
% 2.55/1.50 = ( sub @ A @ id ) )
% 2.55/1.50 => ( ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 2.55/1.50 ( ~ ! [F: subst > term > term] :
% 2.55/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.55/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.55/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.55/1.50 | ~ ! [A: term] :
% 2.55/1.50 ( ~ ( P @ id @ A @ id )
% 2.55/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.55/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.55/1.50 | ~ ! [B: term] :
% 2.55/1.50 ( ~ ( P @ id @ B @ id )
% 2.55/1.50 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 2.55/1.50 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) )
% 2.55/1.50 => ! [P: subst > term > subst > $o,Bound_variable_3232: term] :
% 2.55/1.50 ( ~ ! [F: subst > term > term] :
% 2.55/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.55/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.55/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.55/1.50 | ~ ! [A: term] :
% 2.55/1.50 ( ~ ( P @ id @ A @ id )
% 2.55/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.55/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.55/1.50 | ~ ! [B: term] :
% 2.55/1.50 ( ~ ( P @ id @ B @ id )
% 2.55/1.50 | ( P @ id @ ( sub @ Bound_variable_3232 @ ( push @ B @ id ) ) @ id ) )
% 2.55/1.50 | ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) ) ) ) )
% 2.55/1.50 & termmset_gthm
% 2.55/1.50 & ( hoasinduction_lem3aa
% 2.55/1.50 <=> ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 2.55/1.50 ( ~ ! [F: subst > term > term] :
% 2.55/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.55/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.55/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.55/1.50 | ~ ! [A: term] :
% 2.55/1.50 ( ~ ( P @ id @ A @ id )
% 2.55/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.55/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.55/1.50 | ~ ! [B: term] :
% 2.55/1.50 ( ~ ( P @ id @ B @ id )
% 2.55/1.50 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 2.55/1.50 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) ) )
% 2.55/1.50 & pushprop_lem1v2_gthm
% 2.55/1.50 & hoaslamnotap_gthm
% 2.55/1.50 & hoaslamnotvar_gthm
% 2.55/1.50 & hoasinduction_lem3b_gthm
% 2.55/1.50 & pushprop_lem2v2
% 2.55/1.50 & hoasinduction_lem3a_gthm
% 2.55/1.50 & axclos
% 2.55/1.50 & axassoc
% 2.55/1.50 & ( hoasinduction_lem2v2
% 2.55/1.50 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2820: term,Bound_variable_2822: term] :
% 2.55/1.50 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.55/1.50 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.55/1.50 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.55/1.50 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.55/1.50 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.55/1.50 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.55/1.50 | ~ ! [A: term,B: term] :
% 2.55/1.50 ( ~ ( P @ id @ A @ id )
% 2.55/1.50 | ~ ( P @ id @ B @ id )
% 2.55/1.50 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.55/1.50 | ~ ! [X: term] :
% 2.55/1.50 ( ( Q @ X )
% 2.55/1.50 = ( P @ id @ X @ id ) )
% 2.55/1.50 | ~ ( Q @ Bound_variable_2820 )
% 2.55/1.50 | ~ ( Q @ Bound_variable_2822 )
% 2.55/1.50 | ( Q @ ( ap @ Bound_variable_2820 @ Bound_variable_2822 ) ) ) )
% 2.55/1.50 & pushprop_lthm
% 2.55/1.50 & ( apinj2
% 2.55/1.50 <=> ! [A: term,B: term,C: term,D: term] :
% 2.55/1.50 ( ( ( ap @ A @ C )
% 2.55/1.50 != ( ap @ B @ D ) )
% 2.55/1.50 | ( C = D ) ) )
% 2.55/1.50 & ( apinj1
% 2.55/1.50 <=> ! [A: term,B: term,C: term,D: term] :
% 2.55/1.50 ( ( ( ap @ A @ C )
% 2.55/1.50 != ( ap @ B @ D ) )
% 2.55/1.50 | ( A = B ) ) )
% 2.55/1.50 & ( hoasapinj2_lthm
% 2.55/1.50 <=> ( ! [A: term,B: term,C: term,D: term] :
% 2.55/1.50 ( ( ( ap @ A @ C )
% 2.55/1.50 != ( ap @ B @ D ) )
% 2.55/1.50 | ( C = D ) )
% 2.55/1.50 => ! [A: term,B: term,C: term,D: term] :
% 2.55/1.50 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 2.55/1.50 != ( ap @ ( sub @ B @ id ) @ D ) )
% 2.55/1.50 | ( C = D ) ) ) )
% 2.55/1.50 & ( hoasinduction_lem3v2a
% 2.55/1.50 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 2.55/1.50 ( ~ ! [F: subst > term > term] :
% 2.55/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.55/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.55/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.55/1.50 | ~ ! [A: term] :
% 2.55/1.50 ( ~ ( P @ id @ A @ id )
% 2.55/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.55/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.55/1.50 | ~ ! [X: term] :
% 2.55/1.50 ( ( Q @ X )
% 2.55/1.50 = ( P @ id @ X @ id ) )
% 2.55/1.50 | ~ ! [B: term] :
% 2.55/1.50 ( ~ ( Q @ B )
% 2.55/1.50 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 2.55/1.50 | ( Q @ ( lam @ Bound_variable_2931 ) ) ) )
% 2.55/1.50 & ( hoasapinj1_lthm
% 2.55/1.50 <=> ( ! [A: term] :
% 2.55/1.50 ( A
% 2.55/1.50 = ( sub @ A @ id ) )
% 2.55/1.50 => ( ! [A: term,B: term,C: term,D: term] :
% 2.55/1.50 ( ( ( ap @ A @ C )
% 2.55/1.50 != ( ap @ B @ D ) )
% 2.55/1.50 | ( A = B ) )
% 2.55/1.50 => ! [A: term,B: term,C: term,D: term] :
% 2.55/1.50 ( ( ( ap @ ( sub @ A @ id ) @ C )
% 2.55/1.50 != ( ap @ ( sub @ B @ id ) @ D ) )
% 2.55/1.50 | ( A = B ) ) ) ) )
% 2.55/1.50 & ( hoaslaminj_lthm
% 2.55/1.50 <=> ( ! [A: term,M: subst] :
% 2.55/1.50 ( A
% 2.55/1.50 = ( sub @ one @ ( push @ A @ M ) ) )
% 2.55/1.50 => ( ! [A: term,M: subst] :
% 2.55/1.50 ( M
% 2.55/1.50 = ( comp @ sh @ ( push @ A @ M ) ) )
% 2.55/1.50 => ( ! [A: term,B: term] :
% 2.55/1.50 ( ( ( lam @ A )
% 2.55/1.50 != ( lam @ B ) )
% 2.55/1.50 | ( A = B ) )
% 2.55/1.50 => ! [F: subst > term > term,Bound_variable_2547: subst > term > term,Bound_variable_2549: subst,Bound_variable_2551: term] :
% 2.55/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.55/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.55/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.55/1.50 | ~ ! [M: subst,A: term,N: subst] :
% 2.55/1.50 ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N )
% 2.55/1.50 = ( Bound_variable_2547 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.55/1.50 | ( ( lam @ ( F @ sh @ one ) )
% 2.55/1.50 != ( lam @ ( Bound_variable_2547 @ sh @ one ) ) )
% 2.55/1.50 | ( ( F @ Bound_variable_2549 @ Bound_variable_2551 )
% 2.55/1.50 = ( Bound_variable_2547 @ Bound_variable_2549 @ Bound_variable_2551 ) ) ) ) ) ) )
% 2.55/1.50 & ( axvarcons
% 2.55/1.50 <=> ! [A: term,M: subst] :
% 2.55/1.50 ( A
% 2.55/1.50 = ( sub @ one @ ( push @ A @ M ) ) ) )
% 2.55/1.50 & ( axscons
% 2.55/1.50 <=> ! [M: subst] :
% 2.55/1.50 ( M
% 2.55/1.50 = ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) ) ) )
% 2.55/1.50 & hoasinduction_lem2v2_gthm
% 2.55/1.50 & ( axidr
% 2.55/1.50 <=> ! [M: subst] :
% 2.55/1.50 ( M
% 2.55/1.50 = ( comp @ M @ id ) ) )
% 2.55/1.50 & ( pushprop_lem1
% 2.55/1.50 <=> ! [P: term > $o,K: term > $o,A: term,M: subst,B: term] :
% 2.55/1.50 ( ~ ( P @ A )
% 2.55/1.50 | ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) )
% 2.55/1.50 & ( laminj
% 2.55/1.50 <=> ! [A: term,B: term] :
% 2.55/1.50 ( ( ( lam @ A )
% 2.55/1.50 != ( lam @ B ) )
% 2.55/1.50 | ( A = B ) ) )
% 2.55/1.50 & ( hoasinduction_lem3_lthm
% 2.55/1.50 <=> ( ! [A: term] :
% 2.55/1.50 ( A
% 2.55/1.50 = ( sub @ A @ id ) )
% 2.55/1.50 => ( ! [P: subst > term > subst > $o,Bound_variable_3046: term] :
% 2.55/1.50 ( ~ ! [F: subst > term > term] :
% 2.55/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.55/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.55/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.55/1.50 | ~ ! [A: term] :
% 2.55/1.50 ( ~ ( P @ id @ A @ id )
% 2.55/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.55/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.55/1.50 | ~ ! [B: term] :
% 2.55/1.50 ( ~ ( P @ id @ B @ id )
% 2.55/1.50 | ( P @ id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) )
% 2.55/1.50 | ( P @ id @ ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) )
% 2.55/1.50 => ! [P: subst > term > subst > $o,Bound_variable_3211: term] :
% 2.55/1.50 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.55/1.50 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.55/1.50 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.55/1.50 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.55/1.50 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.55/1.50 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.55/1.50 | ~ ! [F: subst > term > term] :
% 2.55/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.55/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.55/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.55/1.50 | ~ ! [A: term] :
% 2.55/1.50 ( ~ ( P @ id @ A @ id )
% 2.55/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.55/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.55/1.50 | ~ ! [B: term] :
% 2.55/1.50 ( ~ ( P @ id @ B @ id )
% 2.55/1.50 | ( P @ id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) )
% 2.55/1.50 | ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) ) ) ) )
% 2.55/1.50 & ( pushprop_lem0
% 2.55/1.50 <=> ! [P: term > $o,A: term,M: subst] :
% 2.55/1.50 ~ ! [Q: term > $o] :
% 2.55/1.50 ~ ! [X: term] :
% 2.55/1.50 ( ( Q @ X )
% 2.55/1.50 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) )
% 2.55/1.50 & pushprop_gthm
% 2.55/1.50 & axabs
% 2.55/1.50 & ( hoasinduction_lem3v2a_lthm
% 2.55/1.50 <=> ( ! [B: term] :
% 2.55/1.50 ~ ! [F: subst > term > term] :
% 2.55/1.50 ~ ! [A: term,M: subst] :
% 2.55/1.50 ( ( sub @ B @ ( push @ A @ M ) )
% 2.55/1.50 = ( F @ M @ A ) )
% 2.55/1.50 => ( ! [A: term] :
% 2.55/1.50 ( A
% 2.55/1.50 = ( sub @ A @ id ) )
% 2.55/1.50 => ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 2.55/1.50 ( ~ ! [F: subst > term > term] :
% 2.55/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.55/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.55/1.50 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.55/1.50 | ~ ! [A: term] :
% 2.55/1.50 ( ~ ( P @ id @ A @ id )
% 2.55/1.50 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.55/1.50 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.55/1.50 | ~ ! [X: term] :
% 2.55/1.50 ( ( Q @ X )
% 2.55/1.50 = ( P @ id @ X @ id ) )
% 2.55/1.50 | ~ ! [B: term] :
% 2.55/1.50 ( ~ ( Q @ B )
% 2.55/1.50 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 2.55/1.50 | ( Q @ ( lam @ Bound_variable_2931 ) ) ) ) ) )
% 2.55/1.50 & hoasinduction_lem2_lthm
% 2.55/1.50 & hoasapinj2_gthm
% 2.55/1.50 & hoasinduction_lem1_lthm
% 2.55/1.50 & ~ lamnotap
% 2.55/1.50 & hoasapinj1_gthm
% 2.55/1.50 & hoaslamnotvar
% 2.55/1.50 & ( axidl
% 2.55/1.50 <=> ! [M: subst] :
% 2.55/1.50 ( M
% 2.55/1.50 = ( comp @ id @ M ) ) )
% 2.55/1.50 & hoaslaminj_gthm
% 2.55/1.50 & ( induction2_lthm
% 2.55/1.50 <=> ( ! [A: term] :
% 2.55/1.50 ( A
% 2.55/1.50 = ( sub @ A @ id ) )
% 2.55/1.50 => ( ! [P: term > $o,Bound_variable_2340: term,Bound_variable_2342: subst] :
% 2.55/1.50 ( ~ ! [A: term,B: term] :
% 2.55/1.50 ( ~ ( P @ A )
% 2.55/1.50 | ~ ( P @ B )
% 2.55/1.50 | ( P @ ( ap @ A @ B ) ) )
% 2.55/1.50 | ~ ! [A: term] :
% 2.55/1.50 ( ~ ! [B: term] :
% 2.55/1.50 ( ~ ( P @ B )
% 2.55/1.50 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.55/1.50 | ( P @ ( lam @ A ) ) )
% 2.55/1.50 | ~ ! [B: term] :
% 2.55/1.50 ( ~ ( var @ B )
% 2.55/1.50 | ( P @ ( sub @ B @ Bound_variable_2342 ) ) )
% 2.55/1.50 | ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) )
% 2.55/1.50 => ! [P: term > $o,Bound_variable_2367: term] :
% 2.55/1.50 ( ~ ! [A: term] :
% 2.55/1.50 ( ~ ( var @ A )
% 2.55/1.50 | ( P @ A ) )
% 2.55/1.50 | ~ ! [A: term,B: term] :
% 2.55/1.50 ( ~ ( P @ A )
% 2.55/1.50 | ~ ( P @ B )
% 2.55/1.50 | ( P @ ( ap @ A @ B ) ) )
% 2.55/1.50 | ~ ! [A: term] :
% 2.55/1.50 ( ~ ! [B: term] :
% 2.55/1.50 ( ~ ( P @ B )
% 2.55/1.50 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.55/1.50 | ( P @ ( lam @ A ) ) )
% 2.55/1.50 | ( P @ Bound_variable_2367 ) ) ) ) )
% 2.55/1.50 & ( hoasinduction_lem0_lthm
% 2.55/1.50 <=> ! [P: subst > term > subst > $o] :
% 2.55/1.50 ~ ! [Q: term > $o] :
% 2.55/1.50 ~ ! [X: term] :
% 2.55/1.50 ( ( Q @ X )
% 2.55/1.50 = ( P @ id @ X @ id ) ) )
% 2.55/1.50 & ( substmonoid_lthm
% 2.55/1.50 <=> ( ! [M: subst] :
% 2.55/1.50 ( M
% 2.55/1.50 = ( comp @ id @ M ) )
% 2.55/1.50 => ( ! [M: subst] :
% 2.55/1.50 ( M
% 2.55/1.50 = ( comp @ M @ id ) )
% 2.55/1.50 => ( ! [M: subst] :
% 2.55/1.50 ( M
% 2.55/1.50 = ( comp @ id @ M ) )
% 2.55/1.50 & ! [M: subst] :
% 2.55/1.50 ( M
% 2.55/1.50 = ( comp @ M @ id ) ) ) ) ) )
% 2.55/1.50 & pushprop
% 2.55/1.50 & hoasinduction_lem3_gthm
% 2.55/1.50 & hoasinduction_lem2_gthm
% 2.55/1.50 & ( hoasinduction_lem3b
% 2.55/1.50 <=> ! [B: term] :
% 2.55/1.50 ~ ! [F: subst > term > term] :
% 2.55/1.50 ( ( F @ sh @ one )
% 2.55/1.50 != ( sub @ B @ ( push @ one @ sh ) ) ) )
% 2.55/1.50 & ( substmonoid
% 2.55/1.50 <=> ( ! [M: subst] :
% 2.55/1.50 ( M
% 2.55/1.50 = ( comp @ id @ M ) )
% 2.55/1.50 & ! [M: subst] :
% 2.55/1.50 ( M
% 2.55/1.50 = ( comp @ M @ id ) ) ) )
% 2.55/1.50 & lamnotvar
% 2.55/1.50 & ( hoasinduction_lem3a
% 2.55/1.50 <=> ! [P: subst > term > subst > $o,Bound_variable_3232: term] :
% 2.55/1.50 ( ~ ! [F: subst > term > term] :
% 2.55/1.50 ( ~ ! [M: subst,A: term,N: subst] :
% 2.55/1.50 ( ( sub @ ( F @ M @ A ) @ N )
% 2.55/1.51 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.55/1.51 | ~ ! [A: term] :
% 2.55/1.51 ( ~ ( P @ id @ A @ id )
% 2.55/1.51 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.55/1.51 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.55/1.51 | ~ ! [B: term] :
% 2.55/1.51 ( ~ ( P @ id @ B @ id )
% 2.55/1.51 | ( P @ id @ ( sub @ Bound_variable_3232 @ ( push @ B @ id ) ) @ id ) )
% 2.55/1.51 | ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) ) )
% 2.55/1.51 & hoasinduction_lem1_gthm
% 2.55/1.51 & ( hoasinduction_no_psi_cond
% 2.55/1.51 <=> ! [P: subst > term > subst > $o,Bound_variable_3295: term] :
% 2.55/1.51 ( ~ ! [A: term,B: term] :
% 2.55/1.51 ( ~ ( P @ id @ A @ id )
% 2.55/1.51 | ~ ( P @ id @ B @ id )
% 2.55/1.51 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.55/1.51 | ~ ! [F: subst > term > term] :
% 2.55/1.51 ( ~ ! [M: subst,A: term,N: subst] :
% 2.55/1.51 ( ( sub @ ( F @ M @ A ) @ N )
% 2.55/1.51 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.55/1.51 | ~ ! [A: term] :
% 2.55/1.51 ( ~ ( P @ id @ A @ id )
% 2.55/1.51 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.55/1.51 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.55/1.51 | ( P @ id @ Bound_variable_3295 @ id ) ) )
% 2.55/1.51 & induction2_gthm
% 2.55/1.51 & pushprop_lem2v2_lthm
% 2.55/1.51 & ~ ( hoasvar @ ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) )
% 2.55/1.51 & ( hoaslamnotap
% 2.55/1.51 <=> ! [F: subst > term > term,Bound_variable_2603: term,Bound_variable_2605: term] :
% 2.55/1.51 ( ~ ! [M: subst,A: term,N: subst] :
% 2.55/1.51 ( ( sub @ ( F @ M @ A ) @ N )
% 2.55/1.51 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.55/1.51 | ( ( lam @ ( F @ sh @ one ) )
% 2.55/1.51 != ( ap @ ( sub @ Bound_variable_2603 @ id ) @ Bound_variable_2605 ) ) ) )
% 2.55/1.51 & substmonoid_gthm
% 2.55/1.51 & ulamvarsh
% 2.55/1.51 & ( induction2
% 2.55/1.51 <=> ! [P: term > $o,Bound_variable_2367: term] :
% 2.55/1.51 ( ~ ! [A: term] :
% 2.55/1.51 ( ~ ( var @ A )
% 2.55/1.51 | ( P @ A ) )
% 2.55/1.51 | ~ ! [A: term,B: term] :
% 2.55/1.51 ( ~ ( P @ A )
% 2.55/1.51 | ~ ( P @ B )
% 2.55/1.51 | ( P @ ( ap @ A @ B ) ) )
% 2.55/1.51 | ~ ! [A: term] :
% 2.55/1.51 ( ~ ! [B: term] :
% 2.55/1.51 ( ~ ( P @ B )
% 2.55/1.51 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.55/1.51 | ( P @ ( lam @ A ) ) )
% 2.55/1.51 | ( P @ Bound_variable_2367 ) ) )
% 2.55/1.51 & pushprop_lem3v2
% 2.55/1.51 & pushprop_lem2v2_gthm
% 2.55/1.51 & ( pushprop_lem1_lthm
% 2.55/1.51 <=> ( ! [A: term,M: subst] :
% 2.55/1.51 ( A
% 2.55/1.51 = ( sub @ one @ ( push @ A @ M ) ) )
% 2.55/1.51 => ( ! [A: term,M: subst] :
% 2.55/1.51 ( M
% 2.55/1.51 = ( comp @ sh @ ( push @ A @ M ) ) )
% 2.55/1.51 => ! [P: term > $o,K: term > $o,A: term,M: subst,B: term] :
% 2.55/1.51 ( ~ ( P @ A )
% 2.55/1.51 | ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) ) ) )
% 2.55/1.51 & ( hoasinduction_lem3v2
% 2.55/1.51 <=> ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2910: term] :
% 2.55/1.51 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.55/1.51 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.55/1.51 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.55/1.51 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.55/1.51 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.55/1.51 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.55/1.51 | ~ ! [F: subst > term > term] :
% 2.55/1.51 ( ~ ! [M: subst,A: term,N: subst] :
% 2.55/1.51 ( ( sub @ ( F @ M @ A ) @ N )
% 2.55/1.51 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.55/1.51 | ~ ! [A: term] :
% 2.55/1.51 ( ~ ( P @ id @ A @ id )
% 2.55/1.51 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.55/1.51 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.55/1.51 | ~ ! [X: term] :
% 2.55/1.51 ( ( Q @ X )
% 2.55/1.51 = ( P @ id @ X @ id ) )
% 2.55/1.51 | ~ ! [B: term] :
% 2.55/1.51 ( ~ ( Q @ B )
% 2.55/1.51 | ( Q @ ( sub @ Bound_variable_2910 @ ( push @ B @ id ) ) ) )
% 2.55/1.51 | ( Q @ ( lam @ Bound_variable_2910 ) ) ) )
% 2.55/1.51 & ( axshiftcons
% 2.55/1.51 <=> ! [A: term,M: subst] :
% 2.55/1.51 ( M
% 2.55/1.51 = ( comp @ sh @ ( push @ A @ M ) ) ) )
% 2.55/1.51 & ( termmset
% 2.55/1.51 <=> ! [A: term] :
% 2.55/1.51 ( A
% 2.55/1.51 = ( sub @ A @ id ) ) )
% 2.55/1.51 & ( pushprop_lem0_lthm
% 2.55/1.51 <=> ! [P: term > $o,A: term,M: subst] :
% 2.55/1.51 ~ ! [Q: term > $o] :
% 2.55/1.51 ~ ! [X: term] :
% 2.55/1.51 ( ( Q @ X )
% 2.55/1.51 = ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) )
% 2.55/1.51 & hoasapnotvar_lthm
% 2.55/1.51 & ( hoasinduction_lem3v2_lthm
% 2.55/1.51 <=> ( ! [A: term] :
% 2.55/1.51 ( A
% 2.55/1.51 = ( sub @ A @ id ) )
% 2.55/1.51 => ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2910: term] :
% 2.55/1.51 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.55/1.51 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.55/1.51 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.55/1.51 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.55/1.51 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.55/1.51 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.55/1.51 | ~ ! [F: subst > term > term] :
% 2.55/1.51 ( ~ ! [M: subst,A: term,N: subst] :
% 2.55/1.51 ( ( sub @ ( F @ M @ A ) @ N )
% 2.55/1.51 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.55/1.51 | ~ ! [A: term] :
% 2.55/1.51 ( ~ ( P @ id @ A @ id )
% 2.55/1.51 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.55/1.51 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.55/1.51 | ~ ! [X: term] :
% 2.55/1.51 ( ( Q @ X )
% 2.55/1.51 = ( P @ id @ X @ id ) )
% 2.55/1.51 | ~ ! [B: term] :
% 2.55/1.51 ( ~ ( Q @ B )
% 2.55/1.51 | ( Q @ ( sub @ Bound_variable_2910 @ ( push @ B @ id ) ) ) )
% 2.55/1.51 | ( Q @ ( lam @ Bound_variable_2910 ) ) ) ) )
% 2.55/1.51 & ( axvarid
% 2.55/1.51 <=> ! [A: term] :
% 2.55/1.51 ( A
% 2.55/1.51 = ( sub @ A @ id ) ) )
% 2.55/1.51 & ( hoasinduction_lthm_3
% 2.55/1.51 <=> ( ! [P: subst > term > subst > $o] :
% 2.55/1.51 ~ ! [Q: term > $o] :
% 2.55/1.51 ~ ! [X: term] :
% 2.55/1.51 ( ( Q @ X )
% 2.55/1.51 = ( P @ id @ X @ id ) )
% 2.55/1.51 => ( ! [P: term > $o,Bound_variable_2367: term] :
% 2.55/1.51 ( ~ ! [A: term] :
% 2.55/1.51 ( ~ ( var @ A )
% 2.55/1.51 | ( P @ A ) )
% 2.55/1.51 | ~ ! [A: term,B: term] :
% 2.55/1.51 ( ~ ( P @ A )
% 2.55/1.51 | ~ ( P @ B )
% 2.55/1.51 | ( P @ ( ap @ A @ B ) ) )
% 2.55/1.51 | ~ ! [A: term] :
% 2.55/1.51 ( ~ ! [B: term] :
% 2.55/1.51 ( ~ ( P @ B )
% 2.55/1.51 | ( P @ ( sub @ A @ ( push @ B @ id ) ) ) )
% 2.55/1.51 | ( P @ ( lam @ A ) ) )
% 2.55/1.51 | ( P @ Bound_variable_2367 ) )
% 2.55/1.51 => ( ! [A: term] :
% 2.55/1.51 ( A
% 2.55/1.51 = ( sub @ A @ id ) )
% 2.55/1.51 => ( ! [P: subst > term > subst > $o,Q: term > $o,Bound_variable_2931: term] :
% 2.55/1.51 ( ~ ! [F: subst > term > term] :
% 2.55/1.51 ( ~ ! [M: subst,A: term,N: subst] :
% 2.55/1.51 ( ( sub @ ( F @ M @ A ) @ N )
% 2.55/1.51 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.55/1.51 | ~ ! [A: term] :
% 2.55/1.51 ( ~ ( P @ id @ A @ id )
% 2.55/1.51 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.55/1.51 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.55/1.51 | ~ ! [X: term] :
% 2.55/1.51 ( ( Q @ X )
% 2.55/1.51 = ( P @ id @ X @ id ) )
% 2.55/1.51 | ~ ! [B: term] :
% 2.55/1.51 ( ~ ( Q @ B )
% 2.55/1.51 | ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) )
% 2.55/1.51 | ( Q @ ( lam @ Bound_variable_2931 ) ) )
% 2.55/1.51 => ! [P: subst > term > subst > $o,Bound_variable_3283: term] :
% 2.55/1.51 ( ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.55/1.51 ( ~ ( P @ M @ A @ ( comp @ K @ N ) )
% 2.55/1.51 | ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) )
% 2.55/1.51 | ~ ! [M: subst,A: term,N: subst,K: subst] :
% 2.55/1.51 ( ~ ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N )
% 2.55/1.51 | ( P @ M @ A @ ( comp @ K @ N ) ) )
% 2.55/1.51 | ~ ! [A: term] :
% 2.55/1.51 ( ~ ( var @ ( sub @ A @ id ) )
% 2.55/1.51 | ( P @ id @ A @ id ) )
% 2.55/1.51 | ~ ! [A: term,B: term] :
% 2.55/1.51 ( ~ ( P @ id @ A @ id )
% 2.55/1.51 | ~ ( P @ id @ B @ id )
% 2.55/1.51 | ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) )
% 2.55/1.51 | ~ ! [F: subst > term > term] :
% 2.55/1.51 ( ~ ! [M: subst,A: term,N: subst] :
% 2.55/1.51 ( ( sub @ ( F @ M @ A ) @ N )
% 2.55/1.51 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) )
% 2.55/1.51 | ~ ! [A: term] :
% 2.55/1.51 ( ~ ( P @ id @ A @ id )
% 2.55/1.51 | ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.55/1.51 | ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) )
% 2.55/1.51 | ( P @ id @ Bound_variable_3283 @ id ) ) ) ) ) ) ) ) ).
% 2.55/1.51
% 2.55/1.51 thf(hoasinduction_lem3aaa,conjecture,
% 2.55/1.51 ( hoasinduction_lem3aaa
% 2.55/1.51 = ( ! [P: subst > term > subst > $o] :
% 2.55/1.51 ( ! [F: subst > term > term] :
% 2.55/1.51 ( ? [C: term] :
% 2.55/1.51 ! [M: subst,A: term,N: subst] :
% 2.55/1.51 ( ( ( sub @ ( F @ M @ A ) @ N )
% 2.55/1.51 = ( sub @ ( sub @ C @ ( push @ A @ M ) ) @ N ) )
% 2.55/1.51 & ( ( sub @ C @ ( push @ ( sub @ A @ N ) @ ( comp @ M @ N ) ) )
% 2.55/1.51 = ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) )
% 2.55/1.51 => ( ! [A: term] :
% 2.55/1.51 ( ( P @ id @ A @ id )
% 2.55/1.51 => ( P @ id @ ( F @ id @ A ) @ id ) )
% 2.55/1.51 => ( P @ id
% 2.55/1.51 @ ( hoaslam @ id
% 2.55/1.51 @ ^ [M: subst,A: term] : ( F @ M @ A ) )
% 2.55/1.51 @ id ) ) )
% 2.55/1.51 => ! [A: term] :
% 2.55/1.51 ( ! [B: term] :
% 2.55/1.51 ( ( P @ id @ B @ id )
% 2.55/1.51 => ( P @ id @ ( sub @ A @ ( push @ B @ id ) ) @ id ) )
% 2.55/1.51 => ( P @ id @ ( lam @ ( sub @ A @ ( push @ one @ sh ) ) ) @ id ) ) ) ) ) ).
% 2.55/1.51 ------------------------
% 2.55/1.52 % (17363)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_17021 for (2999ds/2Mi)
% 2.55/1.52 % (17363)Instruction limit reached!
% 2.55/1.52 % (17363)------------------------------
% 2.55/1.52 % (17363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.52 % (17363)Termination reason: Unknown
% 2.55/1.52 % (17363)Termination phase: shuffling
% 2.55/1.52
% 2.55/1.52 % (17363)Memory used [KB]: 1151
% 2.55/1.52 % (17363)Time elapsed: 0.002 s
% 2.55/1.52 % (17363)Instructions burned: 2 (million)
% 2.55/1.52 % (17363)------------------------------
% 2.55/1.52 % (17363)------------------------------
% 2.55/1.52 % (17359)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_17021 for (2999ds/183Mi)
% 2.55/1.53 % (17362)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_17021 for (2999ds/2Mi)
% 2.55/1.53 % (17362)Instruction limit reached!
% 2.55/1.53 % (17362)------------------------------
% 2.55/1.53 % (17362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.53 % (17362)Termination reason: Unknown
% 2.55/1.53 % (17362)Termination phase: shuffling
% 2.55/1.53
% 2.55/1.53 % (17362)Memory used [KB]: 1279
% 2.55/1.53 % (17362)Time elapsed: 0.003 s
% 2.55/1.53 % (17362)Instructions burned: 3 (million)
% 2.55/1.53 % (17362)------------------------------
% 2.55/1.53 % (17362)------------------------------
% 2.55/1.53 % (17360)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_17021 for (2999ds/4Mi)
% 2.55/1.53 % (17361)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_17021 for (2999ds/27Mi)
% 2.55/1.53 % (17364)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_17021 for (2999ds/275Mi)
% 2.55/1.53 % (17365)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_17021 for (2999ds/18Mi)
% 2.55/1.53 % (17366)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_17021 for (2999ds/3Mi)
% 2.55/1.53 % (17360)Instruction limit reached!
% 2.55/1.53 % (17360)------------------------------
% 2.55/1.53 % (17360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.53 % (17360)Termination reason: Unknown
% 2.55/1.53 % (17360)Termination phase: shuffling
% 2.55/1.53
% 2.55/1.53 % (17360)Memory used [KB]: 1279
% 2.55/1.53 % (17360)Time elapsed: 0.005 s
% 2.55/1.53 % (17360)Instructions burned: 5 (million)
% 2.55/1.53 % (17360)------------------------------
% 2.55/1.53 % (17360)------------------------------
% 2.55/1.54 % (17366)Instruction limit reached!
% 2.55/1.54 % (17366)------------------------------
% 2.55/1.54 % (17366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.54 % (17366)Termination reason: Unknown
% 2.55/1.54 % (17366)Termination phase: shuffling
% 2.55/1.54
% 2.55/1.54 % (17366)Memory used [KB]: 1279
% 2.55/1.54 % (17366)Time elapsed: 0.003 s
% 2.55/1.54 % (17366)Instructions burned: 6 (million)
% 2.55/1.54 % (17366)------------------------------
% 2.55/1.54 % (17366)------------------------------
% 2.55/1.54 % (17367)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_17021 for (2999ds/37Mi)
% 2.55/1.54 % (17365)Instruction limit reached!
% 2.55/1.54 % (17365)------------------------------
% 2.55/1.54 % (17365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.54 % (17365)Termination reason: Unknown
% 2.55/1.54 % (17365)Termination phase: shuffling
% 2.55/1.54
% 2.55/1.54 % (17365)Memory used [KB]: 2046
% 2.55/1.54 % (17365)Time elapsed: 0.012 s
% 2.55/1.54 % (17365)Instructions burned: 18 (million)
% 2.55/1.54 % (17365)------------------------------
% 2.55/1.54 % (17365)------------------------------
% 2.55/1.54 % (17369)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_17021 for (2999ds/3Mi)
% 2.55/1.55 % (17369)Instruction limit reached!
% 2.55/1.55 % (17369)------------------------------
% 2.55/1.55 % (17369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.55 % (17369)Termination reason: Unknown
% 2.55/1.55 % (17369)Termination phase: shuffling
% 2.55/1.55
% 2.55/1.55 % (17369)Memory used [KB]: 1279
% 2.55/1.55 % (17369)Time elapsed: 0.002 s
% 2.55/1.55 % (17369)Instructions burned: 4 (million)
% 2.55/1.55 % (17369)------------------------------
% 2.55/1.55 % (17369)------------------------------
% 2.55/1.55 % (17361)Instruction limit reached!
% 2.55/1.55 % (17361)------------------------------
% 2.55/1.55 % (17361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.55 % (17361)Termination reason: Unknown
% 2.55/1.55 % (17361)Termination phase: Property scanning
% 2.55/1.55
% 2.55/1.55 % (17361)Memory used [KB]: 2174
% 2.55/1.55 % (17361)Time elapsed: 0.018 s
% 2.55/1.55 % (17361)Instructions burned: 27 (million)
% 2.55/1.55 % (17361)------------------------------
% 2.55/1.55 % (17361)------------------------------
% 2.55/1.55 % (17368)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_17021 for (2999ds/15Mi)
% 2.55/1.55 % (17367)Instruction limit reached!
% 2.55/1.55 % (17367)------------------------------
% 2.55/1.55 % (17367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.55 % (17367)Termination reason: Unknown
% 2.55/1.55 % (17367)Termination phase: Property scanning
% 2.55/1.55
% 2.55/1.55 % (17367)Memory used [KB]: 1918
% 2.55/1.55 % (17367)Time elapsed: 0.013 s
% 2.55/1.55 % (17367)Instructions burned: 39 (million)
% 2.55/1.55 % (17367)------------------------------
% 2.55/1.55 % (17367)------------------------------
% 2.55/1.56 % (17371)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_17021 for (2999ds/7Mi)
% 2.55/1.56 % (17364)Refutation not found, incomplete strategy
% 2.55/1.56 % (17364)------------------------------
% 2.55/1.56 % (17364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.56 % (17364)Termination reason: Refutation not found, incomplete strategy
% 2.55/1.56
% 2.55/1.56
% 2.55/1.56 % (17364)Memory used [KB]: 6652
% 2.55/1.56 % (17364)Time elapsed: 0.027 s
% 2.55/1.56 % (17364)Instructions burned: 43 (million)
% 2.55/1.56 % (17364)------------------------------
% 2.55/1.56 % (17364)------------------------------
% 2.55/1.56 % (17371)Instruction limit reached!
% 2.55/1.56 % (17371)------------------------------
% 2.55/1.56 % (17371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.56 % (17371)Termination reason: Unknown
% 2.55/1.56 % (17371)Termination phase: shuffling
% 2.55/1.56
% 2.55/1.56 % (17371)Memory used [KB]: 1407
% 2.55/1.56 % (17371)Time elapsed: 0.003 s
% 2.55/1.56 % (17371)Instructions burned: 7 (million)
% 2.55/1.56 % (17371)------------------------------
% 2.55/1.56 % (17371)------------------------------
% 2.55/1.56 % (17368)Instruction limit reached!
% 2.55/1.56 % (17368)------------------------------
% 2.55/1.56 % (17368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.56 % (17368)Termination reason: Unknown
% 2.55/1.56 % (17368)Termination phase: shuffling
% 2.55/1.56
% 2.55/1.56 % (17368)Memory used [KB]: 1791
% 2.55/1.56 % (17368)Time elapsed: 0.009 s
% 2.55/1.56 % (17368)Instructions burned: 15 (million)
% 2.55/1.56 % (17368)------------------------------
% 2.55/1.56 % (17368)------------------------------
% 2.55/1.56 % (17370)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_17021 for (2999ds/1041Mi)
% 2.55/1.56 % (17373)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_17021 for (2999ds/3Mi)
% 2.55/1.56 % (17373)Instruction limit reached!
% 2.55/1.56 % (17373)------------------------------
% 2.55/1.56 % (17373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.56 % (17373)Termination reason: Unknown
% 2.55/1.56 % (17373)Termination phase: shuffling
% 2.55/1.56
% 2.55/1.56 % (17373)Memory used [KB]: 1279
% 2.55/1.56 % (17373)Time elapsed: 0.003 s
% 2.55/1.56 % (17373)Instructions burned: 4 (million)
% 2.55/1.56 % (17373)------------------------------
% 2.55/1.56 % (17373)------------------------------
% 2.55/1.56 % (17372)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_17021 for (2999ds/16Mi)
% 2.55/1.57 % (17374)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_17021 for (2999ds/3Mi)
% 2.55/1.57 % (17374)Instruction limit reached!
% 2.55/1.57 % (17374)------------------------------
% 2.55/1.57 % (17374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.57 % (17374)Termination reason: Unknown
% 2.55/1.57 % (17374)Termination phase: shuffling
% 2.55/1.57
% 2.55/1.57 % (17374)Memory used [KB]: 1279
% 2.55/1.57 % (17374)Time elapsed: 0.002 s
% 2.55/1.57 % (17374)Instructions burned: 4 (million)
% 2.55/1.57 % (17374)------------------------------
% 2.55/1.57 % (17374)------------------------------
% 2.55/1.57 % (17377)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_17021 for (2999ds/4Mi)
% 2.55/1.57 % (17376)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_17021 for (2999ds/3Mi)
% 2.55/1.57 % (17372)Instruction limit reached!
% 2.55/1.57 % (17372)------------------------------
% 2.55/1.57 % (17372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.57 % (17372)Termination reason: Unknown
% 2.55/1.57 % (17372)Termination phase: shuffling
% 2.55/1.57
% 2.55/1.57 % (17372)Memory used [KB]: 1918
% 2.55/1.57 % (17372)Time elapsed: 0.011 s
% 2.55/1.57 % (17372)Instructions burned: 16 (million)
% 2.55/1.57 % (17372)------------------------------
% 2.55/1.57 % (17372)------------------------------
% 2.55/1.57 % (17377)Instruction limit reached!
% 2.55/1.57 % (17377)------------------------------
% 2.55/1.57 % (17377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.57 % (17377)Termination reason: Unknown
% 2.55/1.57 % (17377)Termination phase: shuffling
% 2.55/1.57
% 2.55/1.57 % (17377)Memory used [KB]: 1279
% 2.55/1.57 % (17377)Time elapsed: 0.003 s
% 2.55/1.57 % (17377)Instructions burned: 4 (million)
% 2.55/1.57 % (17377)------------------------------
% 2.55/1.57 % (17377)------------------------------
% 2.55/1.57 % (17376)Instruction limit reached!
% 2.55/1.57 % (17376)------------------------------
% 2.55/1.57 % (17376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.57 % (17376)Termination reason: Unknown
% 2.55/1.57 % (17376)Termination phase: shuffling
% 2.55/1.57
% 2.55/1.57 % (17376)Memory used [KB]: 1279
% 2.55/1.57 % (17376)Time elapsed: 0.003 s
% 2.55/1.57 % (17376)Instructions burned: 5 (million)
% 2.55/1.57 % (17376)------------------------------
% 2.55/1.57 % (17376)------------------------------
% 2.55/1.57 % (17375)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_17021 for (2999ds/7Mi)
% 2.55/1.58 % (17378)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_17021 for (2999ds/18Mi)
% 2.55/1.58 % (17359)Instruction limit reached!
% 2.55/1.58 % (17359)------------------------------
% 2.55/1.58 % (17359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.58 % (17359)Termination reason: Unknown
% 2.55/1.58 % (17359)Termination phase: Property scanning
% 2.55/1.58
% 2.55/1.58 % (17359)Memory used [KB]: 4605
% 2.55/1.58 % (17359)Time elapsed: 0.055 s
% 2.55/1.58 % (17359)Instructions burned: 185 (million)
% 2.55/1.58 % (17359)------------------------------
% 2.55/1.58 % (17359)------------------------------
% 2.55/1.58 % (17375)Instruction limit reached!
% 2.55/1.58 % (17375)------------------------------
% 2.55/1.58 % (17375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.58 % (17375)Termination reason: Unknown
% 2.55/1.58 % (17375)Termination phase: shuffling
% 2.55/1.58
% 2.55/1.58 % (17375)Memory used [KB]: 1407
% 2.55/1.58 % (17375)Time elapsed: 0.006 s
% 2.55/1.58 % (17375)Instructions burned: 7 (million)
% 2.55/1.58 % (17375)------------------------------
% 2.55/1.58 % (17375)------------------------------
% 2.55/1.58 % (17378)Instruction limit reached!
% 2.55/1.58 % (17378)------------------------------
% 2.55/1.58 % (17378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.58 % (17378)Termination reason: Unknown
% 2.55/1.58 % (17378)Termination phase: shuffling
% 2.55/1.58
% 2.55/1.58 % (17378)Memory used [KB]: 2046
% 2.55/1.58 % (17378)Time elapsed: 0.007 s
% 2.55/1.58 % (17378)Instructions burned: 20 (million)
% 2.55/1.58 % (17378)------------------------------
% 2.55/1.58 % (17378)------------------------------
% 2.55/1.58 % (17380)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_17021 for (2999ds/6Mi)
% 2.55/1.59 % (17381)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_17021 for (2999ds/902Mi)
% 2.55/1.59 % (17380)Instruction limit reached!
% 2.55/1.59 % (17380)------------------------------
% 2.55/1.59 % (17380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.59 % (17380)Termination reason: Unknown
% 2.55/1.59 % (17380)Termination phase: shuffling
% 2.55/1.59
% 2.55/1.59 % (17380)Memory used [KB]: 1407
% 2.55/1.59 % (17380)Time elapsed: 0.004 s
% 2.55/1.59 % (17380)Instructions burned: 7 (million)
% 2.55/1.59 % (17380)------------------------------
% 2.55/1.59 % (17380)------------------------------
% 2.55/1.59 % (17382)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_17021 for (2999ds/21Mi)
% 2.55/1.59 % (17379)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_17021 for (2999ds/710Mi)
% 2.55/1.59 % (17384)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_17021 for (2999ds/6Mi)
% 2.55/1.59 % (17384)Instruction limit reached!
% 2.55/1.59 % (17384)------------------------------
% 2.55/1.59 % (17384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.59 % (17384)Termination reason: Unknown
% 2.55/1.59 % (17384)Termination phase: shuffling
% 2.55/1.59
% 2.55/1.59 % (17384)Memory used [KB]: 1407
% 2.55/1.59 % (17384)Time elapsed: 0.003 s
% 2.55/1.59 % (17384)Instructions burned: 7 (million)
% 2.55/1.59 % (17384)------------------------------
% 2.55/1.59 % (17384)------------------------------
% 2.55/1.60 % (17382)Instruction limit reached!
% 2.55/1.60 % (17382)------------------------------
% 2.55/1.60 % (17382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.55/1.60 % (17382)Termination reason: Unknown
% 2.55/1.60 % (17382)Termination phase: shuffling
% 2.55/1.60
% 2.55/1.60 % (17382)Memory used [KB]: 2046
% 2.55/1.60 % (17382)Time elapsed: 0.008 s
% 2.55/1.60 % (17382)Instructions burned: 22 (million)
% 2.55/1.60 % (17382)------------------------------
% 2.55/1.60 % (17382)------------------------------
% 2.59/1.60 % (17385)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_17021 for (2999ds/377Mi)
% 2.59/1.60 % (17383)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_17021 for (2999ds/5Mi)
% 2.59/1.60 % (17383)Instruction limit reached!
% 2.59/1.60 % (17383)------------------------------
% 2.59/1.60 % (17383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.60 % (17383)Termination reason: Unknown
% 2.59/1.60 % (17383)Termination phase: shuffling
% 2.59/1.60
% 2.59/1.60 % (17383)Memory used [KB]: 1279
% 2.59/1.60 % (17383)Time elapsed: 0.005 s
% 2.59/1.60 % (17383)Instructions burned: 5 (million)
% 2.59/1.60 % (17383)------------------------------
% 2.59/1.60 % (17383)------------------------------
% 2.59/1.60 % (17386)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_17021 for (2999ds/779Mi)
% 2.59/1.61 % (17387)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_17021 for (2999ds/19Mi)
% 2.59/1.61 % (17387)Instruction limit reached!
% 2.59/1.61 % (17387)------------------------------
% 2.59/1.61 % (17387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.61 % (17387)Termination reason: Unknown
% 2.59/1.61 % (17387)Termination phase: shuffling
% 2.59/1.61
% 2.59/1.61 % (17387)Memory used [KB]: 1663
% 2.59/1.61 % (17387)Time elapsed: 0.008 s
% 2.59/1.61 % (17387)Instructions burned: 22 (million)
% 2.59/1.61 % (17387)------------------------------
% 2.59/1.61 % (17387)------------------------------
% 2.59/1.62 % (17388)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_17021 for (2999ds/879Mi)
% 2.59/1.62 % (17389)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_17021 for (2999ds/17Mi)
% 2.59/1.63 % (17389)Instruction limit reached!
% 2.59/1.63 % (17389)------------------------------
% 2.59/1.63 % (17389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.63 % (17389)Termination reason: Unknown
% 2.59/1.63 % (17389)Termination phase: shuffling
% 2.59/1.63
% 2.59/1.63 % (17389)Memory used [KB]: 2046
% 2.59/1.63 % (17389)Time elapsed: 0.008 s
% 2.59/1.63 % (17389)Instructions burned: 18 (million)
% 2.59/1.63 % (17389)------------------------------
% 2.59/1.63 % (17389)------------------------------
% 2.59/1.64 % (17390)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_17021 for (2998ds/3Mi)
% 2.59/1.64 % (17390)Instruction limit reached!
% 2.59/1.64 % (17390)------------------------------
% 2.59/1.64 % (17390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.64 % (17390)Termination reason: Unknown
% 2.59/1.64 % (17390)Termination phase: shuffling
% 2.59/1.64
% 2.59/1.64 % (17390)Memory used [KB]: 1279
% 2.59/1.64 % (17390)Time elapsed: 0.003 s
% 2.59/1.64 % (17390)Instructions burned: 4 (million)
% 2.59/1.64 % (17390)------------------------------
% 2.59/1.64 % (17390)------------------------------
% 2.59/1.65 % (17381)Refutation not found, incomplete strategy
% 2.59/1.65 % (17381)------------------------------
% 2.59/1.65 % (17381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.65 % (17381)Termination reason: Refutation not found, incomplete strategy
% 2.59/1.65
% 2.59/1.65
% 2.59/1.65 % (17381)Memory used [KB]: 9338
% 2.59/1.65 % (17381)Time elapsed: 0.066 s
% 2.59/1.65 % (17381)Instructions burned: 208 (million)
% 2.59/1.65 % (17381)------------------------------
% 2.59/1.65 % (17381)------------------------------
% 2.59/1.65 % (17391)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_17021 for (2998ds/30Mi)
% 2.59/1.66 % (17391)Instruction limit reached!
% 2.59/1.66 % (17391)------------------------------
% 2.59/1.66 % (17391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.66 % (17391)Termination reason: Unknown
% 2.59/1.66 % (17391)Termination phase: Property scanning
% 2.59/1.66
% 2.59/1.66 % (17391)Memory used [KB]: 2174
% 2.59/1.66 % (17391)Time elapsed: 0.012 s
% 2.59/1.66 % (17391)Instructions burned: 31 (million)
% 2.59/1.66 % (17391)------------------------------
% 2.59/1.66 % (17391)------------------------------
% 2.59/1.66 % (17392)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_17021 for (2998ds/127Mi)
% 2.59/1.67 % (17393)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_17021 for (2998ds/100Mi)
% 2.59/1.70 % (17393)Instruction limit reached!
% 2.59/1.70 % (17393)------------------------------
% 2.59/1.70 % (17393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.70 % (17393)Termination reason: Unknown
% 2.59/1.70 % (17393)Termination phase: Saturation
% 2.59/1.70
% 2.59/1.70 % (17393)Memory used [KB]: 6524
% 2.59/1.70 % (17393)Time elapsed: 0.029 s
% 2.59/1.70 % (17393)Instructions burned: 103 (million)
% 2.59/1.70 % (17393)------------------------------
% 2.59/1.70 % (17393)------------------------------
% 2.59/1.70 % (17392)Instruction limit reached!
% 2.59/1.70 % (17392)------------------------------
% 2.59/1.70 % (17392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.70 % (17392)Termination reason: Unknown
% 2.59/1.70 % (17392)Termination phase: Property scanning
% 2.59/1.70
% 2.59/1.70 % (17392)Memory used [KB]: 4221
% 2.59/1.70 % (17392)Time elapsed: 0.040 s
% 2.59/1.70 % (17392)Instructions burned: 128 (million)
% 2.59/1.70 % (17392)------------------------------
% 2.59/1.70 % (17392)------------------------------
% 2.59/1.71 % (17394)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_17021 for (2998ds/3Mi)
% 2.59/1.71 % (17394)Instruction limit reached!
% 2.59/1.71 % (17394)------------------------------
% 2.59/1.71 % (17394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.71 % (17394)Termination reason: Unknown
% 2.59/1.71 % (17394)Termination phase: shuffling
% 2.59/1.71
% 2.59/1.71 % (17394)Memory used [KB]: 1151
% 2.59/1.71 % (17394)Time elapsed: 0.002 s
% 2.59/1.71 % (17394)Instructions burned: 3 (million)
% 2.59/1.71 % (17394)------------------------------
% 2.59/1.71 % (17394)------------------------------
% 2.59/1.71 % (17395)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_17021 for (2998ds/20Mi)
% 2.59/1.71 % (17385)Instruction limit reached!
% 2.59/1.71 % (17385)------------------------------
% 2.59/1.71 % (17385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.71 % (17385)Termination reason: Unknown
% 2.59/1.71 % (17385)Termination phase: Saturation
% 2.59/1.71
% 2.59/1.71 % (17385)Memory used [KB]: 10362
% 2.59/1.71 % (17385)Time elapsed: 0.118 s
% 2.59/1.71 % (17385)Instructions burned: 378 (million)
% 2.59/1.71 % (17385)------------------------------
% 2.59/1.71 % (17385)------------------------------
% 2.59/1.72 % (17395)Instruction limit reached!
% 2.59/1.72 % (17395)------------------------------
% 2.59/1.72 % (17395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.72 % (17395)Termination reason: Unknown
% 2.59/1.72 % (17395)Termination phase: shuffling
% 2.59/1.72
% 2.59/1.72 % (17395)Memory used [KB]: 2174
% 2.59/1.72 % (17395)Time elapsed: 0.008 s
% 2.59/1.72 % (17395)Instructions burned: 21 (million)
% 2.59/1.72 % (17395)------------------------------
% 2.59/1.72 % (17395)------------------------------
% 2.59/1.72 % (17396)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_17021 for (2997ds/86Mi)
% 2.59/1.72 % (17397)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_17021 for (2997ds/107Mi)
% 2.59/1.73 % (17398)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_17021 for (2997ds/39Mi)
% 2.59/1.74 % (17398)Instruction limit reached!
% 2.59/1.74 % (17398)------------------------------
% 2.59/1.74 % (17398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.74 % (17398)Termination reason: Unknown
% 2.59/1.74 % (17398)Termination phase: Property scanning
% 2.59/1.74
% 2.59/1.74 % (17398)Memory used [KB]: 1918
% 2.59/1.74 % (17398)Time elapsed: 0.013 s
% 2.59/1.74 % (17398)Instructions burned: 39 (million)
% 2.59/1.74 % (17398)------------------------------
% 2.59/1.74 % (17398)------------------------------
% 2.59/1.74 % (17396)Instruction limit reached!
% 2.59/1.74 % (17396)------------------------------
% 2.59/1.74 % (17396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.74 % (17396)Termination reason: Unknown
% 2.59/1.74 % (17396)Termination phase: Preprocessing 3
% 2.59/1.74
% 2.59/1.74 % (17396)Memory used [KB]: 4093
% 2.59/1.74 % (17396)Time elapsed: 0.026 s
% 2.59/1.74 % (17396)Instructions burned: 87 (million)
% 2.59/1.74 % (17396)------------------------------
% 2.59/1.74 % (17396)------------------------------
% 2.59/1.75 % (17399)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_17021 for (2997ds/448Mi)
% 2.59/1.75 % (17400)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_17021 for (2997ds/46Mi)
% 2.59/1.76 % (17397)Instruction limit reached!
% 2.59/1.76 % (17397)------------------------------
% 2.59/1.76 % (17397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.76 % (17397)Termination reason: Unknown
% 2.59/1.76 % (17397)Termination phase: Property scanning
% 2.59/1.76
% 2.59/1.76 % (17397)Memory used [KB]: 4349
% 2.59/1.76 % (17397)Time elapsed: 0.034 s
% 2.59/1.76 % (17397)Instructions burned: 108 (million)
% 2.59/1.76 % (17397)------------------------------
% 2.59/1.76 % (17397)------------------------------
% 2.59/1.77 % (17400)Instruction limit reached!
% 2.59/1.77 % (17400)------------------------------
% 2.59/1.77 % (17400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.77 % (17400)Termination reason: Unknown
% 2.59/1.77 % (17400)Termination phase: Naming
% 2.59/1.77
% 2.59/1.77 % (17400)Memory used [KB]: 2430
% 2.59/1.77 % (17400)Time elapsed: 0.015 s
% 2.59/1.77 % (17400)Instructions burned: 48 (million)
% 2.59/1.77 % (17400)------------------------------
% 2.59/1.77 % (17400)------------------------------
% 2.59/1.77 % (17401)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_17021 for (2997ds/98Mi)
% 2.59/1.78 % (17402)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_17021 for (2997ds/507Mi)
% 2.59/1.79 % (17386)Instruction limit reached!
% 2.59/1.79 % (17386)------------------------------
% 2.59/1.79 % (17386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.79 % (17386)Termination reason: Unknown
% 2.59/1.79 % (17386)Termination phase: Saturation
% 2.59/1.79
% 2.59/1.79 % (17386)Memory used [KB]: 6652
% 2.59/1.79 % (17386)Time elapsed: 0.192 s
% 2.59/1.79 % (17386)Instructions burned: 781 (million)
% 2.59/1.79 % (17386)------------------------------
% 2.59/1.79 % (17386)------------------------------
% 2.59/1.79 % (17401)Instruction limit reached!
% 2.59/1.79 % (17401)------------------------------
% 2.59/1.79 % (17401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.79 % (17401)Termination reason: Unknown
% 2.59/1.79 % (17401)Termination phase: Saturation
% 2.59/1.79
% 2.59/1.79 % (17401)Memory used [KB]: 2046
% 2.59/1.79 % (17401)Time elapsed: 0.029 s
% 2.59/1.79 % (17401)Instructions burned: 100 (million)
% 2.59/1.79 % (17401)------------------------------
% 2.59/1.79 % (17401)------------------------------
% 2.59/1.80 % (17404)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_17021 for (2997ds/39Mi)
% 2.59/1.80 % (17403)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_17021 for (2997ds/149Mi)
% 2.59/1.82 % (17404)Instruction limit reached!
% 2.59/1.82 % (17404)------------------------------
% 2.59/1.82 % (17404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.82 % (17404)Termination reason: Unknown
% 2.59/1.82 % (17404)Termination phase: Preprocessing 1
% 2.59/1.82
% 2.59/1.82 % (17404)Memory used [KB]: 2302
% 2.59/1.82 % (17404)Time elapsed: 0.013 s
% 2.59/1.82 % (17404)Instructions burned: 41 (million)
% 2.59/1.82 % (17404)------------------------------
% 2.59/1.82 % (17404)------------------------------
% 2.59/1.82 % (17379)Instruction limit reached!
% 2.59/1.82 % (17379)------------------------------
% 2.59/1.82 % (17379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.82 % (17379)Termination reason: Unknown
% 2.59/1.82 % (17379)Termination phase: Saturation
% 2.59/1.82
% 2.59/1.82 % (17379)Memory used [KB]: 11513
% 2.59/1.82 % (17379)Time elapsed: 0.235 s
% 2.59/1.82 % (17379)Instructions burned: 711 (million)
% 2.59/1.82 % (17379)------------------------------
% 2.59/1.82 % (17379)------------------------------
% 2.59/1.83 % (17405)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_17021 for (2996ds/6Mi)
% 2.59/1.83 % (17405)Instruction limit reached!
% 2.59/1.83 % (17405)------------------------------
% 2.59/1.83 % (17405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.83 % (17405)Termination reason: Unknown
% 2.59/1.83 % (17405)Termination phase: shuffling
% 2.59/1.83
% 2.59/1.83 % (17405)Memory used [KB]: 1407
% 2.59/1.83 % (17405)Time elapsed: 0.003 s
% 2.59/1.83 % (17405)Instructions burned: 6 (million)
% 2.59/1.83 % (17405)------------------------------
% 2.59/1.83 % (17405)------------------------------
% 2.59/1.83 % (17406)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_17021 for (2996ds/1087Mi)
% 2.59/1.84 % (17407)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_17021 for (2996ds/47Mi)
% 2.59/1.85 % (17403)Instruction limit reached!
% 2.59/1.85 % (17403)------------------------------
% 2.59/1.85 % (17403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.85 % (17403)Termination reason: Unknown
% 2.59/1.85 % (17403)Termination phase: Property scanning
% 2.59/1.85
% 2.59/1.85 % (17403)Memory used [KB]: 7803
% 2.59/1.85 % (17403)Time elapsed: 0.047 s
% 2.59/1.85 % (17403)Instructions burned: 150 (million)
% 2.59/1.85 % (17403)------------------------------
% 2.59/1.85 % (17403)------------------------------
% 2.59/1.85 % (17407)Instruction limit reached!
% 2.59/1.85 % (17407)------------------------------
% 2.59/1.85 % (17407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.85 % (17407)Termination reason: Unknown
% 2.59/1.85 % (17407)Termination phase: Naming
% 2.59/1.85
% 2.59/1.85 % (17407)Memory used [KB]: 2686
% 2.59/1.85 % (17407)Time elapsed: 0.015 s
% 2.59/1.85 % (17407)Instructions burned: 48 (million)
% 2.59/1.85 % (17407)------------------------------
% 2.59/1.85 % (17407)------------------------------
% 2.59/1.85 % (17402)Refutation not found, incomplete strategy
% 2.59/1.85 % (17402)------------------------------
% 2.59/1.85 % (17402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.85 % (17402)Termination reason: Refutation not found, incomplete strategy
% 2.59/1.85
% 2.59/1.85
% 2.59/1.85 % (17402)Memory used [KB]: 9978
% 2.59/1.85 % (17402)Time elapsed: 0.079 s
% 2.59/1.85 % (17402)Instructions burned: 281 (million)
% 2.59/1.85 % (17402)------------------------------
% 2.59/1.85 % (17402)------------------------------
% 2.59/1.86 % (17409)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_17021 for (2996ds/432Mi)
% 2.59/1.86 % (17408)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_17021 for (2996ds/44Mi)
% 2.59/1.86 % (17410)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_17021 for (2996ds/62Mi)
% 2.59/1.87 % (17408)Instruction limit reached!
% 2.59/1.87 % (17408)------------------------------
% 2.59/1.87 % (17408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.87 % (17408)Termination reason: Unknown
% 2.59/1.87 % (17408)Termination phase: Property scanning
% 2.59/1.87
% 2.59/1.87 % (17408)Memory used [KB]: 1918
% 2.59/1.87 % (17408)Time elapsed: 0.013 s
% 2.59/1.87 % (17408)Instructions burned: 45 (million)
% 2.59/1.87 % (17408)------------------------------
% 2.59/1.87 % (17408)------------------------------
% 2.59/1.88 % (17370)Instruction limit reached!
% 2.59/1.88 % (17370)------------------------------
% 2.59/1.88 % (17370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.88 % (17370)Termination reason: Unknown
% 2.59/1.88 % (17370)Termination phase: Saturation
% 2.59/1.88
% 2.59/1.88 % (17370)Memory used [KB]: 7931
% 2.59/1.88 % (17370)Time elapsed: 0.322 s
% 2.59/1.88 % (17370)Instructions burned: 1042 (million)
% 2.59/1.88 % (17370)------------------------------
% 2.59/1.88 % (17370)------------------------------
% 2.59/1.88 % (17410)Instruction limit reached!
% 2.59/1.88 % (17410)------------------------------
% 2.59/1.88 % (17410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.88 % (17410)Termination reason: Unknown
% 2.59/1.88 % (17410)Termination phase: Property scanning
% 2.59/1.88
% 2.59/1.88 % (17410)Memory used [KB]: 1918
% 2.59/1.88 % (17410)Time elapsed: 0.017 s
% 2.59/1.88 % (17410)Instructions burned: 63 (million)
% 2.59/1.88 % (17410)------------------------------
% 2.59/1.88 % (17410)------------------------------
% 2.59/1.88 % (17411)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_17021 for (2996ds/31Mi)
% 2.59/1.89 % (17399)Instruction limit reached!
% 2.59/1.89 % (17399)------------------------------
% 2.59/1.89 % (17399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.89 % (17399)Termination reason: Unknown
% 2.59/1.89 % (17399)Termination phase: Saturation
% 2.59/1.89
% 2.59/1.89 % (17399)Memory used [KB]: 7291
% 2.59/1.89 % (17399)Time elapsed: 0.140 s
% 2.59/1.89 % (17399)Instructions burned: 450 (million)
% 2.59/1.89 % (17399)------------------------------
% 2.59/1.89 % (17399)------------------------------
% 2.59/1.89 % (17413)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_17021 for (2996ds/453Mi)
% 2.59/1.89 % (17411)Instruction limit reached!
% 2.59/1.89 % (17411)------------------------------
% 2.59/1.89 % (17411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.89 % (17411)Termination reason: Unknown
% 2.59/1.89 % (17411)Termination phase: Property scanning
% 2.59/1.89
% 2.59/1.89 % (17411)Memory used [KB]: 2174
% 2.59/1.89 % (17411)Time elapsed: 0.011 s
% 2.59/1.89 % (17411)Instructions burned: 33 (million)
% 2.59/1.89 % (17411)------------------------------
% 2.59/1.89 % (17411)------------------------------
% 2.59/1.90 % (17414)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_17021 for (2996ds/71Mi)
% 2.59/1.90 % (17412)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_17021 for (2996ds/96Mi)
% 2.59/1.90 % (17415)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_17021 for (2996ds/83Mi)
% 2.59/1.92 % (17388)Instruction limit reached!
% 2.59/1.92 % (17388)------------------------------
% 2.59/1.92 % (17388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.92 % (17388)Termination reason: Unknown
% 2.59/1.92 % (17388)Termination phase: Saturation
% 2.59/1.92
% 2.59/1.92 % (17388)Memory used [KB]: 11513
% 2.59/1.92 % (17388)Time elapsed: 0.305 s
% 2.59/1.92 % (17414)Instruction limit reached!
% 2.59/1.92 % (17414)------------------------------
% 2.59/1.92 % (17414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.92 % (17388)Instructions burned: 880 (million)
% 2.59/1.92 % (17414)Termination reason: Unknown
% 2.59/1.92 % (17388)------------------------------
% 2.59/1.92 % (17388)------------------------------
% 2.59/1.92 % (17414)Termination phase: Preprocessing 3
% 2.59/1.92
% 2.59/1.92 % (17414)Memory used [KB]: 3454
% 2.59/1.92 % (17414)Time elapsed: 0.024 s
% 2.59/1.92 % (17414)Instructions burned: 74 (million)
% 2.59/1.92 % (17414)------------------------------
% 2.59/1.92 % (17414)------------------------------
% 2.59/1.93 % (17415)Instruction limit reached!
% 2.59/1.93 % (17415)------------------------------
% 2.59/1.93 % (17415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.93 % (17415)Termination reason: Unknown
% 2.59/1.93 % (17415)Termination phase: Saturation
% 2.59/1.93
% 2.59/1.93 % (17415)Memory used [KB]: 7036
% 2.59/1.93 % (17415)Time elapsed: 0.025 s
% 2.59/1.93 % (17415)Instructions burned: 83 (million)
% 2.59/1.93 % (17415)------------------------------
% 2.59/1.93 % (17415)------------------------------
% 2.59/1.93 % (17416)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_17021 for (2995ds/11Mi)
% 2.59/1.93 % (17417)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_17021 for (2995ds/41Mi)
% 2.59/1.93 % (17416)Instruction limit reached!
% 2.59/1.93 % (17416)------------------------------
% 2.59/1.93 % (17416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.93 % (17416)Termination reason: Unknown
% 2.59/1.93 % (17416)Termination phase: shuffling
% 2.59/1.93
% 2.59/1.93 % (17416)Memory used [KB]: 1535
% 2.59/1.93 % (17416)Time elapsed: 0.005 s
% 2.59/1.93 % (17416)Instructions burned: 12 (million)
% 2.59/1.93 % (17416)------------------------------
% 2.59/1.93 % (17416)------------------------------
% 2.59/1.94 % (17418)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_17021 for (2995ds/6Mi)
% 2.59/1.94 % (17418)Instruction limit reached!
% 2.59/1.94 % (17418)------------------------------
% 2.59/1.94 % (17418)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.94 % (17418)Termination reason: Unknown
% 2.59/1.94 % (17418)Termination phase: shuffling
% 2.59/1.94
% 2.59/1.94 % (17418)Memory used [KB]: 1407
% 2.59/1.94 % (17418)Time elapsed: 0.003 s
% 2.59/1.94 % (17418)Instructions burned: 7 (million)
% 2.59/1.94 % (17418)------------------------------
% 2.59/1.94 % (17418)------------------------------
% 2.59/1.94 % (17417)Instruction limit reached!
% 2.59/1.94 % (17417)------------------------------
% 2.59/1.94 % (17417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.94 % (17417)Termination reason: Unknown
% 2.59/1.94 % (17417)Termination phase: Property scanning
% 2.59/1.94
% 2.59/1.94 % (17417)Memory used [KB]: 1918
% 2.59/1.94 % (17417)Time elapsed: 0.013 s
% 2.59/1.94 % (17417)Instructions burned: 43 (million)
% 2.59/1.94 % (17417)------------------------------
% 2.59/1.94 % (17417)------------------------------
% 2.59/1.94 % (17419)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_17021 for (2995ds/150Mi)
% 2.59/1.95 % (17420)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_17021 for (2995ds/343Mi)
% 2.59/1.95 % (17412)Instruction limit reached!
% 2.59/1.95 % (17412)------------------------------
% 2.59/1.95 % (17412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.95 % (17412)Termination reason: Unknown
% 2.59/1.95 % (17412)Termination phase: Property scanning
% 2.59/1.95
% 2.59/1.95 % (17412)Memory used [KB]: 4221
% 2.59/1.95 % (17412)Time elapsed: 0.054 s
% 2.59/1.95 % (17412)Instructions burned: 96 (million)
% 2.59/1.95 % (17412)------------------------------
% 2.59/1.95 % (17412)------------------------------
% 2.59/1.95 % (17421)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_17021 for (2995ds/109Mi)
% 2.59/1.97 % (17422)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_17021 for (2995ds/253Mi)
% 2.59/1.97 % (17409)Instruction limit reached!
% 2.59/1.97 % (17409)------------------------------
% 2.59/1.97 % (17409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.97 % (17409)Termination reason: Unknown
% 2.59/1.97 % (17409)Termination phase: Saturation
% 2.59/1.97
% 2.59/1.97 % (17409)Memory used [KB]: 2430
% 2.59/1.97 % (17409)Time elapsed: 0.111 s
% 2.59/1.97 % (17409)Instructions burned: 435 (million)
% 2.59/1.97 % (17409)------------------------------
% 2.59/1.97 % (17409)------------------------------
% 2.59/1.98 % (17423)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_17021 for (2995ds/140Mi)
% 2.59/1.98 % (17419)Instruction limit reached!
% 2.59/1.98 % (17419)------------------------------
% 2.59/1.98 % (17419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.98 % (17419)Termination reason: Unknown
% 2.59/1.98 % (17419)Termination phase: Property scanning
% 2.59/1.98
% 2.59/1.98 % (17419)Memory used [KB]: 4221
% 2.59/1.98 % (17419)Time elapsed: 0.042 s
% 2.59/1.98 % (17419)Instructions burned: 151 (million)
% 2.59/1.98 % (17419)------------------------------
% 2.59/1.98 % (17419)------------------------------
% 2.59/1.99 % (17421)Instruction limit reached!
% 2.59/1.99 % (17421)------------------------------
% 2.59/1.99 % (17421)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/1.99 % (17421)Termination reason: Unknown
% 2.59/1.99 % (17421)Termination phase: Property scanning
% 2.59/1.99
% 2.59/1.99 % (17421)Memory used [KB]: 4221
% 2.59/1.99 % (17421)Time elapsed: 0.036 s
% 2.59/1.99 % (17421)Instructions burned: 112 (million)
% 2.59/1.99 % (17421)------------------------------
% 2.59/1.99 % (17421)------------------------------
% 2.59/1.99 % (17424)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_17021 for (2995ds/614Mi)
% 2.59/2.00 % (17425)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_17021 for (2995ds/202Mi)
% 2.59/2.00 % (17413)Instruction limit reached!
% 2.59/2.00 % (17413)------------------------------
% 2.59/2.00 % (17413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.59/2.00 % (17413)Termination reason: Unknown
% 2.59/2.00 % (17413)Termination phase: Saturation
% 2.59/2.00
% 2.59/2.00 % (17413)Memory used [KB]: 6652
% 2.59/2.00 % (17413)Time elapsed: 0.114 s
% 2.59/2.00 % (17413)Instructions burned: 457 (million)
% 2.59/2.00 % (17413)------------------------------
% 2.59/2.00 % (17413)------------------------------
% 6.01/2.02 % (17423)Instruction limit reached!
% 6.01/2.02 % (17423)------------------------------
% 6.01/2.02 % (17423)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.01/2.02 % (17423)Termination reason: Unknown
% 6.01/2.02 % (17423)Termination phase: Property scanning
% 6.01/2.02
% 6.01/2.02 % (17423)Memory used [KB]: 4221
% 6.01/2.02 % (17423)Time elapsed: 0.039 s
% 6.01/2.02 % (17423)Instructions burned: 140 (million)
% 6.01/2.02 % (17423)------------------------------
% 6.01/2.02 % (17423)------------------------------
% 6.01/2.02 % (17426)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_17021 for (2994ds/339Mi)
% 6.01/2.03 % (17427)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_17021 for (2994ds/283Mi)
% 6.01/2.04 % (17420)Instruction limit reached!
% 6.01/2.04 % (17420)------------------------------
% 6.01/2.04 % (17420)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.01/2.04 % (17420)Termination reason: Unknown
% 6.01/2.04 % (17420)Termination phase: Saturation
% 6.01/2.04
% 6.01/2.04 % (17420)Memory used [KB]: 7547
% 6.01/2.04 % (17420)Time elapsed: 0.099 s
% 6.01/2.04 % (17420)Instructions burned: 344 (million)
% 6.01/2.04 % (17420)------------------------------
% 6.01/2.04 % (17420)------------------------------
% 6.01/2.05 % (17428)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_17021 for (2994ds/134Mi)
% 6.01/2.06 % (17425)Instruction limit reached!
% 6.01/2.06 % (17425)------------------------------
% 6.01/2.06 % (17425)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.01/2.06 % (17425)Termination reason: Unknown
% 6.01/2.06 % (17425)Termination phase: Saturation
% 6.01/2.06
% 6.01/2.06 % (17425)Memory used [KB]: 4477
% 6.01/2.06 % (17425)Time elapsed: 0.057 s
% 6.01/2.06 % (17425)Instructions burned: 204 (million)
% 6.01/2.06 % (17425)------------------------------
% 6.01/2.06 % (17425)------------------------------
% 6.01/2.06 % (17422)Instruction limit reached!
% 6.01/2.06 % (17422)------------------------------
% 6.01/2.06 % (17422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.01/2.06 % (17422)Termination reason: Unknown
% 6.01/2.06 % (17422)Termination phase: Saturation
% 6.01/2.06
% 6.01/2.06 % (17422)Memory used [KB]: 7164
% 6.01/2.06 % (17422)Time elapsed: 0.094 s
% 6.01/2.06 % (17422)Instructions burned: 253 (million)
% 6.01/2.06 % (17422)------------------------------
% 6.01/2.06 % (17422)------------------------------
% 6.01/2.07 % (17429)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_17021 for (2994ds/298Mi)
% 6.01/2.07 % (17430)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_17021 for (2994ds/192Mi)
% 6.01/2.09 % (17428)Instruction limit reached!
% 6.01/2.09 % (17428)------------------------------
% 6.01/2.09 % (17428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.01/2.09 % (17428)Termination reason: Unknown
% 6.01/2.09 % (17428)Termination phase: Property scanning
% 6.01/2.09
% 6.01/2.09 % (17428)Memory used [KB]: 4093
% 6.01/2.09 % (17428)Time elapsed: 0.038 s
% 6.01/2.09 % (17428)Instructions burned: 135 (million)
% 6.01/2.09 % (17428)------------------------------
% 6.01/2.09 % (17428)------------------------------
% 6.01/2.10 % (17427)Instruction limit reached!
% 6.01/2.10 % (17427)------------------------------
% 6.01/2.10 % (17427)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.01/2.10 % (17427)Termination reason: Unknown
% 6.01/2.10 % (17427)Termination phase: Saturation
% 6.01/2.10
% 6.01/2.10 % (17427)Memory used [KB]: 6780
% 6.01/2.10 % (17427)Time elapsed: 0.074 s
% 6.01/2.10 % (17427)Instructions burned: 284 (million)
% 6.01/2.10 % (17427)------------------------------
% 6.01/2.10 % (17427)------------------------------
% 6.01/2.10 % (17431)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_17021 for (2994ds/258Mi)
% 6.01/2.11 % (17432)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_17021 for (2994ds/90Mi)
% 6.01/2.11 % (17426)Instruction limit reached!
% 6.01/2.11 % (17426)------------------------------
% 6.01/2.11 % (17426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.01/2.11 % (17426)Termination reason: Unknown
% 6.01/2.11 % (17426)Termination phase: Saturation
% 6.01/2.11
% 6.01/2.11 % (17426)Memory used [KB]: 9466
% 6.01/2.11 % (17426)Time elapsed: 0.093 s
% 6.01/2.11 % (17426)Instructions burned: 342 (million)
% 6.01/2.11 % (17426)------------------------------
% 6.01/2.11 % (17426)------------------------------
% 6.62/2.12 % (17433)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_17021 for (2993ds/231Mi)
% 6.62/2.13 % (17430)Instruction limit reached!
% 6.62/2.13 % (17430)------------------------------
% 6.62/2.13 % (17430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.62/2.13 % (17430)Termination reason: Unknown
% 6.62/2.13 % (17430)Termination phase: Property scanning
% 6.62/2.13
% 6.62/2.13 % (17430)Memory used [KB]: 4605
% 6.62/2.13 % (17430)Time elapsed: 0.057 s
% 6.62/2.13 % (17430)Instructions burned: 195 (million)
% 6.62/2.13 % (17430)------------------------------
% 6.62/2.13 % (17430)------------------------------
% 6.62/2.14 % (17434)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_17021 for (2993ds/458Mi)
% 6.62/2.14 % (17432)Instruction limit reached!
% 6.62/2.14 % (17432)------------------------------
% 6.62/2.14 % (17432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.62/2.14 % (17432)Termination reason: Unknown
% 6.62/2.14 % (17432)Termination phase: Preprocessing 3
% 6.62/2.14
% 6.62/2.14 % (17432)Memory used [KB]: 4093
% 6.62/2.14 % (17432)Time elapsed: 0.028 s
% 6.62/2.14 % (17432)Instructions burned: 92 (million)
% 6.62/2.14 % (17432)------------------------------
% 6.62/2.14 % (17432)------------------------------
% 6.62/2.14 % (17429)Instruction limit reached!
% 6.62/2.14 % (17429)------------------------------
% 6.62/2.14 % (17429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.62/2.14 % (17429)Termination reason: Unknown
% 6.62/2.14 % (17429)Termination phase: Saturation
% 6.62/2.14
% 6.62/2.14 % (17429)Memory used [KB]: 6652
% 6.62/2.14 % (17429)Time elapsed: 0.077 s
% 6.62/2.14 % (17429)Instructions burned: 299 (million)
% 6.62/2.14 % (17429)------------------------------
% 6.62/2.14 % (17429)------------------------------
% 6.62/2.15 % (17435)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_17021 for (2993ds/31Mi)
% 6.62/2.15 % (17436)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_17021 for (2993ds/297Mi)
% 6.62/2.16 % (17435)Instruction limit reached!
% 6.62/2.16 % (17435)------------------------------
% 6.62/2.16 % (17435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.62/2.16 % (17435)Termination reason: Unknown
% 6.62/2.16 % (17435)Termination phase: Property scanning
% 6.62/2.16
% 6.62/2.16 % (17435)Memory used [KB]: 2174
% 6.62/2.16 % (17435)Time elapsed: 0.011 s
% 6.62/2.16 % (17435)Instructions burned: 34 (million)
% 6.62/2.16 % (17435)------------------------------
% 6.62/2.16 % (17435)------------------------------
% 6.62/2.17 % (17437)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_17021 for (2993ds/987Mi)
% 6.62/2.17 % (17431)Instruction limit reached!
% 6.62/2.17 % (17431)------------------------------
% 6.62/2.17 % (17431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.62/2.17 % (17431)Termination reason: Unknown
% 6.62/2.17 % (17431)Termination phase: Property scanning
% 6.62/2.17
% 6.62/2.17 % (17431)Memory used [KB]: 7803
% 6.62/2.17 % (17431)Time elapsed: 0.068 s
% 6.62/2.17 % (17431)Instructions burned: 259 (million)
% 6.62/2.17 % (17431)------------------------------
% 6.62/2.17 % (17431)------------------------------
% 6.62/2.17 % (17406)Instruction limit reached!
% 6.62/2.17 % (17406)------------------------------
% 6.62/2.17 % (17406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.62/2.17 % (17406)Termination reason: Unknown
% 6.62/2.17 % (17406)Termination phase: Saturation
% 6.62/2.17
% 6.62/2.17 % (17406)Memory used [KB]: 12153
% 6.62/2.17 % (17406)Time elapsed: 0.339 s
% 6.62/2.17 % (17406)Instructions burned: 1088 (million)
% 6.62/2.17 % (17406)------------------------------
% 6.62/2.17 % (17406)------------------------------
% 6.62/2.17 % (17424)Instruction limit reached!
% 6.62/2.17 % (17424)------------------------------
% 6.62/2.17 % (17424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.62/2.17 % (17424)Termination reason: Unknown
% 6.62/2.17 % (17424)Termination phase: Saturation
% 6.62/2.17
% 6.62/2.17 % (17424)Memory used [KB]: 12025
% 6.62/2.17 % (17424)Time elapsed: 0.181 s
% 6.62/2.17 % (17424)Instructions burned: 614 (million)
% 6.62/2.17 % (17424)------------------------------
% 6.62/2.17 % (17424)------------------------------
% 6.62/2.18 % (17438)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_17021 for (2993ds/182Mi)
% 6.62/2.18 % (17433)Instruction limit reached!
% 6.62/2.18 % (17433)------------------------------
% 6.62/2.18 % (17433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.62/2.18 % (17433)Termination reason: Unknown
% 6.62/2.18 % (17433)Termination phase: Saturation
% 6.62/2.18
% 6.62/2.18 % (17433)Memory used [KB]: 7036
% 6.62/2.18 % (17433)Time elapsed: 0.059 s
% 6.62/2.18 % (17433)Instructions burned: 232 (million)
% 6.62/2.18 % (17433)------------------------------
% 6.62/2.18 % (17433)------------------------------
% 6.62/2.18 % (17439)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_17021 for (2993ds/182Mi)
% 6.62/2.18 % (17440)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_17021 for (2993ds/154Mi)
% 6.62/2.19 % (17441)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_17021 for (2993ds/79Mi)
% 7.10/2.21 % (17441)Instruction limit reached!
% 7.10/2.21 % (17441)------------------------------
% 7.10/2.21 % (17441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.10/2.21 % (17441)Termination reason: Unknown
% 7.10/2.21 % (17441)Termination phase: Preprocessing 3
% 7.10/2.21
% 7.10/2.21 % (17441)Memory used [KB]: 3837
% 7.10/2.21 % (17441)Time elapsed: 0.024 s
% 7.10/2.21 % (17441)Instructions burned: 79 (million)
% 7.10/2.21 % (17441)------------------------------
% 7.10/2.21 % (17441)------------------------------
% 7.10/2.22 % (17442)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_17021 for (2992ds/216Mi)
% 7.10/2.22 % (17440)Instruction limit reached!
% 7.10/2.22 % (17440)------------------------------
% 7.10/2.22 % (17440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.10/2.22 % (17440)Termination reason: Unknown
% 7.10/2.22 % (17440)Termination phase: Saturation
% 7.10/2.22
% 7.10/2.22 % (17440)Memory used [KB]: 2430
% 7.10/2.22 % (17440)Time elapsed: 0.040 s
% 7.10/2.22 % (17440)Instructions burned: 155 (million)
% 7.10/2.22 % (17440)------------------------------
% 7.10/2.22 % (17440)------------------------------
% 7.10/2.23 % (17438)Instruction limit reached!
% 7.10/2.23 % (17438)------------------------------
% 7.10/2.23 % (17438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.10/2.23 % (17438)Termination reason: Unknown
% 7.10/2.23 % (17438)Termination phase: Property scanning
% 7.10/2.23
% 7.10/2.23 % (17438)Memory used [KB]: 7803
% 7.10/2.23 % (17438)Time elapsed: 0.051 s
% 7.10/2.23 % (17438)Instructions burned: 184 (million)
% 7.10/2.23 % (17438)------------------------------
% 7.10/2.23 % (17438)------------------------------
% 7.10/2.23 % (17443)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_17021 for (2992ds/114Mi)
% 7.10/2.24 % (17436)Instruction limit reached!
% 7.10/2.24 % (17436)------------------------------
% 7.10/2.24 % (17436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.10/2.24 % (17436)Termination reason: Unknown
% 7.10/2.24 % (17436)Termination phase: Saturation
% 7.10/2.24
% 7.10/2.24 % (17436)Memory used [KB]: 7291
% 7.10/2.24 % (17436)Time elapsed: 0.086 s
% 7.10/2.24 % (17436)Instructions burned: 298 (million)
% 7.10/2.24 % (17436)------------------------------
% 7.10/2.24 % (17436)------------------------------
% 7.10/2.24 % (17444)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_17021 for (2992ds/922Mi)
% 7.10/2.24 % (17439)Instruction limit reached!
% 7.10/2.24 % (17439)------------------------------
% 7.10/2.24 % (17439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.10/2.24 % (17439)Termination reason: Unknown
% 7.10/2.24 % (17439)Termination phase: Saturation
% 7.10/2.24
% 7.10/2.24 % (17439)Memory used [KB]: 9083
% 7.10/2.24 % (17439)Time elapsed: 0.056 s
% 7.10/2.24 % (17439)Instructions burned: 184 (million)
% 7.10/2.24 % (17439)------------------------------
% 7.10/2.24 % (17439)------------------------------
% 7.10/2.25 % (17445)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_17021 for (2992ds/182Mi)
% 7.10/2.25 % (17446)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_17021 for (2992ds/164Mi)
% 7.10/2.26 % (17443)Instruction limit reached!
% 7.10/2.26 % (17443)------------------------------
% 7.10/2.26 % (17443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.10/2.26 % (17443)Termination reason: Unknown
% 7.10/2.26 % (17443)Termination phase: Property scanning
% 7.10/2.26
% 7.10/2.26 % (17443)Memory used [KB]: 4349
% 7.10/2.26 % (17443)Time elapsed: 0.033 s
% 7.10/2.26 % (17443)Instructions burned: 115 (million)
% 7.10/2.26 % (17443)------------------------------
% 7.10/2.26 % (17443)------------------------------
% 7.10/2.27 % (17447)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_17021 for (2992ds/50Mi)
% 7.10/2.28 % (17434)Instruction limit reached!
% 7.10/2.28 % (17434)------------------------------
% 7.10/2.28 % (17434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.10/2.28 % (17434)Termination reason: Unknown
% 7.10/2.28 % (17434)Termination phase: Saturation
% 7.10/2.28
% 7.10/2.28 % (17434)Memory used [KB]: 10490
% 7.10/2.28 % (17434)Time elapsed: 0.145 s
% 7.10/2.28 % (17434)Instructions burned: 459 (million)
% 7.10/2.28 % (17434)------------------------------
% 7.10/2.28 % (17434)------------------------------
% 7.10/2.28 % (17442)Instruction limit reached!
% 7.10/2.28 % (17442)------------------------------
% 7.10/2.28 % (17442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.10/2.28 % (17442)Termination reason: Unknown
% 7.10/2.28 % (17442)Termination phase: Saturation
% 7.10/2.28
% 7.10/2.28 % (17442)Memory used [KB]: 6652
% 7.10/2.28 % (17442)Time elapsed: 0.062 s
% 7.10/2.28 % (17442)Instructions burned: 218 (million)
% 7.10/2.28 % (17442)------------------------------
% 7.10/2.28 % (17442)------------------------------
% 7.10/2.29 % (17447)Instruction limit reached!
% 7.10/2.29 % (17447)------------------------------
% 7.10/2.29 % (17447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.10/2.29 % (17447)Termination reason: Unknown
% 7.10/2.29 % (17447)Termination phase: Property scanning
% 7.10/2.29
% 7.10/2.29 % (17447)Memory used [KB]: 1918
% 7.10/2.29 % (17447)Time elapsed: 0.015 s
% 7.10/2.29 % (17447)Instructions burned: 52 (million)
% 7.10/2.29 % (17447)------------------------------
% 7.10/2.29 % (17447)------------------------------
% 7.10/2.29 % (17448)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_17021 for (2992ds/368Mi)
% 7.10/2.29 % (17445)Instruction limit reached!
% 7.10/2.29 % (17445)------------------------------
% 7.10/2.29 % (17445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.10/2.29 % (17445)Termination reason: Unknown
% 7.10/2.29 % (17445)Termination phase: Saturation
% 7.10/2.29
% 7.10/2.29 % (17445)Memory used [KB]: 6652
% 7.10/2.29 % (17445)Time elapsed: 0.047 s
% 7.10/2.29 % (17445)Instructions burned: 182 (million)
% 7.10/2.29 % (17445)------------------------------
% 7.10/2.29 % (17445)------------------------------
% 7.10/2.29 % (17449)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_17021 for (2992ds/1021Mi)
% 7.10/2.29 % (17446)Instruction limit reached!
% 7.10/2.29 % (17446)------------------------------
% 7.10/2.29 % (17446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.10/2.29 % (17446)Termination reason: Unknown
% 7.10/2.29 % (17446)Termination phase: Saturation
% 7.10/2.29
% 7.10/2.29 % (17446)Memory used [KB]: 2558
% 7.10/2.29 % (17446)Time elapsed: 0.047 s
% 7.10/2.29 % (17446)Instructions burned: 165 (million)
% 7.10/2.29 % (17446)------------------------------
% 7.10/2.29 % (17446)------------------------------
% 7.81/2.30 % (17450)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_17021 for (2992ds/267Mi)
% 7.81/2.30 % (17451)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_17021 for (2992ds/204Mi)
% 7.81/2.30 % (17452)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_17021 for (2992ds/26Mi)
% 7.81/2.31 % (17452)Instruction limit reached!
% 7.81/2.31 % (17452)------------------------------
% 7.81/2.31 % (17452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.81/2.31 % (17452)Termination reason: Unknown
% 7.81/2.31 % (17452)Termination phase: shuffling
% 7.81/2.31
% 7.81/2.31 % (17452)Memory used [KB]: 1791
% 7.81/2.31 % (17452)Time elapsed: 0.009 s
% 7.81/2.31 % (17452)Instructions burned: 27 (million)
% 7.81/2.31 % (17452)------------------------------
% 7.81/2.31 % (17452)------------------------------
% 7.81/2.32 % (17453)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_17021 for (2992ds/53Mi)
% 7.81/2.33 % (17453)Instruction limit reached!
% 7.81/2.33 % (17453)------------------------------
% 7.81/2.33 % (17453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.81/2.33 % (17453)Termination reason: Unknown
% 7.81/2.33 % (17453)Termination phase: Property scanning
% 7.81/2.33
% 7.81/2.33 % (17453)Memory used [KB]: 1918
% 7.81/2.33 % (17453)Time elapsed: 0.015 s
% 7.81/2.33 % (17453)Instructions burned: 55 (million)
% 7.81/2.33 % (17453)------------------------------
% 7.81/2.33 % (17453)------------------------------
% 7.81/2.34 % (17454)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_17021 for (2991ds/4436Mi)
% 7.81/2.36 % (17451)Instruction limit reached!
% 7.81/2.36 % (17451)------------------------------
% 7.81/2.36 % (17451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.81/2.36 % (17451)Termination reason: Unknown
% 7.81/2.36 % (17451)Termination phase: Property scanning
% 7.81/2.36
% 7.81/2.36 % (17451)Memory used [KB]: 4605
% 7.81/2.36 % (17451)Time elapsed: 0.056 s
% 7.81/2.36 % (17451)Instructions burned: 205 (million)
% 7.81/2.36 % (17451)------------------------------
% 7.81/2.36 % (17451)------------------------------
% 7.81/2.36 % (17450)Instruction limit reached!
% 7.81/2.36 % (17450)------------------------------
% 7.81/2.36 % (17450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.81/2.36 % (17450)Termination reason: Unknown
% 7.81/2.36 % (17450)Termination phase: Saturation
% 7.81/2.36
% 7.81/2.36 % (17450)Memory used [KB]: 6780
% 7.81/2.36 % (17450)Time elapsed: 0.068 s
% 7.81/2.36 % (17450)Instructions burned: 267 (million)
% 7.81/2.36 % (17450)------------------------------
% 7.81/2.36 % (17450)------------------------------
% 7.81/2.37 % (17455)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_17021 for (2991ds/1539Mi)
% 7.81/2.37 % (17456)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_17021 for (2991ds/408Mi)
% 8.00/2.40 % (17448)Instruction limit reached!
% 8.00/2.40 % (17448)------------------------------
% 8.00/2.40 % (17448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.00/2.40 % (17448)Termination reason: Unknown
% 8.00/2.40 % (17448)Termination phase: Saturation
% 8.00/2.40
% 8.00/2.40 % (17448)Memory used [KB]: 11513
% 8.00/2.40 % (17448)Time elapsed: 0.108 s
% 8.00/2.40 % (17448)Instructions burned: 369 (million)
% 8.00/2.40 % (17448)------------------------------
% 8.00/2.40 % (17448)------------------------------
% 8.00/2.41 % (17457)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_17021 for (2991ds/5205Mi)
% 8.00/2.41 % (17437)Instruction limit reached!
% 8.00/2.41 % (17437)------------------------------
% 8.00/2.41 % (17437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.00/2.41 % (17437)Termination reason: Unknown
% 8.00/2.41 % (17437)Termination phase: Saturation
% 8.00/2.41
% 8.00/2.41 % (17437)Memory used [KB]: 7547
% 8.00/2.42 % (17437)Time elapsed: 0.250 s
% 8.00/2.42 % (17437)Instructions burned: 988 (million)
% 8.00/2.42 % (17437)------------------------------
% 8.00/2.42 % (17437)------------------------------
% 8.00/2.42 % (17458)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_17021 for (2991ds/1913Mi)
% 8.00/2.49 % (17456)Instruction limit reached!
% 8.00/2.49 % (17456)------------------------------
% 8.00/2.49 % (17456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.00/2.49 % (17456)Termination reason: Unknown
% 8.00/2.49 % (17456)Termination phase: Saturation
% 8.00/2.49
% 8.00/2.49 % (17456)Memory used [KB]: 11129
% 8.00/2.49 % (17456)Time elapsed: 0.121 s
% 8.00/2.49 % (17456)Instructions burned: 409 (million)
% 8.00/2.49 % (17456)------------------------------
% 8.00/2.49 % (17456)------------------------------
% 8.50/2.50 % (17460)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_17021 for (2990ds/4350Mi)
% 8.50/2.52 % (17444)Instruction limit reached!
% 8.50/2.52 % (17444)------------------------------
% 8.50/2.52 % (17444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.50/2.52 % (17444)Termination reason: Unknown
% 8.50/2.52 % (17444)Termination phase: Saturation
% 8.50/2.52
% 8.50/2.52 % (17444)Memory used [KB]: 12665
% 8.50/2.52 % (17444)Time elapsed: 0.282 s
% 8.50/2.52 % (17444)Instructions burned: 923 (million)
% 8.50/2.52 % (17444)------------------------------
% 8.50/2.52 % (17444)------------------------------
% 8.50/2.53 % (17461)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_17021 for (2990ds/68Mi)
% 8.50/2.55 % (17461)Instruction limit reached!
% 8.50/2.55 % (17461)------------------------------
% 8.50/2.55 % (17461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.50/2.55 % (17461)Termination reason: Unknown
% 8.50/2.55 % (17461)Termination phase: Preprocessing 3
% 8.50/2.55
% 8.50/2.55 % (17461)Memory used [KB]: 3070
% 8.50/2.55 % (17461)Time elapsed: 0.021 s
% 8.50/2.55 % (17461)Instructions burned: 69 (million)
% 8.50/2.55 % (17461)------------------------------
% 8.50/2.55 % (17461)------------------------------
% 8.50/2.56 % (17462)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_17021 for (2989ds/358Mi)
% 8.83/2.60 % (17449)Instruction limit reached!
% 8.83/2.60 % (17449)------------------------------
% 8.83/2.60 % (17449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.83/2.60 % (17449)Termination reason: Unknown
% 8.83/2.60 % (17449)Termination phase: Saturation
% 8.83/2.60
% 8.83/2.60 % (17449)Memory used [KB]: 12409
% 8.83/2.60 % (17449)Time elapsed: 0.310 s
% 8.83/2.60 % (17449)Instructions burned: 1021 (million)
% 8.83/2.60 % (17449)------------------------------
% 8.83/2.60 % (17449)------------------------------
% 8.83/2.61 % (17463)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_17021 for (2988ds/31Mi)
% 8.83/2.62 % (17463)Instruction limit reached!
% 8.83/2.62 % (17463)------------------------------
% 8.83/2.62 % (17463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.83/2.62 % (17463)Termination reason: Unknown
% 8.83/2.62 % (17463)Termination phase: Property scanning
% 8.83/2.62
% 8.83/2.62 % (17463)Memory used [KB]: 2174
% 8.83/2.62 % (17463)Time elapsed: 0.012 s
% 8.83/2.62 % (17463)Instructions burned: 34 (million)
% 8.83/2.62 % (17463)------------------------------
% 8.83/2.62 % (17463)------------------------------
% 8.83/2.63 % (17464)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_17021 for (2988ds/279Mi)
% 8.83/2.66 % (17462)Instruction limit reached!
% 8.83/2.66 % (17462)------------------------------
% 8.83/2.66 % (17462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.83/2.66 % (17462)Termination reason: Unknown
% 8.83/2.66 % (17462)Termination phase: Saturation
% 8.83/2.66
% 8.83/2.66 % (17462)Memory used [KB]: 9594
% 8.83/2.66 % (17462)Time elapsed: 0.103 s
% 8.83/2.66 % (17462)Instructions burned: 359 (million)
% 8.83/2.66 % (17462)------------------------------
% 8.83/2.66 % (17462)------------------------------
% 8.83/2.67 % (17465)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_17021 for (2988ds/258Mi)
% 9.27/2.70 % (17464)Instruction limit reached!
% 9.27/2.70 % (17464)------------------------------
% 9.27/2.70 % (17464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.27/2.70 % (17464)Termination reason: Unknown
% 9.27/2.70 % (17464)Termination phase: Saturation
% 9.27/2.70
% 9.27/2.70 % (17464)Memory used [KB]: 7675
% 9.27/2.70 % (17464)Time elapsed: 0.071 s
% 9.27/2.70 % (17464)Instructions burned: 283 (million)
% 9.27/2.70 % (17464)------------------------------
% 9.27/2.70 % (17464)------------------------------
% 9.27/2.71 % (17466)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_17021 for (2987ds/26Mi)
% 9.27/2.72 % (17466)Instruction limit reached!
% 9.27/2.72 % (17466)------------------------------
% 9.27/2.72 % (17466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.27/2.72 % (17466)Termination reason: Unknown
% 9.27/2.72 % (17466)Termination phase: shuffling
% 9.27/2.72
% 9.27/2.72 % (17466)Memory used [KB]: 1791
% 9.27/2.72 % (17466)Time elapsed: 0.009 s
% 9.27/2.72 % (17466)Instructions burned: 27 (million)
% 9.27/2.72 % (17466)------------------------------
% 9.27/2.72 % (17466)------------------------------
% 9.27/2.73 % (17467)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_17021 for (2987ds/995Mi)
% 9.27/2.74 % (17465)Instruction limit reached!
% 9.27/2.74 % (17465)------------------------------
% 9.27/2.74 % (17465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.27/2.74 % (17465)Termination reason: Unknown
% 9.27/2.74 % (17465)Termination phase: Saturation
% 9.27/2.74
% 9.27/2.74 % (17465)Memory used [KB]: 9722
% 9.27/2.74 % (17465)Time elapsed: 0.075 s
% 9.27/2.74 % (17465)Instructions burned: 259 (million)
% 9.27/2.74 % (17465)------------------------------
% 9.27/2.74 % (17465)------------------------------
% 9.27/2.75 % (17468)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_17021 for (2987ds/373Mi)
% 9.47/2.80 % (17455)Instruction limit reached!
% 9.47/2.80 % (17455)------------------------------
% 9.47/2.80 % (17455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.47/2.80 % (17455)Termination reason: Unknown
% 9.47/2.80 % (17455)Termination phase: Saturation
% 9.47/2.80
% 9.47/2.80 % (17455)Memory used [KB]: 12025
% 9.47/2.80 % (17455)Time elapsed: 0.439 s
% 9.47/2.80 % (17455)Instructions burned: 1541 (million)
% 9.47/2.80 % (17455)------------------------------
% 9.47/2.80 % (17455)------------------------------
% 9.47/2.81 % (17469)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_17021 for (2986ds/253Mi)
% 9.47/2.86 % (17468)Instruction limit reached!
% 9.47/2.86 % (17468)------------------------------
% 9.47/2.86 % (17468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.47/2.86 % (17468)Termination reason: Unknown
% 9.47/2.86 % (17468)Termination phase: Saturation
% 9.47/2.86
% 9.47/2.86 % (17468)Memory used [KB]: 10234
% 9.47/2.86 % (17468)Time elapsed: 0.111 s
% 9.47/2.86 % (17468)Instructions burned: 373 (million)
% 9.47/2.86 % (17468)------------------------------
% 9.47/2.86 % (17468)------------------------------
% 9.47/2.87 % (17470)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_17021 for (2986ds/832Mi)
% 9.47/2.88 % (17469)Instruction limit reached!
% 9.47/2.88 % (17469)------------------------------
% 9.47/2.88 % (17469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.47/2.88 % (17469)Termination reason: Unknown
% 9.47/2.88 % (17469)Termination phase: Saturation
% 9.47/2.88
% 9.47/2.88 % (17469)Memory used [KB]: 6780
% 9.47/2.88 % (17469)Time elapsed: 0.066 s
% 9.47/2.88 % (17469)Instructions burned: 253 (million)
% 9.47/2.88 % (17469)------------------------------
% 9.47/2.88 % (17469)------------------------------
% 9.47/2.89 % (17471)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_17021 for (2986ds/668Mi)
% 10.11/2.95 % (17470)Refutation not found, incomplete strategy
% 10.11/2.95 % (17470)------------------------------
% 10.11/2.95 % (17470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.11/2.95 % (17470)Termination reason: Refutation not found, incomplete strategy
% 10.11/2.95
% 10.11/2.95
% 10.11/2.95 % (17470)Memory used [KB]: 9594
% 10.11/2.95 % (17470)Time elapsed: 0.076 s
% 10.11/2.95 % (17470)Instructions burned: 273 (million)
% 10.11/2.95 % (17470)------------------------------
% 10.11/2.95 % (17470)------------------------------
% 10.11/2.96 % (17472)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_17021 for (2985ds/40Mi)
% 10.11/2.97 % (17472)Instruction limit reached!
% 10.11/2.97 % (17472)------------------------------
% 10.11/2.97 % (17472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.11/2.97 % (17472)Termination reason: Unknown
% 10.11/2.97 % (17472)Termination phase: Property scanning
% 10.11/2.97
% 10.11/2.97 % (17472)Memory used [KB]: 1918
% 10.11/2.97 % (17472)Time elapsed: 0.013 s
% 10.11/2.97 % (17472)Instructions burned: 43 (million)
% 10.11/2.97 % (17472)------------------------------
% 10.11/2.97 % (17472)------------------------------
% 10.11/2.97 % (17467)Instruction limit reached!
% 10.11/2.97 % (17467)------------------------------
% 10.11/2.97 % (17467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.11/2.97 % (17467)Termination reason: Unknown
% 10.11/2.97 % (17467)Termination phase: Saturation
% 10.11/2.97
% 10.11/2.97 % (17467)Memory used [KB]: 6652
% 10.11/2.97 % (17467)Time elapsed: 0.246 s
% 10.11/2.97 % (17467)Instructions burned: 996 (million)
% 10.11/2.97 % (17467)------------------------------
% 10.11/2.97 % (17467)------------------------------
% 10.11/2.98 % (17473)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_17021 for (2985ds/294Mi)
% 10.11/2.98 % (17474)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_17021 for (2985ds/187Mi)
% 10.11/3.01 % (17458)Instruction limit reached!
% 10.11/3.01 % (17458)------------------------------
% 10.11/3.01 % (17458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.11/3.01 % (17458)Termination reason: Unknown
% 10.11/3.01 % (17458)Termination phase: Saturation
% 10.11/3.01
% 10.11/3.01 % (17458)Memory used [KB]: 6524
% 10.11/3.01 % (17458)Time elapsed: 0.607 s
% 10.11/3.01 % (17458)Instructions burned: 1914 (million)
% 10.11/3.01 % (17458)------------------------------
% 10.11/3.01 % (17458)------------------------------
% 12.43/3.02 % (17475)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_17021 for (2985ds/371Mi)
% 12.43/3.03 % (17474)Instruction limit reached!
% 12.43/3.03 % (17474)------------------------------
% 12.43/3.03 % (17474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.43/3.03 % (17474)Termination reason: Unknown
% 12.43/3.03 % (17474)Termination phase: Property scanning
% 12.43/3.03
% 12.43/3.03 % (17474)Memory used [KB]: 4605
% 12.43/3.03 % (17474)Time elapsed: 0.051 s
% 12.43/3.03 % (17474)Instructions burned: 187 (million)
% 12.43/3.03 % (17474)------------------------------
% 12.43/3.03 % (17474)------------------------------
% 12.43/3.04 % (17475)Refutation not found, incomplete strategy
% 12.43/3.04 % (17475)------------------------------
% 12.43/3.04 % (17475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.43/3.04 % (17475)Termination reason: Refutation not found, incomplete strategy
% 12.43/3.04
% 12.43/3.04
% 12.43/3.04 % (17475)Memory used [KB]: 6780
% 12.43/3.04 % (17475)Time elapsed: 0.018 s
% 12.43/3.04 % (17475)Instructions burned: 55 (million)
% 12.43/3.04 % (17475)------------------------------
% 12.43/3.04 % (17475)------------------------------
% 12.43/3.04 % (17476)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_17021 for (2984ds/1827Mi)
% 12.43/3.05 % (17477)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_17021 for (2984ds/70Mi)
% 12.43/3.05 % (17471)Instruction limit reached!
% 12.43/3.05 % (17471)------------------------------
% 12.43/3.05 % (17471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.43/3.05 % (17471)Termination reason: Unknown
% 12.43/3.05 % (17471)Termination phase: Saturation
% 12.43/3.05
% 12.43/3.05 % (17471)Memory used [KB]: 11129
% 12.43/3.05 % (17471)Time elapsed: 0.164 s
% 12.43/3.05 % (17471)Instructions burned: 670 (million)
% 12.43/3.05 % (17471)------------------------------
% 12.43/3.05 % (17471)------------------------------
% 12.43/3.05 % (17473)Instruction limit reached!
% 12.43/3.05 % (17473)------------------------------
% 12.43/3.05 % (17473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.43/3.05 % (17473)Termination reason: Unknown
% 12.43/3.05 % (17473)Termination phase: Saturation
% 12.43/3.05
% 12.43/3.05 % (17473)Memory used [KB]: 7547
% 12.43/3.05 % (17473)Time elapsed: 0.073 s
% 12.43/3.05 % (17473)Instructions burned: 295 (million)
% 12.43/3.05 % (17473)------------------------------
% 12.43/3.05 % (17473)------------------------------
% 12.43/3.06 % (17478)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_17021 for (2984ds/316Mi)
% 12.43/3.06 % (17479)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_17021 for (2984ds/932Mi)
% 12.43/3.06 % (17477)Instruction limit reached!
% 12.43/3.06 % (17477)------------------------------
% 12.43/3.06 % (17477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.43/3.06 % (17477)Termination reason: Unknown
% 12.43/3.06 % (17477)Termination phase: Property scanning
% 12.43/3.06
% 12.43/3.06 % (17477)Memory used [KB]: 1918
% 12.43/3.06 % (17477)Time elapsed: 0.019 s
% 12.43/3.06 % (17477)Instructions burned: 70 (million)
% 12.43/3.06 % (17477)------------------------------
% 12.43/3.06 % (17477)------------------------------
% 12.43/3.07 % (17480)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_17021 for (2984ds/4714Mi)
% 13.50/3.14 % (17478)Instruction limit reached!
% 13.50/3.14 % (17478)------------------------------
% 13.50/3.14 % (17478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.50/3.14 % (17478)Termination reason: Unknown
% 13.50/3.14 % (17478)Termination phase: Saturation
% 13.50/3.14
% 13.50/3.14 % (17478)Memory used [KB]: 7291
% 13.50/3.14 % (17478)Time elapsed: 0.084 s
% 13.50/3.14 % (17478)Instructions burned: 317 (million)
% 13.50/3.14 % (17478)------------------------------
% 13.50/3.14 % (17478)------------------------------
% 13.50/3.15 % (17481)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_17021 for (2983ds/8250Mi)
% 13.87/3.29 % (17479)Instruction limit reached!
% 13.87/3.29 % (17479)------------------------------
% 13.87/3.29 % (17479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.87/3.29 % (17479)Termination reason: Unknown
% 13.87/3.29 % (17479)Termination phase: Saturation
% 13.87/3.29
% 13.87/3.29 % (17479)Memory used [KB]: 8315
% 13.87/3.29 % (17479)Time elapsed: 0.252 s
% 13.87/3.29 % (17479)Instructions burned: 933 (million)
% 13.87/3.29 % (17479)------------------------------
% 13.87/3.29 % (17479)------------------------------
% 14.40/3.30 % (17482)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_17021 for (2982ds/770Mi)
% 14.40/3.32 % (17482)Refutation not found, incomplete strategy
% 14.40/3.32 % (17482)------------------------------
% 14.40/3.32 % (17482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.40/3.32 % (17482)Termination reason: Refutation not found, incomplete strategy
% 14.40/3.32
% 14.40/3.32
% 14.40/3.32 % (17482)Memory used [KB]: 6652
% 14.40/3.32 % (17482)Time elapsed: 0.014 s
% 14.40/3.32 % (17482)Instructions burned: 42 (million)
% 14.40/3.32 % (17482)------------------------------
% 14.40/3.32 % (17482)------------------------------
% 14.40/3.33 % (17483)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_17021 for (2982ds/794Mi)
% 14.71/3.49 % (17454)First to succeed.
% 15.02/3.53 % (17454)Refutation found. Thanks to Tanya!
% 15.02/3.53 % SZS status Theorem for DTF2THF_17021
% 15.02/3.53 % SZS output start Proof for DTF2THF_17021
% 15.02/3.53 thf(type_def_5, type, term: $tType).
% 15.02/3.53 thf(type_def_7, type, subst: $tType).
% 15.02/3.53 thf(type_def_8, type, d_term: $tType).
% 15.02/3.53 thf(type_def_9, type, d_subst: $tType).
% 15.02/3.53 thf(func_def_0, type, term: $tType).
% 15.02/3.53 thf(func_def_1, type, subst: $tType).
% 15.02/3.53 thf(func_def_2, type, one: term).
% 15.02/3.53 thf(func_def_3, type, ap: term > term > term).
% 15.02/3.53 thf(func_def_4, type, lam: term > term).
% 15.02/3.53 thf(func_def_5, type, sub: term > subst > term).
% 15.02/3.53 thf(func_def_6, type, id: subst).
% 15.02/3.53 thf(func_def_7, type, sh: subst).
% 15.02/3.53 thf(func_def_8, type, push: term > subst > subst).
% 15.02/3.53 thf(func_def_9, type, comp: subst > subst > subst).
% 15.02/3.53 thf(func_def_10, type, var: term > $o).
% 15.02/3.53 thf(func_def_18, type, hoasap: subst > term > subst > term > term).
% 15.02/3.53 thf(func_def_73, type, hoaslam: subst > (subst > term > term) > term).
% 15.02/3.53 thf(func_def_86, type, hoasinduction_p_and_p_prime: (subst > term > subst > $o) > (term > $o) > $o).
% 15.02/3.53 thf(func_def_107, type, hoasvar: subst > term > subst > $o).
% 15.02/3.53 thf(func_def_121, type, pushprop_p_and_p_prime: term > subst > (term > $o) > (term > $o) > $o).
% 15.02/3.53 thf(func_def_124, type, d_term: $tType).
% 15.02/3.53 thf(func_def_125, type, d_subst: $tType).
% 15.02/3.53 thf(func_def_126, type, d2term: d_term > term).
% 15.02/3.53 thf(func_def_127, type, d2subst: d_subst > subst).
% 15.02/3.53 thf(func_def_128, type, d_one: d_term).
% 15.02/3.53 thf(func_def_129, type, d_id: d_subst).
% 15.02/3.53 thf(func_def_141, type, sP0: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_143, type, sP2: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_144, type, sP3: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_145, type, sP4: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_146, type, sP5: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_147, type, sP6: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_148, type, sP7: (term > $o) > $o).
% 15.02/3.53 thf(func_def_149, type, sP8: (term > $o) > $o).
% 15.02/3.53 thf(func_def_153, type, sP12: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_154, type, sP13: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_155, type, sP14: (subst > term > subst > $o) > term > $o).
% 15.02/3.53 thf(func_def_157, type, sP16: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_158, type, sP17: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_159, type, sP18: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_160, type, sP19: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_161, type, sP20: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_162, type, sP21: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_164, type, sP23: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_166, type, sP25: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_167, type, sP26: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_170, type, sP29: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_177, type, sP36: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_178, type, sP37: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_179, type, sP38: term > (term > $o) > $o).
% 15.02/3.53 thf(func_def_183, type, sP42: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_185, type, sP44: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_187, type, sP46: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_188, type, sP47: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_190, type, sP49: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_191, type, sP50: term > (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_192, type, sP51: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_193, type, sP52: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_196, type, sP55: (term > $o) > $o).
% 15.02/3.53 thf(func_def_197, type, sP56: (term > $o) > $o).
% 15.02/3.53 thf(func_def_198, type, sP57: (term > $o) > $o).
% 15.02/3.53 thf(func_def_199, type, sP58: (term > $o) > $o).
% 15.02/3.53 thf(func_def_202, type, sP61: (term > $o) > $o).
% 15.02/3.53 thf(func_def_203, type, sP62: (term > $o) > $o).
% 15.02/3.53 thf(func_def_204, type, sP63: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_205, type, sP64: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_206, type, sP65: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_207, type, sP66: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_208, type, sP67: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_209, type, sP68: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_210, type, sP69: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_211, type, sP70: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_212, type, sP71: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_217, type, sP76: (term > $o) > $o).
% 15.02/3.53 thf(func_def_218, type, sP77: (term > $o) > subst > $o).
% 15.02/3.53 thf(func_def_219, type, sP78: (term > $o) > $o).
% 15.02/3.53 thf(func_def_220, type, sP79: (term > $o) > $o).
% 15.02/3.53 thf(func_def_221, type, sP80: (term > $o) > $o).
% 15.02/3.53 thf(func_def_224, type, sP83: (term > $o) > $o).
% 15.02/3.53 thf(func_def_225, type, sP84: (term > $o) > $o).
% 15.02/3.53 thf(func_def_227, type, sP86: (term > $o) > $o).
% 15.02/3.53 thf(func_def_228, type, sP87: (term > $o) > $o).
% 15.02/3.53 thf(func_def_230, type, sP89: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_231, type, sP90: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_233, type, sP92: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_234, type, sP93: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_235, type, sP94: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_237, type, sP96: (term > $o) > $o).
% 15.02/3.53 thf(func_def_238, type, sP97: (term > $o) > $o).
% 15.02/3.53 thf(func_def_240, type, sP99: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_242, type, sP101: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_243, type, sP102: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_244, type, sP103: (term > $o) > $o).
% 15.02/3.53 thf(func_def_245, type, sP104: (term > $o) > $o).
% 15.02/3.53 thf(func_def_246, type, sP105: (term > $o) > $o).
% 15.02/3.53 thf(func_def_247, type, sP106: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_251, type, sP110: (subst > term > term) > $o).
% 15.02/3.53 thf(func_def_252, type, sP111: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_253, type, sP112: (subst > term > subst > $o) > $o).
% 15.02/3.53 thf(func_def_254, type, sK113: term).
% 15.02/3.53 thf(func_def_255, type, sK114: term > $o).
% 15.02/3.53 thf(func_def_256, type, sK115: (term > $o) > (subst > term > subst > $o) > term).
% 15.02/3.53 thf(func_def_257, type, sK116: (term > $o) > term > term).
% 15.02/3.53 thf(func_def_258, type, sK117: term).
% 15.02/3.53 thf(func_def_259, type, sK118: subst > term > subst > $o).
% 15.02/3.53 thf(func_def_260, type, sK119: term > $o).
% 15.02/3.53 thf(func_def_261, type, sK120: subst > term > subst > $o).
% 15.02/3.53 thf(func_def_262, type, sK121: term).
% 15.02/3.53 thf(func_def_263, type, sK122: (subst > term > subst > $o) > subst > term > term).
% 15.02/3.53 thf(func_def_264, type, sK123: (subst > term > term) > (subst > term > subst > $o) > term).
% 15.02/3.53 thf(func_def_265, type, sK124: (subst > term > term) > term).
% 15.02/3.53 thf(func_def_266, type, sK125: (subst > term > term) > subst).
% 15.02/3.53 thf(func_def_267, type, sK126: (subst > term > term) > subst).
% 15.02/3.53 thf(func_def_268, type, sK127: (term > $o) > term).
% 15.02/3.53 thf(func_def_269, type, sK128: term > (term > $o) > term).
% 15.02/3.53 thf(func_def_270, type, sK129: (term > $o) > term).
% 15.02/3.53 thf(func_def_271, type, sK130: (term > $o) > term).
% 15.02/3.53 thf(func_def_272, type, sK131: (term > $o) > term).
% 15.02/3.53 thf(func_def_273, type, sK132: (subst > term > subst > $o) > term).
% 15.02/3.53 thf(func_def_274, type, sK133: (subst > term > subst > $o) > term).
% 15.02/3.53 thf(func_def_275, type, sK134: (subst > term > term) > (subst > term > subst > $o) > term).
% 15.02/3.53 thf(func_def_276, type, sK135: (subst > term > term) > term).
% 15.02/3.53 thf(func_def_277, type, sK136: (subst > term > term) > subst).
% 15.02/3.53 thf(func_def_278, type, sK137: (subst > term > term) > subst).
% 15.02/3.53 thf(func_def_279, type, sK138: (subst > term > subst > $o) > subst > term > term).
% 15.02/3.53 thf(func_def_280, type, sK139: term).
% 15.02/3.53 thf(func_def_281, type, sK140: subst > term > subst > $o).
% 15.02/3.53 thf(func_def_282, type, sK141: (subst > term > subst > $o) > term > term).
% 15.02/3.53 thf(func_def_283, type, sK142: (subst > term > term) > (subst > term > subst > $o) > term).
% 15.02/3.53 thf(func_def_284, type, sK143: (subst > term > term) > subst).
% 15.02/3.53 thf(func_def_285, type, sK144: (subst > term > term) > term).
% 15.02/3.53 thf(func_def_286, type, sK145: (subst > term > term) > subst).
% 15.02/3.53 thf(func_def_287, type, sK146: (subst > term > subst > $o) > subst > term > term).
% 15.02/3.53 thf(func_def_288, type, sK147: term).
% 15.02/3.53 thf(func_def_289, type, sK148: term > $o).
% 15.02/3.53 thf(func_def_290, type, sK149: (term > $o) > term).
% 15.02/3.53 thf(func_def_291, type, sK150: (term > $o) > term).
% 15.02/3.53 thf(func_def_292, type, sK151: (term > $o) > term).
% 15.02/3.53 thf(func_def_293, type, sK152: (term > $o) > term).
% 15.02/3.54 thf(func_def_294, type, sK153: term > $o).
% 15.02/3.54 thf(func_def_295, type, sK154: subst > term > subst > $o).
% 15.02/3.54 thf(func_def_296, type, sK155: term).
% 15.02/3.54 thf(func_def_297, type, sK156: term > (term > $o) > term).
% 15.02/3.54 thf(func_def_298, type, sK157: (subst > term > subst > $o) > (term > $o) > term).
% 15.02/3.54 thf(func_def_299, type, sK158: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_300, type, sK159: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_301, type, sK160: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_302, type, sK161: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_303, type, sK162: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_304, type, sK163: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_305, type, sK164: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_306, type, sK165: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_307, type, sK166: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_308, type, sK167: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_309, type, sK168: (subst > term > term) > term).
% 15.02/3.54 thf(func_def_310, type, sK169: (subst > term > term) > (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_311, type, sK170: (subst > term > subst > $o) > subst > term > term).
% 15.02/3.54 thf(func_def_312, type, sK171: term).
% 15.02/3.54 thf(func_def_313, type, sK172: term).
% 15.02/3.54 thf(func_def_314, type, sK173: subst > term > subst > $o).
% 15.02/3.54 thf(func_def_315, type, sK174: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_316, type, sK175: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_317, type, sK176: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_318, type, sK177: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_319, type, sK178: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_320, type, sK179: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_321, type, sK180: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_322, type, sK181: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_323, type, sK182: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_324, type, sK183: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_325, type, sK184: term > $o).
% 15.02/3.54 thf(func_def_326, type, sK185: term).
% 15.02/3.54 thf(func_def_327, type, sK186: (term > $o) > term).
% 15.02/3.54 thf(func_def_328, type, sK187: (term > $o) > term).
% 15.02/3.54 thf(func_def_329, type, sK188: (term > $o) > term).
% 15.02/3.54 thf(func_def_330, type, sK189: term > (term > $o) > term).
% 15.02/3.54 thf(func_def_331, type, sK190: (term > $o) > term).
% 15.02/3.54 thf(func_def_332, type, sK191: term).
% 15.02/3.54 thf(func_def_333, type, sK192: subst).
% 15.02/3.54 thf(func_def_334, type, sK193: term > $o).
% 15.02/3.54 thf(func_def_335, type, sK194: (term > $o) > subst > term).
% 15.02/3.54 thf(func_def_336, type, sK195: (term > $o) > term).
% 15.02/3.54 thf(func_def_337, type, sK196: (term > $o) > term).
% 15.02/3.54 thf(func_def_338, type, sK197: term > (term > $o) > term).
% 15.02/3.54 thf(func_def_339, type, sK198: (term > $o) > term).
% 15.02/3.54 thf(func_def_340, type, sK199: subst).
% 15.02/3.54 thf(func_def_341, type, sK200: term > $o).
% 15.02/3.54 thf(func_def_342, type, sK201: term).
% 15.02/3.54 thf(func_def_343, type, sK202: term).
% 15.02/3.54 thf(func_def_344, type, sK203: term > $o).
% 15.02/3.54 thf(func_def_345, type, sK204: (term > $o) > term).
% 15.02/3.54 thf(func_def_346, type, sK205: (term > $o) > term).
% 15.02/3.54 thf(func_def_347, type, sK206: (term > $o) > term).
% 15.02/3.54 thf(func_def_348, type, sK207: term > (term > $o) > term).
% 15.02/3.54 thf(func_def_349, type, sK208: (term > $o) > term).
% 15.02/3.54 thf(func_def_350, type, sK209: (term > $o) > term).
% 15.02/3.54 thf(func_def_351, type, sK210: term > (term > $o) > term).
% 15.02/3.54 thf(func_def_352, type, sK211: (term > $o) > subst > term).
% 15.02/3.54 thf(func_def_353, type, sK212: (term > $o) > term).
% 15.02/3.54 thf(func_def_354, type, sK213: (term > $o) > term).
% 15.02/3.54 thf(func_def_355, type, sK214: (subst > term > subst > $o) > term > term).
% 15.02/3.54 thf(func_def_356, type, sK215: term).
% 15.02/3.54 thf(func_def_357, type, sK216: subst > term > subst > $o).
% 15.02/3.54 thf(func_def_358, type, sK217: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_359, type, sK218: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_360, type, sK219: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_361, type, sK220: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_362, type, sK221: term).
% 15.02/3.54 thf(func_def_363, type, sK222: term).
% 15.02/3.54 thf(func_def_364, type, sK223: subst > term > subst > $o).
% 15.02/3.54 thf(func_def_365, type, sK224: (term > $o) > term).
% 15.02/3.54 thf(func_def_366, type, sK225: term > $o).
% 15.02/3.54 thf(func_def_367, type, sK226: term).
% 15.02/3.54 thf(func_def_368, type, sK227: subst > term > subst > $o).
% 15.02/3.54 thf(func_def_369, type, sK228: term).
% 15.02/3.54 thf(func_def_370, type, sK229: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_371, type, sK230: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_372, type, sK231: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_373, type, sK232: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_374, type, sK233: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_375, type, sK234: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_376, type, sK235: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_377, type, sK236: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_378, type, sK237: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_379, type, sK238: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_380, type, sK239: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_381, type, sK240: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_382, type, sK241: (subst > term > term) > term).
% 15.02/3.54 thf(func_def_383, type, sK242: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_384, type, sK243: (subst > term > term) > (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_385, type, sK244: (subst > term > subst > $o) > subst > term > term).
% 15.02/3.54 thf(func_def_386, type, sK245: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_387, type, sK246: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_388, type, sK247: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_389, type, sK248: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_390, type, sK249: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_391, type, sK250: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_392, type, sK251: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_393, type, sK252: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_394, type, sK253: (subst > term > subst > $o) > subst > term > term).
% 15.02/3.54 thf(func_def_395, type, sK254: (subst > term > term) > term).
% 15.02/3.54 thf(func_def_396, type, sK255: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_397, type, sK256: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_398, type, sK257: (subst > term > term) > (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_399, type, sK258: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_400, type, sK259: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_401, type, sK260: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_402, type, sK261: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_403, type, sK262: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_404, type, sK263: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_405, type, sK264: (term > $o) > term).
% 15.02/3.54 thf(func_def_406, type, sK265: term > (term > $o) > term).
% 15.02/3.54 thf(func_def_407, type, sK266: (term > $o) > term).
% 15.02/3.54 thf(func_def_408, type, sK267: (term > $o) > term).
% 15.02/3.54 thf(func_def_409, type, sK268: (term > $o) > term).
% 15.02/3.54 thf(func_def_410, type, sK269: term).
% 15.02/3.54 thf(func_def_411, type, sK270: term > $o).
% 15.02/3.54 thf(func_def_412, type, sK271: subst).
% 15.02/3.54 thf(func_def_413, type, sK272: term > $o).
% 15.02/3.54 thf(func_def_414, type, sK273: term).
% 15.02/3.54 thf(func_def_415, type, sK274: (term > $o) > subst > term).
% 15.02/3.54 thf(func_def_416, type, sK275: (term > $o) > term).
% 15.02/3.54 thf(func_def_417, type, sK276: (term > $o) > term).
% 15.02/3.54 thf(func_def_418, type, sK277: (term > $o) > term).
% 15.02/3.54 thf(func_def_419, type, sK278: (term > $o) > term).
% 15.02/3.54 thf(func_def_420, type, sK279: (term > $o) > term).
% 15.02/3.54 thf(func_def_421, type, sK280: term > (term > $o) > term).
% 15.02/3.54 thf(func_def_422, type, sK281: (term > $o) > term).
% 15.02/3.54 thf(func_def_423, type, sK282: term > (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_424, type, sK283: subst > term > subst > $o).
% 15.02/3.54 thf(func_def_425, type, sK284: term).
% 15.02/3.54 thf(func_def_426, type, sK285: term).
% 15.02/3.54 thf(func_def_427, type, sK286: subst > term > subst > $o).
% 15.02/3.54 thf(func_def_428, type, sK287: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_429, type, sK288: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_430, type, sK289: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_431, type, sK290: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_432, type, sK291: (subst > term > subst > $o) > subst > term > term).
% 15.02/3.54 thf(func_def_433, type, sK292: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_434, type, sK293: (subst > term > term) > term).
% 15.02/3.54 thf(func_def_435, type, sK294: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_436, type, sK295: (subst > term > term) > (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_437, type, sK296: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_438, type, sK297: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_439, type, sK298: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_440, type, sK299: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_441, type, sK300: term > (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_442, type, sK301: (subst > term > term) > (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_443, type, sK302: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_444, type, sK303: (subst > term > term) > term).
% 15.02/3.54 thf(func_def_445, type, sK304: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_446, type, sK305: (subst > term > subst > $o) > subst > term > term).
% 15.02/3.54 thf(func_def_447, type, sK306: term).
% 15.02/3.54 thf(func_def_448, type, sK307: term > $o).
% 15.02/3.54 thf(func_def_449, type, sK308: subst > term > subst > $o).
% 15.02/3.54 thf(func_def_450, type, sK309: term).
% 15.02/3.54 thf(func_def_451, type, sK310: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_452, type, sK311: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_453, type, sK312: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_454, type, sK313: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_455, type, sK314: (subst > term > subst > $o) > (term > $o) > term).
% 15.02/3.54 thf(func_def_456, type, sK315: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_457, type, sK316: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_458, type, sK317: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_459, type, sK318: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_460, type, sK319: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_461, type, sK320: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_462, type, sK321: term).
% 15.02/3.54 thf(func_def_463, type, sK322: subst > term > subst > $o).
% 15.02/3.54 thf(func_def_464, type, sK323: (subst > term > subst > $o) > term > term).
% 15.02/3.54 thf(func_def_465, type, sK324: (subst > term > term) > (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_466, type, sK325: (subst > term > term) > term > subst).
% 15.02/3.54 thf(func_def_467, type, sK326: (subst > term > term) > term > term).
% 15.02/3.54 thf(func_def_468, type, sK327: (subst > term > term) > term > subst).
% 15.02/3.54 thf(func_def_469, type, sK328: (subst > term > term) > term > subst).
% 15.02/3.54 thf(func_def_470, type, sK329: (subst > term > term) > term > term).
% 15.02/3.54 thf(func_def_471, type, sK330: (subst > term > term) > term > subst).
% 15.02/3.54 thf(func_def_472, type, sK331: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_473, type, sK332: (subst > term > subst > $o) > subst > term > term).
% 15.02/3.54 thf(func_def_474, type, sK333: term).
% 15.02/3.54 thf(func_def_475, type, sK334: subst > term > subst > $o).
% 15.02/3.54 thf(func_def_476, type, sK335: (subst > term > subst > $o) > term > term).
% 15.02/3.54 thf(func_def_477, type, sK336: (subst > term > term) > (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_478, type, sK337: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_479, type, sK338: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_480, type, sK339: (subst > term > term) > term).
% 15.02/3.54 thf(func_def_481, type, sK340: (subst > term > subst > $o) > subst > term > term).
% 15.02/3.54 thf(func_def_482, type, sK341: term).
% 15.02/3.54 thf(func_def_483, type, sK342: term).
% 15.02/3.54 thf(func_def_484, type, sK343: term).
% 15.02/3.54 thf(func_def_485, type, sK344: term).
% 15.02/3.54 thf(func_def_486, type, sK345: term).
% 15.02/3.54 thf(func_def_487, type, sK346: term).
% 15.02/3.54 thf(func_def_488, type, sK347: term).
% 15.02/3.54 thf(func_def_489, type, sK348: term).
% 15.02/3.54 thf(func_def_490, type, sK349: term).
% 15.02/3.54 thf(func_def_491, type, sK350: subst > term > subst > $o).
% 15.02/3.54 thf(func_def_492, type, sK351: term > $o).
% 15.02/3.54 thf(func_def_493, type, sK352: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_494, type, sK353: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_495, type, sK354: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_496, type, sK355: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_497, type, sK356: (term > $o) > (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_498, type, sK357: term > (term > $o) > term).
% 15.02/3.54 thf(func_def_499, type, sK358: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_500, type, sK359: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_501, type, sK360: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_502, type, sK361: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_503, type, sK362: (subst > term > term) > term).
% 15.02/3.54 thf(func_def_504, type, sK363: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_505, type, sK364: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_506, type, sK365: (subst > term > term) > (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_507, type, sK366: (subst > term > subst > $o) > subst > term > term).
% 15.02/3.54 thf(func_def_508, type, sK367: subst).
% 15.02/3.54 thf(func_def_509, type, sK368: term).
% 15.02/3.54 thf(func_def_510, type, sK369: term).
% 15.02/3.54 thf(func_def_511, type, sK370: subst).
% 15.02/3.54 thf(func_def_512, type, sK371: term).
% 15.02/3.54 thf(func_def_513, type, sK372: term).
% 15.02/3.54 thf(func_def_514, type, sK373: subst).
% 15.02/3.54 thf(func_def_515, type, sK374: term).
% 15.02/3.54 thf(func_def_516, type, sK375: subst > term > term).
% 15.02/3.54 thf(func_def_517, type, sK376: subst > term > term).
% 15.02/3.54 thf(func_def_518, type, sK377: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_519, type, sK378: (subst > term > term) > term).
% 15.02/3.54 thf(func_def_520, type, sK379: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_521, type, sK380: (subst > term > term) > term).
% 15.02/3.54 thf(func_def_522, type, sK381: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_523, type, sK382: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_524, type, sK383: subst).
% 15.02/3.54 thf(func_def_525, type, sK384: subst).
% 15.02/3.54 thf(func_def_526, type, sK385: subst).
% 15.02/3.54 thf(func_def_527, type, sK386: subst).
% 15.02/3.54 thf(func_def_528, type, sK387: term).
% 15.02/3.54 thf(func_def_529, type, sK388: term).
% 15.02/3.54 thf(func_def_530, type, sK389: term).
% 15.02/3.54 thf(func_def_531, type, sK390: term).
% 15.02/3.54 thf(func_def_532, type, sK391: term).
% 15.02/3.54 thf(func_def_533, type, sK392: term).
% 15.02/3.54 thf(func_def_534, type, sK393: term).
% 15.02/3.54 thf(func_def_535, type, sK394: term).
% 15.02/3.54 thf(func_def_536, type, sK395: term).
% 15.02/3.54 thf(func_def_537, type, sK396: subst > term > subst > $o).
% 15.02/3.54 thf(func_def_538, type, sK397: term).
% 15.02/3.54 thf(func_def_539, type, sK398: term > $o).
% 15.02/3.54 thf(func_def_540, type, sK399: (term > $o) > term > term).
% 15.02/3.54 thf(func_def_541, type, sK400: (term > $o) > (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_542, type, sK401: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_543, type, sK402: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_544, type, sK403: (subst > term > term) > term).
% 15.02/3.54 thf(func_def_545, type, sK404: (subst > term > term) > (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_546, type, sK405: (subst > term > subst > $o) > subst > term > term).
% 15.02/3.54 thf(func_def_547, type, sK406: term > (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_548, type, sK407: subst > term > subst > $o).
% 15.02/3.54 thf(func_def_549, type, sK408: term).
% 15.02/3.54 thf(func_def_550, type, sK409: subst > term > subst > $o).
% 15.02/3.54 thf(func_def_551, type, sK410: term).
% 15.02/3.54 thf(func_def_552, type, sK411: term > (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_553, type, sK412: (subst > term > term) > term).
% 15.02/3.54 thf(func_def_554, type, sK413: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_555, type, sK414: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_556, type, sK415: (subst > term > term) > (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_557, type, sK416: (subst > term > subst > $o) > subst > term > term).
% 15.02/3.54 thf(func_def_558, type, sK417: (subst > term > subst > $o) > subst > term > term).
% 15.02/3.54 thf(func_def_559, type, sK418: (subst > term > term) > term).
% 15.02/3.54 thf(func_def_560, type, sK419: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_561, type, sK420: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_562, type, sK421: (subst > term > term) > (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_563, type, sK422: term > $o).
% 15.02/3.54 thf(func_def_564, type, sK423: subst > term > subst > $o).
% 15.02/3.54 thf(func_def_565, type, sK424: term).
% 15.02/3.54 thf(func_def_566, type, sK425: term > (term > $o) > term).
% 15.02/3.54 thf(func_def_567, type, sK426: (subst > term > subst > $o) > (term > $o) > term).
% 15.02/3.54 thf(func_def_568, type, sK427: (subst > term > term) > (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_569, type, sK428: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_570, type, sK429: (subst > term > term) > term).
% 15.02/3.54 thf(func_def_571, type, sK430: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_572, type, sK431: (subst > term > subst > $o) > subst > term > term).
% 15.02/3.54 thf(func_def_573, type, sK432: term).
% 15.02/3.54 thf(func_def_574, type, sK433: subst > term > subst > $o).
% 15.02/3.54 thf(func_def_575, type, sK434: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_576, type, sK435: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_577, type, sK436: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_578, type, sK437: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_579, type, sK438: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_580, type, sK439: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_581, type, sK440: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_582, type, sK441: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_583, type, sK442: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_584, type, sK443: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_585, type, sK444: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_586, type, sK445: (subst > term > term) > (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_587, type, sK446: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_588, type, sK447: (subst > term > term) > term).
% 15.02/3.54 thf(func_def_589, type, sK448: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_590, type, sK449: (subst > term > subst > $o) > subst > term > term).
% 15.02/3.54 thf(func_def_591, type, sK450: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_592, type, sK451: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_593, type, sK452: (subst > term > term) > (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_594, type, sK453: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_595, type, sK454: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_596, type, sK455: (subst > term > term) > term).
% 15.02/3.54 thf(func_def_597, type, sK456: (subst > term > subst > $o) > subst > term > term).
% 15.02/3.54 thf(func_def_598, type, sK457: term).
% 15.02/3.54 thf(func_def_599, type, sK458: subst > term > subst > $o).
% 15.02/3.54 thf(func_def_600, type, sK459: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_601, type, sK460: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_602, type, sK461: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_603, type, sK462: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_604, type, sK463: (subst > term > subst > $o) > term > term).
% 15.02/3.54 thf(func_def_605, type, sK464: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_606, type, sK465: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_607, type, sK466: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_608, type, sK467: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_609, type, sK468: (subst > term > term) > (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_610, type, sK469: (subst > term > term) > term).
% 15.02/3.54 thf(func_def_611, type, sK470: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_612, type, sK471: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_613, type, sK472: (subst > term > subst > $o) > subst > term > term).
% 15.02/3.54 thf(func_def_614, type, sK473: (term > $o) > term).
% 15.02/3.54 thf(func_def_615, type, sK474: term).
% 15.02/3.54 thf(func_def_616, type, sK475: term > $o).
% 15.02/3.54 thf(func_def_617, type, sK476: (term > $o) > (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_618, type, sK477: (term > $o) > term > term).
% 15.02/3.54 thf(func_def_619, type, sK478: subst > term > subst > $o).
% 15.02/3.54 thf(func_def_620, type, sK479: term).
% 15.02/3.54 thf(func_def_621, type, sK480: term > $o).
% 15.02/3.54 thf(func_def_622, type, sK481: term).
% 15.02/3.54 thf(func_def_623, type, sK482: subst > term > subst > $o).
% 15.02/3.54 thf(func_def_624, type, sK483: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_625, type, sK484: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_626, type, sK485: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_627, type, sK486: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_628, type, sK487: (term > $o) > term).
% 15.02/3.54 thf(func_def_629, type, sK488: term > (term > $o) > term).
% 15.02/3.54 thf(func_def_630, type, sK489: (term > $o) > term).
% 15.02/3.54 thf(func_def_631, type, sK490: (term > $o) > term).
% 15.02/3.54 thf(func_def_632, type, sK491: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_633, type, sK492: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_634, type, sK493: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_635, type, sK494: (subst > term > subst > $o) > subst).
% 15.02/3.54 thf(func_def_636, type, sK495: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_637, type, sK496: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_638, type, sK497: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_639, type, sK498: (subst > term > term) > (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_640, type, sK499: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_641, type, sK500: (subst > term > term) > term).
% 15.02/3.54 thf(func_def_642, type, sK501: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_643, type, sK502: (subst > term > subst > $o) > subst > term > term).
% 15.02/3.54 thf(func_def_644, type, sK503: (subst > term > subst > $o) > subst > term > term).
% 15.02/3.54 thf(func_def_645, type, sK504: (subst > term > term) > (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_646, type, sK505: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_647, type, sK506: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_648, type, sK507: (subst > term > term) > term).
% 15.02/3.54 thf(func_def_649, type, sK508: subst > term > subst > $o).
% 15.02/3.54 thf(func_def_650, type, sK509: term).
% 15.02/3.54 thf(func_def_651, type, sK510: term > (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_652, type, sK511: (subst > term > term) > (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_653, type, sK512: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_654, type, sK513: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_655, type, sK514: (subst > term > term) > term).
% 15.02/3.54 thf(func_def_656, type, sK515: (subst > term > subst > $o) > subst > term > term).
% 15.02/3.54 thf(func_def_657, type, sK516: term).
% 15.02/3.54 thf(func_def_658, type, sK517: term).
% 15.02/3.54 thf(func_def_659, type, sK518: term).
% 15.02/3.54 thf(func_def_660, type, sK519: term).
% 15.02/3.54 thf(func_def_661, type, sK520: subst).
% 15.02/3.54 thf(func_def_662, type, sK521: term).
% 15.02/3.54 thf(func_def_663, type, sK522: subst > term > subst > $o).
% 15.02/3.54 thf(func_def_664, type, sK523: (term > $o) > term).
% 15.02/3.54 thf(func_def_665, type, sK524: (subst > term > subst > $o) > term > $o).
% 15.02/3.54 thf(func_def_666, type, sK525: subst).
% 15.02/3.54 thf(func_def_667, type, sK526: subst).
% 15.02/3.54 thf(func_def_668, type, sK527: term).
% 15.02/3.54 thf(func_def_669, type, sK528: term).
% 15.02/3.54 thf(func_def_670, type, sK529: term).
% 15.02/3.54 thf(func_def_671, type, sK530: term).
% 15.02/3.54 thf(func_def_672, type, sK531: term).
% 15.02/3.54 thf(func_def_673, type, sK532: term).
% 15.02/3.54 thf(func_def_674, type, sK533: term).
% 15.02/3.54 thf(func_def_675, type, sK534: (subst > term > term) > term).
% 15.02/3.54 thf(func_def_676, type, sK535: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_677, type, sK536: term > subst > term > term).
% 15.02/3.54 thf(func_def_678, type, sK537: term).
% 15.02/3.54 thf(func_def_679, type, sK538: term).
% 15.02/3.54 thf(func_def_680, type, sK539: term).
% 15.02/3.54 thf(func_def_681, type, sK540: term > subst > term > term).
% 15.02/3.54 thf(func_def_682, type, sK541: subst).
% 15.02/3.54 thf(func_def_683, type, sK542: subst).
% 15.02/3.54 thf(func_def_684, type, sK543: term).
% 15.02/3.54 thf(func_def_685, type, sK544: term).
% 15.02/3.54 thf(func_def_686, type, sK545: subst).
% 15.02/3.54 thf(func_def_687, type, sK546: term > (term > $o) > subst > term > $o).
% 15.02/3.54 thf(func_def_688, type, sK547: subst).
% 15.02/3.54 thf(func_def_689, type, sK548: term > $o).
% 15.02/3.54 thf(func_def_690, type, sK549: term).
% 15.02/3.54 thf(func_def_691, type, sK550: (term > $o) > term).
% 15.02/3.54 thf(func_def_692, type, sK551: term).
% 15.02/3.54 thf(func_def_693, type, sK552: term > $o).
% 15.02/3.54 thf(func_def_694, type, sK553: subst).
% 15.02/3.54 thf(func_def_695, type, sK554: term).
% 15.02/3.54 thf(func_def_696, type, sK555: (term > $o) > term).
% 15.02/3.54 thf(func_def_697, type, sK556: term > subst > (term > $o) > term > $o).
% 15.02/3.54 thf(func_def_698, type, sK557: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_699, type, sK558: (subst > term > term) > term).
% 15.02/3.54 thf(func_def_700, type, sK559: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_701, type, sK560: subst > term > term).
% 15.02/3.54 thf(func_def_702, type, sK561: term).
% 15.02/3.54 thf(func_def_703, type, sK562: term).
% 15.02/3.54 thf(func_def_704, type, sK563: term > d_term).
% 15.02/3.54 thf(func_def_705, type, sK564: term).
% 15.02/3.54 thf(func_def_706, type, sK565: term).
% 15.02/3.54 thf(func_def_707, type, sK566: term).
% 15.02/3.54 thf(func_def_708, type, sK567: subst).
% 15.02/3.54 thf(func_def_709, type, sK568: term).
% 15.02/3.54 thf(func_def_710, type, sK569: (subst > term > term) > term).
% 15.02/3.54 thf(func_def_711, type, sK570: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_712, type, sK571: term > subst > term > term).
% 15.02/3.54 thf(func_def_713, type, sK572: term > subst > term > term).
% 15.02/3.54 thf(func_def_714, type, sK573: term).
% 15.02/3.54 thf(func_def_715, type, sK574: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_716, type, sK575: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_717, type, sK576: (subst > term > term) > term).
% 15.02/3.54 thf(func_def_718, type, sK577: (subst > term > term) > term).
% 15.02/3.54 thf(func_def_719, type, sK578: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_720, type, sK579: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_721, type, sK580: subst).
% 15.02/3.54 thf(func_def_722, type, sK581: subst > term > term).
% 15.02/3.54 thf(func_def_723, type, sK582: term).
% 15.02/3.54 thf(func_def_724, type, sK583: subst > term > term).
% 15.02/3.54 thf(func_def_725, type, sK584: term).
% 15.02/3.54 thf(func_def_726, type, sK585: term).
% 15.02/3.54 thf(func_def_727, type, sK586: term).
% 15.02/3.54 thf(func_def_728, type, sK587: term).
% 15.02/3.54 thf(func_def_729, type, sK588: term).
% 15.02/3.54 thf(func_def_730, type, sK589: term).
% 15.02/3.54 thf(func_def_731, type, sK590: (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_732, type, sK591: (subst > term > term) > term).
% 15.02/3.54 thf(func_def_733, type, sK592: term > subst > term > term).
% 15.02/3.54 thf(func_def_734, type, sK593: subst).
% 15.02/3.54 thf(func_def_735, type, sK594: term).
% 15.02/3.54 thf(func_def_736, type, sK595: term).
% 15.02/3.54 thf(func_def_737, type, sK596: subst).
% 15.02/3.54 thf(func_def_738, type, sK597: term).
% 15.02/3.54 thf(func_def_739, type, sK598: term > $o).
% 15.02/3.54 thf(func_def_740, type, sK599: subst).
% 15.02/3.54 thf(func_def_741, type, sK600: term).
% 15.02/3.54 thf(func_def_742, type, sK601: term > $o).
% 15.02/3.54 thf(func_def_743, type, sK602: term).
% 15.02/3.54 thf(func_def_744, type, sK603: term > (term > $o) > (term > $o) > subst > term).
% 15.02/3.54 thf(func_def_745, type, sK604: subst).
% 15.02/3.54 thf(func_def_746, type, sK605: term > $o).
% 15.02/3.54 thf(func_def_747, type, sK606: term > $o).
% 15.02/3.54 thf(func_def_748, type, sK607: term).
% 15.02/3.54 thf(func_def_749, type, sK608: (subst > term > subst > $o) > term > $o).
% 15.02/3.54 thf(func_def_750, type, sK609: subst > term > subst > $o).
% 15.02/3.54 thf(func_def_751, type, sK610: (term > $o) > term).
% 15.02/3.54 thf(func_def_752, type, sK611: term).
% 15.02/3.54 thf(func_def_753, type, sK612: subst).
% 15.02/3.54 thf(func_def_754, type, sK613: term > $o).
% 15.02/3.54 thf(func_def_755, type, sK614: term > $o).
% 15.02/3.54 thf(func_def_756, type, sK615: (term > $o) > (term > $o) > subst > term > term).
% 15.02/3.54 thf(func_def_757, type, sK616: term).
% 15.02/3.54 thf(func_def_758, type, sK617: subst).
% 15.02/3.54 thf(func_def_759, type, sK618: term).
% 15.02/3.54 thf(func_def_760, type, sK619: term).
% 15.02/3.54 thf(func_def_761, type, sK620: term).
% 15.02/3.54 thf(func_def_762, type, sK621: term).
% 15.02/3.54 thf(func_def_763, type, sK622: term).
% 15.02/3.54 thf(func_def_764, type, sK623: subst).
% 15.02/3.54 thf(func_def_765, type, sK624: term).
% 15.02/3.54 thf(func_def_766, type, sK625: subst > term > subst > $o).
% 15.02/3.54 thf(func_def_767, type, sK626: term).
% 15.02/3.54 thf(func_def_768, type, sK627: term).
% 15.02/3.54 thf(func_def_769, type, sK628: term).
% 15.02/3.54 thf(func_def_770, type, sK629: term).
% 15.02/3.54 thf(func_def_771, type, sK630: term).
% 15.02/3.54 thf(func_def_772, type, sK631: term > $o).
% 15.02/3.54 thf(func_def_773, type, sK632: subst).
% 15.02/3.54 thf(func_def_774, type, sK633: term > $o).
% 15.02/3.54 thf(func_def_775, type, sK634: subst).
% 15.02/3.54 thf(func_def_776, type, sK635: term).
% 15.02/3.54 thf(func_def_777, type, sK636: (subst > term > subst > $o) > term > $o).
% 15.02/3.54 thf(func_def_778, type, sK637: term).
% 15.02/3.54 thf(func_def_779, type, sK638: subst > term > subst > $o).
% 15.02/3.54 thf(func_def_780, type, sK639: (term > $o) > term).
% 15.02/3.54 thf(func_def_781, type, sK640: subst).
% 15.02/3.54 thf(func_def_782, type, sK641: subst > term > subst > $o).
% 15.02/3.54 thf(func_def_783, type, sK642: (term > $o) > term).
% 15.02/3.54 thf(func_def_784, type, sK643: (subst > term > subst > $o) > term > $o).
% 15.02/3.54 thf(func_def_785, type, sK644: subst > d_subst).
% 15.02/3.54 thf(func_def_786, type, sK645: (subst > term > term) > (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_787, type, sK646: (subst > term > subst > $o) > subst > term > term).
% 15.02/3.54 thf(func_def_788, type, sK647: (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_789, type, sK648: term > (subst > term > subst > $o) > term).
% 15.02/3.54 thf(func_def_790, type, sK649: term > (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_791, type, sK650: term > (subst > term > term) > term).
% 15.02/3.54 thf(func_def_792, type, sK651: term > (subst > term > term) > subst).
% 15.02/3.54 thf(func_def_793, type, sK652: (subst > term > term) > term).
% 15.02/3.54 thf(func_def_794, type, sK653: subst > term > subst > $o).
% 15.02/3.54 thf(func_def_797, type, ph655: !>[X0: $tType]:(X0)).
% 15.02/3.54 thf(f15089,plain,(
% 15.02/3.54 $false),
% 15.02/3.54 inference(avatar_sat_refutation,[status(thm)],[f2202,f2903,f2934,f3128,f3268,f3464,f8837,f8846,f11474,f14373,f14490,f14981,f15088])).
% 15.02/3.54 thf(f15088,plain,(
% 15.02/3.54 spl654_371 | ~spl654_487),
% 15.02/3.54 inference(avatar_contradiction_clause,[status(thm)],[f15087])).
% 15.02/3.54 thf(f15087,plain,(
% 15.02/3.54 $false | (spl654_371 | ~spl654_487)),
% 15.02/3.54 inference(subsumption_resolution,[status(thm)],[f14495,f8833])).
% 15.02/3.54 thf(f8833,plain,(
% 15.02/3.54 ($true = (sK322 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | ~spl654_487),
% 15.02/3.54 inference(avatar_component_clause,[status(thm)],[f8832])).
% 15.02/3.54 thf(f8832,definition,(
% 15.02/3.54 spl654_487 <=> ($true = (sK322 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[spl654_487])],[avatar_definition])).
% 15.02/3.54 thf(f14495,plain,(
% 15.02/3.54 ($true != (sK322 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))) | spl654_371),
% 15.02/3.54 inference(forward_demodulation,[status(thm)],[f3463,f3865])).
% 15.02/3.54 thf(f3865,plain,(
% 15.02/3.54 ( ! [X97 : term] : (((d2term @ d_one) = X97)) )),
% 15.02/3.54 inference(forward_demodulation,[status(thm)],[f1412,f1314])).
% 15.02/3.54 thf(f1314,plain,(
% 15.02/3.54 ( ! [X227 : d_term] : ((d_one = X227)) )),
% 15.02/3.54 inference(cnf_transformation,[status(thm)],[f749])).
% 15.02/3.54 thf(f749,plain,(
% 15.02/3.54 (hoasapnotvar = $true) & (hoasinduction_lem2v2_gthm = $true) & ((apinj1 = $true) | ((sK517 != sK519) & ((ap @ sK519 @ sK518) = (ap @ sK517 @ sK516)))) & (! [X4 : term,X5 : term,X6 : term,X7 : term] : ((X5 = X7) | ((ap @ X5 @ X4) != (ap @ X7 @ X6))) | (apinj1 != $true)) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (hoaslamnotvar_gthm = $true) & (! [X8 : subst] : ((comp @ X8 @ id) = X8) | (axidr != $true)) & ((axidr = $true) | ((comp @ sK520 @ id) != sK520)) & (termmset_gthm = $true) & ((sP108 = $true) | ((sub @ sK521 @ id) != sK521) | ! [X12 : term > $o] : ((X12 @ (sK523 @ X12)) != (sK522 @ id @ (sK523 @ X12) @ id)) | (sP109 = $true) | (sP107 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | ((sP108 != $true) & ! [X14 : term] : ((sub @ X14 @ id) = X14) & ! [X15 : subst > term > subst > $o] : ! [X17 : term] : ((X15 @ id @ X17 @ id) = (sK524 @ X15 @ X17)) & (sP109 != $true) & (sP107 != $true))) & (hoasinduction_lem3v2_gthm = $true) & ! [X18 : d_subst] : (d_id = X18) & ((! [X19 : subst] : ((comp @ id @ X19) = X19) & ! [X20 : subst] : ((comp @ X20 @ id) = X20)) | (substmonoid != $true)) & ((substmonoid = $true) | ((comp @ id @ sK525) != sK525) | ((comp @ sK526 @ id) != sK526)) & (hoasinduction_lem3a_gthm = $true) & (one = (d2term @ d_one)) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ((sP100 = $true) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | (sP100 != $true)) & ((induction = $true) | (sP98 != $true)) & ((sP98 = $true) | (induction != $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & ((hoasinduction_lem3v2_lthm = $true) | (! [X23 : term] : ((sub @ X23 @ id) = X23) & ($true != sP95))) & ((sK527 != (sub @ sK527 @ id)) | ($true = sP95) | (hoasinduction_lem3v2_lthm != $true)) & (pushprop_lthm_orig = $true) & (hoaslamnotvar_lthm = $true) & (hoaslamnotap_lthm = $true) & ! [X25 : d_term,X26 : d_term] : (((d2term @ X25) != (d2term @ X26)) | (X25 = X26)) & (hoaslamnotvar = $true) & ((hoasinduction_lem2 = $true) | ($true != sP91)) & (($true = sP91) | (hoasinduction_lem2 != $true)) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (axabs = $true) & (! [X27 : term,X28 : term,X29 : term,X30 : term] : (((ap @ (sub @ X27 @ id) @ X30) != (ap @ (sub @ X29 @ id) @ X28)) | (X28 = X30)) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | (((ap @ (sub @ sK528 @ id) @ sK531) = (ap @ (sub @ sK530 @ id) @ sK529)) & (sK529 != sK531))) & ((induction2 = $true) | (sP88 != $true)) & ((sP88 = $true) | (induction2 != $true)) & (induction2_gthm = $true) & (($true = sP85) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP85)) & (hoasinduction_lem1v2_gthm = $true) & ((sP81 = $true) | (sK532 != (sub @ sK532 @ id)) | ($true = sP82) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ((sP81 != $true) & ! [X36 : term] : ((sub @ X36 @ id) = X36) & ($true != sP82))) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lem3v2_f = $true) | ! [X38 : subst > term > term] : ((sub @ sK533 @ (push @ (sK534 @ X38) @ (sK535 @ X38))) != (X38 @ (sK535 @ X38) @ (sK534 @ X38)))) & (! [X41 : term] : ! [X43 : term,X44 : subst] : ((sK536 @ X41 @ X44 @ X43) = (sub @ X41 @ (push @ X43 @ X44))) | (hoasinduction_lem3v2_f != $true)) & (axclos = $true) & (! [X45 : term,X46 : term] : ((X45 = X46) | ((lam @ X46) != (lam @ X45))) | (laminj != $true)) & ((laminj = $true) | ((sK537 != sK538) & ((lam @ sK538) = (lam @ sK537)))) & (pushprop_lem3v2_lthm = $true) & (axassoc = $true) & (ulamvar1 != $true) & ((hoasinduction_lem3b_lthm = $true) | ! [X50 : subst > term > term] : ((sub @ sK539 @ (push @ one @ sh)) != (X50 @ sh @ one))) & (! [X51 : term] : ((sK540 @ X51 @ sh @ one) = (sub @ X51 @ (push @ one @ sh))) | (hoasinduction_lem3b_lthm != $true)) & ((sP72 = $true) | ($true = sP75) | (sP74 = $true) | ($true = sP73) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | ((sP72 != $true) & ($true != sP75) & (sP74 != $true) & ($true != sP73))) & ((induction2lem_lthm = $true) | ((sP60 != $true) & (sP59 != $true) & ! [X53 : subst] : ((comp @ X53 @ id) = X53) & ! [X54 : subst,X55 : term] : ((comp @ sh @ (push @ X55 @ X54)) = X54) & ! [X56 : term,X57 : subst] : ((sub @ one @ (push @ X56 @ X57)) = X56))) & ((sP60 = $true) | (sP59 = $true) | (sK541 != (comp @ sK541 @ id)) | (sK542 != (comp @ sh @ (push @ sK543 @ sK542))) | (sK544 != (sub @ one @ (push @ sK544 @ sK545))) | (induction2lem_lthm != $true)) & (! [X63 : subst,X64 : term > $o,X65 : term] : ! [X67 : term] : ((sK546 @ X65 @ X64 @ X63 @ X67) = (X64 @ (sub @ X67 @ (push @ X65 @ X63)))) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ! [X71 : term > $o] : ((X71 @ (sK550 @ X71)) != (sK548 @ (sub @ (sK550 @ X71) @ (push @ sK549 @ sK547))))) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (apnotvar = $true) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (hoasinduction_gthm = $true) & (axapp = $true) & ((hoasinduction_lem3_lthm = $true) | ((sP54 != $true) & ! [X73 : term] : ((sub @ X73 @ id) = X73) & ($true != sP53))) & ((sP54 = $true) | ((sub @ sK551 @ id) != sK551) | ($true = sP53) | (hoasinduction_lem3_lthm != $true)) & ((pushprop_lem0 = $true) | ! [X78 : term > $o] : ((X78 @ (sK555 @ X78)) != (sK552 @ (sub @ (sK555 @ X78) @ (push @ sK554 @ sK553))))) & (! [X80 : term > $o,X81 : subst,X82 : term] : ! [X84 : term] : ((sK556 @ X82 @ X81 @ X80 @ X84) = (X80 @ (sub @ X84 @ (push @ X82 @ X81)))) | (pushprop_lem0 != $true)) & (induction2lem_gthm = $true) & (($true = sP48) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | ($true != sP48)) & ((hoasinduction_lem3aaa = $true) | ($true != sP45)) & (($true = sP45) | (hoasinduction_lem3aaa != $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasinduction_lem3a = $true) | ($true != sP43)) & (($true = sP43) | (hoasinduction_lem3a != $true)) & (! [X85 : subst > term > term,X86 : term,X87 : term] : (((ap @ (sub @ X86 @ id) @ X87) != (lam @ (X85 @ sh @ one))) | ((sub @ (X85 @ (sK559 @ X85) @ (sK558 @ X85)) @ (sK557 @ X85)) != (X85 @ (comp @ (sK559 @ X85) @ (sK557 @ X85)) @ (sub @ (sK558 @ X85) @ (sK557 @ X85))))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | (((lam @ (sK560 @ sh @ one)) = (ap @ (sub @ sK561 @ id) @ sK562)) & ! [X94 : subst,X95 : term,X96 : subst] : ((sub @ (sK560 @ X96 @ X95) @ X94) = (sK560 @ (comp @ X96 @ X94) @ (sub @ X95 @ X94))))) & (hoasinduction_lem1 = $true) & (pushprop_lem2v2_gthm = $true) & ! [X97 : term] : ((d2term @ (sK563 @ X97)) = X97) & ((sP41 = $true) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (sP41 != $true)) & (lamnotvar = $true) & (axvarshift = $true) & (hoasinduction_lem3b_gthm = $true) & (pushprop = $true) & ! [X99 : d_subst,X100 : d_subst] : ((X99 = X100) | ((d2subst @ X100) != (d2subst @ X99))) & (ulamvarind = $true) & (substmonoid_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (pushprop_lem2v2_lthm = $true) & ((shinj = $true) | ((sK564 != sK565) & ((sub @ sK564 @ sh) = (sub @ sK565 @ sh)))) & (! [X103 : term,X104 : term] : ((X103 = X104) | ((sub @ X104 @ sh) != (sub @ X103 @ sh))) | (shinj != $true)) & ((axshiftcons = $true) | ((comp @ sh @ (push @ sK566 @ sK567)) != sK567)) & (! [X107 : term,X108 : subst] : ((comp @ sh @ (push @ X107 @ X108)) = X108) | (axshiftcons != $true)) & (hoasapinj1_gthm = $true) & ((var @ (d2term @ d_one)) != $true) & (hoasinduction_lem1_lthm = $true) & ((sP39 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP39 != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ! [X110 : subst > term > term] : ((sub @ sK568 @ (push @ (sK569 @ X110) @ (sK570 @ X110))) != (X110 @ (sK570 @ X110) @ (sK569 @ X110)))) & (! [X113 : term] : ! [X115 : term,X116 : subst] : ((sK571 @ X113 @ X116 @ X115) = (sub @ X113 @ (push @ X115 @ X116))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((d2subst @ d_id) = id) & (pushprop_lem1v2_gthm = $true) & (! [X117 : term] : ((sK572 @ X117 @ sh @ one) = (sub @ X117 @ (push @ one @ sh))) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ! [X120 : subst > term > term] : ((X120 @ sh @ one) != (sub @ sK573 @ (push @ one @ sh)))) & ((sP35 = $true) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | (sP35 != $true)) & (! [X121 : subst,X122 : subst > term > term,X123 : term,X124 : subst > term > term] : (((X122 @ (comp @ (sK575 @ X122) @ (sK574 @ X122)) @ (sub @ (sK576 @ X122) @ (sK574 @ X122))) != (sub @ (X122 @ (sK575 @ X122) @ (sK576 @ X122)) @ (sK574 @ X122))) | ((lam @ (X124 @ sh @ one)) != (lam @ (X122 @ sh @ one))) | ((sub @ (X124 @ (sK578 @ X124) @ (sK577 @ X124)) @ (sK579 @ X124)) != (X124 @ (comp @ (sK578 @ X124) @ (sK579 @ X124)) @ (sub @ (sK577 @ X124) @ (sK579 @ X124)))) | ((X124 @ X121 @ X123) = (X122 @ X121 @ X123))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | (! [X135 : subst,X136 : subst,X137 : term] : ((sK581 @ (comp @ X136 @ X135) @ (sub @ X137 @ X135)) = (sub @ (sK581 @ X136 @ X137) @ X135)) & ((lam @ (sK583 @ sh @ one)) = (lam @ (sK581 @ sh @ one))) & ! [X138 : term,X139 : subst,X140 : subst] : ((sub @ (sK583 @ X139 @ X138) @ X140) = (sK583 @ (comp @ X139 @ X140) @ (sub @ X138 @ X140))) & ((sK583 @ sK580 @ sK582) != (sK581 @ sK580 @ sK582)))) & (hoaslamnotap_gthm = $true) & ((substmonoid_lthm = $true) | ($true != sP33)) & (($true = sP33) | (substmonoid_lthm != $true)) & (! [X141 : term,X142 : term,X143 : term,X144 : term] : (((ap @ X142 @ X141) != (ap @ X143 @ X144)) | (X141 = X144)) | (apinj2 != $true)) & ((apinj2 = $true) | (((ap @ sK586 @ sK587) = (ap @ sK585 @ sK584)) & (sK587 != sK584))) & (hoasinduction_lem2_gthm = $true) & (pushprop_lem3v2 = $true) & (pushprop_lem1_gthm = $true) & ((hoasapinj1_lthm = $true) | ($true != sP32)) & (($true = sP32) | (hoasapinj1_lthm != $true)) & (($true = sP30) | ((sub @ sK588 @ id) != sK588) | ! [X151 : subst > term > term] : ((sub @ sK589 @ (push @ (sK591 @ X151) @ (sK590 @ X151))) != (X151 @ (sK590 @ X151) @ (sK591 @ X151))) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (($true != sP30) & ! [X154 : term] : ((sub @ X154 @ id) = X154) & ! [X155 : term] : ! [X157 : subst,X158 : term] : ((sK592 @ X155 @ X157 @ X158) = (sub @ X155 @ (push @ X158 @ X157))))) & (((comp @ sh @ (push @ sK594 @ sK593)) != sK593) | ((sub @ one @ (push @ sK595 @ sK596)) != sK595) | ! [X163 : term,X164 : term > $o,X165 : subst,X166 : term,X167 : term > $o] : (((X167 @ (sub @ X163 @ (push @ X166 @ X165))) = $true) | ($true != (X164 @ X163))) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X168 : subst,X169 : term] : ((comp @ sh @ (push @ X169 @ X168)) = X168) & ! [X170 : term,X171 : subst] : ((sub @ one @ (push @ X170 @ X171)) = X170) & (((sK601 @ (sub @ sK597 @ (push @ sK600 @ sK599))) != $true) & ($true = (sK598 @ sK597))))) & (($true = sP27) | ($true = sP28) | ((sub @ sK602 @ id) != sK602) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (($true != sP27) & ($true != sP28) & ! [X178 : term] : ((sub @ X178 @ id) = X178))) & (hoasinduction_lem1v2 = $true) & (! [X179 : subst,X180 : term > $o,X181 : term > $o,X182 : term] : (((X180 @ (sub @ (sK603 @ X182 @ X181 @ X180 @ X179) @ (push @ X182 @ X179))) != (X181 @ (sK603 @ X182 @ X181 @ X180 @ X179))) | ((X181 @ one) = $true) | ($true != (X180 @ X182))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | (! [X188 : term] : ((sK605 @ (sub @ X188 @ (push @ sK607 @ sK604))) = (sK606 @ X188)) & ($true != (sK606 @ one)) & ($true = (sK605 @ sK607)))) & (lamnotap != $true) & (hoasapnotvar_gthm = $true) & (! [X189 : subst > term > subst > $o] : ! [X191 : term] : ((X189 @ id @ X191 @ id) = (sK608 @ X189 @ X191)) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ! [X193 : term > $o] : ((sK609 @ id @ (sK610 @ X193) @ id) != (X193 @ (sK610 @ X193)))) & ((d2subst @ d_id) = sh) & ((pushprop_lem1v2_lthm = $true) | ((! [X199 : term] : ((sK614 @ X199) = (sK613 @ (sub @ X199 @ (push @ sK611 @ sK612)))) & ($true != (sK614 @ one)) & ($true = (sK613 @ sK611))) & ! [X200 : term,X201 : subst] : ((sub @ one @ (push @ X200 @ X201)) = X200))) & (! [X202 : term,X203 : subst,X204 : term > $o,X205 : term > $o] : (((X204 @ (sub @ (sK615 @ X205 @ X204 @ X203 @ X202) @ (push @ X202 @ X203))) != (X205 @ (sK615 @ X205 @ X204 @ X203 @ X202))) | ((X205 @ one) = $true) | ((X204 @ X202) != $true)) | (sK616 != (sub @ one @ (push @ sK616 @ sK617))) | (pushprop_lem1v2_lthm != $true)) & (hoasinduction_lem1_gthm = $true) & (pushprop_lem0_gthm = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & ((axvarid = $true) | ((sub @ sK618 @ id) != sK618)) & (! [X210 : term] : ((sub @ X210 @ id) = X210) | (axvarid != $true)) & ((sP24 = $true) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | (sP24 != $true)) & ((hoasapinj1 = $true) | (((ap @ (sub @ sK622 @ id) @ sK619) = (ap @ (sub @ sK621 @ id) @ sK620)) & (sK621 != sK622))) & (! [X215 : term,X216 : term,X217 : term,X218 : term] : (((ap @ (sub @ X217 @ id) @ X216) != (ap @ (sub @ X218 @ id) @ X215)) | (X217 = X218)) | (hoasapinj1 != $true)) & (pushprop_gthm = $true) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & ((axscons = $true) | (sK623 != (push @ (sub @ one @ sK623) @ (comp @ sh @ sK623)))) & (! [X220 : subst] : ((push @ (sub @ one @ X220) @ (comp @ sh @ X220)) = X220) | (axscons != $true)) & ((hoasinduction = $true) | ($true != sP22)) & (($true = sP22) | (hoasinduction != $true)) & (pushprop_lem2v2 = $true) & ((hoasinduction_no_psi_cond = $true) | (((sK625 @ id @ sK624 @ id) != $true) & ((sP17 @ sK625) != $true) & ((sP16 @ sK625) != $true))) & (! [X223 : term,X224 : subst > term > subst > $o] : (($true = (X224 @ id @ X223 @ id)) | ($true = (sP17 @ X224)) | ((sP16 @ X224) = $true)) | (hoasinduction_no_psi_cond != $true)) & (hoasinduction_lem3_gthm = $true) & ((termmset = $true) | (sK626 != (sub @ sK626 @ id))) & (! [X226 : term] : ((sub @ X226 @ id) = X226) | (termmset != $true)) & ! [X227 : d_term] : (d_one = X227) & (ulamvarsh = $true) & (hoasapinj2_gthm = $true) & (axmap = $true) & ((sP15 = $true) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | (sP15 != $true)) & (! [X228 : term] : ((sub @ X228 @ id) = X228) | (sK627 != (sub @ sK627 @ id)) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (((sub @ sK628 @ id) != sK628) & ! [X231 : term] : ((sub @ X231 @ id) = X231))) & ((pushprop_lem1 = $true) | (((sK633 @ sK630) = $true) & ($true != (sK631 @ (sub @ sK630 @ (push @ sK629 @ sK632)))))) & (! [X237 : term,X238 : term,X239 : term > $o,X240 : subst,X241 : term > $o] : (($true != (X241 @ X238)) | ((X239 @ (sub @ X238 @ (push @ X237 @ X240))) = $true)) | (pushprop_lem1 != $true)) & ((axvarcons = $true) | ((sub @ one @ (push @ sK635 @ sK634)) != sK635)) & (! [X244 : subst,X245 : term] : ((sub @ one @ (push @ X245 @ X244)) = X245) | (axvarcons != $true)) & ((hoasinduction_lthm_3 = $true) | (($true != sP11) & ($true != sP9) & ! [X246 : term] : ((sub @ X246 @ id) = X246) & ! [X247 : subst > term > subst > $o] : ! [X249 : term] : ((sK636 @ X247 @ X249) = (X247 @ id @ X249 @ id)) & (sP10 != $true))) & (($true = sP11) | ($true = sP9) | ((sub @ sK637 @ id) != sK637) | ! [X252 : term > $o] : ((X252 @ (sK639 @ X252)) != (sK638 @ id @ (sK639 @ X252) @ id)) | (sP10 = $true) | (hoasinduction_lthm_3 != $true)) & (pushprop_lthm = $true) & (! [X254 : subst] : ((comp @ id @ X254) = X254) | (axidl != $true)) & ((axidl = $true) | (sK640 != (comp @ id @ sK640))) & ((hoasinduction_lem3aa = $true) | (sP1 != $true)) & ((sP1 = $true) | (hoasinduction_lem3aa != $true)) & (hoaslaminj_gthm = $true) & ((hoasinduction_lem0 = $true) | ! [X257 : term > $o] : ((sK641 @ id @ (sK642 @ X257) @ id) != (X257 @ (sK642 @ X257)))) & (! [X259 : subst > term > subst > $o] : ! [X261 : term] : ((X259 @ id @ X261 @ id) = (sK643 @ X259 @ X261)) | (hoasinduction_lem0 != $true)) & ! [X262 : subst] : ((d2subst @ (sK644 @ X262)) = X262)),
% 15.02/3.54 inference(skolemisation,[status(esa),new_symbols(skolem,[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,sK591,sK592,sK593,sK594,sK595,sK596,sK597,sK598,sK599,sK600,sK601,sK602,sK603,sK604,sK605,sK606,sK607,sK608,sK609,sK610,sK611,sK612,sK613,sK614,sK615,sK616,sK617,sK618,sK619,sK620,sK621,sK622,sK623,sK624,sK625,sK626,sK627,sK628,sK629,sK630,sK631,sK632,sK633,sK634,sK635,sK636,sK637,sK638,sK639,sK640,sK641,sK642,sK643,sK644])],[f673,f748,f747,f746,f745,f744,f743,f742,f741,f740,f739,f738,f737,f736,f735,f734,f733,f732,f731,f730,f729,f728,f727,f726,f725,f724,f723,f722,f721,f720,f719,f718,f717,f716,f715,f714,f713,f712,f711,f710,f709,f708,f707,f706,f705,f704,f703,f702,f701,f700,f699,f698,f697,f696,f695,f694,f693,f692,f691,f690,f689,f688,f687,f686,f685,f684,f683,f682,f681,f680,f679,f678,f677,f676,f675,f674])).
% 15.02/3.54 thf(f674,plain,(
% 15.02/3.54 ? [X0 : term,X1 : term,X2 : term,X3 : term] : ((X1 != X3) & ((ap @ X1 @ X0) = (ap @ X3 @ X2))) => ((sK517 != sK519) & ((ap @ sK519 @ sK518) = (ap @ sK517 @ sK516)))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f675,plain,(
% 15.02/3.54 ? [X9 : subst] : ((comp @ X9 @ id) != X9) => ((comp @ sK520 @ id) != sK520)),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f676,plain,(
% 15.02/3.54 ? [X10 : term] : ((sub @ X10 @ id) != X10) => ((sub @ sK521 @ id) != sK521)),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f677,plain,(
% 15.02/3.54 ? [X11 : subst > term > subst > $o] : ! [X12 : term > $o] : ? [X13 : term] : ((X12 @ X13) != (X11 @ id @ X13 @ id)) => ! [X12 : term > $o] : ? [X13 : term] : ((X12 @ X13) != (sK522 @ id @ X13 @ id))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f678,plain,(
% 15.02/3.54 ! [X12 : term > $o] : (? [X13 : term] : ((X12 @ X13) != (sK522 @ id @ X13 @ id)) => ((X12 @ (sK523 @ X12)) != (sK522 @ id @ (sK523 @ X12) @ id)))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f679,plain,(
% 15.02/3.54 ! [X15 : subst > term > subst > $o] : (? [X16 : term > $o] : ! [X17 : term] : ((X15 @ id @ X17 @ id) = (X16 @ X17)) => ! [X17 : term] : ((X15 @ id @ X17 @ id) = (sK524 @ X15 @ X17)))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f680,plain,(
% 15.02/3.54 ? [X21 : subst] : ((comp @ id @ X21) != X21) => ((comp @ id @ sK525) != sK525)),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f681,plain,(
% 15.02/3.54 ? [X22 : subst] : ((comp @ X22 @ id) != X22) => ((comp @ sK526 @ id) != sK526)),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f682,plain,(
% 15.02/3.54 ? [X24 : term] : ((sub @ X24 @ id) != X24) => (sK527 != (sub @ sK527 @ id))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f683,plain,(
% 15.02/3.54 ? [X31 : term,X32 : term,X33 : term,X34 : term] : (((ap @ (sub @ X31 @ id) @ X34) = (ap @ (sub @ X33 @ id) @ X32)) & (X32 != X34)) => (((ap @ (sub @ sK528 @ id) @ sK531) = (ap @ (sub @ sK530 @ id) @ sK529)) & (sK529 != sK531))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f684,plain,(
% 15.02/3.54 ? [X35 : term] : ((sub @ X35 @ id) != X35) => (sK532 != (sub @ sK532 @ id))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f685,plain,(
% 15.02/3.54 ? [X37 : term] : ! [X38 : subst > term > term] : ? [X39 : term,X40 : subst] : ((sub @ X37 @ (push @ X39 @ X40)) != (X38 @ X40 @ X39)) => ! [X38 : subst > term > term] : ? [X40 : subst,X39 : term] : ((X38 @ X40 @ X39) != (sub @ sK533 @ (push @ X39 @ X40)))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f686,plain,(
% 15.02/3.54 ! [X38 : subst > term > term] : (? [X40 : subst,X39 : term] : ((X38 @ X40 @ X39) != (sub @ sK533 @ (push @ X39 @ X40))) => ((sub @ sK533 @ (push @ (sK534 @ X38) @ (sK535 @ X38))) != (X38 @ (sK535 @ X38) @ (sK534 @ X38))))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f687,plain,(
% 15.02/3.54 ! [X41 : term] : (? [X42 : subst > term > term] : ! [X43 : term,X44 : subst] : ((X42 @ X44 @ X43) = (sub @ X41 @ (push @ X43 @ X44))) => ! [X44 : subst,X43 : term] : ((sK536 @ X41 @ X44 @ X43) = (sub @ X41 @ (push @ X43 @ X44))))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f688,plain,(
% 15.02/3.54 ? [X47 : term,X48 : term] : ((X47 != X48) & ((lam @ X48) = (lam @ X47))) => ((sK537 != sK538) & ((lam @ sK538) = (lam @ sK537)))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f689,plain,(
% 15.02/3.54 ? [X49 : term] : ! [X50 : subst > term > term] : ((X50 @ sh @ one) != (sub @ X49 @ (push @ one @ sh))) => ! [X50 : subst > term > term] : ((sub @ sK539 @ (push @ one @ sh)) != (X50 @ sh @ one))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f690,plain,(
% 15.02/3.54 ! [X51 : term] : (? [X52 : subst > term > term] : ((sub @ X51 @ (push @ one @ sh)) = (X52 @ sh @ one)) => ((sK540 @ X51 @ sh @ one) = (sub @ X51 @ (push @ one @ sh))))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f691,plain,(
% 15.02/3.54 ? [X58 : subst] : ((comp @ X58 @ id) != X58) => (sK541 != (comp @ sK541 @ id))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f692,plain,(
% 15.02/3.54 ? [X59 : subst,X60 : term] : ((comp @ sh @ (push @ X60 @ X59)) != X59) => (sK542 != (comp @ sh @ (push @ sK543 @ sK542)))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f693,plain,(
% 15.02/3.54 ? [X61 : term,X62 : subst] : ((sub @ one @ (push @ X61 @ X62)) != X61) => (sK544 != (sub @ one @ (push @ sK544 @ sK545)))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f694,plain,(
% 15.02/3.54 ! [X63 : subst,X64 : term > $o,X65 : term] : (? [X66 : term > $o] : ! [X67 : term] : ((X64 @ (sub @ X67 @ (push @ X65 @ X63))) = (X66 @ X67)) => ! [X67 : term] : ((sK546 @ X65 @ X64 @ X63 @ X67) = (X64 @ (sub @ X67 @ (push @ X65 @ X63)))))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f695,plain,(
% 15.02/3.54 ? [X68 : subst,X69 : term > $o,X70 : term] : ! [X71 : term > $o] : ? [X72 : term] : ((X71 @ X72) != (X69 @ (sub @ X72 @ (push @ X70 @ X68)))) => ! [X71 : term > $o] : ? [X72 : term] : ((X71 @ X72) != (sK548 @ (sub @ X72 @ (push @ sK549 @ sK547))))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f696,plain,(
% 15.02/3.54 ! [X71 : term > $o] : (? [X72 : term] : ((X71 @ X72) != (sK548 @ (sub @ X72 @ (push @ sK549 @ sK547)))) => ((X71 @ (sK550 @ X71)) != (sK548 @ (sub @ (sK550 @ X71) @ (push @ sK549 @ sK547)))))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f697,plain,(
% 15.02/3.54 ? [X74 : term] : ((sub @ X74 @ id) != X74) => ((sub @ sK551 @ id) != sK551)),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f698,plain,(
% 15.02/3.54 ? [X75 : term > $o,X76 : subst,X77 : term] : ! [X78 : term > $o] : ? [X79 : term] : ((X78 @ X79) != (X75 @ (sub @ X79 @ (push @ X77 @ X76)))) => ! [X78 : term > $o] : ? [X79 : term] : ((X78 @ X79) != (sK552 @ (sub @ X79 @ (push @ sK554 @ sK553))))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f699,plain,(
% 15.02/3.54 ! [X78 : term > $o] : (? [X79 : term] : ((X78 @ X79) != (sK552 @ (sub @ X79 @ (push @ sK554 @ sK553)))) => ((X78 @ (sK555 @ X78)) != (sK552 @ (sub @ (sK555 @ X78) @ (push @ sK554 @ sK553)))))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f700,plain,(
% 15.02/3.54 ! [X80 : term > $o,X81 : subst,X82 : term] : (? [X83 : term > $o] : ! [X84 : term] : ((X83 @ X84) = (X80 @ (sub @ X84 @ (push @ X82 @ X81)))) => ! [X84 : term] : ((sK556 @ X82 @ X81 @ X80 @ X84) = (X80 @ (sub @ X84 @ (push @ X82 @ X81)))))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f701,plain,(
% 15.02/3.54 ! [X85 : subst > term > term] : (? [X88 : subst,X89 : term,X90 : subst] : ((sub @ (X85 @ X90 @ X89) @ X88) != (X85 @ (comp @ X90 @ X88) @ (sub @ X89 @ X88))) => ((sub @ (X85 @ (sK559 @ X85) @ (sK558 @ X85)) @ (sK557 @ X85)) != (X85 @ (comp @ (sK559 @ X85) @ (sK557 @ X85)) @ (sub @ (sK558 @ X85) @ (sK557 @ X85)))))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f702,plain,(
% 15.02/3.54 ? [X91 : subst > term > term,X92 : term,X93 : term] : (((lam @ (X91 @ sh @ one)) = (ap @ (sub @ X92 @ id) @ X93)) & ! [X94 : subst,X95 : term,X96 : subst] : ((sub @ (X91 @ X96 @ X95) @ X94) = (X91 @ (comp @ X96 @ X94) @ (sub @ X95 @ X94)))) => (((lam @ (sK560 @ sh @ one)) = (ap @ (sub @ sK561 @ id) @ sK562)) & ! [X96 : subst,X95 : term,X94 : subst] : ((sub @ (sK560 @ X96 @ X95) @ X94) = (sK560 @ (comp @ X96 @ X94) @ (sub @ X95 @ X94))))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f703,plain,(
% 15.02/3.54 ! [X97 : term] : (? [X98 : d_term] : ((d2term @ X98) = X97) => ((d2term @ (sK563 @ X97)) = X97))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f704,plain,(
% 15.02/3.54 ? [X101 : term,X102 : term] : ((X101 != X102) & ((sub @ X101 @ sh) = (sub @ X102 @ sh))) => ((sK564 != sK565) & ((sub @ sK564 @ sh) = (sub @ sK565 @ sh)))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f705,plain,(
% 15.02/3.54 ? [X105 : term,X106 : subst] : ((comp @ sh @ (push @ X105 @ X106)) != X106) => ((comp @ sh @ (push @ sK566 @ sK567)) != sK567)),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f706,plain,(
% 15.02/3.54 ? [X109 : term] : ! [X110 : subst > term > term] : ? [X111 : term,X112 : subst] : ((X110 @ X112 @ X111) != (sub @ X109 @ (push @ X111 @ X112))) => ! [X110 : subst > term > term] : ? [X112 : subst,X111 : term] : ((sub @ sK568 @ (push @ X111 @ X112)) != (X110 @ X112 @ X111))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f707,plain,(
% 15.02/3.54 ! [X110 : subst > term > term] : (? [X112 : subst,X111 : term] : ((sub @ sK568 @ (push @ X111 @ X112)) != (X110 @ X112 @ X111)) => ((sub @ sK568 @ (push @ (sK569 @ X110) @ (sK570 @ X110))) != (X110 @ (sK570 @ X110) @ (sK569 @ X110))))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f708,plain,(
% 15.02/3.54 ! [X113 : term] : (? [X114 : subst > term > term] : ! [X115 : term,X116 : subst] : ((X114 @ X116 @ X115) = (sub @ X113 @ (push @ X115 @ X116))) => ! [X116 : subst,X115 : term] : ((sK571 @ X113 @ X116 @ X115) = (sub @ X113 @ (push @ X115 @ X116))))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f709,plain,(
% 15.02/3.54 ! [X117 : term] : (? [X118 : subst > term > term] : ((X118 @ sh @ one) = (sub @ X117 @ (push @ one @ sh))) => ((sK572 @ X117 @ sh @ one) = (sub @ X117 @ (push @ one @ sh))))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f710,plain,(
% 15.02/3.54 ? [X119 : term] : ! [X120 : subst > term > term] : ((X120 @ sh @ one) != (sub @ X119 @ (push @ one @ sh))) => ! [X120 : subst > term > term] : ((X120 @ sh @ one) != (sub @ sK573 @ (push @ one @ sh)))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f711,plain,(
% 15.02/3.54 ! [X122 : subst > term > term] : (? [X125 : subst,X126 : subst,X127 : term] : ((X122 @ (comp @ X126 @ X125) @ (sub @ X127 @ X125)) != (sub @ (X122 @ X126 @ X127) @ X125)) => ((X122 @ (comp @ (sK575 @ X122) @ (sK574 @ X122)) @ (sub @ (sK576 @ X122) @ (sK574 @ X122))) != (sub @ (X122 @ (sK575 @ X122) @ (sK576 @ X122)) @ (sK574 @ X122))))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f712,plain,(
% 15.02/3.54 ! [X124 : subst > term > term] : (? [X128 : term,X129 : subst,X130 : subst] : ((sub @ (X124 @ X129 @ X128) @ X130) != (X124 @ (comp @ X129 @ X130) @ (sub @ X128 @ X130))) => ((sub @ (X124 @ (sK578 @ X124) @ (sK577 @ X124)) @ (sK579 @ X124)) != (X124 @ (comp @ (sK578 @ X124) @ (sK579 @ X124)) @ (sub @ (sK577 @ X124) @ (sK579 @ X124)))))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f713,plain,(
% 15.02/3.54 ? [X131 : subst,X132 : subst > term > term,X133 : term,X134 : subst > term > term] : (! [X135 : subst,X136 : subst,X137 : term] : ((X132 @ (comp @ X136 @ X135) @ (sub @ X137 @ X135)) = (sub @ (X132 @ X136 @ X137) @ X135)) & ((lam @ (X132 @ sh @ one)) = (lam @ (X134 @ sh @ one))) & ! [X138 : term,X139 : subst,X140 : subst] : ((X134 @ (comp @ X139 @ X140) @ (sub @ X138 @ X140)) = (sub @ (X134 @ X139 @ X138) @ X140)) & ((X132 @ X131 @ X133) != (X134 @ X131 @ X133))) => (! [X137 : term,X136 : subst,X135 : subst] : ((sK581 @ (comp @ X136 @ X135) @ (sub @ X137 @ X135)) = (sub @ (sK581 @ X136 @ X137) @ X135)) & ((lam @ (sK583 @ sh @ one)) = (lam @ (sK581 @ sh @ one))) & ! [X140 : subst,X139 : subst,X138 : term] : ((sub @ (sK583 @ X139 @ X138) @ X140) = (sK583 @ (comp @ X139 @ X140) @ (sub @ X138 @ X140))) & ((sK583 @ sK580 @ sK582) != (sK581 @ sK580 @ sK582)))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f714,plain,(
% 15.02/3.54 ? [X145 : term,X146 : term,X147 : term,X148 : term] : (((ap @ X147 @ X148) = (ap @ X146 @ X145)) & (X145 != X148)) => (((ap @ sK586 @ sK587) = (ap @ sK585 @ sK584)) & (sK587 != sK584))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f715,plain,(
% 15.02/3.54 ? [X149 : term] : ((sub @ X149 @ id) != X149) => ((sub @ sK588 @ id) != sK588)),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f716,plain,(
% 15.02/3.54 ? [X150 : term] : ! [X151 : subst > term > term] : ? [X152 : subst,X153 : term] : ((sub @ X150 @ (push @ X153 @ X152)) != (X151 @ X152 @ X153)) => ! [X151 : subst > term > term] : ? [X153 : term,X152 : subst] : ((sub @ sK589 @ (push @ X153 @ X152)) != (X151 @ X152 @ X153))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f717,plain,(
% 15.02/3.54 ! [X151 : subst > term > term] : (? [X153 : term,X152 : subst] : ((sub @ sK589 @ (push @ X153 @ X152)) != (X151 @ X152 @ X153)) => ((sub @ sK589 @ (push @ (sK591 @ X151) @ (sK590 @ X151))) != (X151 @ (sK590 @ X151) @ (sK591 @ X151))))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f718,plain,(
% 15.02/3.54 ! [X155 : term] : (? [X156 : subst > term > term] : ! [X157 : subst,X158 : term] : ((X156 @ X157 @ X158) = (sub @ X155 @ (push @ X158 @ X157))) => ! [X158 : term,X157 : subst] : ((sK592 @ X155 @ X157 @ X158) = (sub @ X155 @ (push @ X158 @ X157))))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f719,plain,(
% 15.02/3.54 ? [X159 : subst,X160 : term] : ((comp @ sh @ (push @ X160 @ X159)) != X159) => ((comp @ sh @ (push @ sK594 @ sK593)) != sK593)),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f720,plain,(
% 15.02/3.54 ? [X161 : term,X162 : subst] : ((sub @ one @ (push @ X161 @ X162)) != X161) => ((sub @ one @ (push @ sK595 @ sK596)) != sK595)),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f721,plain,(
% 15.02/3.54 ? [X172 : term,X173 : term > $o,X174 : subst,X175 : term,X176 : term > $o] : (($true != (X176 @ (sub @ X172 @ (push @ X175 @ X174)))) & ((X173 @ X172) = $true)) => (((sK601 @ (sub @ sK597 @ (push @ sK600 @ sK599))) != $true) & ($true = (sK598 @ sK597)))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f722,plain,(
% 15.02/3.54 ? [X177 : term] : ((sub @ X177 @ id) != X177) => ((sub @ sK602 @ id) != sK602)),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f723,plain,(
% 15.02/3.54 ! [X179 : subst,X180 : term > $o,X181 : term > $o,X182 : term] : (? [X183 : term] : ((X181 @ X183) != (X180 @ (sub @ X183 @ (push @ X182 @ X179)))) => ((X180 @ (sub @ (sK603 @ X182 @ X181 @ X180 @ X179) @ (push @ X182 @ X179))) != (X181 @ (sK603 @ X182 @ X181 @ X180 @ X179))))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f724,plain,(
% 15.02/3.54 ? [X184 : subst,X185 : term > $o,X186 : term > $o,X187 : term] : (! [X188 : term] : ((X185 @ (sub @ X188 @ (push @ X187 @ X184))) = (X186 @ X188)) & ($true != (X186 @ one)) & ((X185 @ X187) = $true)) => (! [X188 : term] : ((sK605 @ (sub @ X188 @ (push @ sK607 @ sK604))) = (sK606 @ X188)) & ($true != (sK606 @ one)) & ($true = (sK605 @ sK607)))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f725,plain,(
% 15.02/3.54 ! [X189 : subst > term > subst > $o] : (? [X190 : term > $o] : ! [X191 : term] : ((X190 @ X191) = (X189 @ id @ X191 @ id)) => ! [X191 : term] : ((X189 @ id @ X191 @ id) = (sK608 @ X189 @ X191)))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f726,plain,(
% 15.02/3.54 ? [X192 : subst > term > subst > $o] : ! [X193 : term > $o] : ? [X194 : term] : ((X193 @ X194) != (X192 @ id @ X194 @ id)) => ! [X193 : term > $o] : ? [X194 : term] : ((X193 @ X194) != (sK609 @ id @ X194 @ id))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f727,plain,(
% 15.02/3.54 ! [X193 : term > $o] : (? [X194 : term] : ((X193 @ X194) != (sK609 @ id @ X194 @ id)) => ((sK609 @ id @ (sK610 @ X193) @ id) != (X193 @ (sK610 @ X193))))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f728,plain,(
% 15.02/3.54 ? [X195 : term,X196 : subst,X197 : term > $o,X198 : term > $o] : (! [X199 : term] : ((X198 @ X199) = (X197 @ (sub @ X199 @ (push @ X195 @ X196)))) & ($true != (X198 @ one)) & ((X197 @ X195) = $true)) => (! [X199 : term] : ((sK614 @ X199) = (sK613 @ (sub @ X199 @ (push @ sK611 @ sK612)))) & ($true != (sK614 @ one)) & ($true = (sK613 @ sK611)))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f729,plain,(
% 15.02/3.54 ! [X202 : term,X203 : subst,X204 : term > $o,X205 : term > $o] : (? [X206 : term] : ((X205 @ X206) != (X204 @ (sub @ X206 @ (push @ X202 @ X203)))) => ((X204 @ (sub @ (sK615 @ X205 @ X204 @ X203 @ X202) @ (push @ X202 @ X203))) != (X205 @ (sK615 @ X205 @ X204 @ X203 @ X202))))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f730,plain,(
% 15.02/3.54 ? [X207 : term,X208 : subst] : ((sub @ one @ (push @ X207 @ X208)) != X207) => (sK616 != (sub @ one @ (push @ sK616 @ sK617)))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f731,plain,(
% 15.02/3.54 ? [X209 : term] : ((sub @ X209 @ id) != X209) => ((sub @ sK618 @ id) != sK618)),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f732,plain,(
% 15.02/3.54 ? [X211 : term,X212 : term,X213 : term,X214 : term] : (((ap @ (sub @ X213 @ id) @ X212) = (ap @ (sub @ X214 @ id) @ X211)) & (X213 != X214)) => (((ap @ (sub @ sK622 @ id) @ sK619) = (ap @ (sub @ sK621 @ id) @ sK620)) & (sK621 != sK622))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f733,plain,(
% 15.02/3.54 ? [X219 : subst] : ((push @ (sub @ one @ X219) @ (comp @ sh @ X219)) != X219) => (sK623 != (push @ (sub @ one @ sK623) @ (comp @ sh @ sK623)))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f734,plain,(
% 15.02/3.54 ? [X221 : term,X222 : subst > term > subst > $o] : (((X222 @ id @ X221 @ id) != $true) & ($true != (sP17 @ X222)) & ((sP16 @ X222) != $true)) => (((sK625 @ id @ sK624 @ id) != $true) & ((sP17 @ sK625) != $true) & ((sP16 @ sK625) != $true))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f735,plain,(
% 15.02/3.54 ? [X225 : term] : ((sub @ X225 @ id) != X225) => (sK626 != (sub @ sK626 @ id))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f736,plain,(
% 15.02/3.54 ? [X229 : term] : ((sub @ X229 @ id) != X229) => (sK627 != (sub @ sK627 @ id))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f737,plain,(
% 15.02/3.54 ? [X230 : term] : ((sub @ X230 @ id) != X230) => ((sub @ sK628 @ id) != sK628)),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f738,plain,(
% 15.02/3.54 ? [X232 : term,X233 : term,X234 : term > $o,X235 : subst,X236 : term > $o] : (($true = (X236 @ X233)) & ($true != (X234 @ (sub @ X233 @ (push @ X232 @ X235))))) => (((sK633 @ sK630) = $true) & ($true != (sK631 @ (sub @ sK630 @ (push @ sK629 @ sK632)))))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f739,plain,(
% 15.02/3.54 ? [X242 : subst,X243 : term] : ((sub @ one @ (push @ X243 @ X242)) != X243) => ((sub @ one @ (push @ sK635 @ sK634)) != sK635)),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f740,plain,(
% 15.02/3.54 ! [X247 : subst > term > subst > $o] : (? [X248 : term > $o] : ! [X249 : term] : ((X248 @ X249) = (X247 @ id @ X249 @ id)) => ! [X249 : term] : ((sK636 @ X247 @ X249) = (X247 @ id @ X249 @ id)))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f741,plain,(
% 15.02/3.54 ? [X250 : term] : ((sub @ X250 @ id) != X250) => ((sub @ sK637 @ id) != sK637)),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f742,plain,(
% 15.02/3.54 ? [X251 : subst > term > subst > $o] : ! [X252 : term > $o] : ? [X253 : term] : ((X251 @ id @ X253 @ id) != (X252 @ X253)) => ! [X252 : term > $o] : ? [X253 : term] : ((sK638 @ id @ X253 @ id) != (X252 @ X253))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f743,plain,(
% 15.02/3.54 ! [X252 : term > $o] : (? [X253 : term] : ((sK638 @ id @ X253 @ id) != (X252 @ X253)) => ((X252 @ (sK639 @ X252)) != (sK638 @ id @ (sK639 @ X252) @ id)))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f744,plain,(
% 15.02/3.54 ? [X255 : subst] : ((comp @ id @ X255) != X255) => (sK640 != (comp @ id @ sK640))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f745,plain,(
% 15.02/3.54 ? [X256 : subst > term > subst > $o] : ! [X257 : term > $o] : ? [X258 : term] : ((X257 @ X258) != (X256 @ id @ X258 @ id)) => ! [X257 : term > $o] : ? [X258 : term] : ((X257 @ X258) != (sK641 @ id @ X258 @ id))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f746,plain,(
% 15.02/3.54 ! [X257 : term > $o] : (? [X258 : term] : ((X257 @ X258) != (sK641 @ id @ X258 @ id)) => ((sK641 @ id @ (sK642 @ X257) @ id) != (X257 @ (sK642 @ X257))))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f747,plain,(
% 15.02/3.54 ! [X259 : subst > term > subst > $o] : (? [X260 : term > $o] : ! [X261 : term] : ((X259 @ id @ X261 @ id) = (X260 @ X261)) => ! [X261 : term] : ((X259 @ id @ X261 @ id) = (sK643 @ X259 @ X261)))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f748,plain,(
% 15.02/3.54 ! [X262 : subst] : (? [X263 : d_subst] : ((d2subst @ X263) = X262) => ((d2subst @ (sK644 @ X262)) = X262))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f673,plain,(
% 15.02/3.54 (hoasapnotvar = $true) & (hoasinduction_lem2v2_gthm = $true) & ((apinj1 = $true) | ? [X0 : term,X1 : term,X2 : term,X3 : term] : ((X1 != X3) & ((ap @ X1 @ X0) = (ap @ X3 @ X2)))) & (! [X4 : term,X5 : term,X6 : term,X7 : term] : ((X5 = X7) | ((ap @ X5 @ X4) != (ap @ X7 @ X6))) | (apinj1 != $true)) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (hoaslamnotvar_gthm = $true) & (! [X8 : subst] : ((comp @ X8 @ id) = X8) | (axidr != $true)) & ((axidr = $true) | ? [X9 : subst] : ((comp @ X9 @ id) != X9)) & (termmset_gthm = $true) & ((sP108 = $true) | ? [X10 : term] : ((sub @ X10 @ id) != X10) | ? [X11 : subst > term > subst > $o] : ! [X12 : term > $o] : ? [X13 : term] : ((X12 @ X13) != (X11 @ id @ X13 @ id)) | (sP109 = $true) | (sP107 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | ((sP108 != $true) & ! [X14 : term] : ((sub @ X14 @ id) = X14) & ! [X15 : subst > term > subst > $o] : ? [X16 : term > $o] : ! [X17 : term] : ((X15 @ id @ X17 @ id) = (X16 @ X17)) & (sP109 != $true) & (sP107 != $true))) & (hoasinduction_lem3v2_gthm = $true) & ! [X18 : d_subst] : (d_id = X18) & ((! [X19 : subst] : ((comp @ id @ X19) = X19) & ! [X20 : subst] : ((comp @ X20 @ id) = X20)) | (substmonoid != $true)) & ((substmonoid = $true) | ? [X21 : subst] : ((comp @ id @ X21) != X21) | ? [X22 : subst] : ((comp @ X22 @ id) != X22)) & (hoasinduction_lem3a_gthm = $true) & (one = (d2term @ d_one)) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ((sP100 = $true) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | (sP100 != $true)) & ((induction = $true) | (sP98 != $true)) & ((sP98 = $true) | (induction != $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & ((hoasinduction_lem3v2_lthm = $true) | (! [X23 : term] : ((sub @ X23 @ id) = X23) & ($true != sP95))) & (? [X24 : term] : ((sub @ X24 @ id) != X24) | ($true = sP95) | (hoasinduction_lem3v2_lthm != $true)) & (pushprop_lthm_orig = $true) & (hoaslamnotvar_lthm = $true) & (hoaslamnotap_lthm = $true) & ! [X25 : d_term,X26 : d_term] : (((d2term @ X25) != (d2term @ X26)) | (X25 = X26)) & (hoaslamnotvar = $true) & ((hoasinduction_lem2 = $true) | ($true != sP91)) & (($true = sP91) | (hoasinduction_lem2 != $true)) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (axabs = $true) & (! [X27 : term,X28 : term,X29 : term,X30 : term] : (((ap @ (sub @ X27 @ id) @ X30) != (ap @ (sub @ X29 @ id) @ X28)) | (X28 = X30)) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ? [X31 : term,X32 : term,X33 : term,X34 : term] : (((ap @ (sub @ X31 @ id) @ X34) = (ap @ (sub @ X33 @ id) @ X32)) & (X32 != X34))) & ((induction2 = $true) | (sP88 != $true)) & ((sP88 = $true) | (induction2 != $true)) & (induction2_gthm = $true) & (($true = sP85) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP85)) & (hoasinduction_lem1v2_gthm = $true) & ((sP81 = $true) | ? [X35 : term] : ((sub @ X35 @ id) != X35) | ($true = sP82) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ((sP81 != $true) & ! [X36 : term] : ((sub @ X36 @ id) = X36) & ($true != sP82))) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lem3v2_f = $true) | ? [X37 : term] : ! [X38 : subst > term > term] : ? [X39 : term,X40 : subst] : ((sub @ X37 @ (push @ X39 @ X40)) != (X38 @ X40 @ X39))) & (! [X41 : term] : ? [X42 : subst > term > term] : ! [X43 : term,X44 : subst] : ((X42 @ X44 @ X43) = (sub @ X41 @ (push @ X43 @ X44))) | (hoasinduction_lem3v2_f != $true)) & (axclos = $true) & (! [X45 : term,X46 : term] : ((X45 = X46) | ((lam @ X46) != (lam @ X45))) | (laminj != $true)) & ((laminj = $true) | ? [X47 : term,X48 : term] : ((X47 != X48) & ((lam @ X48) = (lam @ X47)))) & (pushprop_lem3v2_lthm = $true) & (axassoc = $true) & (ulamvar1 != $true) & ((hoasinduction_lem3b_lthm = $true) | ? [X49 : term] : ! [X50 : subst > term > term] : ((X50 @ sh @ one) != (sub @ X49 @ (push @ one @ sh)))) & (! [X51 : term] : ? [X52 : subst > term > term] : ((sub @ X51 @ (push @ one @ sh)) = (X52 @ sh @ one)) | (hoasinduction_lem3b_lthm != $true)) & ((sP72 = $true) | ($true = sP75) | (sP74 = $true) | ($true = sP73) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | ((sP72 != $true) & ($true != sP75) & (sP74 != $true) & ($true != sP73))) & ((induction2lem_lthm = $true) | ((sP60 != $true) & (sP59 != $true) & ! [X53 : subst] : ((comp @ X53 @ id) = X53) & ! [X54 : subst,X55 : term] : ((comp @ sh @ (push @ X55 @ X54)) = X54) & ! [X56 : term,X57 : subst] : ((sub @ one @ (push @ X56 @ X57)) = X56))) & ((sP60 = $true) | (sP59 = $true) | ? [X58 : subst] : ((comp @ X58 @ id) != X58) | ? [X59 : subst,X60 : term] : ((comp @ sh @ (push @ X60 @ X59)) != X59) | ? [X61 : term,X62 : subst] : ((sub @ one @ (push @ X61 @ X62)) != X61) | (induction2lem_lthm != $true)) & (! [X63 : subst,X64 : term > $o,X65 : term] : ? [X66 : term > $o] : ! [X67 : term] : ((X64 @ (sub @ X67 @ (push @ X65 @ X63))) = (X66 @ X67)) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X68 : subst,X69 : term > $o,X70 : term] : ! [X71 : term > $o] : ? [X72 : term] : ((X71 @ X72) != (X69 @ (sub @ X72 @ (push @ X70 @ X68))))) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (apnotvar = $true) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (hoasinduction_gthm = $true) & (axapp = $true) & ((hoasinduction_lem3_lthm = $true) | ((sP54 != $true) & ! [X73 : term] : ((sub @ X73 @ id) = X73) & ($true != sP53))) & ((sP54 = $true) | ? [X74 : term] : ((sub @ X74 @ id) != X74) | ($true = sP53) | (hoasinduction_lem3_lthm != $true)) & ((pushprop_lem0 = $true) | ? [X75 : term > $o,X76 : subst,X77 : term] : ! [X78 : term > $o] : ? [X79 : term] : ((X78 @ X79) != (X75 @ (sub @ X79 @ (push @ X77 @ X76))))) & (! [X80 : term > $o,X81 : subst,X82 : term] : ? [X83 : term > $o] : ! [X84 : term] : ((X83 @ X84) = (X80 @ (sub @ X84 @ (push @ X82 @ X81)))) | (pushprop_lem0 != $true)) & (induction2lem_gthm = $true) & (($true = sP48) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | ($true != sP48)) & ((hoasinduction_lem3aaa = $true) | ($true != sP45)) & (($true = sP45) | (hoasinduction_lem3aaa != $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasinduction_lem3a = $true) | ($true != sP43)) & (($true = sP43) | (hoasinduction_lem3a != $true)) & (! [X85 : subst > term > term,X86 : term,X87 : term] : (((ap @ (sub @ X86 @ id) @ X87) != (lam @ (X85 @ sh @ one))) | ? [X88 : subst,X89 : term,X90 : subst] : ((sub @ (X85 @ X90 @ X89) @ X88) != (X85 @ (comp @ X90 @ X88) @ (sub @ X89 @ X88)))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X91 : subst > term > term,X92 : term,X93 : term] : (((lam @ (X91 @ sh @ one)) = (ap @ (sub @ X92 @ id) @ X93)) & ! [X94 : subst,X95 : term,X96 : subst] : ((sub @ (X91 @ X96 @ X95) @ X94) = (X91 @ (comp @ X96 @ X94) @ (sub @ X95 @ X94))))) & (hoasinduction_lem1 = $true) & (pushprop_lem2v2_gthm = $true) & ! [X97 : term] : ? [X98 : d_term] : ((d2term @ X98) = X97) & ((sP41 = $true) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (sP41 != $true)) & (lamnotvar = $true) & (axvarshift = $true) & (hoasinduction_lem3b_gthm = $true) & (pushprop = $true) & ! [X99 : d_subst,X100 : d_subst] : ((X99 = X100) | ((d2subst @ X100) != (d2subst @ X99))) & (ulamvarind = $true) & (substmonoid_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (pushprop_lem2v2_lthm = $true) & ((shinj = $true) | ? [X101 : term,X102 : term] : ((X101 != X102) & ((sub @ X101 @ sh) = (sub @ X102 @ sh)))) & (! [X103 : term,X104 : term] : ((X103 = X104) | ((sub @ X104 @ sh) != (sub @ X103 @ sh))) | (shinj != $true)) & ((axshiftcons = $true) | ? [X105 : term,X106 : subst] : ((comp @ sh @ (push @ X105 @ X106)) != X106)) & (! [X107 : term,X108 : subst] : ((comp @ sh @ (push @ X107 @ X108)) = X108) | (axshiftcons != $true)) & (hoasapinj1_gthm = $true) & ((var @ (d2term @ d_one)) != $true) & (hoasinduction_lem1_lthm = $true) & ((sP39 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP39 != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X109 : term] : ! [X110 : subst > term > term] : ? [X111 : term,X112 : subst] : ((X110 @ X112 @ X111) != (sub @ X109 @ (push @ X111 @ X112)))) & (! [X113 : term] : ? [X114 : subst > term > term] : ! [X115 : term,X116 : subst] : ((X114 @ X116 @ X115) = (sub @ X113 @ (push @ X115 @ X116))) | (hoasinduction_lem3v2_f_lthm != $true)) & ((d2subst @ d_id) = id) & (pushprop_lem1v2_gthm = $true) & (! [X117 : term] : ? [X118 : subst > term > term] : ((X118 @ sh @ one) = (sub @ X117 @ (push @ one @ sh))) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ? [X119 : term] : ! [X120 : subst > term > term] : ((X120 @ sh @ one) != (sub @ X119 @ (push @ one @ sh)))) & ((sP35 = $true) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | (sP35 != $true)) & (! [X121 : subst,X122 : subst > term > term,X123 : term,X124 : subst > term > term] : (? [X125 : subst,X126 : subst,X127 : term] : ((X122 @ (comp @ X126 @ X125) @ (sub @ X127 @ X125)) != (sub @ (X122 @ X126 @ X127) @ X125)) | ((lam @ (X124 @ sh @ one)) != (lam @ (X122 @ sh @ one))) | ? [X128 : term,X129 : subst,X130 : subst] : ((sub @ (X124 @ X129 @ X128) @ X130) != (X124 @ (comp @ X129 @ X130) @ (sub @ X128 @ X130))) | ((X124 @ X121 @ X123) = (X122 @ X121 @ X123))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X131 : subst,X132 : subst > term > term,X133 : term,X134 : subst > term > term] : (! [X135 : subst,X136 : subst,X137 : term] : ((X132 @ (comp @ X136 @ X135) @ (sub @ X137 @ X135)) = (sub @ (X132 @ X136 @ X137) @ X135)) & ((lam @ (X132 @ sh @ one)) = (lam @ (X134 @ sh @ one))) & ! [X138 : term,X139 : subst,X140 : subst] : ((X134 @ (comp @ X139 @ X140) @ (sub @ X138 @ X140)) = (sub @ (X134 @ X139 @ X138) @ X140)) & ((X132 @ X131 @ X133) != (X134 @ X131 @ X133)))) & (hoaslamnotap_gthm = $true) & ((substmonoid_lthm = $true) | ($true != sP33)) & (($true = sP33) | (substmonoid_lthm != $true)) & (! [X141 : term,X142 : term,X143 : term,X144 : term] : (((ap @ X142 @ X141) != (ap @ X143 @ X144)) | (X141 = X144)) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X145 : term,X146 : term,X147 : term,X148 : term] : (((ap @ X147 @ X148) = (ap @ X146 @ X145)) & (X145 != X148))) & (hoasinduction_lem2_gthm = $true) & (pushprop_lem3v2 = $true) & (pushprop_lem1_gthm = $true) & ((hoasapinj1_lthm = $true) | ($true != sP32)) & (($true = sP32) | (hoasapinj1_lthm != $true)) & (($true = sP30) | ? [X149 : term] : ((sub @ X149 @ id) != X149) | ? [X150 : term] : ! [X151 : subst > term > term] : ? [X152 : subst,X153 : term] : ((sub @ X150 @ (push @ X153 @ X152)) != (X151 @ X152 @ X153)) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (($true != sP30) & ! [X154 : term] : ((sub @ X154 @ id) = X154) & ! [X155 : term] : ? [X156 : subst > term > term] : ! [X157 : subst,X158 : term] : ((X156 @ X157 @ X158) = (sub @ X155 @ (push @ X158 @ X157))))) & (? [X159 : subst,X160 : term] : ((comp @ sh @ (push @ X160 @ X159)) != X159) | ? [X161 : term,X162 : subst] : ((sub @ one @ (push @ X161 @ X162)) != X161) | ! [X163 : term,X164 : term > $o,X165 : subst,X166 : term,X167 : term > $o] : (((X167 @ (sub @ X163 @ (push @ X166 @ X165))) = $true) | ($true != (X164 @ X163))) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X168 : subst,X169 : term] : ((comp @ sh @ (push @ X169 @ X168)) = X168) & ! [X170 : term,X171 : subst] : ((sub @ one @ (push @ X170 @ X171)) = X170) & ? [X172 : term,X173 : term > $o,X174 : subst,X175 : term,X176 : term > $o] : (($true != (X176 @ (sub @ X172 @ (push @ X175 @ X174)))) & ((X173 @ X172) = $true)))) & (($true = sP27) | ($true = sP28) | ? [X177 : term] : ((sub @ X177 @ id) != X177) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (($true != sP27) & ($true != sP28) & ! [X178 : term] : ((sub @ X178 @ id) = X178))) & (hoasinduction_lem1v2 = $true) & (! [X179 : subst,X180 : term > $o,X181 : term > $o,X182 : term] : (? [X183 : term] : ((X181 @ X183) != (X180 @ (sub @ X183 @ (push @ X182 @ X179)))) | ((X181 @ one) = $true) | ($true != (X180 @ X182))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X184 : subst,X185 : term > $o,X186 : term > $o,X187 : term] : (! [X188 : term] : ((X185 @ (sub @ X188 @ (push @ X187 @ X184))) = (X186 @ X188)) & ($true != (X186 @ one)) & ((X185 @ X187) = $true))) & (lamnotap != $true) & (hoasapnotvar_gthm = $true) & (! [X189 : subst > term > subst > $o] : ? [X190 : term > $o] : ! [X191 : term] : ((X190 @ X191) = (X189 @ id @ X191 @ id)) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X192 : subst > term > subst > $o] : ! [X193 : term > $o] : ? [X194 : term] : ((X193 @ X194) != (X192 @ id @ X194 @ id))) & ((d2subst @ d_id) = sh) & ((pushprop_lem1v2_lthm = $true) | (? [X195 : term,X196 : subst,X197 : term > $o,X198 : term > $o] : (! [X199 : term] : ((X198 @ X199) = (X197 @ (sub @ X199 @ (push @ X195 @ X196)))) & ($true != (X198 @ one)) & ((X197 @ X195) = $true)) & ! [X200 : term,X201 : subst] : ((sub @ one @ (push @ X200 @ X201)) = X200))) & (! [X202 : term,X203 : subst,X204 : term > $o,X205 : term > $o] : (? [X206 : term] : ((X205 @ X206) != (X204 @ (sub @ X206 @ (push @ X202 @ X203)))) | ((X205 @ one) = $true) | ((X204 @ X202) != $true)) | ? [X207 : term,X208 : subst] : ((sub @ one @ (push @ X207 @ X208)) != X207) | (pushprop_lem1v2_lthm != $true)) & (hoasinduction_lem1_gthm = $true) & (pushprop_lem0_gthm = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & ((axvarid = $true) | ? [X209 : term] : ((sub @ X209 @ id) != X209)) & (! [X210 : term] : ((sub @ X210 @ id) = X210) | (axvarid != $true)) & ((sP24 = $true) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | (sP24 != $true)) & ((hoasapinj1 = $true) | ? [X211 : term,X212 : term,X213 : term,X214 : term] : (((ap @ (sub @ X213 @ id) @ X212) = (ap @ (sub @ X214 @ id) @ X211)) & (X213 != X214))) & (! [X215 : term,X216 : term,X217 : term,X218 : term] : (((ap @ (sub @ X217 @ id) @ X216) != (ap @ (sub @ X218 @ id) @ X215)) | (X217 = X218)) | (hoasapinj1 != $true)) & (pushprop_gthm = $true) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & ((axscons = $true) | ? [X219 : subst] : ((push @ (sub @ one @ X219) @ (comp @ sh @ X219)) != X219)) & (! [X220 : subst] : ((push @ (sub @ one @ X220) @ (comp @ sh @ X220)) = X220) | (axscons != $true)) & ((hoasinduction = $true) | ($true != sP22)) & (($true = sP22) | (hoasinduction != $true)) & (pushprop_lem2v2 = $true) & ((hoasinduction_no_psi_cond = $true) | ? [X221 : term,X222 : subst > term > subst > $o] : (((X222 @ id @ X221 @ id) != $true) & ($true != (sP17 @ X222)) & ((sP16 @ X222) != $true))) & (! [X223 : term,X224 : subst > term > subst > $o] : (($true = (X224 @ id @ X223 @ id)) | ($true = (sP17 @ X224)) | ((sP16 @ X224) = $true)) | (hoasinduction_no_psi_cond != $true)) & (hoasinduction_lem3_gthm = $true) & ((termmset = $true) | ? [X225 : term] : ((sub @ X225 @ id) != X225)) & (! [X226 : term] : ((sub @ X226 @ id) = X226) | (termmset != $true)) & ! [X227 : d_term] : (d_one = X227) & (ulamvarsh = $true) & (hoasapinj2_gthm = $true) & (axmap = $true) & ((sP15 = $true) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | (sP15 != $true)) & (! [X228 : term] : ((sub @ X228 @ id) = X228) | ? [X229 : term] : ((sub @ X229 @ id) != X229) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X230 : term] : ((sub @ X230 @ id) != X230) & ! [X231 : term] : ((sub @ X231 @ id) = X231))) & ((pushprop_lem1 = $true) | ? [X232 : term,X233 : term,X234 : term > $o,X235 : subst,X236 : term > $o] : (($true = (X236 @ X233)) & ($true != (X234 @ (sub @ X233 @ (push @ X232 @ X235)))))) & (! [X237 : term,X238 : term,X239 : term > $o,X240 : subst,X241 : term > $o] : (($true != (X241 @ X238)) | ((X239 @ (sub @ X238 @ (push @ X237 @ X240))) = $true)) | (pushprop_lem1 != $true)) & ((axvarcons = $true) | ? [X242 : subst,X243 : term] : ((sub @ one @ (push @ X243 @ X242)) != X243)) & (! [X244 : subst,X245 : term] : ((sub @ one @ (push @ X245 @ X244)) = X245) | (axvarcons != $true)) & ((hoasinduction_lthm_3 = $true) | (($true != sP11) & ($true != sP9) & ! [X246 : term] : ((sub @ X246 @ id) = X246) & ! [X247 : subst > term > subst > $o] : ? [X248 : term > $o] : ! [X249 : term] : ((X248 @ X249) = (X247 @ id @ X249 @ id)) & (sP10 != $true))) & (($true = sP11) | ($true = sP9) | ? [X250 : term] : ((sub @ X250 @ id) != X250) | ? [X251 : subst > term > subst > $o] : ! [X252 : term > $o] : ? [X253 : term] : ((X251 @ id @ X253 @ id) != (X252 @ X253)) | (sP10 = $true) | (hoasinduction_lthm_3 != $true)) & (pushprop_lthm = $true) & (! [X254 : subst] : ((comp @ id @ X254) = X254) | (axidl != $true)) & ((axidl = $true) | ? [X255 : subst] : ((comp @ id @ X255) != X255)) & ((hoasinduction_lem3aa = $true) | (sP1 != $true)) & ((sP1 = $true) | (hoasinduction_lem3aa != $true)) & (hoaslaminj_gthm = $true) & ((hoasinduction_lem0 = $true) | ? [X256 : subst > term > subst > $o] : ! [X257 : term > $o] : ? [X258 : term] : ((X257 @ X258) != (X256 @ id @ X258 @ id))) & (! [X259 : subst > term > subst > $o] : ? [X260 : term > $o] : ! [X261 : term] : ((X259 @ id @ X261 @ id) = (X260 @ X261)) | (hoasinduction_lem0 != $true)) & ! [X262 : subst] : ? [X263 : d_subst] : ((d2subst @ X263) = X262)),
% 15.02/3.54 inference(rectify,[status(thm)],[f672])).
% 15.02/3.54 thf(f672,plain,(
% 15.02/3.54 (hoasapnotvar = $true) & (hoasinduction_lem2v2_gthm = $true) & ((apinj1 = $true) | ? [X261 : term,X262 : term,X263 : term,X264 : term] : ((X262 != X264) & ((ap @ X264 @ X263) = (ap @ X262 @ X261)))) & (! [X261 : term,X262 : term,X263 : term,X264 : term] : ((X262 = X264) | ((ap @ X264 @ X263) != (ap @ X262 @ X261))) | (apinj1 != $true)) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (hoaslamnotvar_gthm = $true) & (! [X52 : subst] : ((comp @ X52 @ id) = X52) | (axidr != $true)) & ((axidr = $true) | ? [X52 : subst] : ((comp @ X52 @ id) != X52)) & (termmset_gthm = $true) & ((sP108 = $true) | ? [X10 : term] : ((sub @ X10 @ id) != X10) | ? [X0 : subst > term > subst > $o] : ! [X1 : term > $o] : ? [X2 : term] : ((X0 @ id @ X2 @ id) != (X1 @ X2)) | (sP109 = $true) | (sP107 = $true) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | ((sP108 != $true) & ! [X10 : term] : ((sub @ X10 @ id) = X10) & ! [X0 : subst > term > subst > $o] : ? [X1 : term > $o] : ! [X2 : term] : ((X0 @ id @ X2 @ id) = (X1 @ X2)) & (sP109 != $true) & (sP107 != $true))) & (hoasinduction_lem3v2_gthm = $true) & ! [X291 : d_subst] : (d_id = X291) & ((! [X79 : subst] : ((comp @ id @ X79) = X79) & ! [X80 : subst] : ((comp @ X80 @ id) = X80)) | (substmonoid != $true)) & ((substmonoid = $true) | ? [X79 : subst] : ((comp @ id @ X79) != X79) | ? [X80 : subst] : ((comp @ X80 @ id) != X80)) & (hoasinduction_lem3a_gthm = $true) & (one = (d2term @ d_one)) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ((sP100 = $true) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | (sP100 != $true)) & ((induction = $true) | (sP98 != $true)) & ((sP98 = $true) | (induction != $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & ((hoasinduction_lem3v2_lthm = $true) | (! [X98 : term] : ((sub @ X98 @ id) = X98) & ($true != sP95))) & (? [X98 : term] : ((sub @ X98 @ id) != X98) | ($true = sP95) | (hoasinduction_lem3v2_lthm != $true)) & (pushprop_lthm_orig = $true) & (hoaslamnotvar_lthm = $true) & (hoaslamnotap_lthm = $true) & ! [X234 : d_term,X235 : d_term] : (((d2term @ X234) != (d2term @ X235)) | (X234 = X235)) & (hoaslamnotvar = $true) & ((hoasinduction_lem2 = $true) | ($true != sP91)) & (($true = sP91) | (hoasinduction_lem2 != $true)) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (axabs = $true) & (! [X480 : term,X481 : term,X482 : term,X483 : term] : (((ap @ (sub @ X482 @ id) @ X481) != (ap @ (sub @ X480 @ id) @ X483)) | (X481 = X483)) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ? [X480 : term,X481 : term,X482 : term,X483 : term] : (((ap @ (sub @ X482 @ id) @ X481) = (ap @ (sub @ X480 @ id) @ X483)) & (X481 != X483))) & ((induction2 = $true) | (sP88 != $true)) & ((sP88 = $true) | (induction2 != $true)) & (induction2_gthm = $true) & (($true = sP85) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP85)) & (hoasinduction_lem1v2_gthm = $true) & ((sP81 = $true) | ? [X128 : term] : ((sub @ X128 @ id) != X128) | ($true = sP82) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ((sP81 != $true) & ! [X128 : term] : ((sub @ X128 @ id) = X128) & ($true != sP82))) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lem3v2_f = $true) | ? [X280 : term] : ! [X281 : subst > term > term] : ? [X282 : term,X283 : subst] : ((X281 @ X283 @ X282) != (sub @ X280 @ (push @ X282 @ X283)))) & (! [X280 : term] : ? [X281 : subst > term > term] : ! [X282 : term,X283 : subst] : ((X281 @ X283 @ X282) = (sub @ X280 @ (push @ X282 @ X283))) | (hoasinduction_lem3v2_f != $true)) & (axclos = $true) & (! [X30 : term,X31 : term] : ((X30 = X31) | ((lam @ X30) != (lam @ X31))) | (laminj != $true)) & ((laminj = $true) | ? [X30 : term,X31 : term] : ((X30 != X31) & ((lam @ X30) = (lam @ X31)))) & (pushprop_lem3v2_lthm = $true) & (axassoc = $true) & (ulamvar1 != $true) & ((hoasinduction_lem3b_lthm = $true) | ? [X339 : term] : ! [X340 : subst > term > term] : ((X340 @ sh @ one) != (sub @ X339 @ (push @ one @ sh)))) & (! [X339 : term] : ? [X340 : subst > term > term] : ((X340 @ sh @ one) = (sub @ X339 @ (push @ one @ sh))) | (hoasinduction_lem3b_lthm != $true)) & ((sP72 = $true) | ($true = sP75) | (sP74 = $true) | ($true = sP73) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | ((sP72 != $true) & ($true != sP75) & (sP74 != $true) & ($true != sP73))) & ((induction2lem_lthm = $true) | ((sP60 != $true) & (sP59 != $true) & ! [X510 : subst] : ((comp @ X510 @ id) = X510) & ! [X508 : subst,X509 : term] : ((comp @ sh @ (push @ X509 @ X508)) = X508) & ! [X506 : term,X507 : subst] : ((sub @ one @ (push @ X506 @ X507)) = X506))) & ((sP60 = $true) | (sP59 = $true) | ? [X510 : subst] : ((comp @ X510 @ id) != X510) | ? [X508 : subst,X509 : term] : ((comp @ sh @ (push @ X509 @ X508)) != X508) | ? [X506 : term,X507 : subst] : ((sub @ one @ (push @ X506 @ X507)) != X506) | (induction2lem_lthm != $true)) & (! [X144 : subst,X145 : term > $o,X146 : term] : ? [X147 : term > $o] : ! [X148 : term] : ((X145 @ (sub @ X148 @ (push @ X146 @ X144))) = (X147 @ X148)) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X144 : subst,X145 : term > $o,X146 : term] : ! [X147 : term > $o] : ? [X148 : term] : ((X145 @ (sub @ X148 @ (push @ X146 @ X144))) != (X147 @ X148))) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (apnotvar = $true) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (hoasinduction_gthm = $true) & (axapp = $true) & ((hoasinduction_lem3_lthm = $true) | ((sP54 != $true) & ! [X424 : term] : ((sub @ X424 @ id) = X424) & ($true != sP53))) & ((sP54 = $true) | ? [X424 : term] : ((sub @ X424 @ id) != X424) | ($true = sP53) | (hoasinduction_lem3_lthm != $true)) & ((pushprop_lem0 = $true) | ? [X119 : term > $o,X120 : subst,X121 : term] : ! [X122 : term > $o] : ? [X123 : term] : ((X122 @ X123) != (X119 @ (sub @ X123 @ (push @ X121 @ X120))))) & (! [X119 : term > $o,X120 : subst,X121 : term] : ? [X122 : term > $o] : ! [X123 : term] : ((X122 @ X123) = (X119 @ (sub @ X123 @ (push @ X121 @ X120)))) | (pushprop_lem0 != $true)) & (induction2lem_gthm = $true) & (($true = sP48) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | ($true != sP48)) & ((hoasinduction_lem3aaa = $true) | ($true != sP45)) & (($true = sP45) | (hoasinduction_lem3aaa != $true)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasinduction_lem3a = $true) | ($true != sP43)) & (($true = sP43) | (hoasinduction_lem3a != $true)) & (! [X341 : subst > term > term,X342 : term,X343 : term] : (((ap @ (sub @ X342 @ id) @ X343) != (lam @ (X341 @ sh @ one))) | ? [X344 : subst,X345 : term,X346 : subst] : ((sub @ (X341 @ X346 @ X345) @ X344) != (X341 @ (comp @ X346 @ X344) @ (sub @ X345 @ X344)))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X341 : subst > term > term,X342 : term,X343 : term] : (((ap @ (sub @ X342 @ id) @ X343) = (lam @ (X341 @ sh @ one))) & ! [X344 : subst,X345 : term,X346 : subst] : ((sub @ (X341 @ X346 @ X345) @ X344) = (X341 @ (comp @ X346 @ X344) @ (sub @ X345 @ X344))))) & (hoasinduction_lem1 = $true) & (pushprop_lem2v2_gthm = $true) & ! [X422 : term] : ? [X423 : d_term] : ((d2term @ X423) = X422) & ((sP41 = $true) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (sP41 != $true)) & (lamnotvar = $true) & (axvarshift = $true) & (hoasinduction_lem3b_gthm = $true) & (pushprop = $true) & ! [X265 : d_subst,X266 : d_subst] : ((X265 = X266) | ((d2subst @ X266) != (d2subst @ X265))) & (ulamvarind = $true) & (substmonoid_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (pushprop_lem2v2_lthm = $true) & ((shinj = $true) | ? [X328 : term,X329 : term] : ((X328 != X329) & ((sub @ X329 @ sh) = (sub @ X328 @ sh)))) & (! [X328 : term,X329 : term] : ((X328 = X329) | ((sub @ X329 @ sh) != (sub @ X328 @ sh))) | (shinj != $true)) & ((axshiftcons = $true) | ? [X117 : term,X118 : subst] : ((comp @ sh @ (push @ X117 @ X118)) != X118)) & (! [X117 : term,X118 : subst] : ((comp @ sh @ (push @ X117 @ X118)) = X118) | (axshiftcons != $true)) & (hoasapinj1_gthm = $true) & ((var @ (d2term @ d_one)) != $true) & (hoasinduction_lem1_lthm = $true) & ((sP39 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP39 != $true)) & ((hoasinduction_lem3v2_f_lthm = $true) | ? [X124 : term] : ! [X125 : subst > term > term] : ? [X126 : term,X127 : subst] : ((sub @ X124 @ (push @ X126 @ X127)) != (X125 @ X127 @ X126))) & (! [X124 : term] : ? [X125 : subst > term > term] : ! [X126 : term,X127 : subst] : ((sub @ X124 @ (push @ X126 @ X127)) = (X125 @ X127 @ X126)) | (hoasinduction_lem3v2_f_lthm != $true)) & ((d2subst @ d_id) = id) & (pushprop_lem1v2_gthm = $true) & (! [X529 : term] : ? [X530 : subst > term > term] : ((X530 @ sh @ one) = (sub @ X529 @ (push @ one @ sh))) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ? [X529 : term] : ! [X530 : subst > term > term] : ((X530 @ sh @ one) != (sub @ X529 @ (push @ one @ sh)))) & ((sP35 = $true) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | (sP35 != $true)) & (! [X404 : subst,X405 : subst > term > term,X406 : term,X407 : subst > term > term] : (? [X411 : subst,X412 : subst,X413 : term] : ((X405 @ (comp @ X412 @ X411) @ (sub @ X413 @ X411)) != (sub @ (X405 @ X412 @ X413) @ X411)) | ((lam @ (X407 @ sh @ one)) != (lam @ (X405 @ sh @ one))) | ? [X408 : term,X409 : subst,X410 : subst] : ((X407 @ (comp @ X409 @ X410) @ (sub @ X408 @ X410)) != (sub @ (X407 @ X409 @ X408) @ X410)) | ((X407 @ X404 @ X406) = (X405 @ X404 @ X406))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X404 : subst,X405 : subst > term > term,X406 : term,X407 : subst > term > term] : (! [X411 : subst,X412 : subst,X413 : term] : ((X405 @ (comp @ X412 @ X411) @ (sub @ X413 @ X411)) = (sub @ (X405 @ X412 @ X413) @ X411)) & ((lam @ (X407 @ sh @ one)) = (lam @ (X405 @ sh @ one))) & ! [X408 : term,X409 : subst,X410 : subst] : ((X407 @ (comp @ X409 @ X410) @ (sub @ X408 @ X410)) = (sub @ (X407 @ X409 @ X408) @ X410)) & ((X407 @ X404 @ X406) != (X405 @ X404 @ X406)))) & (hoaslamnotap_gthm = $true) & ((substmonoid_lthm = $true) | ($true != sP33)) & (($true = sP33) | (substmonoid_lthm != $true)) & (! [X48 : term,X49 : term,X50 : term,X51 : term] : (((ap @ X49 @ X48) != (ap @ X50 @ X51)) | (X48 = X51)) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X48 : term,X49 : term,X50 : term,X51 : term] : (((ap @ X49 @ X48) = (ap @ X50 @ X51)) & (X48 != X51))) & (hoasinduction_lem2_gthm = $true) & (pushprop_lem3v2 = $true) & (pushprop_lem1_gthm = $true) & ((hoasapinj1_lthm = $true) | ($true != sP32)) & (($true = sP32) | (hoasapinj1_lthm != $true)) & (($true = sP30) | ? [X469 : term] : ((sub @ X469 @ id) != X469) | ? [X465 : term] : ! [X466 : subst > term > term] : ? [X467 : subst,X468 : term] : ((sub @ X465 @ (push @ X468 @ X467)) != (X466 @ X467 @ X468)) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (($true != sP30) & ! [X469 : term] : ((sub @ X469 @ id) = X469) & ! [X465 : term] : ? [X466 : subst > term > term] : ! [X467 : subst,X468 : term] : ((sub @ X465 @ (push @ X468 @ X467)) = (X466 @ X467 @ X468)))) & (? [X151 : subst,X152 : term] : ((comp @ sh @ (push @ X152 @ X151)) != X151) | ? [X149 : term,X150 : subst] : ((sub @ one @ (push @ X149 @ X150)) != X149) | ! [X153 : term,X154 : term > $o,X155 : subst,X156 : term,X157 : term > $o] : (((X157 @ (sub @ X153 @ (push @ X156 @ X155))) = $true) | ($true != (X154 @ X153))) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X151 : subst,X152 : term] : ((comp @ sh @ (push @ X152 @ X151)) = X151) & ! [X149 : term,X150 : subst] : ((sub @ one @ (push @ X149 @ X150)) = X149) & ? [X153 : term,X154 : term > $o,X155 : subst,X156 : term,X157 : term > $o] : (((X157 @ (sub @ X153 @ (push @ X156 @ X155))) != $true) & ($true = (X154 @ X153))))) & (($true = sP27) | ($true = sP28) | ? [X81 : term] : ((sub @ X81 @ id) != X81) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (($true != sP27) & ($true != sP28) & ! [X81 : term] : ((sub @ X81 @ id) = X81))) & (hoasinduction_lem1v2 = $true) & (! [X399 : subst,X400 : term > $o,X401 : term > $o,X402 : term] : (? [X403 : term] : ((X400 @ (sub @ X403 @ (push @ X402 @ X399))) != (X401 @ X403)) | ($true = (X401 @ one)) | ($true != (X400 @ X402))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X399 : subst,X400 : term > $o,X401 : term > $o,X402 : term] : (! [X403 : term] : ((X400 @ (sub @ X403 @ (push @ X402 @ X399))) = (X401 @ X403)) & ($true != (X401 @ one)) & ($true = (X400 @ X402)))) & (lamnotap != $true) & (hoasapnotvar_gthm = $true) & (! [X449 : subst > term > subst > $o] : ? [X450 : term > $o] : ! [X451 : term] : ((X449 @ id @ X451 @ id) = (X450 @ X451)) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X449 : subst > term > subst > $o] : ! [X450 : term > $o] : ? [X451 : term] : ((X449 @ id @ X451 @ id) != (X450 @ X451))) & ((d2subst @ d_id) = sh) & ((pushprop_lem1v2_lthm = $true) | (? [X286 : term,X287 : subst,X288 : term > $o,X289 : term > $o] : (! [X290 : term] : ((X288 @ (sub @ X290 @ (push @ X286 @ X287))) = (X289 @ X290)) & ((X289 @ one) != $true) & ($true = (X288 @ X286))) & ! [X284 : term,X285 : subst] : ((sub @ one @ (push @ X284 @ X285)) = X284))) & (! [X286 : term,X287 : subst,X288 : term > $o,X289 : term > $o] : (? [X290 : term] : ((X288 @ (sub @ X290 @ (push @ X286 @ X287))) != (X289 @ X290)) | ((X289 @ one) = $true) | ($true != (X288 @ X286))) | ? [X284 : term,X285 : subst] : ((sub @ one @ (push @ X284 @ X285)) != X284) | (pushprop_lem1v2_lthm != $true)) & (hoasinduction_lem1_gthm = $true) & (pushprop_lem0_gthm = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & ((axvarid = $true) | ? [X236 : term] : ((sub @ X236 @ id) != X236)) & (! [X236 : term] : ((sub @ X236 @ id) = X236) | (axvarid != $true)) & ((sP24 = $true) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | (sP24 != $true)) & ((hoasapinj1 = $true) | ? [X486 : term,X487 : term,X488 : term,X489 : term] : (((ap @ (sub @ X489 @ id) @ X486) = (ap @ (sub @ X488 @ id) @ X487)) & (X488 != X489))) & (! [X486 : term,X487 : term,X488 : term,X489 : term] : (((ap @ (sub @ X489 @ id) @ X486) != (ap @ (sub @ X488 @ id) @ X487)) | (X488 = X489)) | (hoasapinj1 != $true)) & (pushprop_gthm = $true) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & ((axscons = $true) | ? [X267 : subst] : ((push @ (sub @ one @ X267) @ (comp @ sh @ X267)) != X267)) & (! [X267 : subst] : ((push @ (sub @ one @ X267) @ (comp @ sh @ X267)) = X267) | (axscons != $true)) & ((hoasinduction = $true) | ($true != sP22)) & (($true = sP22) | (hoasinduction != $true)) & (pushprop_lem2v2 = $true) & ((hoasinduction_no_psi_cond = $true) | ? [X330 : term,X331 : subst > term > subst > $o] : (((X331 @ id @ X330 @ id) != $true) & ((sP17 @ X331) != $true) & ((sP16 @ X331) != $true))) & (! [X330 : term,X331 : subst > term > subst > $o] : (((X331 @ id @ X330 @ id) = $true) | ((sP17 @ X331) = $true) | ((sP16 @ X331) = $true)) | (hoasinduction_no_psi_cond != $true)) & (hoasinduction_lem3_gthm = $true) & ((termmset = $true) | ? [X394 : term] : ((sub @ X394 @ id) != X394)) & (! [X394 : term] : ((sub @ X394 @ id) = X394) | (termmset != $true)) & ! [X531 : d_term] : (d_one = X531) & (ulamvarsh = $true) & (hoasapinj2_gthm = $true) & (axmap = $true) & ((sP15 = $true) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | (sP15 != $true)) & (! [X254 : term] : ((sub @ X254 @ id) = X254) | ? [X253 : term] : ((sub @ X253 @ id) != X253) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X254 : term] : ((sub @ X254 @ id) != X254) & ! [X253 : term] : ((sub @ X253 @ id) = X253))) & ((pushprop_lem1 = $true) | ? [X275 : term,X276 : term,X277 : term > $o,X278 : subst,X279 : term > $o] : (((X279 @ X276) = $true) & ((X277 @ (sub @ X276 @ (push @ X275 @ X278))) != $true))) & (! [X275 : term,X276 : term,X277 : term > $o,X278 : subst,X279 : term > $o] : (((X279 @ X276) != $true) | ((X277 @ (sub @ X276 @ (push @ X275 @ X278))) = $true)) | (pushprop_lem1 != $true)) & ((axvarcons = $true) | ? [X77 : subst,X78 : term] : ((sub @ one @ (push @ X78 @ X77)) != X78)) & (! [X77 : subst,X78 : term] : ((sub @ one @ (push @ X78 @ X77)) = X78) | (axvarcons != $true)) & ((hoasinduction_lthm_3 = $true) | (($true != sP11) & ($true != sP9) & ! [X357 : term] : ((sub @ X357 @ id) = X357) & ! [X347 : subst > term > subst > $o] : ? [X348 : term > $o] : ! [X349 : term] : ((X347 @ id @ X349 @ id) = (X348 @ X349)) & (sP10 != $true))) & (($true = sP11) | ($true = sP9) | ? [X357 : term] : ((sub @ X357 @ id) != X357) | ? [X347 : subst > term > subst > $o] : ! [X348 : term > $o] : ? [X349 : term] : ((X347 @ id @ X349 @ id) != (X348 @ X349)) | (sP10 = $true) | (hoasinduction_lthm_3 != $true)) & (pushprop_lthm = $true) & (! [X528 : subst] : ((comp @ id @ X528) = X528) | (axidl != $true)) & ((axidl = $true) | ? [X528 : subst] : ((comp @ id @ X528) != X528)) & ((hoasinduction_lem3aa = $true) | (sP1 != $true)) & ((sP1 = $true) | (hoasinduction_lem3aa != $true)) & (hoaslaminj_gthm = $true) & ((hoasinduction_lem0 = $true) | ? [X525 : subst > term > subst > $o] : ! [X526 : term > $o] : ? [X527 : term] : ((X525 @ id @ X527 @ id) != (X526 @ X527))) & (! [X525 : subst > term > subst > $o] : ? [X526 : term > $o] : ! [X527 : term] : ((X525 @ id @ X527 @ id) = (X526 @ X527)) | (hoasinduction_lem0 != $true)) & ! [X484 : subst] : ? [X485 : d_subst] : ((d2subst @ X485) = X484)),
% 15.02/3.54 inference(flattening,[status(thm)],[f671])).
% 15.02/3.54 thf(f671,plain,(
% 15.02/3.54 (hoasapnotvar = $true) & (hoasinduction_lem2v2_gthm = $true) & (((apinj1 = $true) | ? [X261 : term,X262 : term,X263 : term,X264 : term] : ((X262 != X264) & ((ap @ X264 @ X263) = (ap @ X262 @ X261)))) & (! [X261 : term,X262 : term,X263 : term,X264 : term] : ((X262 = X264) | ((ap @ X264 @ X263) != (ap @ X262 @ X261))) | (apinj1 != $true))) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (hoaslamnotvar_gthm = $true) & ((! [X52 : subst] : ((comp @ X52 @ id) = X52) | (axidr != $true)) & ((axidr = $true) | ? [X52 : subst] : ((comp @ X52 @ id) != X52))) & (termmset_gthm = $true) & ((((sP108 = $true) | ? [X10 : term] : ((sub @ X10 @ id) != X10) | ? [X0 : subst > term > subst > $o] : ! [X1 : term > $o] : ? [X2 : term] : ((X0 @ id @ X2 @ id) != (X1 @ X2)) | (sP109 = $true) | (sP107 = $true)) | (hoasinduction_no_psi_cond_lthm != $true)) & ((hoasinduction_no_psi_cond_lthm = $true) | ((sP108 != $true) & ! [X10 : term] : ((sub @ X10 @ id) = X10) & ! [X0 : subst > term > subst > $o] : ? [X1 : term > $o] : ! [X2 : term] : ((X0 @ id @ X2 @ id) = (X1 @ X2)) & (sP109 != $true) & (sP107 != $true)))) & (hoasinduction_lem3v2_gthm = $true) & ! [X291 : d_subst] : (d_id = X291) & (((! [X79 : subst] : ((comp @ id @ X79) = X79) & ! [X80 : subst] : ((comp @ X80 @ id) = X80)) | (substmonoid != $true)) & ((substmonoid = $true) | (? [X79 : subst] : ((comp @ id @ X79) != X79) | ? [X80 : subst] : ((comp @ X80 @ id) != X80)))) & (hoasinduction_lem3a_gthm = $true) & (one = (d2term @ d_one)) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (((sP100 = $true) | (hoasinduction_lem3aa_lthm != $true)) & ((hoasinduction_lem3aa_lthm = $true) | (sP100 != $true))) & (((induction = $true) | (sP98 != $true)) & ((sP98 = $true) | (induction != $true))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (((hoasinduction_lem3v2_lthm = $true) | (! [X98 : term] : ((sub @ X98 @ id) = X98) & ($true != sP95))) & ((? [X98 : term] : ((sub @ X98 @ id) != X98) | ($true = sP95)) | (hoasinduction_lem3v2_lthm != $true))) & (pushprop_lthm_orig = $true) & (hoaslamnotvar_lthm = $true) & (hoaslamnotap_lthm = $true) & ! [X234 : d_term,X235 : d_term] : (((d2term @ X234) != (d2term @ X235)) | (X234 = X235)) & (hoaslamnotvar = $true) & (((hoasinduction_lem2 = $true) | ($true != sP91)) & (($true = sP91) | (hoasinduction_lem2 != $true))) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (axabs = $true) & ((! [X480 : term,X481 : term,X482 : term,X483 : term] : (((ap @ (sub @ X482 @ id) @ X481) != (ap @ (sub @ X480 @ id) @ X483)) | (X481 = X483)) | (hoasapinj2 != $true)) & ((hoasapinj2 = $true) | ? [X480 : term,X481 : term,X482 : term,X483 : term] : (((ap @ (sub @ X482 @ id) @ X481) = (ap @ (sub @ X480 @ id) @ X483)) & (X481 != X483)))) & (((induction2 = $true) | (sP88 != $true)) & ((sP88 = $true) | (induction2 != $true))) & (induction2_gthm = $true) & ((($true = sP85) | (induction2lem != $true)) & ((induction2lem = $true) | ($true != sP85))) & (hoasinduction_lem1v2_gthm = $true) & ((((sP81 = $true) | ? [X128 : term] : ((sub @ X128 @ id) != X128) | ($true = sP82)) | (induction2_lthm != $true)) & ((induction2_lthm = $true) | ((sP81 != $true) & ! [X128 : term] : ((sub @ X128 @ id) = X128) & ($true != sP82)))) & (hoasapnotvar_lthm = $true) & (((hoasinduction_lem3v2_f = $true) | ? [X280 : term] : ! [X281 : subst > term > term] : ? [X282 : term,X283 : subst] : ((X281 @ X283 @ X282) != (sub @ X280 @ (push @ X282 @ X283)))) & (! [X280 : term] : ? [X281 : subst > term > term] : ! [X282 : term,X283 : subst] : ((X281 @ X283 @ X282) = (sub @ X280 @ (push @ X282 @ X283))) | (hoasinduction_lem3v2_f != $true))) & (axclos = $true) & ((! [X30 : term,X31 : term] : ((X30 = X31) | ((lam @ X30) != (lam @ X31))) | (laminj != $true)) & ((laminj = $true) | ? [X30 : term,X31 : term] : ((X30 != X31) & ((lam @ X30) = (lam @ X31))))) & (pushprop_lem3v2_lthm = $true) & (axassoc = $true) & (ulamvar1 != $true) & (((hoasinduction_lem3b_lthm = $true) | ? [X339 : term] : ! [X340 : subst > term > term] : ((X340 @ sh @ one) != (sub @ X339 @ (push @ one @ sh)))) & (! [X339 : term] : ? [X340 : subst > term > term] : ((X340 @ sh @ one) = (sub @ X339 @ (push @ one @ sh))) | (hoasinduction_lem3b_lthm != $true))) & ((((sP72 = $true) | ($true = sP75) | (sP74 = $true) | ($true = sP73)) | (hoasinduction_lthm != $true)) & ((hoasinduction_lthm = $true) | ((sP72 != $true) & ($true != sP75) & (sP74 != $true) & ($true != sP73)))) & (((induction2lem_lthm = $true) | ((sP60 != $true) & (sP59 != $true) & ! [X510 : subst] : ((comp @ X510 @ id) = X510) & ! [X508 : subst,X509 : term] : ((comp @ sh @ (push @ X509 @ X508)) = X508) & ! [X506 : term,X507 : subst] : ((sub @ one @ (push @ X506 @ X507)) = X506))) & (((sP60 = $true) | (sP59 = $true) | ? [X510 : subst] : ((comp @ X510 @ id) != X510) | ? [X508 : subst,X509 : term] : ((comp @ sh @ (push @ X509 @ X508)) != X508) | ? [X506 : term,X507 : subst] : ((sub @ one @ (push @ X506 @ X507)) != X506)) | (induction2lem_lthm != $true))) & ((! [X144 : subst,X145 : term > $o,X146 : term] : ? [X147 : term > $o] : ! [X148 : term] : ((X145 @ (sub @ X148 @ (push @ X146 @ X144))) = (X147 @ X148)) | (pushprop_lem0_lthm != $true)) & ((pushprop_lem0_lthm = $true) | ? [X144 : subst,X145 : term > $o,X146 : term] : ! [X147 : term > $o] : ? [X148 : term] : ((X145 @ (sub @ X148 @ (push @ X146 @ X144))) != (X147 @ X148)))) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (apnotvar = $true) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (hoasinduction_gthm = $true) & (axapp = $true) & (((hoasinduction_lem3_lthm = $true) | ((sP54 != $true) & ! [X424 : term] : ((sub @ X424 @ id) = X424) & ($true != sP53))) & (((sP54 = $true) | ? [X424 : term] : ((sub @ X424 @ id) != X424) | ($true = sP53)) | (hoasinduction_lem3_lthm != $true))) & (((pushprop_lem0 = $true) | ? [X119 : term > $o,X120 : subst,X121 : term] : ! [X122 : term > $o] : ? [X123 : term] : ((X122 @ X123) != (X119 @ (sub @ X123 @ (push @ X121 @ X120))))) & (! [X119 : term > $o,X120 : subst,X121 : term] : ? [X122 : term > $o] : ! [X123 : term] : ((X122 @ X123) = (X119 @ (sub @ X123 @ (push @ X121 @ X120)))) | (pushprop_lem0 != $true))) & (induction2lem_gthm = $true) & ((($true = sP48) | (hoasinduction_lem2v2 != $true)) & ((hoasinduction_lem2v2 = $true) | ($true != sP48))) & (((hoasinduction_lem3aaa = $true) | ($true != sP45)) & (($true = sP45) | (hoasinduction_lem3aaa != $true))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (((hoasinduction_lem3a = $true) | ($true != sP43)) & (($true = sP43) | (hoasinduction_lem3a != $true))) & ((! [X341 : subst > term > term,X342 : term,X343 : term] : (((ap @ (sub @ X342 @ id) @ X343) != (lam @ (X341 @ sh @ one))) | ? [X344 : subst,X345 : term,X346 : subst] : ((sub @ (X341 @ X346 @ X345) @ X344) != (X341 @ (comp @ X346 @ X344) @ (sub @ X345 @ X344)))) | (hoaslamnotap != $true)) & ((hoaslamnotap = $true) | ? [X341 : subst > term > term,X342 : term,X343 : term] : (((ap @ (sub @ X342 @ id) @ X343) = (lam @ (X341 @ sh @ one))) & ! [X344 : subst,X345 : term,X346 : subst] : ((sub @ (X341 @ X346 @ X345) @ X344) = (X341 @ (comp @ X346 @ X344) @ (sub @ X345 @ X344)))))) & (hoasinduction_lem1 = $true) & (pushprop_lem2v2_gthm = $true) & ! [X422 : term] : ? [X423 : d_term] : ((d2term @ X423) = X422) & (((sP41 = $true) | (hoasapinj2_lthm != $true)) & ((hoasapinj2_lthm = $true) | (sP41 != $true))) & (lamnotvar = $true) & (axvarshift = $true) & (hoasinduction_lem3b_gthm = $true) & (pushprop = $true) & ! [X265 : d_subst,X266 : d_subst] : ((X265 = X266) | ((d2subst @ X266) != (d2subst @ X265))) & (ulamvarind = $true) & (substmonoid_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (pushprop_lem2v2_lthm = $true) & (((shinj = $true) | ? [X328 : term,X329 : term] : ((X328 != X329) & ((sub @ X329 @ sh) = (sub @ X328 @ sh)))) & (! [X328 : term,X329 : term] : ((X328 = X329) | ((sub @ X329 @ sh) != (sub @ X328 @ sh))) | (shinj != $true))) & (((axshiftcons = $true) | ? [X117 : term,X118 : subst] : ((comp @ sh @ (push @ X117 @ X118)) != X118)) & (! [X117 : term,X118 : subst] : ((comp @ sh @ (push @ X117 @ X118)) = X118) | (axshiftcons != $true))) & (hoasapinj1_gthm = $true) & ((var @ (d2term @ d_one)) != $true) & (hoasinduction_lem1_lthm = $true) & (((sP39 = $true) | (hoasinduction_lem3v2 != $true)) & ((hoasinduction_lem3v2 = $true) | (sP39 != $true))) & (((hoasinduction_lem3v2_f_lthm = $true) | ? [X124 : term] : ! [X125 : subst > term > term] : ? [X126 : term,X127 : subst] : ((sub @ X124 @ (push @ X126 @ X127)) != (X125 @ X127 @ X126))) & (! [X124 : term] : ? [X125 : subst > term > term] : ! [X126 : term,X127 : subst] : ((sub @ X124 @ (push @ X126 @ X127)) = (X125 @ X127 @ X126)) | (hoasinduction_lem3v2_f_lthm != $true))) & ((d2subst @ d_id) = id) & (pushprop_lem1v2_gthm = $true) & ((! [X529 : term] : ? [X530 : subst > term > term] : ((X530 @ sh @ one) = (sub @ X529 @ (push @ one @ sh))) | (hoasinduction_lem3b != $true)) & ((hoasinduction_lem3b = $true) | ? [X529 : term] : ! [X530 : subst > term > term] : ((X530 @ sh @ one) != (sub @ X529 @ (push @ one @ sh))))) & (((sP35 = $true) | (hoaslaminj_lthm != $true)) & ((hoaslaminj_lthm = $true) | (sP35 != $true))) & ((! [X404 : subst,X405 : subst > term > term,X406 : term,X407 : subst > term > term] : (? [X411 : subst,X412 : subst,X413 : term] : ((X405 @ (comp @ X412 @ X411) @ (sub @ X413 @ X411)) != (sub @ (X405 @ X412 @ X413) @ X411)) | ((lam @ (X407 @ sh @ one)) != (lam @ (X405 @ sh @ one))) | ? [X408 : term,X409 : subst,X410 : subst] : ((X407 @ (comp @ X409 @ X410) @ (sub @ X408 @ X410)) != (sub @ (X407 @ X409 @ X408) @ X410)) | ((X407 @ X404 @ X406) = (X405 @ X404 @ X406))) | (hoaslaminj != $true)) & ((hoaslaminj = $true) | ? [X404 : subst,X405 : subst > term > term,X406 : term,X407 : subst > term > term] : (! [X411 : subst,X412 : subst,X413 : term] : ((X405 @ (comp @ X412 @ X411) @ (sub @ X413 @ X411)) = (sub @ (X405 @ X412 @ X413) @ X411)) & ((lam @ (X407 @ sh @ one)) = (lam @ (X405 @ sh @ one))) & ! [X408 : term,X409 : subst,X410 : subst] : ((X407 @ (comp @ X409 @ X410) @ (sub @ X408 @ X410)) = (sub @ (X407 @ X409 @ X408) @ X410)) & ((X407 @ X404 @ X406) != (X405 @ X404 @ X406))))) & (hoaslamnotap_gthm = $true) & (((substmonoid_lthm = $true) | ($true != sP33)) & (($true = sP33) | (substmonoid_lthm != $true))) & ((! [X48 : term,X49 : term,X50 : term,X51 : term] : (((ap @ X49 @ X48) != (ap @ X50 @ X51)) | (X48 = X51)) | (apinj2 != $true)) & ((apinj2 = $true) | ? [X48 : term,X49 : term,X50 : term,X51 : term] : (((ap @ X49 @ X48) = (ap @ X50 @ X51)) & (X48 != X51)))) & (hoasinduction_lem2_gthm = $true) & (pushprop_lem3v2 = $true) & (pushprop_lem1_gthm = $true) & (((hoasapinj1_lthm = $true) | ($true != sP32)) & (($true = sP32) | (hoasapinj1_lthm != $true))) & (((($true = sP30) | ? [X469 : term] : ((sub @ X469 @ id) != X469) | ? [X465 : term] : ! [X466 : subst > term > term] : ? [X467 : subst,X468 : term] : ((sub @ X465 @ (push @ X468 @ X467)) != (X466 @ X467 @ X468))) | (hoasinduction_lem3v2a_lthm != $true)) & ((hoasinduction_lem3v2a_lthm = $true) | (($true != sP30) & ! [X469 : term] : ((sub @ X469 @ id) = X469) & ! [X465 : term] : ? [X466 : subst > term > term] : ! [X467 : subst,X468 : term] : ((sub @ X465 @ (push @ X468 @ X467)) = (X466 @ X467 @ X468))))) & (((? [X151 : subst,X152 : term] : ((comp @ sh @ (push @ X152 @ X151)) != X151) | ? [X149 : term,X150 : subst] : ((sub @ one @ (push @ X149 @ X150)) != X149) | ! [X153 : term,X154 : term > $o,X155 : subst,X156 : term,X157 : term > $o] : (((X157 @ (sub @ X153 @ (push @ X156 @ X155))) = $true) | ($true != (X154 @ X153)))) | (pushprop_lem1_lthm != $true)) & ((pushprop_lem1_lthm = $true) | (! [X151 : subst,X152 : term] : ((comp @ sh @ (push @ X152 @ X151)) = X151) & ! [X149 : term,X150 : subst] : ((sub @ one @ (push @ X149 @ X150)) = X149) & ? [X153 : term,X154 : term > $o,X155 : subst,X156 : term,X157 : term > $o] : (((X157 @ (sub @ X153 @ (push @ X156 @ X155))) != $true) & ($true = (X154 @ X153)))))) & (((($true = sP27) | ($true = sP28) | ? [X81 : term] : ((sub @ X81 @ id) != X81)) | (hoasinduction_lem3a_lthm != $true)) & ((hoasinduction_lem3a_lthm = $true) | (($true != sP27) & ($true != sP28) & ! [X81 : term] : ((sub @ X81 @ id) = X81)))) & (hoasinduction_lem1v2 = $true) & ((! [X399 : subst,X400 : term > $o,X401 : term > $o,X402 : term] : (? [X403 : term] : ((X400 @ (sub @ X403 @ (push @ X402 @ X399))) != (X401 @ X403)) | ($true = (X401 @ one)) | ($true != (X400 @ X402))) | (pushprop_lem1v2 != $true)) & ((pushprop_lem1v2 = $true) | ? [X399 : subst,X400 : term > $o,X401 : term > $o,X402 : term] : (! [X403 : term] : ((X400 @ (sub @ X403 @ (push @ X402 @ X399))) = (X401 @ X403)) & ($true != (X401 @ one)) & ($true = (X400 @ X402))))) & (lamnotap != $true) & (hoasapnotvar_gthm = $true) & ((! [X449 : subst > term > subst > $o] : ? [X450 : term > $o] : ! [X451 : term] : ((X449 @ id @ X451 @ id) = (X450 @ X451)) | (hoasinduction_lem0_lthm != $true)) & ((hoasinduction_lem0_lthm = $true) | ? [X449 : subst > term > subst > $o] : ! [X450 : term > $o] : ? [X451 : term] : ((X449 @ id @ X451 @ id) != (X450 @ X451)))) & ((d2subst @ d_id) = sh) & (((pushprop_lem1v2_lthm = $true) | (? [X286 : term,X287 : subst,X288 : term > $o,X289 : term > $o] : (! [X290 : term] : ((X288 @ (sub @ X290 @ (push @ X286 @ X287))) = (X289 @ X290)) & ((X289 @ one) != $true) & ($true = (X288 @ X286))) & ! [X284 : term,X285 : subst] : ((sub @ one @ (push @ X284 @ X285)) = X284))) & ((! [X286 : term,X287 : subst,X288 : term > $o,X289 : term > $o] : (? [X290 : term] : ((X288 @ (sub @ X290 @ (push @ X286 @ X287))) != (X289 @ X290)) | ((X289 @ one) = $true) | ($true != (X288 @ X286))) | ? [X284 : term,X285 : subst] : ((sub @ one @ (push @ X284 @ X285)) != X284)) | (pushprop_lem1v2_lthm != $true))) & (hoasinduction_lem1_gthm = $true) & (pushprop_lem0_gthm = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (((axvarid = $true) | ? [X236 : term] : ((sub @ X236 @ id) != X236)) & (! [X236 : term] : ((sub @ X236 @ id) = X236) | (axvarid != $true))) & (((sP24 = $true) | (hoasinduction_lem3v2a != $true)) & ((hoasinduction_lem3v2a = $true) | (sP24 != $true))) & (((hoasapinj1 = $true) | ? [X486 : term,X487 : term,X488 : term,X489 : term] : (((ap @ (sub @ X489 @ id) @ X486) = (ap @ (sub @ X488 @ id) @ X487)) & (X488 != X489))) & (! [X486 : term,X487 : term,X488 : term,X489 : term] : (((ap @ (sub @ X489 @ id) @ X486) != (ap @ (sub @ X488 @ id) @ X487)) | (X488 = X489)) | (hoasapinj1 != $true))) & (pushprop_gthm = $true) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (((axscons = $true) | ? [X267 : subst] : ((push @ (sub @ one @ X267) @ (comp @ sh @ X267)) != X267)) & (! [X267 : subst] : ((push @ (sub @ one @ X267) @ (comp @ sh @ X267)) = X267) | (axscons != $true))) & (((hoasinduction = $true) | ($true != sP22)) & (($true = sP22) | (hoasinduction != $true))) & (pushprop_lem2v2 = $true) & (((hoasinduction_no_psi_cond = $true) | ? [X330 : term,X331 : subst > term > subst > $o] : (((X331 @ id @ X330 @ id) != $true) & ((sP17 @ X331) != $true) & ((sP16 @ X331) != $true))) & (! [X330 : term,X331 : subst > term > subst > $o] : (((X331 @ id @ X330 @ id) = $true) | ((sP17 @ X331) = $true) | ((sP16 @ X331) = $true)) | (hoasinduction_no_psi_cond != $true))) & (hoasinduction_lem3_gthm = $true) & (((termmset = $true) | ? [X394 : term] : ((sub @ X394 @ id) != X394)) & (! [X394 : term] : ((sub @ X394 @ id) = X394) | (termmset != $true))) & ! [X531 : d_term] : (d_one = X531) & (ulamvarsh = $true) & (hoasapinj2_gthm = $true) & (axmap = $true) & (((sP15 = $true) | (hoasinduction_lem3 != $true)) & ((hoasinduction_lem3 = $true) | (sP15 != $true))) & (((! [X254 : term] : ((sub @ X254 @ id) = X254) | ? [X253 : term] : ((sub @ X253 @ id) != X253)) | (termmset_lthm != $true)) & ((termmset_lthm = $true) | (? [X254 : term] : ((sub @ X254 @ id) != X254) & ! [X253 : term] : ((sub @ X253 @ id) = X253)))) & (((pushprop_lem1 = $true) | ? [X275 : term,X276 : term,X277 : term > $o,X278 : subst,X279 : term > $o] : (((X279 @ X276) = $true) & ((X277 @ (sub @ X276 @ (push @ X275 @ X278))) != $true))) & (! [X275 : term,X276 : term,X277 : term > $o,X278 : subst,X279 : term > $o] : (((X279 @ X276) != $true) | ((X277 @ (sub @ X276 @ (push @ X275 @ X278))) = $true)) | (pushprop_lem1 != $true))) & (((axvarcons = $true) | ? [X77 : subst,X78 : term] : ((sub @ one @ (push @ X78 @ X77)) != X78)) & (! [X77 : subst,X78 : term] : ((sub @ one @ (push @ X78 @ X77)) = X78) | (axvarcons != $true))) & (((hoasinduction_lthm_3 = $true) | (($true != sP11) & ($true != sP9) & ! [X357 : term] : ((sub @ X357 @ id) = X357) & ! [X347 : subst > term > subst > $o] : ? [X348 : term > $o] : ! [X349 : term] : ((X347 @ id @ X349 @ id) = (X348 @ X349)) & (sP10 != $true))) & ((($true = sP11) | ($true = sP9) | ? [X357 : term] : ((sub @ X357 @ id) != X357) | ? [X347 : subst > term > subst > $o] : ! [X348 : term > $o] : ? [X349 : term] : ((X347 @ id @ X349 @ id) != (X348 @ X349)) | (sP10 = $true)) | (hoasinduction_lthm_3 != $true))) & (pushprop_lthm = $true) & ((! [X528 : subst] : ((comp @ id @ X528) = X528) | (axidl != $true)) & ((axidl = $true) | ? [X528 : subst] : ((comp @ id @ X528) != X528))) & (((hoasinduction_lem3aa = $true) | (sP1 != $true)) & ((sP1 = $true) | (hoasinduction_lem3aa != $true))) & (hoaslaminj_gthm = $true) & (((hoasinduction_lem0 = $true) | ? [X525 : subst > term > subst > $o] : ! [X526 : term > $o] : ? [X527 : term] : ((X525 @ id @ X527 @ id) != (X526 @ X527))) & (! [X525 : subst > term > subst > $o] : ? [X526 : term > $o] : ! [X527 : term] : ((X525 @ id @ X527 @ id) = (X526 @ X527)) | (hoasinduction_lem0 != $true))) & ! [X484 : subst] : ? [X485 : d_subst] : ((d2subst @ X485) = X484)),
% 15.02/3.54 inference(nnf_transformation,[status(thm)],[f126])).
% 15.02/3.54 thf(f126,plain,(
% 15.02/3.54 (hoasapnotvar = $true) & (hoasinduction_lem2v2_gthm = $true) & ((apinj1 = $true) <=> ! [X261 : term,X262 : term,X263 : term,X264 : term] : ((X262 = X264) | ((ap @ X264 @ X263) != (ap @ X262 @ X261)))) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (hoaslamnotvar_gthm = $true) & (! [X52 : subst] : ((comp @ X52 @ id) = X52) <=> (axidr = $true)) & (termmset_gthm = $true) & (((sP108 = $true) | ? [X10 : term] : ((sub @ X10 @ id) != X10) | ? [X0 : subst > term > subst > $o] : ! [X1 : term > $o] : ? [X2 : term] : ((X0 @ id @ X2 @ id) != (X1 @ X2)) | (sP109 = $true) | (sP107 = $true)) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (hoasinduction_lem3v2_gthm = $true) & ! [X291 : d_subst] : (d_id = X291) & ((! [X79 : subst] : ((comp @ id @ X79) = X79) & ! [X80 : subst] : ((comp @ X80 @ id) = X80)) <=> (substmonoid = $true)) & (hoasinduction_lem3a_gthm = $true) & (one = (d2term @ d_one)) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ((sP100 = $true) <=> (hoasinduction_lem3aa_lthm = $true)) & ((induction = $true) <=> (sP98 = $true)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & ((hoasinduction_lem3v2_lthm = $true) <=> (? [X98 : term] : ((sub @ X98 @ id) != X98) | ($true = sP95))) & (pushprop_lthm_orig = $true) & (hoaslamnotvar_lthm = $true) & (hoaslamnotap_lthm = $true) & ! [X234 : d_term,X235 : d_term] : (((d2term @ X234) != (d2term @ X235)) | (X234 = X235)) & (hoaslamnotvar = $true) & ((hoasinduction_lem2 = $true) <=> ($true = sP91)) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (axabs = $true) & (! [X480 : term,X481 : term,X482 : term,X483 : term] : (((ap @ (sub @ X482 @ id) @ X481) != (ap @ (sub @ X480 @ id) @ X483)) | (X481 = X483)) <=> (hoasapinj2 = $true)) & ((induction2 = $true) <=> (sP88 = $true)) & (induction2_gthm = $true) & (($true = sP85) <=> (induction2lem = $true)) & (hoasinduction_lem1v2_gthm = $true) & (((sP81 = $true) | ? [X128 : term] : ((sub @ X128 @ id) != X128) | ($true = sP82)) <=> (induction2_lthm = $true)) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X280 : term] : ? [X281 : subst > term > term] : ! [X282 : term,X283 : subst] : ((X281 @ X283 @ X282) = (sub @ X280 @ (push @ X282 @ X283)))) & (axclos = $true) & (! [X30 : term,X31 : term] : ((X30 = X31) | ((lam @ X30) != (lam @ X31))) <=> (laminj = $true)) & (pushprop_lem3v2_lthm = $true) & (axassoc = $true) & (ulamvar1 != $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X339 : term] : ? [X340 : subst > term > term] : ((X340 @ sh @ one) = (sub @ X339 @ (push @ one @ sh)))) & (((sP72 = $true) | ($true = sP75) | (sP74 = $true) | ($true = sP73)) <=> (hoasinduction_lthm = $true)) & ((induction2lem_lthm = $true) <=> ((sP60 = $true) | (sP59 = $true) | ? [X510 : subst] : ((comp @ X510 @ id) != X510) | ? [X508 : subst,X509 : term] : ((comp @ sh @ (push @ X509 @ X508)) != X508) | ? [X506 : term,X507 : subst] : ((sub @ one @ (push @ X506 @ X507)) != X506))) & (! [X144 : subst,X145 : term > $o,X146 : term] : ? [X147 : term > $o] : ! [X148 : term] : ((X145 @ (sub @ X148 @ (push @ X146 @ X144))) = (X147 @ X148)) <=> (pushprop_lem0_lthm = $true)) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (apnotvar = $true) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (hoasinduction_gthm = $true) & (axapp = $true) & ((hoasinduction_lem3_lthm = $true) <=> ((sP54 = $true) | ? [X424 : term] : ((sub @ X424 @ id) != X424) | ($true = sP53))) & ((pushprop_lem0 = $true) <=> ! [X119 : term > $o,X120 : subst,X121 : term] : ? [X122 : term > $o] : ! [X123 : term] : ((X122 @ X123) = (X119 @ (sub @ X123 @ (push @ X121 @ X120))))) & (induction2lem_gthm = $true) & (($true = sP48) <=> (hoasinduction_lem2v2 = $true)) & ((hoasinduction_lem3aaa = $true) <=> ($true = sP45)) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasinduction_lem3a = $true) <=> ($true = sP43)) & (! [X341 : subst > term > term,X342 : term,X343 : term] : (((ap @ (sub @ X342 @ id) @ X343) != (lam @ (X341 @ sh @ one))) | ? [X344 : subst,X345 : term,X346 : subst] : ((sub @ (X341 @ X346 @ X345) @ X344) != (X341 @ (comp @ X346 @ X344) @ (sub @ X345 @ X344)))) <=> (hoaslamnotap = $true)) & (hoasinduction_lem1 = $true) & (pushprop_lem2v2_gthm = $true) & ! [X422 : term] : ? [X423 : d_term] : ((d2term @ X423) = X422) & ((sP41 = $true) <=> (hoasapinj2_lthm = $true)) & (lamnotvar = $true) & (axvarshift = $true) & (hoasinduction_lem3b_gthm = $true) & (pushprop = $true) & ! [X265 : d_subst,X266 : d_subst] : ((X265 = X266) | ((d2subst @ X266) != (d2subst @ X265))) & (ulamvarind = $true) & (substmonoid_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (pushprop_lem2v2_lthm = $true) & ((shinj = $true) <=> ! [X328 : term,X329 : term] : ((X328 = X329) | ((sub @ X329 @ sh) != (sub @ X328 @ sh)))) & ((axshiftcons = $true) <=> ! [X117 : term,X118 : subst] : ((comp @ sh @ (push @ X117 @ X118)) = X118)) & (hoasapinj1_gthm = $true) & ((var @ (d2term @ d_one)) != $true) & (hoasinduction_lem1_lthm = $true) & ((sP39 = $true) <=> (hoasinduction_lem3v2 = $true)) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X124 : term] : ? [X125 : subst > term > term] : ! [X126 : term,X127 : subst] : ((sub @ X124 @ (push @ X126 @ X127)) = (X125 @ X127 @ X126))) & ((d2subst @ d_id) = id) & (pushprop_lem1v2_gthm = $true) & (! [X529 : term] : ? [X530 : subst > term > term] : ((X530 @ sh @ one) = (sub @ X529 @ (push @ one @ sh))) <=> (hoasinduction_lem3b = $true)) & ((sP35 = $true) <=> (hoaslaminj_lthm = $true)) & (! [X404 : subst,X405 : subst > term > term,X406 : term,X407 : subst > term > term] : (? [X411 : subst,X412 : subst,X413 : term] : ((X405 @ (comp @ X412 @ X411) @ (sub @ X413 @ X411)) != (sub @ (X405 @ X412 @ X413) @ X411)) | ((lam @ (X407 @ sh @ one)) != (lam @ (X405 @ sh @ one))) | ? [X408 : term,X409 : subst,X410 : subst] : ((X407 @ (comp @ X409 @ X410) @ (sub @ X408 @ X410)) != (sub @ (X407 @ X409 @ X408) @ X410)) | ((X407 @ X404 @ X406) = (X405 @ X404 @ X406))) <=> (hoaslaminj = $true)) & (hoaslamnotap_gthm = $true) & ((substmonoid_lthm = $true) <=> ($true = sP33)) & (! [X48 : term,X49 : term,X50 : term,X51 : term] : (((ap @ X49 @ X48) != (ap @ X50 @ X51)) | (X48 = X51)) <=> (apinj2 = $true)) & (hoasinduction_lem2_gthm = $true) & (pushprop_lem3v2 = $true) & (pushprop_lem1_gthm = $true) & ((hoasapinj1_lthm = $true) <=> ($true = sP32)) & ((($true = sP30) | ? [X469 : term] : ((sub @ X469 @ id) != X469) | ? [X465 : term] : ! [X466 : subst > term > term] : ? [X467 : subst,X468 : term] : ((sub @ X465 @ (push @ X468 @ X467)) != (X466 @ X467 @ X468))) <=> (hoasinduction_lem3v2a_lthm = $true)) & ((? [X151 : subst,X152 : term] : ((comp @ sh @ (push @ X152 @ X151)) != X151) | ? [X149 : term,X150 : subst] : ((sub @ one @ (push @ X149 @ X150)) != X149) | ! [X153 : term,X154 : term > $o,X155 : subst,X156 : term,X157 : term > $o] : (((X157 @ (sub @ X153 @ (push @ X156 @ X155))) = $true) | ($true != (X154 @ X153)))) <=> (pushprop_lem1_lthm = $true)) & ((($true = sP27) | ($true = sP28) | ? [X81 : term] : ((sub @ X81 @ id) != X81)) <=> (hoasinduction_lem3a_lthm = $true)) & (hoasinduction_lem1v2 = $true) & (! [X399 : subst,X400 : term > $o,X401 : term > $o,X402 : term] : (? [X403 : term] : ((X400 @ (sub @ X403 @ (push @ X402 @ X399))) != (X401 @ X403)) | ($true = (X401 @ one)) | ($true != (X400 @ X402))) <=> (pushprop_lem1v2 = $true)) & (lamnotap != $true) & (hoasapnotvar_gthm = $true) & (! [X449 : subst > term > subst > $o] : ? [X450 : term > $o] : ! [X451 : term] : ((X449 @ id @ X451 @ id) = (X450 @ X451)) <=> (hoasinduction_lem0_lthm = $true)) & ((d2subst @ d_id) = sh) & ((pushprop_lem1v2_lthm = $true) <=> (! [X286 : term,X287 : subst,X288 : term > $o,X289 : term > $o] : (? [X290 : term] : ((X288 @ (sub @ X290 @ (push @ X286 @ X287))) != (X289 @ X290)) | ((X289 @ one) = $true) | ($true != (X288 @ X286))) | ? [X284 : term,X285 : subst] : ((sub @ one @ (push @ X284 @ X285)) != X284))) & (hoasinduction_lem1_gthm = $true) & (pushprop_lem0_gthm = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & ((axvarid = $true) <=> ! [X236 : term] : ((sub @ X236 @ id) = X236)) & ((sP24 = $true) <=> (hoasinduction_lem3v2a = $true)) & ((hoasapinj1 = $true) <=> ! [X486 : term,X487 : term,X488 : term,X489 : term] : (((ap @ (sub @ X489 @ id) @ X486) != (ap @ (sub @ X488 @ id) @ X487)) | (X488 = X489))) & (pushprop_gthm = $true) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & ((axscons = $true) <=> ! [X267 : subst] : ((push @ (sub @ one @ X267) @ (comp @ sh @ X267)) = X267)) & ((hoasinduction = $true) <=> ($true = sP22)) & (pushprop_lem2v2 = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X330 : term,X331 : subst > term > subst > $o] : (((X331 @ id @ X330 @ id) = $true) | ((sP17 @ X331) = $true) | ((sP16 @ X331) = $true))) & (hoasinduction_lem3_gthm = $true) & ((termmset = $true) <=> ! [X394 : term] : ((sub @ X394 @ id) = X394)) & ! [X531 : d_term] : (d_one = X531) & (ulamvarsh = $true) & (hoasapinj2_gthm = $true) & (axmap = $true) & ((sP15 = $true) <=> (hoasinduction_lem3 = $true)) & ((! [X254 : term] : ((sub @ X254 @ id) = X254) | ? [X253 : term] : ((sub @ X253 @ id) != X253)) <=> (termmset_lthm = $true)) & ((pushprop_lem1 = $true) <=> ! [X275 : term,X276 : term,X277 : term > $o,X278 : subst,X279 : term > $o] : (((X279 @ X276) != $true) | ((X277 @ (sub @ X276 @ (push @ X275 @ X278))) = $true))) & ((axvarcons = $true) <=> ! [X77 : subst,X78 : term] : ((sub @ one @ (push @ X78 @ X77)) = X78)) & ((hoasinduction_lthm_3 = $true) <=> (($true = sP11) | ($true = sP9) | ? [X357 : term] : ((sub @ X357 @ id) != X357) | ? [X347 : subst > term > subst > $o] : ! [X348 : term > $o] : ? [X349 : term] : ((X347 @ id @ X349 @ id) != (X348 @ X349)) | (sP10 = $true))) & (pushprop_lthm = $true) & (! [X528 : subst] : ((comp @ id @ X528) = X528) <=> (axidl = $true)) & ((hoasinduction_lem3aa = $true) <=> (sP1 = $true)) & (hoaslaminj_gthm = $true) & ((hoasinduction_lem0 = $true) <=> ! [X525 : subst > term > subst > $o] : ? [X526 : term > $o] : ! [X527 : term] : ((X525 @ id @ X527 @ id) = (X526 @ X527))) & ! [X484 : subst] : ? [X485 : d_subst] : ((d2subst @ X485) = X484)),
% 15.02/3.54 inference(definition_folding,[status(thm)],[f13,f125,f124,f123,f122,f121,f120,f119,f118,f117,f116,f115,f114,f113,f112,f111,f110,f109,f108,f107,f106,f105,f104,f103,f102,f101,f100,f99,f98,f97,f96,f95,f94,f93,f92,f91,f90,f89,f88,f87,f86,f85,f84,f83,f82,f81,f80,f79,f78,f77,f76,f75,f74,f73,f72,f71,f70,f69,f68,f67,f66,f65,f64,f63,f62,f61,f60,f59,f58,f57,f56,f55,f54,f53,f52,f51,f50,f49,f48,f47,f46,f45,f44,f43,f42,f41,f40,f39,f38,f37,f36,f35,f34,f33,f32,f31,f30,f29,f28,f27,f26,f25,f24,f23,f22,f21,f20,f19,f18,f17,f16])).
% 15.02/3.54 thf(f16,plain,(
% 15.02/3.54 ! [X498 : subst > term > subst > $o] : (($true = (sP0 @ X498)) <=> ? [X501 : subst > term > term] : (! [X505 : term] : (($true != (X498 @ id @ X505 @ id)) | ($true = (X498 @ id @ (X501 @ id @ X505) @ id))) & ($true != (X498 @ id @ (lam @ (X501 @ sh @ one)) @ id)) & ! [X502 : subst,X503 : subst,X504 : term] : ((X501 @ (comp @ X502 @ X503) @ (sub @ X504 @ X503)) = (sub @ (X501 @ X502 @ X504) @ X503))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f17,plain,(
% 15.02/3.54 (sP1 = $true) <=> ! [X498 : subst > term > subst > $o,X499 : term] : (($true = (sP0 @ X498)) | ? [X500 : term] : (($true != (X498 @ id @ (sub @ X499 @ (push @ X500 @ id)) @ id)) & ($true = (X498 @ id @ X500 @ id))) | ($true = (X498 @ id @ (lam @ (sub @ X499 @ (push @ one @ sh))) @ id)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f18,plain,(
% 15.02/3.54 ! [X358 : subst > term > subst > $o] : (($true = (sP2 @ X358)) <=> ! [X362 : subst > term > term] : (? [X363 : term] : (((X358 @ id @ (X362 @ id @ X363) @ id) != $true) & ((X358 @ id @ X363 @ id) = $true)) | ($true = (X358 @ id @ (lam @ (X362 @ sh @ one)) @ id)) | ? [X364 : subst,X365 : subst,X366 : term] : ((sub @ (X362 @ X364 @ X366) @ X365) != (X362 @ (comp @ X364 @ X365) @ (sub @ X366 @ X365)))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f19,plain,(
% 15.02/3.54 ! [X369 : subst > term > subst > $o] : (((sP3 @ X369) = $true) <=> ? [X380 : subst > term > term] : (! [X381 : term] : (($true != (X369 @ id @ X381 @ id)) | ((X369 @ id @ (X380 @ id @ X381) @ id) = $true)) & ! [X382 : subst,X383 : term,X384 : subst] : ((X380 @ (comp @ X382 @ X384) @ (sub @ X383 @ X384)) = (sub @ (X380 @ X382 @ X383) @ X384)) & ($true != (X369 @ id @ (lam @ (X380 @ sh @ one)) @ id))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f20,plain,(
% 15.02/3.54 ! [X369 : subst > term > subst > $o] : (((sP4 @ X369) = $true) <=> ? [X374 : term,X375 : term] : (((X369 @ id @ X375 @ id) = $true) & ($true = (X369 @ id @ X374 @ id)) & ((X369 @ id @ (ap @ (sub @ X374 @ id) @ X375) @ id) != $true)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f21,plain,(
% 15.02/3.54 ! [X369 : subst > term > subst > $o] : (($true = (sP5 @ X369)) <=> ? [X385 : term] : (($true != (X369 @ id @ X385 @ id)) & ($true = (var @ (sub @ X385 @ id)))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f22,plain,(
% 15.02/3.54 ! [X369 : subst > term > subst > $o] : (($true = (sP6 @ X369)) <=> ? [X370 : term,X371 : subst,X372 : subst,X373 : subst] : (($true != (X369 @ X373 @ X370 @ (comp @ X372 @ X371))) & ($true = (X369 @ (comp @ X373 @ X372) @ (sub @ X370 @ X372) @ X371))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f23,plain,(
% 15.02/3.54 ! [X351 : term > $o] : (($true = (sP7 @ X351)) <=> ! [X353 : term,X354 : term] : (((X351 @ X353) != $true) | ($true = (X351 @ (ap @ X354 @ X353))) | ($true != (X351 @ X354))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f24,plain,(
% 15.02/3.54 ! [X351 : term > $o] : (($true = (sP8 @ X351)) <=> ! [X355 : term] : (($true = (X351 @ (lam @ X355))) | ? [X356 : term] : (((X351 @ (sub @ X355 @ (push @ X356 @ id))) != $true) & ((X351 @ X356) = $true))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f25,plain,(
% 15.02/3.54 ($true = sP9) <=> ! [X368 : term,X369 : subst > term > subst > $o] : (((sP4 @ X369) = $true) | ? [X376 : subst,X377 : subst,X378 : subst,X379 : term] : (((X369 @ X378 @ X379 @ (comp @ X376 @ X377)) = $true) & ((X369 @ (comp @ X378 @ X376) @ (sub @ X379 @ X376) @ X377) != $true)) | ((sP3 @ X369) = $true) | ($true = (sP6 @ X369)) | ($true = (X369 @ id @ X368 @ id)) | ($true = (sP5 @ X369)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f26,plain,(
% 15.02/3.54 (sP10 = $true) <=> ? [X358 : subst > term > subst > $o,X359 : term,X360 : term > $o] : (($true != (X360 @ (lam @ X359))) & ! [X361 : term] : ((X360 @ X361) = (X358 @ id @ X361 @ id)) & ! [X367 : term] : (((X360 @ X367) != $true) | ($true = (X360 @ (sub @ X359 @ (push @ X367 @ id))))) & ($true = (sP2 @ X358)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f27,plain,(
% 15.02/3.54 ($true = sP11) <=> ? [X350 : term,X351 : term > $o] : (($true != (X351 @ X350)) & ($true = (sP7 @ X351)) & ! [X352 : term] : (((X351 @ X352) = $true) | ((var @ X352) != $true)) & ($true = (sP8 @ X351)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f28,plain,(
% 15.02/3.54 ! [X33 : subst > term > subst > $o] : (((sP12 @ X33) = $true) <=> ? [X42 : subst > term > term] : (((X33 @ id @ (lam @ (X42 @ sh @ one)) @ id) != $true) & ! [X43 : term] : (($true != (X33 @ id @ X43 @ id)) | ((X33 @ id @ (X42 @ id @ X43) @ id) = $true)) & ! [X44 : term,X45 : subst,X46 : subst] : ((X42 @ (comp @ X46 @ X45) @ (sub @ X44 @ X45)) = (sub @ (X42 @ X46 @ X44) @ X45))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f29,plain,(
% 15.02/3.54 ! [X33 : subst > term > subst > $o] : (($true = (sP13 @ X33)) <=> ? [X34 : term,X35 : subst,X36 : subst,X37 : subst] : (((X33 @ X36 @ X34 @ (comp @ X37 @ X35)) != $true) & ((X33 @ (comp @ X36 @ X37) @ (sub @ X34 @ X37) @ X35) = $true)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f30,plain,(
% 15.02/3.54 ! [X32 : term,X33 : subst > term > subst > $o] : (((sP14 @ X33 @ X32) = $true) <=> ? [X47 : term] : (((X33 @ id @ (sub @ X32 @ (push @ X47 @ id)) @ id) != $true) & ($true = (X33 @ id @ X47 @ id))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f31,plain,(
% 15.02/3.54 (sP15 = $true) <=> ! [X32 : term,X33 : subst > term > subst > $o] : (((sP12 @ X33) = $true) | ? [X38 : subst,X39 : subst,X40 : subst,X41 : term] : (($true != (X33 @ (comp @ X39 @ X40) @ (sub @ X41 @ X40) @ X38)) & ($true = (X33 @ X39 @ X41 @ (comp @ X40 @ X38)))) | ($true = (X33 @ id @ (lam @ X32) @ id)) | ((sP14 @ X33 @ X32) = $true) | ($true = (sP13 @ X33)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f32,plain,(
% 15.02/3.54 ! [X331 : subst > term > subst > $o] : (((sP16 @ X331) = $true) <=> ? [X332 : subst > term > term] : (($true != (X331 @ id @ (lam @ (X332 @ sh @ one)) @ id)) & ! [X333 : term] : (((X331 @ id @ X333 @ id) != $true) | ((X331 @ id @ (X332 @ id @ X333) @ id) = $true)) & ! [X334 : subst,X335 : subst,X336 : term] : ((sub @ (X332 @ X335 @ X336) @ X334) = (X332 @ (comp @ X335 @ X334) @ (sub @ X336 @ X334)))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f33,plain,(
% 15.02/3.54 ! [X331 : subst > term > subst > $o] : (((sP17 @ X331) = $true) <=> ? [X337 : term,X338 : term] : (((X331 @ id @ (ap @ (sub @ X337 @ id) @ X338) @ id) != $true) & ((X331 @ id @ X338 @ id) = $true) & ((X331 @ id @ X337 @ id) = $true)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f34,plain,(
% 15.02/3.54 ! [X293 : subst > term > subst > $o] : (($true = (sP18 @ X293)) <=> ? [X294 : subst > term > term] : (($true != (X293 @ id @ (lam @ (X294 @ sh @ one)) @ id)) & ! [X298 : term] : (($true != (X293 @ id @ X298 @ id)) | ($true = (X293 @ id @ (X294 @ id @ X298) @ id))) & ! [X295 : subst,X296 : term,X297 : subst] : ((X294 @ (comp @ X295 @ X297) @ (sub @ X296 @ X297)) = (sub @ (X294 @ X295 @ X296) @ X297))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f35,plain,(
% 15.02/3.54 ! [X293 : subst > term > subst > $o] : (($true = (sP19 @ X293)) <=> ? [X304 : term,X305 : term] : (($true != (X293 @ id @ (ap @ (sub @ X304 @ id) @ X305) @ id)) & ($true = (X293 @ id @ X305 @ id)) & ($true = (X293 @ id @ X304 @ id))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f36,plain,(
% 15.02/3.54 ! [X293 : subst > term > subst > $o] : (($true = (sP20 @ X293)) <=> ? [X299 : subst,X300 : subst,X301 : term,X302 : subst] : (($true != (X293 @ (comp @ X302 @ X300) @ (sub @ X301 @ X300) @ X299)) & ((X293 @ X302 @ X301 @ (comp @ X300 @ X299)) = $true)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f37,plain,(
% 15.02/3.54 ! [X293 : subst > term > subst > $o] : (((sP21 @ X293) = $true) <=> ? [X303 : term] : (($true = (var @ (sub @ X303 @ id))) & ((X293 @ id @ X303 @ id) != $true)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f38,plain,(
% 15.02/3.54 ($true = sP22) <=> ! [X292 : term,X293 : subst > term > subst > $o] : (? [X306 : term,X307 : subst,X308 : subst,X309 : subst] : (($true = (X293 @ (comp @ X308 @ X307) @ (sub @ X306 @ X307) @ X309)) & ((X293 @ X308 @ X306 @ (comp @ X307 @ X309)) != $true)) | ((sP21 @ X293) = $true) | ((X293 @ id @ X292 @ id) = $true) | ($true = (sP19 @ X293)) | ($true = (sP18 @ X293)) | ($true = (sP20 @ X293)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f39,plain,(
% 15.02/3.54 ! [X159 : subst > term > subst > $o] : (((sP23 @ X159) = $true) <=> ? [X162 : subst > term > term] : (! [X163 : term] : (($true != (X159 @ id @ X163 @ id)) | ($true = (X159 @ id @ (X162 @ id @ X163) @ id))) & ((X159 @ id @ (lam @ (X162 @ sh @ one)) @ id) != $true) & ! [X164 : subst,X165 : term,X166 : subst] : ((sub @ (X162 @ X166 @ X165) @ X164) = (X162 @ (comp @ X166 @ X164) @ (sub @ X165 @ X164)))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f40,plain,(
% 15.02/3.54 (sP24 = $true) <=> ! [X158 : term > $o,X159 : subst > term > subst > $o,X160 : term] : (? [X167 : term] : (($true != (X158 @ (sub @ X160 @ (push @ X167 @ id)))) & ((X158 @ X167) = $true)) | ? [X161 : term] : ((X158 @ X161) != (X159 @ id @ X161 @ id)) | ($true = (X158 @ (lam @ X160))) | ((sP23 @ X159) = $true))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f41,plain,(
% 15.02/3.54 ! [X82 : subst > term > subst > $o] : (($true = (sP25 @ X82)) <=> ! [X84 : subst > term > term] : (? [X85 : term,X86 : subst,X87 : subst] : ((sub @ (X84 @ X87 @ X85) @ X86) != (X84 @ (comp @ X87 @ X86) @ (sub @ X85 @ X86))) | ($true = (X82 @ id @ (lam @ (X84 @ sh @ one)) @ id)) | ? [X88 : term] : (((X82 @ id @ (X84 @ id @ X88) @ id) != $true) & ($true = (X82 @ id @ X88 @ id)))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f42,plain,(
% 15.02/3.54 ! [X90 : subst > term > subst > $o] : (($true = (sP26 @ X90)) <=> ? [X92 : subst > term > term] : (! [X94 : term,X95 : subst,X96 : subst] : ((sub @ (X92 @ X96 @ X94) @ X95) = (X92 @ (comp @ X96 @ X95) @ (sub @ X94 @ X95))) & ! [X93 : term] : (($true = (X90 @ id @ (X92 @ id @ X93) @ id)) | ($true != (X90 @ id @ X93 @ id))) & ($true != (X90 @ id @ (lam @ (X92 @ sh @ one)) @ id))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f43,plain,(
% 15.02/3.54 ($true = sP27) <=> ! [X90 : subst > term > subst > $o,X91 : term] : (? [X97 : term] : (($true = (X90 @ id @ X97 @ id)) & ($true != (X90 @ id @ (sub @ X91 @ (push @ X97 @ id)) @ id))) | ((X90 @ id @ (lam @ X91) @ id) = $true) | ($true = (sP26 @ X90)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f44,plain,(
% 15.02/3.54 ($true = sP28) <=> ? [X82 : subst > term > subst > $o,X83 : term] : (((X82 @ id @ (lam @ (sub @ X83 @ (push @ one @ sh))) @ id) != $true) & ! [X89 : term] : (($true = (X82 @ id @ (sub @ X83 @ (push @ X89 @ id)) @ id)) | ((X82 @ id @ X89 @ id) != $true)) & ($true = (sP25 @ X82)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f45,plain,(
% 15.02/3.54 ! [X470 : subst > term > subst > $o] : (($true = (sP29 @ X470)) <=> ? [X473 : subst > term > term] : (! [X475 : subst,X476 : subst,X477 : term] : ((X473 @ (comp @ X476 @ X475) @ (sub @ X477 @ X475)) = (sub @ (X473 @ X476 @ X477) @ X475)) & ((X470 @ id @ (lam @ (X473 @ sh @ one)) @ id) != $true) & ! [X474 : term] : (((X470 @ id @ X474 @ id) != $true) | ((X470 @ id @ (X473 @ id @ X474) @ id) = $true))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f46,plain,(
% 15.02/3.54 ($true = sP30) <=> ! [X470 : subst > term > subst > $o,X471 : term,X472 : term > $o] : (($true = (sP29 @ X470)) | ? [X479 : term] : (((X472 @ (sub @ X471 @ (push @ X479 @ id))) != $true) & ($true = (X472 @ X479))) | ? [X478 : term] : ((X470 @ id @ X478 @ id) != (X472 @ X478)) | ((X472 @ (lam @ X471)) = $true))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f47,plain,(
% 15.02/3.54 (sP31 = $true) <=> ! [X73 : term,X74 : term,X75 : term,X76 : term] : ((X73 = X74) | ((ap @ (sub @ X74 @ id) @ X76) != (ap @ (sub @ X73 @ id) @ X75)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f48,plain,(
% 15.02/3.54 ($true = sP32) <=> ((sP31 = $true) | ? [X69 : term,X70 : term,X71 : term,X72 : term] : (((ap @ X69 @ X70) = (ap @ X71 @ X72)) & (X69 != X71)) | ? [X68 : term] : ((sub @ X68 @ id) != X68))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f49,plain,(
% 15.02/3.54 ($true = sP33) <=> (? [X396 : subst] : ((comp @ X396 @ id) != X396) | ? [X395 : subst] : ((comp @ id @ X395) != X395) | (! [X397 : subst] : ((comp @ id @ X397) = X397) & ! [X398 : subst] : ((comp @ X398 @ id) = X398)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f50,plain,(
% 15.02/3.54 (sP34 = $true) <=> ! [X243 : subst,X244 : term,X245 : subst > term > term,X246 : subst > term > term] : (((lam @ (X246 @ sh @ one)) != (lam @ (X245 @ sh @ one))) | ((X246 @ X243 @ X244) = (X245 @ X243 @ X244)) | ? [X250 : subst,X251 : term,X252 : subst] : ((X245 @ (comp @ X250 @ X252) @ (sub @ X251 @ X252)) != (sub @ (X245 @ X250 @ X251) @ X252)) | ? [X247 : term,X248 : subst,X249 : subst] : ((sub @ (X246 @ X248 @ X247) @ X249) != (X246 @ (comp @ X248 @ X249) @ (sub @ X247 @ X249))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f51,plain,(
% 15.02/3.54 (sP35 = $true) <=> (? [X237 : subst,X238 : term] : ((sub @ one @ (push @ X238 @ X237)) != X238) | (sP34 = $true) | ? [X239 : term,X240 : subst] : ((comp @ sh @ (push @ X239 @ X240)) != X240) | ? [X241 : term,X242 : term] : ((X241 != X242) & ((lam @ X241) = (lam @ X242))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f52,plain,(
% 15.02/3.54 ! [X311 : subst > term > subst > $o] : (((sP36 @ X311) = $true) <=> ? [X323 : subst > term > term] : (((X311 @ id @ (lam @ (X323 @ sh @ one)) @ id) != $true) & ! [X325 : term,X326 : subst,X327 : subst] : ((X323 @ (comp @ X327 @ X326) @ (sub @ X325 @ X326)) = (sub @ (X323 @ X327 @ X325) @ X326)) & ! [X324 : term] : (((X311 @ id @ (X323 @ id @ X324) @ id) = $true) | ($true != (X311 @ id @ X324 @ id)))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f53,plain,(
% 15.02/3.54 ! [X311 : subst > term > subst > $o] : (((sP37 @ X311) = $true) <=> ? [X319 : subst,X320 : subst,X321 : term,X322 : subst] : (((X311 @ X322 @ X321 @ (comp @ X319 @ X320)) = $true) & ((X311 @ (comp @ X322 @ X319) @ (sub @ X321 @ X319) @ X320) != $true)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f54,plain,(
% 15.02/3.54 ! [X312 : term > $o,X310 : term] : (($true = (sP38 @ X310 @ X312)) <=> ? [X314 : term] : (((X312 @ X314) = $true) & ((X312 @ (sub @ X310 @ (push @ X314 @ id))) != $true)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f55,plain,(
% 15.02/3.54 (sP39 = $true) <=> ! [X310 : term,X311 : subst > term > subst > $o,X312 : term > $o] : (((sP36 @ X311) = $true) | ? [X315 : subst,X316 : subst,X317 : subst,X318 : term] : (($true != (X311 @ X316 @ X318 @ (comp @ X317 @ X315))) & ((X311 @ (comp @ X316 @ X317) @ (sub @ X318 @ X317) @ X315) = $true)) | ($true = (sP38 @ X310 @ X312)) | ((X312 @ (lam @ X310)) = $true) | ((sP37 @ X311) = $true) | ? [X313 : term] : ((X312 @ X313) != (X311 @ id @ X313 @ id)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f56,plain,(
% 15.02/3.54 (sP40 = $true) <=> ! [X536 : term,X537 : term,X538 : term,X539 : term] : (((ap @ (sub @ X536 @ id) @ X539) != (ap @ (sub @ X537 @ id) @ X538)) | (X538 = X539))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f57,plain,(
% 15.02/3.54 (sP41 = $true) <=> (? [X532 : term,X533 : term,X534 : term,X535 : term] : (((ap @ X532 @ X534) = (ap @ X535 @ X533)) & (X533 != X534)) | (sP40 = $true))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f58,plain,(
% 15.02/3.54 ! [X491 : subst > term > subst > $o] : (($true = (sP42 @ X491)) <=> ? [X493 : subst > term > term] : (! [X497 : term] : (((X491 @ id @ (X493 @ id @ X497) @ id) = $true) | ((X491 @ id @ X497 @ id) != $true)) & ((X491 @ id @ (lam @ (X493 @ sh @ one)) @ id) != $true) & ! [X494 : subst,X495 : subst,X496 : term] : ((X493 @ (comp @ X494 @ X495) @ (sub @ X496 @ X495)) = (sub @ (X493 @ X494 @ X496) @ X495))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f59,plain,(
% 15.02/3.54 ($true = sP43) <=> ! [X490 : term,X491 : subst > term > subst > $o] : (($true = (sP42 @ X491)) | ? [X492 : term] : (((X491 @ id @ (sub @ X490 @ (push @ X492 @ id)) @ id) != $true) & ((X491 @ id @ X492 @ id) = $true)) | ($true = (X491 @ id @ (lam @ X490) @ id)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f60,plain,(
% 15.02/3.54 ! [X223 : subst > term > subst > $o] : (((sP44 @ X223) = $true) <=> ? [X225 : term,X226 : subst > term > term] : (! [X233 : term] : (((X223 @ id @ (X226 @ id @ X233) @ id) = $true) | ($true != (X223 @ id @ X233 @ id))) & ! [X227 : subst,X228 : term,X229 : subst] : ((sub @ (sub @ X225 @ (push @ X228 @ X229)) @ X227) = (sub @ (X226 @ X229 @ X228) @ X227)) & ($true != (X223 @ id @ (lam @ (X226 @ sh @ one)) @ id)) & ! [X230 : subst,X231 : term,X232 : subst] : ((sub @ X225 @ (push @ (sub @ X231 @ X232) @ (comp @ X230 @ X232))) = (X226 @ (comp @ X230 @ X232) @ (sub @ X231 @ X232)))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f61,plain,(
% 15.02/3.54 ($true = sP45) <=> ! [X222 : term,X223 : subst > term > subst > $o] : (((sP44 @ X223) = $true) | ? [X224 : term] : (((X223 @ id @ X224 @ id) = $true) & ($true != (X223 @ id @ (sub @ X222 @ (push @ X224 @ id)) @ id))) | ($true = (X223 @ id @ (lam @ (sub @ X222 @ (push @ one @ sh))) @ id)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f62,plain,(
% 15.02/3.54 ! [X55 : subst > term > subst > $o] : (((sP46 @ X55) = $true) <=> ? [X61 : term,X62 : term] : (((X55 @ id @ X62 @ id) = $true) & ((X55 @ id @ (ap @ (sub @ X62 @ id) @ X61) @ id) != $true) & ($true = (X55 @ id @ X61 @ id))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f63,plain,(
% 15.02/3.54 ! [X55 : subst > term > subst > $o] : (((sP47 @ X55) = $true) <=> ? [X57 : subst,X58 : term,X59 : subst,X60 : subst] : (((X55 @ (comp @ X60 @ X57) @ (sub @ X58 @ X57) @ X59) != $true) & ($true = (X55 @ X60 @ X58 @ (comp @ X57 @ X59)))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f64,plain,(
% 15.02/3.54 ($true = sP48) <=> ! [X53 : term,X54 : term > $o,X55 : subst > term > subst > $o,X56 : term] : (? [X64 : subst,X65 : term,X66 : subst,X67 : subst] : (((X55 @ X66 @ X65 @ (comp @ X67 @ X64)) != $true) & ((X55 @ (comp @ X66 @ X67) @ (sub @ X65 @ X67) @ X64) = $true)) | ((sP46 @ X55) = $true) | ((X54 @ (ap @ X53 @ X56)) = $true) | ((X54 @ X53) != $true) | ? [X63 : term] : ((X55 @ id @ X63 @ id) != (X54 @ X63)) | ((X54 @ X56) != $true) | ((sP47 @ X55) = $true))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f65,plain,(
% 15.02/3.54 ! [X434 : subst > term > subst > $o] : (((sP49 @ X434) = $true) <=> ? [X444 : subst > term > term] : (! [X445 : term] : (((X434 @ id @ (X444 @ id @ X445) @ id) = $true) | ((X434 @ id @ X445 @ id) != $true)) & ((X434 @ id @ (lam @ (X444 @ sh @ one)) @ id) != $true) & ! [X446 : subst,X447 : term,X448 : subst] : ((X444 @ (comp @ X448 @ X446) @ (sub @ X447 @ X446)) = (sub @ (X444 @ X448 @ X447) @ X446))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f66,plain,(
% 15.02/3.54 ! [X434 : subst > term > subst > $o,X433 : term] : (($true = (sP50 @ X433 @ X434)) <=> ? [X435 : term] : (($true = (X434 @ id @ X435 @ id)) & ((X434 @ id @ (sub @ X433 @ (push @ X435 @ id)) @ id) != $true)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f67,plain,(
% 15.02/3.54 ! [X434 : subst > term > subst > $o] : (($true = (sP51 @ X434)) <=> ? [X436 : subst,X437 : term,X438 : subst,X439 : subst] : (($true != (X434 @ (comp @ X436 @ X439) @ (sub @ X437 @ X439) @ X438)) & ((X434 @ X436 @ X437 @ (comp @ X439 @ X438)) = $true)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f68,plain,(
% 15.02/3.54 ! [X425 : subst > term > subst > $o] : (((sP52 @ X425) = $true) <=> ! [X427 : subst > term > term] : (? [X428 : subst,X429 : term,X430 : subst] : ((X427 @ (comp @ X430 @ X428) @ (sub @ X429 @ X428)) != (sub @ (X427 @ X430 @ X429) @ X428)) | ($true = (X425 @ id @ (lam @ (X427 @ sh @ one)) @ id)) | ? [X431 : term] : (($true = (X425 @ id @ X431 @ id)) & ((X425 @ id @ (X427 @ id @ X431) @ id) != $true))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f69,plain,(
% 15.02/3.54 ($true = sP53) <=> ! [X433 : term,X434 : subst > term > subst > $o] : (((sP49 @ X434) = $true) | ((X434 @ id @ (lam @ X433) @ id) = $true) | ? [X440 : subst,X441 : term,X442 : subst,X443 : subst] : (((X434 @ (comp @ X442 @ X440) @ (sub @ X441 @ X440) @ X443) = $true) & ((X434 @ X442 @ X441 @ (comp @ X440 @ X443)) != $true)) | ($true = (sP51 @ X434)) | ($true = (sP50 @ X433 @ X434)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f70,plain,(
% 15.02/3.54 (sP54 = $true) <=> ? [X425 : subst > term > subst > $o,X426 : term] : (($true != (X425 @ id @ (lam @ (sub @ X426 @ (push @ one @ sh))) @ id)) & ! [X432 : term] : (($true = (X425 @ id @ (sub @ X426 @ (push @ X432 @ id)) @ id)) | ((X425 @ id @ X432 @ id) != $true)) & ((sP52 @ X425) = $true))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f71,plain,(
% 15.02/3.54 ! [X518 : term > $o] : (((sP55 @ X518) = $true) <=> ? [X520 : term] : (! [X521 : term] : (($true != (X518 @ X521)) | ($true = (X518 @ (sub @ X520 @ (push @ X521 @ id))))) & ((X518 @ (lam @ X520)) != $true)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f72,plain,(
% 15.02/3.54 ! [X518 : term > $o] : (((sP56 @ X518) = $true) <=> ? [X522 : term,X523 : term] : (($true != (X518 @ (ap @ X523 @ X522))) & ((X518 @ X522) = $true) & ((X518 @ X523) = $true)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f73,plain,(
% 15.02/3.54 ! [X512 : term > $o] : (($true = (sP57 @ X512)) <=> ! [X515 : term,X516 : term] : (((X512 @ (ap @ X516 @ X515)) = $true) | ((X512 @ X515) != $true) | ($true != (X512 @ X516))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f74,plain,(
% 15.02/3.54 ! [X512 : term > $o] : (((sP58 @ X512) = $true) <=> ! [X514 : term] : (((X512 @ X514) = $true) | ((var @ X514) != $true)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f75,plain,(
% 15.02/3.54 (sP59 = $true) <=> ! [X517 : subst,X518 : term > $o,X519 : term] : (((sP56 @ X518) = $true) | ($true = (X518 @ (sub @ X519 @ X517))) | ? [X524 : term] : (($true != (X518 @ (sub @ X524 @ X517))) & ((var @ X524) = $true)) | ((sP55 @ X518) = $true))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f76,plain,(
% 15.02/3.54 (sP60 = $true) <=> ? [X511 : term,X512 : term > $o] : (($true = (sP57 @ X512)) & ((X512 @ X511) != $true) & ! [X513 : term] : (($true != (X512 @ X513)) | ((X512 @ (lam @ X513)) = $true)) & ((sP58 @ X512) = $true))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f77,plain,(
% 15.02/3.54 ! [X168 : term > $o] : (($true = (sP61 @ X168)) <=> ! [X172 : term,X173 : term] : (((X168 @ X172) != $true) | ((X168 @ (ap @ X173 @ X172)) = $true) | ($true != (X168 @ X173))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f78,plain,(
% 15.02/3.54 ! [X168 : term > $o] : (((sP62 @ X168) = $true) <=> ! [X170 : term] : (((X168 @ (lam @ X170)) = $true) | ? [X171 : term] : (((X168 @ X171) = $true) & ($true != (X168 @ (sub @ X170 @ (push @ X171 @ id)))))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f79,plain,(
% 15.02/3.54 ! [X177 : subst > term > subst > $o] : (($true = (sP63 @ X177)) <=> ! [X186 : term,X187 : term] : (($true != (X177 @ id @ X187 @ id)) | ($true != (X177 @ id @ X186 @ id)) | ($true = (X177 @ id @ (ap @ (sub @ X187 @ id) @ X186) @ id))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f80,plain,(
% 15.02/3.54 ! [X177 : subst > term > subst > $o] : (($true = (sP64 @ X177)) <=> ! [X178 : subst,X179 : subst,X180 : term,X181 : subst] : (((X177 @ X179 @ X180 @ (comp @ X181 @ X178)) != $true) | ((X177 @ (comp @ X179 @ X181) @ (sub @ X180 @ X181) @ X178) = $true)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f81,plain,(
% 15.02/3.54 ! [X189 : subst > term > subst > $o] : (($true = (sP65 @ X189)) <=> ! [X199 : subst > term > term] : (? [X200 : term,X201 : subst,X202 : subst] : ((sub @ (X199 @ X201 @ X200) @ X202) != (X199 @ (comp @ X201 @ X202) @ (sub @ X200 @ X202))) | ? [X203 : term] : (((X189 @ id @ X203 @ id) = $true) & ((X189 @ id @ (X199 @ id @ X203) @ id) != $true)) | ((X189 @ id @ (lam @ (X199 @ sh @ one)) @ id) = $true)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f82,plain,(
% 15.02/3.54 ! [X189 : subst > term > subst > $o] : (((sP66 @ X189) = $true) <=> ! [X194 : subst,X195 : subst,X196 : term,X197 : subst] : (((X189 @ (comp @ X197 @ X195) @ (sub @ X196 @ X195) @ X194) != $true) | ((X189 @ X197 @ X196 @ (comp @ X195 @ X194)) = $true)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f83,plain,(
% 15.02/3.54 ! [X189 : subst > term > subst > $o] : (($true = (sP67 @ X189)) <=> ! [X190 : subst,X191 : term,X192 : subst,X193 : subst] : (((X189 @ X193 @ X191 @ (comp @ X190 @ X192)) != $true) | ((X189 @ (comp @ X193 @ X190) @ (sub @ X191 @ X190) @ X192) = $true)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f84,plain,(
% 15.02/3.54 ! [X204 : subst > term > subst > $o] : (((sP68 @ X204) = $true) <=> ? [X217 : subst > term > term] : (! [X218 : subst,X219 : term,X220 : subst] : ((sub @ (X217 @ X220 @ X219) @ X218) = (X217 @ (comp @ X220 @ X218) @ (sub @ X219 @ X218))) & ! [X221 : term] : (($true != (X204 @ id @ X221 @ id)) | ((X204 @ id @ (X217 @ id @ X221) @ id) = $true)) & ((X204 @ id @ (lam @ (X217 @ sh @ one)) @ id) != $true)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f85,plain,(
% 15.02/3.54 ! [X204 : subst > term > subst > $o] : (($true = (sP69 @ X204)) <=> ? [X206 : term,X207 : term] : (($true = (X204 @ id @ X206 @ id)) & ($true != (X204 @ id @ (ap @ (sub @ X207 @ id) @ X206) @ id)) & ($true = (X204 @ id @ X207 @ id))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f86,plain,(
% 15.02/3.54 ! [X204 : subst > term > subst > $o] : (($true = (sP70 @ X204)) <=> ? [X212 : subst,X213 : subst,X214 : term,X215 : subst] : (((X204 @ (comp @ X213 @ X212) @ (sub @ X214 @ X212) @ X215) != $true) & ($true = (X204 @ X213 @ X214 @ (comp @ X212 @ X215)))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f87,plain,(
% 15.02/3.54 ! [X204 : subst > term > subst > $o] : (($true = (sP71 @ X204)) <=> ? [X208 : subst,X209 : subst,X210 : subst,X211 : term] : (($true = (X204 @ (comp @ X210 @ X208) @ (sub @ X211 @ X208) @ X209)) & ((X204 @ X210 @ X211 @ (comp @ X208 @ X209)) != $true)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f88,plain,(
% 15.02/3.54 (sP72 = $true) <=> ! [X204 : subst > term > subst > $o,X205 : term] : (? [X216 : term] : (($true = (var @ (sub @ X216 @ id))) & ((X204 @ id @ X216 @ id) != $true)) | ($true = (sP71 @ X204)) | ((sP68 @ X204) = $true) | ($true = (sP70 @ X204)) | ($true = (X204 @ id @ X205 @ id)) | ($true = (sP69 @ X204)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f89,plain,(
% 15.02/3.54 ($true = sP73) <=> ? [X168 : term > $o,X169 : term] : (($true != (X168 @ X169)) & ($true = (sP61 @ X168)) & ! [X174 : term] : (((var @ X174) != $true) | ((X168 @ X174) = $true)) & ((sP62 @ X168) = $true))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f90,plain,(
% 15.02/3.54 (sP74 = $true) <=> ? [X175 : term,X176 : term,X177 : subst > term > subst > $o] : (($true = (X177 @ id @ X175 @ id)) & ! [X182 : subst,X183 : subst,X184 : term,X185 : subst] : (($true = (X177 @ X185 @ X184 @ (comp @ X183 @ X182))) | ($true != (X177 @ (comp @ X185 @ X183) @ (sub @ X184 @ X183) @ X182))) & ($true = (sP63 @ X177)) & ($true = (X177 @ id @ X176 @ id)) & ($true = (sP64 @ X177)) & ((X177 @ id @ (ap @ X175 @ X176) @ id) != $true))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f91,plain,(
% 15.02/3.54 ($true = sP75) <=> ? [X188 : term,X189 : subst > term > subst > $o] : (! [X198 : term] : (((X189 @ id @ (sub @ X188 @ (push @ X198 @ id)) @ id) = $true) | ($true != (X189 @ id @ X198 @ id))) & ($true = (sP67 @ X189)) & ((X189 @ id @ (lam @ X188) @ id) != $true) & ((sP66 @ X189) = $true) & ($true = (sP65 @ X189)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f92,plain,(
% 15.02/3.54 ! [X130 : term > $o] : (((sP76 @ X130) = $true) <=> ! [X134 : term,X135 : term] : (((X130 @ X134) != $true) | ($true != (X130 @ X135)) | ((X130 @ (ap @ X134 @ X135)) = $true)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f93,plain,(
% 15.02/3.54 ! [X129 : subst,X130 : term > $o] : (((sP77 @ X130 @ X129) = $true) <=> ! [X136 : term] : (((var @ X136) != $true) | ($true = (X130 @ (sub @ X136 @ X129)))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f94,plain,(
% 15.02/3.54 ! [X130 : term > $o] : (($true = (sP78 @ X130)) <=> ! [X132 : term] : (? [X133 : term] : (($true != (X130 @ (sub @ X132 @ (push @ X133 @ id)))) & ((X130 @ X133) = $true)) | ((X130 @ (lam @ X132)) = $true)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f95,plain,(
% 15.02/3.54 ! [X138 : term > $o] : (($true = (sP79 @ X138)) <=> ? [X142 : term] : (! [X143 : term] : (((X138 @ X143) != $true) | ((X138 @ (sub @ X142 @ (push @ X143 @ id))) = $true)) & ($true != (X138 @ (lam @ X142)))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f96,plain,(
% 15.02/3.54 ! [X138 : term > $o] : (((sP80 @ X138) = $true) <=> ? [X140 : term,X141 : term] : (((X138 @ X140) = $true) & ((X138 @ (ap @ X140 @ X141)) != $true) & ($true = (X138 @ X141))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f97,plain,(
% 15.02/3.54 (sP81 = $true) <=> ! [X137 : term,X138 : term > $o] : (? [X139 : term] : (((var @ X139) = $true) & ((X138 @ X139) != $true)) | ($true = (sP79 @ X138)) | ((sP80 @ X138) = $true) | ($true = (X138 @ X137)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f98,plain,(
% 15.02/3.54 ($true = sP82) <=> ? [X129 : subst,X130 : term > $o,X131 : term] : (($true = (sP78 @ X130)) & ((sP77 @ X130 @ X129) = $true) & ($true != (X130 @ (sub @ X131 @ X129))) & ((sP76 @ X130) = $true))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f99,plain,(
% 15.02/3.54 ! [X388 : term > $o] : (($true = (sP83 @ X388)) <=> ? [X392 : term] : (((X388 @ (lam @ X392)) != $true) & ! [X393 : term] : (($true != (X388 @ X393)) | ((X388 @ (sub @ X392 @ (push @ X393 @ id))) = $true))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f100,plain,(
% 15.02/3.54 ! [X388 : term > $o] : (($true = (sP84 @ X388)) <=> ? [X390 : term,X391 : term] : (((X388 @ X390) = $true) & ((X388 @ (ap @ X391 @ X390)) != $true) & ($true = (X388 @ X391))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f101,plain,(
% 15.02/3.54 ($true = sP85) <=> ! [X386 : term,X387 : subst,X388 : term > $o] : (($true = (sP83 @ X388)) | ($true = (X388 @ (sub @ X386 @ X387))) | ? [X389 : term] : (($true = (var @ X389)) & ((X388 @ (sub @ X389 @ X387)) != $true)) | ($true = (sP84 @ X388)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f102,plain,(
% 15.02/3.54 ! [X268 : term > $o] : (($true = (sP86 @ X268)) <=> ? [X270 : term] : (! [X271 : term] : (($true = (X268 @ (sub @ X270 @ (push @ X271 @ id)))) | ($true != (X268 @ X271))) & ((X268 @ (lam @ X270)) != $true)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f103,plain,(
% 15.02/3.54 ! [X268 : term > $o] : (($true = (sP87 @ X268)) <=> ? [X272 : term,X273 : term] : (($true = (X268 @ X272)) & ((X268 @ (ap @ X273 @ X272)) != $true) & ((X268 @ X273) = $true)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f104,plain,(
% 15.02/3.54 (sP88 = $true) <=> ! [X268 : term > $o,X269 : term] : (? [X274 : term] : (($true != (X268 @ X274)) & ((var @ X274) = $true)) | ($true = (sP87 @ X268)) | ((X268 @ X269) = $true) | ($true = (sP86 @ X268)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f105,plain,(
% 15.02/3.54 ! [X454 : subst > term > subst > $o] : (($true = (sP89 @ X454)) <=> ? [X463 : term,X464 : term] : (($true = (X454 @ id @ X463 @ id)) & ($true != (X454 @ id @ (ap @ (sub @ X463 @ id) @ X464) @ id)) & ((X454 @ id @ X464 @ id) = $true)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f106,plain,(
% 15.02/3.54 ! [X454 : subst > term > subst > $o] : (($true = (sP90 @ X454)) <=> ? [X459 : subst,X460 : term,X461 : subst,X462 : subst] : (((X454 @ X461 @ X460 @ (comp @ X459 @ X462)) = $true) & ((X454 @ (comp @ X461 @ X459) @ (sub @ X460 @ X459) @ X462) != $true)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f107,plain,(
% 15.02/3.54 ($true = sP91) <=> ! [X452 : term,X453 : term,X454 : subst > term > subst > $o] : (((X454 @ id @ X453 @ id) != $true) | ($true = (sP89 @ X454)) | ((X454 @ id @ X452 @ id) != $true) | ? [X455 : subst,X456 : subst,X457 : term,X458 : subst] : (((X454 @ X458 @ X457 @ (comp @ X455 @ X456)) != $true) & ($true = (X454 @ (comp @ X458 @ X455) @ (sub @ X457 @ X455) @ X456))) | ((X454 @ id @ (ap @ X452 @ X453) @ id) = $true) | ($true = (sP90 @ X454)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f108,plain,(
% 15.02/3.54 ! [X100 : subst > term > subst > $o] : (($true = (sP92 @ X100)) <=> ? [X103 : subst > term > term] : (! [X104 : subst,X105 : subst,X106 : term] : ((X103 @ (comp @ X105 @ X104) @ (sub @ X106 @ X104)) = (sub @ (X103 @ X105 @ X106) @ X104)) & ! [X107 : term] : (((X100 @ id @ X107 @ id) != $true) | ($true = (X100 @ id @ (X103 @ id @ X107) @ id))) & ($true != (X100 @ id @ (lam @ (X103 @ sh @ one)) @ id))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f109,plain,(
% 15.02/3.54 ! [X100 : subst > term > subst > $o] : (((sP93 @ X100) = $true) <=> ? [X108 : subst,X109 : term,X110 : subst,X111 : subst] : (((X100 @ (comp @ X108 @ X110) @ (sub @ X109 @ X110) @ X111) != $true) & ((X100 @ X108 @ X109 @ (comp @ X110 @ X111)) = $true)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f110,plain,(
% 15.02/3.54 ! [X100 : subst > term > subst > $o] : (((sP94 @ X100) = $true) <=> ? [X113 : subst,X114 : subst,X115 : term,X116 : subst] : (($true = (X100 @ (comp @ X114 @ X113) @ (sub @ X115 @ X113) @ X116)) & ($true != (X100 @ X114 @ X115 @ (comp @ X113 @ X116)))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f111,plain,(
% 15.02/3.54 ($true = sP95) <=> ! [X99 : term > $o,X100 : subst > term > subst > $o,X101 : term] : (((X99 @ (lam @ X101)) = $true) | ? [X102 : term] : (((X99 @ (sub @ X101 @ (push @ X102 @ id))) != $true) & ((X99 @ X102) = $true)) | ($true = (sP92 @ X100)) | ((sP94 @ X100) = $true) | ? [X112 : term] : ((X100 @ id @ X112 @ id) != (X99 @ X112)) | ((sP93 @ X100) = $true))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f112,plain,(
% 15.02/3.54 ! [X256 : term > $o] : (((sP96 @ X256) = $true) <=> ? [X258 : term,X259 : term] : (((X256 @ X258) = $true) & ((X256 @ (ap @ X259 @ X258)) != $true) & ($true = (X256 @ X259))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f113,plain,(
% 15.02/3.54 ! [X256 : term > $o] : (((sP97 @ X256) = $true) <=> ? [X260 : term] : (($true != (X256 @ X260)) & ((var @ X260) = $true)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f114,plain,(
% 15.02/3.54 (sP98 = $true) <=> ! [X255 : term,X256 : term > $o] : (((sP96 @ X256) = $true) | ? [X257 : term] : (($true = (X256 @ X257)) & ((X256 @ (lam @ X257)) != $true)) | ((X256 @ X255) = $true) | ((sP97 @ X256) = $true))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f115,plain,(
% 15.02/3.54 ! [X415 : subst > term > subst > $o] : (($true = (sP99 @ X415)) <=> ? [X417 : subst > term > term] : (! [X421 : term] : (($true != (X415 @ id @ X421 @ id)) | ((X415 @ id @ (X417 @ id @ X421) @ id) = $true)) & ((X415 @ id @ (lam @ (X417 @ sh @ one)) @ id) != $true) & ! [X418 : subst,X419 : term,X420 : subst] : ((sub @ (X417 @ X418 @ X419) @ X420) = (X417 @ (comp @ X418 @ X420) @ (sub @ X419 @ X420)))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f116,plain,(
% 15.02/3.54 (sP100 = $true) <=> ! [X414 : term,X415 : subst > term > subst > $o] : (($true = (sP99 @ X415)) | ((X415 @ id @ (lam @ (sub @ X414 @ (push @ one @ sh))) @ id) = $true) | ? [X416 : term] : (((X415 @ id @ X416 @ id) = $true) & ((X415 @ id @ (sub @ X414 @ (push @ X416 @ id)) @ id) != $true)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f117,plain,(
% 15.02/3.54 ! [X21 : subst > term > subst > $o] : (($true = (sP101 @ X21)) <=> ? [X25 : subst > term > term] : (((X21 @ id @ (lam @ (X25 @ sh @ one)) @ id) != $true) & ! [X26 : term] : (((X21 @ id @ X26 @ id) != $true) | ((X21 @ id @ (X25 @ id @ X26) @ id) = $true)) & ! [X27 : term,X28 : subst,X29 : subst] : ((X25 @ (comp @ X28 @ X29) @ (sub @ X27 @ X29)) = (sub @ (X25 @ X28 @ X27) @ X29))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f118,plain,(
% 15.02/3.54 ! [X21 : subst > term > subst > $o] : (($true = (sP102 @ X21)) <=> ? [X23 : term,X24 : term] : (((X21 @ id @ X24 @ id) = $true) & ($true != (X21 @ id @ (ap @ (sub @ X23 @ id) @ X24) @ id)) & ($true = (X21 @ id @ X23 @ id))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f119,plain,(
% 15.02/3.54 ! [X4 : term > $o] : (($true = (sP103 @ X4)) <=> ! [X5 : term,X6 : term] : (((X4 @ X5) != $true) | ((X4 @ X6) != $true) | ($true = (X4 @ (ap @ X5 @ X6)))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f120,plain,(
% 15.02/3.54 ! [X4 : term > $o] : (($true = (sP104 @ X4)) <=> ! [X7 : term] : (($true != (var @ X7)) | ((X4 @ X7) = $true)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f121,plain,(
% 15.02/3.54 ! [X4 : term > $o] : (((sP105 @ X4) = $true) <=> ! [X8 : term] : (((X4 @ (lam @ X8)) = $true) | ? [X9 : term] : (($true != (X4 @ (sub @ X8 @ (push @ X9 @ id)))) & ($true = (X4 @ X9)))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f122,plain,(
% 15.02/3.54 ! [X12 : subst > term > subst > $o] : (((sP106 @ X12) = $true) <=> ! [X15 : subst > term > term] : (? [X16 : term] : (((X12 @ id @ (X15 @ id @ X16) @ id) != $true) & ($true = (X12 @ id @ X16 @ id))) | ($true = (X12 @ id @ (lam @ (X15 @ sh @ one)) @ id)) | ? [X17 : term,X18 : subst,X19 : subst] : ((sub @ (X15 @ X19 @ X17) @ X18) != (X15 @ (comp @ X19 @ X18) @ (sub @ X17 @ X18)))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f123,plain,(
% 15.02/3.54 (sP107 = $true) <=> ! [X21 : subst > term > subst > $o,X22 : term] : (($true = (sP102 @ X21)) | ($true = (X21 @ id @ X22 @ id)) | ($true = (sP101 @ X21)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f124,plain,(
% 15.02/3.54 (sP108 = $true) <=> ? [X11 : term,X12 : subst > term > subst > $o,X13 : term > $o] : (! [X14 : term] : ((X13 @ X14) = (X12 @ id @ X14 @ id)) & ! [X20 : term] : (($true = (X13 @ (sub @ X11 @ (push @ X20 @ id)))) | ((X13 @ X20) != $true)) & ((X13 @ (lam @ X11)) != $true) & ((sP106 @ X12) = $true))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f125,plain,(
% 15.02/3.54 (sP109 = $true) <=> ? [X3 : term,X4 : term > $o] : (((sP105 @ X4) = $true) & ($true = (sP104 @ X4)) & ($true != (X4 @ X3)) & ($true = (sP103 @ X4)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f13,plain,(
% 15.02/3.54 (hoasapnotvar = $true) & (hoasinduction_lem2v2_gthm = $true) & ((apinj1 = $true) <=> ! [X261 : term,X262 : term,X263 : term,X264 : term] : ((X262 = X264) | ((ap @ X264 @ X263) != (ap @ X262 @ X261)))) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (hoaslamnotvar_gthm = $true) & (! [X52 : subst] : ((comp @ X52 @ id) = X52) <=> (axidr = $true)) & (termmset_gthm = $true) & ((? [X11 : term,X12 : subst > term > subst > $o,X13 : term > $o] : (! [X14 : term] : ((X13 @ X14) = (X12 @ id @ X14 @ id)) & ! [X20 : term] : (($true = (X13 @ (sub @ X11 @ (push @ X20 @ id)))) | ((X13 @ X20) != $true)) & ((X13 @ (lam @ X11)) != $true) & ! [X15 : subst > term > term] : (? [X16 : term] : (((X12 @ id @ (X15 @ id @ X16) @ id) != $true) & ($true = (X12 @ id @ X16 @ id))) | ($true = (X12 @ id @ (lam @ (X15 @ sh @ one)) @ id)) | ? [X17 : term,X18 : subst,X19 : subst] : ((sub @ (X15 @ X19 @ X17) @ X18) != (X15 @ (comp @ X19 @ X18) @ (sub @ X17 @ X18))))) | ? [X10 : term] : ((sub @ X10 @ id) != X10) | ? [X0 : subst > term > subst > $o] : ! [X1 : term > $o] : ? [X2 : term] : ((X0 @ id @ X2 @ id) != (X1 @ X2)) | ? [X3 : term,X4 : term > $o] : (! [X8 : term] : (((X4 @ (lam @ X8)) = $true) | ? [X9 : term] : (($true != (X4 @ (sub @ X8 @ (push @ X9 @ id)))) & ($true = (X4 @ X9)))) & ! [X7 : term] : (($true != (var @ X7)) | ((X4 @ X7) = $true)) & ($true != (X4 @ X3)) & ! [X5 : term,X6 : term] : (((X4 @ X5) != $true) | ((X4 @ X6) != $true) | ($true = (X4 @ (ap @ X5 @ X6))))) | ! [X21 : subst > term > subst > $o,X22 : term] : (? [X23 : term,X24 : term] : (((X21 @ id @ X24 @ id) = $true) & ($true != (X21 @ id @ (ap @ (sub @ X23 @ id) @ X24) @ id)) & ($true = (X21 @ id @ X23 @ id))) | ($true = (X21 @ id @ X22 @ id)) | ? [X25 : subst > term > term] : (((X21 @ id @ (lam @ (X25 @ sh @ one)) @ id) != $true) & ! [X26 : term] : (((X21 @ id @ X26 @ id) != $true) | ((X21 @ id @ (X25 @ id @ X26) @ id) = $true)) & ! [X27 : term,X28 : subst,X29 : subst] : ((X25 @ (comp @ X28 @ X29) @ (sub @ X27 @ X29)) = (sub @ (X25 @ X28 @ X27) @ X29))))) <=> (hoasinduction_no_psi_cond_lthm = $true)) & (hoasinduction_lem3v2_gthm = $true) & ! [X291 : d_subst] : (d_id = X291) & ((! [X79 : subst] : ((comp @ id @ X79) = X79) & ! [X80 : subst] : ((comp @ X80 @ id) = X80)) <=> (substmonoid = $true)) & (hoasinduction_lem3a_gthm = $true) & (one = (d2term @ d_one)) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (! [X414 : term,X415 : subst > term > subst > $o] : (? [X417 : subst > term > term] : (! [X421 : term] : (($true != (X415 @ id @ X421 @ id)) | ((X415 @ id @ (X417 @ id @ X421) @ id) = $true)) & ((X415 @ id @ (lam @ (X417 @ sh @ one)) @ id) != $true) & ! [X418 : subst,X419 : term,X420 : subst] : ((sub @ (X417 @ X418 @ X419) @ X420) = (X417 @ (comp @ X418 @ X420) @ (sub @ X419 @ X420)))) | ((X415 @ id @ (lam @ (sub @ X414 @ (push @ one @ sh))) @ id) = $true) | ? [X416 : term] : (((X415 @ id @ X416 @ id) = $true) & ((X415 @ id @ (sub @ X414 @ (push @ X416 @ id)) @ id) != $true))) <=> (hoasinduction_lem3aa_lthm = $true)) & ((induction = $true) <=> ! [X255 : term,X256 : term > $o] : (? [X258 : term,X259 : term] : (((X256 @ X258) = $true) & ((X256 @ (ap @ X259 @ X258)) != $true) & ($true = (X256 @ X259))) | ? [X257 : term] : (($true = (X256 @ X257)) & ((X256 @ (lam @ X257)) != $true)) | ((X256 @ X255) = $true) | ? [X260 : term] : (($true != (X256 @ X260)) & ((var @ X260) = $true)))) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & ((hoasinduction_lem3v2_lthm = $true) <=> (? [X98 : term] : ((sub @ X98 @ id) != X98) | ! [X99 : term > $o,X100 : subst > term > subst > $o,X101 : term] : (((X99 @ (lam @ X101)) = $true) | ? [X102 : term] : (((X99 @ (sub @ X101 @ (push @ X102 @ id))) != $true) & ((X99 @ X102) = $true)) | ? [X103 : subst > term > term] : (! [X104 : subst,X105 : subst,X106 : term] : ((X103 @ (comp @ X105 @ X104) @ (sub @ X106 @ X104)) = (sub @ (X103 @ X105 @ X106) @ X104)) & ! [X107 : term] : (((X100 @ id @ X107 @ id) != $true) | ($true = (X100 @ id @ (X103 @ id @ X107) @ id))) & ($true != (X100 @ id @ (lam @ (X103 @ sh @ one)) @ id))) | ? [X113 : subst,X114 : subst,X115 : term,X116 : subst] : (($true = (X100 @ (comp @ X114 @ X113) @ (sub @ X115 @ X113) @ X116)) & ($true != (X100 @ X114 @ X115 @ (comp @ X113 @ X116)))) | ? [X112 : term] : ((X100 @ id @ X112 @ id) != (X99 @ X112)) | ? [X108 : subst,X109 : term,X110 : subst,X111 : subst] : (((X100 @ (comp @ X108 @ X110) @ (sub @ X109 @ X110) @ X111) != $true) & ((X100 @ X108 @ X109 @ (comp @ X110 @ X111)) = $true))))) & (pushprop_lthm_orig = $true) & (hoaslamnotvar_lthm = $true) & (hoaslamnotap_lthm = $true) & ! [X234 : d_term,X235 : d_term] : (((d2term @ X234) != (d2term @ X235)) | (X234 = X235)) & (hoaslamnotvar = $true) & ((hoasinduction_lem2 = $true) <=> ! [X452 : term,X453 : term,X454 : subst > term > subst > $o] : (((X454 @ id @ X453 @ id) != $true) | ? [X463 : term,X464 : term] : (($true = (X454 @ id @ X463 @ id)) & ($true != (X454 @ id @ (ap @ (sub @ X463 @ id) @ X464) @ id)) & ((X454 @ id @ X464 @ id) = $true)) | ((X454 @ id @ X452 @ id) != $true) | ? [X455 : subst,X456 : subst,X457 : term,X458 : subst] : (((X454 @ X458 @ X457 @ (comp @ X455 @ X456)) != $true) & ($true = (X454 @ (comp @ X458 @ X455) @ (sub @ X457 @ X455) @ X456))) | ((X454 @ id @ (ap @ X452 @ X453) @ id) = $true) | ? [X459 : subst,X460 : term,X461 : subst,X462 : subst] : (((X454 @ X461 @ X460 @ (comp @ X459 @ X462)) = $true) & ((X454 @ (comp @ X461 @ X459) @ (sub @ X460 @ X459) @ X462) != $true)))) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (axabs = $true) & (! [X480 : term,X481 : term,X482 : term,X483 : term] : (((ap @ (sub @ X482 @ id) @ X481) != (ap @ (sub @ X480 @ id) @ X483)) | (X481 = X483)) <=> (hoasapinj2 = $true)) & ((induction2 = $true) <=> ! [X268 : term > $o,X269 : term] : (? [X274 : term] : (($true != (X268 @ X274)) & ((var @ X274) = $true)) | ? [X272 : term,X273 : term] : (($true = (X268 @ X272)) & ((X268 @ (ap @ X273 @ X272)) != $true) & ((X268 @ X273) = $true)) | ((X268 @ X269) = $true) | ? [X270 : term] : (! [X271 : term] : (($true = (X268 @ (sub @ X270 @ (push @ X271 @ id)))) | ($true != (X268 @ X271))) & ((X268 @ (lam @ X270)) != $true)))) & (induction2_gthm = $true) & (! [X386 : term,X387 : subst,X388 : term > $o] : (? [X392 : term] : (((X388 @ (lam @ X392)) != $true) & ! [X393 : term] : (($true != (X388 @ X393)) | ((X388 @ (sub @ X392 @ (push @ X393 @ id))) = $true))) | ($true = (X388 @ (sub @ X386 @ X387))) | ? [X389 : term] : (($true = (var @ X389)) & ((X388 @ (sub @ X389 @ X387)) != $true)) | ? [X390 : term,X391 : term] : (((X388 @ X390) = $true) & ((X388 @ (ap @ X391 @ X390)) != $true) & ($true = (X388 @ X391)))) <=> (induction2lem = $true)) & (hoasinduction_lem1v2_gthm = $true) & ((! [X137 : term,X138 : term > $o] : (? [X139 : term] : (((var @ X139) = $true) & ((X138 @ X139) != $true)) | ? [X142 : term] : (! [X143 : term] : (((X138 @ X143) != $true) | ((X138 @ (sub @ X142 @ (push @ X143 @ id))) = $true)) & ($true != (X138 @ (lam @ X142)))) | ? [X140 : term,X141 : term] : (((X138 @ X140) = $true) & ((X138 @ (ap @ X140 @ X141)) != $true) & ($true = (X138 @ X141))) | ($true = (X138 @ X137))) | ? [X128 : term] : ((sub @ X128 @ id) != X128) | ? [X129 : subst,X130 : term > $o,X131 : term] : (! [X132 : term] : (? [X133 : term] : (($true != (X130 @ (sub @ X132 @ (push @ X133 @ id)))) & ((X130 @ X133) = $true)) | ((X130 @ (lam @ X132)) = $true)) & ! [X136 : term] : (((var @ X136) != $true) | ($true = (X130 @ (sub @ X136 @ X129)))) & ($true != (X130 @ (sub @ X131 @ X129))) & ! [X134 : term,X135 : term] : (((X130 @ X134) != $true) | ($true != (X130 @ X135)) | ((X130 @ (ap @ X134 @ X135)) = $true)))) <=> (induction2_lthm = $true)) & (hoasapnotvar_lthm = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X280 : term] : ? [X281 : subst > term > term] : ! [X282 : term,X283 : subst] : ((X281 @ X283 @ X282) = (sub @ X280 @ (push @ X282 @ X283)))) & (axclos = $true) & (! [X30 : term,X31 : term] : ((X30 = X31) | ((lam @ X30) != (lam @ X31))) <=> (laminj = $true)) & (pushprop_lem3v2_lthm = $true) & (axassoc = $true) & (ulamvar1 != $true) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X339 : term] : ? [X340 : subst > term > term] : ((X340 @ sh @ one) = (sub @ X339 @ (push @ one @ sh)))) & ((! [X204 : subst > term > subst > $o,X205 : term] : (? [X216 : term] : (($true = (var @ (sub @ X216 @ id))) & ((X204 @ id @ X216 @ id) != $true)) | ? [X208 : subst,X209 : subst,X210 : subst,X211 : term] : (($true = (X204 @ (comp @ X210 @ X208) @ (sub @ X211 @ X208) @ X209)) & ((X204 @ X210 @ X211 @ (comp @ X208 @ X209)) != $true)) | ? [X217 : subst > term > term] : (! [X218 : subst,X219 : term,X220 : subst] : ((sub @ (X217 @ X220 @ X219) @ X218) = (X217 @ (comp @ X220 @ X218) @ (sub @ X219 @ X218))) & ! [X221 : term] : (($true != (X204 @ id @ X221 @ id)) | ((X204 @ id @ (X217 @ id @ X221) @ id) = $true)) & ((X204 @ id @ (lam @ (X217 @ sh @ one)) @ id) != $true)) | ? [X212 : subst,X213 : subst,X214 : term,X215 : subst] : (((X204 @ (comp @ X213 @ X212) @ (sub @ X214 @ X212) @ X215) != $true) & ($true = (X204 @ X213 @ X214 @ (comp @ X212 @ X215)))) | ($true = (X204 @ id @ X205 @ id)) | ? [X206 : term,X207 : term] : (($true = (X204 @ id @ X206 @ id)) & ($true != (X204 @ id @ (ap @ (sub @ X207 @ id) @ X206) @ id)) & ($true = (X204 @ id @ X207 @ id)))) | ? [X188 : term,X189 : subst > term > subst > $o] : (! [X198 : term] : (((X189 @ id @ (sub @ X188 @ (push @ X198 @ id)) @ id) = $true) | ($true != (X189 @ id @ X198 @ id))) & ! [X190 : subst,X191 : term,X192 : subst,X193 : subst] : (((X189 @ X193 @ X191 @ (comp @ X190 @ X192)) != $true) | ((X189 @ (comp @ X193 @ X190) @ (sub @ X191 @ X190) @ X192) = $true)) & ((X189 @ id @ (lam @ X188) @ id) != $true) & ! [X194 : subst,X195 : subst,X196 : term,X197 : subst] : (((X189 @ (comp @ X197 @ X195) @ (sub @ X196 @ X195) @ X194) != $true) | ((X189 @ X197 @ X196 @ (comp @ X195 @ X194)) = $true)) & ! [X199 : subst > term > term] : (? [X200 : term,X201 : subst,X202 : subst] : ((sub @ (X199 @ X201 @ X200) @ X202) != (X199 @ (comp @ X201 @ X202) @ (sub @ X200 @ X202))) | ? [X203 : term] : (((X189 @ id @ X203 @ id) = $true) & ((X189 @ id @ (X199 @ id @ X203) @ id) != $true)) | ((X189 @ id @ (lam @ (X199 @ sh @ one)) @ id) = $true))) | ? [X175 : term,X176 : term,X177 : subst > term > subst > $o] : (($true = (X177 @ id @ X175 @ id)) & ! [X182 : subst,X183 : subst,X184 : term,X185 : subst] : (($true = (X177 @ X185 @ X184 @ (comp @ X183 @ X182))) | ($true != (X177 @ (comp @ X185 @ X183) @ (sub @ X184 @ X183) @ X182))) & ! [X186 : term,X187 : term] : (($true != (X177 @ id @ X187 @ id)) | ($true != (X177 @ id @ X186 @ id)) | ($true = (X177 @ id @ (ap @ (sub @ X187 @ id) @ X186) @ id))) & ($true = (X177 @ id @ X176 @ id)) & ! [X178 : subst,X179 : subst,X180 : term,X181 : subst] : (((X177 @ X179 @ X180 @ (comp @ X181 @ X178)) != $true) | ((X177 @ (comp @ X179 @ X181) @ (sub @ X180 @ X181) @ X178) = $true)) & ((X177 @ id @ (ap @ X175 @ X176) @ id) != $true)) | ? [X168 : term > $o,X169 : term] : (($true != (X168 @ X169)) & ! [X172 : term,X173 : term] : (((X168 @ X172) != $true) | ((X168 @ (ap @ X173 @ X172)) = $true) | ($true != (X168 @ X173))) & ! [X174 : term] : (((var @ X174) != $true) | ((X168 @ X174) = $true)) & ! [X170 : term] : (((X168 @ (lam @ X170)) = $true) | ? [X171 : term] : (((X168 @ X171) = $true) & ($true != (X168 @ (sub @ X170 @ (push @ X171 @ id)))))))) <=> (hoasinduction_lthm = $true)) & ((induction2lem_lthm = $true) <=> (? [X511 : term,X512 : term > $o] : (! [X515 : term,X516 : term] : (((X512 @ (ap @ X516 @ X515)) = $true) | ((X512 @ X515) != $true) | ($true != (X512 @ X516))) & ((X512 @ X511) != $true) & ! [X513 : term] : (($true != (X512 @ X513)) | ((X512 @ (lam @ X513)) = $true)) & ! [X514 : term] : (((X512 @ X514) = $true) | ((var @ X514) != $true))) | ! [X517 : subst,X518 : term > $o,X519 : term] : (? [X522 : term,X523 : term] : (($true != (X518 @ (ap @ X523 @ X522))) & ((X518 @ X522) = $true) & ((X518 @ X523) = $true)) | ($true = (X518 @ (sub @ X519 @ X517))) | ? [X524 : term] : (($true != (X518 @ (sub @ X524 @ X517))) & ((var @ X524) = $true)) | ? [X520 : term] : (! [X521 : term] : (($true != (X518 @ X521)) | ($true = (X518 @ (sub @ X520 @ (push @ X521 @ id))))) & ((X518 @ (lam @ X520)) != $true))) | ? [X510 : subst] : ((comp @ X510 @ id) != X510) | ? [X508 : subst,X509 : term] : ((comp @ sh @ (push @ X509 @ X508)) != X508) | ? [X506 : term,X507 : subst] : ((sub @ one @ (push @ X506 @ X507)) != X506))) & (! [X144 : subst,X145 : term > $o,X146 : term] : ? [X147 : term > $o] : ! [X148 : term] : ((X145 @ (sub @ X148 @ (push @ X146 @ X144))) = (X147 @ X148)) <=> (pushprop_lem0_lthm = $true)) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & (pushprop_p_and_p_prime = (^[Y0 : term]: ((^[Y1 : subst]: ((^[Y2 : term > $o]: ((^[Y3 : term > $o]: (!! @ term @ (^[Y4 : term]: ((Y2 @ (sub @ Y4 @ (push @ Y0 @ Y1))) = (Y3 @ Y4)))))))))))) & (apnotvar = $true) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (hoasinduction_gthm = $true) & (axapp = $true) & ((hoasinduction_lem3_lthm = $true) <=> (? [X425 : subst > term > subst > $o,X426 : term] : (($true != (X425 @ id @ (lam @ (sub @ X426 @ (push @ one @ sh))) @ id)) & ! [X432 : term] : (($true = (X425 @ id @ (sub @ X426 @ (push @ X432 @ id)) @ id)) | ((X425 @ id @ X432 @ id) != $true)) & ! [X427 : subst > term > term] : (? [X428 : subst,X429 : term,X430 : subst] : ((X427 @ (comp @ X430 @ X428) @ (sub @ X429 @ X428)) != (sub @ (X427 @ X430 @ X429) @ X428)) | ($true = (X425 @ id @ (lam @ (X427 @ sh @ one)) @ id)) | ? [X431 : term] : (($true = (X425 @ id @ X431 @ id)) & ((X425 @ id @ (X427 @ id @ X431) @ id) != $true)))) | ? [X424 : term] : ((sub @ X424 @ id) != X424) | ! [X433 : term,X434 : subst > term > subst > $o] : (? [X444 : subst > term > term] : (! [X445 : term] : (((X434 @ id @ (X444 @ id @ X445) @ id) = $true) | ((X434 @ id @ X445 @ id) != $true)) & ((X434 @ id @ (lam @ (X444 @ sh @ one)) @ id) != $true) & ! [X446 : subst,X447 : term,X448 : subst] : ((X444 @ (comp @ X448 @ X446) @ (sub @ X447 @ X446)) = (sub @ (X444 @ X448 @ X447) @ X446))) | ((X434 @ id @ (lam @ X433) @ id) = $true) | ? [X440 : subst,X441 : term,X442 : subst,X443 : subst] : (((X434 @ (comp @ X442 @ X440) @ (sub @ X441 @ X440) @ X443) = $true) & ((X434 @ X442 @ X441 @ (comp @ X440 @ X443)) != $true)) | ? [X436 : subst,X437 : term,X438 : subst,X439 : subst] : (($true != (X434 @ (comp @ X436 @ X439) @ (sub @ X437 @ X439) @ X438)) & ((X434 @ X436 @ X437 @ (comp @ X439 @ X438)) = $true)) | ? [X435 : term] : (($true = (X434 @ id @ X435 @ id)) & ((X434 @ id @ (sub @ X433 @ (push @ X435 @ id)) @ id) != $true))))) & ((pushprop_lem0 = $true) <=> ! [X119 : term > $o,X120 : subst,X121 : term] : ? [X122 : term > $o] : ! [X123 : term] : ((X122 @ X123) = (X119 @ (sub @ X123 @ (push @ X121 @ X120))))) & (induction2lem_gthm = $true) & (! [X53 : term,X54 : term > $o,X55 : subst > term > subst > $o,X56 : term] : (? [X64 : subst,X65 : term,X66 : subst,X67 : subst] : (((X55 @ X66 @ X65 @ (comp @ X67 @ X64)) != $true) & ((X55 @ (comp @ X66 @ X67) @ (sub @ X65 @ X67) @ X64) = $true)) | ? [X61 : term,X62 : term] : (((X55 @ id @ X62 @ id) = $true) & ((X55 @ id @ (ap @ (sub @ X62 @ id) @ X61) @ id) != $true) & ($true = (X55 @ id @ X61 @ id))) | ((X54 @ (ap @ X53 @ X56)) = $true) | ((X54 @ X53) != $true) | ? [X63 : term] : ((X55 @ id @ X63 @ id) != (X54 @ X63)) | ((X54 @ X56) != $true) | ? [X57 : subst,X58 : term,X59 : subst,X60 : subst] : (((X55 @ (comp @ X60 @ X57) @ (sub @ X58 @ X57) @ X59) != $true) & ($true = (X55 @ X60 @ X58 @ (comp @ X57 @ X59))))) <=> (hoasinduction_lem2v2 = $true)) & ((hoasinduction_lem3aaa = $true) <=> ! [X222 : term,X223 : subst > term > subst > $o] : (? [X225 : term,X226 : subst > term > term] : (! [X233 : term] : (((X223 @ id @ (X226 @ id @ X233) @ id) = $true) | ($true != (X223 @ id @ X233 @ id))) & ! [X227 : subst,X228 : term,X229 : subst] : ((sub @ (sub @ X225 @ (push @ X228 @ X229)) @ X227) = (sub @ (X226 @ X229 @ X228) @ X227)) & ($true != (X223 @ id @ (lam @ (X226 @ sh @ one)) @ id)) & ! [X230 : subst,X231 : term,X232 : subst] : ((sub @ X225 @ (push @ (sub @ X231 @ X232) @ (comp @ X230 @ X232))) = (X226 @ (comp @ X230 @ X232) @ (sub @ X231 @ X232)))) | ? [X224 : term] : (((X223 @ id @ X224 @ id) = $true) & ($true != (X223 @ id @ (sub @ X222 @ (push @ X224 @ id)) @ id))) | ($true = (X223 @ id @ (lam @ (sub @ X222 @ (push @ one @ sh))) @ id)))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((hoasinduction_lem3a = $true) <=> ! [X490 : term,X491 : subst > term > subst > $o] : (? [X493 : subst > term > term] : (! [X497 : term] : (((X491 @ id @ (X493 @ id @ X497) @ id) = $true) | ((X491 @ id @ X497 @ id) != $true)) & ((X491 @ id @ (lam @ (X493 @ sh @ one)) @ id) != $true) & ! [X494 : subst,X495 : subst,X496 : term] : ((X493 @ (comp @ X494 @ X495) @ (sub @ X496 @ X495)) = (sub @ (X493 @ X494 @ X496) @ X495))) | ? [X492 : term] : (((X491 @ id @ (sub @ X490 @ (push @ X492 @ id)) @ id) != $true) & ((X491 @ id @ X492 @ id) = $true)) | ($true = (X491 @ id @ (lam @ X490) @ id)))) & (! [X341 : subst > term > term,X342 : term,X343 : term] : (((ap @ (sub @ X342 @ id) @ X343) != (lam @ (X341 @ sh @ one))) | ? [X344 : subst,X345 : term,X346 : subst] : ((sub @ (X341 @ X346 @ X345) @ X344) != (X341 @ (comp @ X346 @ X344) @ (sub @ X345 @ X344)))) <=> (hoaslamnotap = $true)) & (hoasinduction_lem1 = $true) & (pushprop_lem2v2_gthm = $true) & ! [X422 : term] : ? [X423 : d_term] : ((d2term @ X423) = X422) & ((? [X532 : term,X533 : term,X534 : term,X535 : term] : (((ap @ X532 @ X534) = (ap @ X535 @ X533)) & (X533 != X534)) | ! [X536 : term,X537 : term,X538 : term,X539 : term] : (((ap @ (sub @ X536 @ id) @ X539) != (ap @ (sub @ X537 @ id) @ X538)) | (X538 = X539))) <=> (hoasapinj2_lthm = $true)) & (lamnotvar = $true) & (axvarshift = $true) & (hoasinduction_lem3b_gthm = $true) & (pushprop = $true) & ! [X265 : d_subst,X266 : d_subst] : ((X265 = X266) | ((d2subst @ X266) != (d2subst @ X265))) & (ulamvarind = $true) & (substmonoid_gthm = $true) & (hoasinduction_lem2_lthm = $true) & (pushprop_lem2v2_lthm = $true) & ((shinj = $true) <=> ! [X328 : term,X329 : term] : ((X328 = X329) | ((sub @ X329 @ sh) != (sub @ X328 @ sh)))) & ((axshiftcons = $true) <=> ! [X117 : term,X118 : subst] : ((comp @ sh @ (push @ X117 @ X118)) = X118)) & (hoasapinj1_gthm = $true) & ((var @ (d2term @ d_one)) != $true) & (hoasinduction_lem1_lthm = $true) & (! [X310 : term,X311 : subst > term > subst > $o,X312 : term > $o] : (? [X323 : subst > term > term] : (((X311 @ id @ (lam @ (X323 @ sh @ one)) @ id) != $true) & ! [X325 : term,X326 : subst,X327 : subst] : ((X323 @ (comp @ X327 @ X326) @ (sub @ X325 @ X326)) = (sub @ (X323 @ X327 @ X325) @ X326)) & ! [X324 : term] : (((X311 @ id @ (X323 @ id @ X324) @ id) = $true) | ($true != (X311 @ id @ X324 @ id)))) | ? [X315 : subst,X316 : subst,X317 : subst,X318 : term] : (($true != (X311 @ X316 @ X318 @ (comp @ X317 @ X315))) & ((X311 @ (comp @ X316 @ X317) @ (sub @ X318 @ X317) @ X315) = $true)) | ? [X314 : term] : (((X312 @ X314) = $true) & ((X312 @ (sub @ X310 @ (push @ X314 @ id))) != $true)) | ((X312 @ (lam @ X310)) = $true) | ? [X319 : subst,X320 : subst,X321 : term,X322 : subst] : (((X311 @ X322 @ X321 @ (comp @ X319 @ X320)) = $true) & ((X311 @ (comp @ X322 @ X319) @ (sub @ X321 @ X319) @ X320) != $true)) | ? [X313 : term] : ((X312 @ X313) != (X311 @ id @ X313 @ id))) <=> (hoasinduction_lem3v2 = $true)) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X124 : term] : ? [X125 : subst > term > term] : ! [X126 : term,X127 : subst] : ((sub @ X124 @ (push @ X126 @ X127)) = (X125 @ X127 @ X126))) & ((d2subst @ d_id) = id) & (pushprop_lem1v2_gthm = $true) & (! [X529 : term] : ? [X530 : subst > term > term] : ((X530 @ sh @ one) = (sub @ X529 @ (push @ one @ sh))) <=> (hoasinduction_lem3b = $true)) & ((? [X237 : subst,X238 : term] : ((sub @ one @ (push @ X238 @ X237)) != X238) | ! [X243 : subst,X244 : term,X245 : subst > term > term,X246 : subst > term > term] : (((lam @ (X246 @ sh @ one)) != (lam @ (X245 @ sh @ one))) | ((X246 @ X243 @ X244) = (X245 @ X243 @ X244)) | ? [X250 : subst,X251 : term,X252 : subst] : ((X245 @ (comp @ X250 @ X252) @ (sub @ X251 @ X252)) != (sub @ (X245 @ X250 @ X251) @ X252)) | ? [X247 : term,X248 : subst,X249 : subst] : ((sub @ (X246 @ X248 @ X247) @ X249) != (X246 @ (comp @ X248 @ X249) @ (sub @ X247 @ X249)))) | ? [X239 : term,X240 : subst] : ((comp @ sh @ (push @ X239 @ X240)) != X240) | ? [X241 : term,X242 : term] : ((X241 != X242) & ((lam @ X241) = (lam @ X242)))) <=> (hoaslaminj_lthm = $true)) & (! [X404 : subst,X405 : subst > term > term,X406 : term,X407 : subst > term > term] : (? [X411 : subst,X412 : subst,X413 : term] : ((X405 @ (comp @ X412 @ X411) @ (sub @ X413 @ X411)) != (sub @ (X405 @ X412 @ X413) @ X411)) | ((lam @ (X407 @ sh @ one)) != (lam @ (X405 @ sh @ one))) | ? [X408 : term,X409 : subst,X410 : subst] : ((X407 @ (comp @ X409 @ X410) @ (sub @ X408 @ X410)) != (sub @ (X407 @ X409 @ X408) @ X410)) | ((X407 @ X404 @ X406) = (X405 @ X404 @ X406))) <=> (hoaslaminj = $true)) & (hoaslamnotap_gthm = $true) & ((substmonoid_lthm = $true) <=> (? [X396 : subst] : ((comp @ X396 @ id) != X396) | ? [X395 : subst] : ((comp @ id @ X395) != X395) | (! [X397 : subst] : ((comp @ id @ X397) = X397) & ! [X398 : subst] : ((comp @ X398 @ id) = X398)))) & (! [X48 : term,X49 : term,X50 : term,X51 : term] : (((ap @ X49 @ X48) != (ap @ X50 @ X51)) | (X48 = X51)) <=> (apinj2 = $true)) & (hoasinduction_lem2_gthm = $true) & (pushprop_lem3v2 = $true) & (pushprop_lem1_gthm = $true) & ((hoasapinj1_lthm = $true) <=> (! [X73 : term,X74 : term,X75 : term,X76 : term] : ((X73 = X74) | ((ap @ (sub @ X74 @ id) @ X76) != (ap @ (sub @ X73 @ id) @ X75))) | ? [X69 : term,X70 : term,X71 : term,X72 : term] : (((ap @ X69 @ X70) = (ap @ X71 @ X72)) & (X69 != X71)) | ? [X68 : term] : ((sub @ X68 @ id) != X68))) & ((! [X470 : subst > term > subst > $o,X471 : term,X472 : term > $o] : (? [X473 : subst > term > term] : (! [X475 : subst,X476 : subst,X477 : term] : ((X473 @ (comp @ X476 @ X475) @ (sub @ X477 @ X475)) = (sub @ (X473 @ X476 @ X477) @ X475)) & ((X470 @ id @ (lam @ (X473 @ sh @ one)) @ id) != $true) & ! [X474 : term] : (((X470 @ id @ X474 @ id) != $true) | ((X470 @ id @ (X473 @ id @ X474) @ id) = $true))) | ? [X479 : term] : (((X472 @ (sub @ X471 @ (push @ X479 @ id))) != $true) & ($true = (X472 @ X479))) | ? [X478 : term] : ((X470 @ id @ X478 @ id) != (X472 @ X478)) | ((X472 @ (lam @ X471)) = $true)) | ? [X469 : term] : ((sub @ X469 @ id) != X469) | ? [X465 : term] : ! [X466 : subst > term > term] : ? [X467 : subst,X468 : term] : ((sub @ X465 @ (push @ X468 @ X467)) != (X466 @ X467 @ X468))) <=> (hoasinduction_lem3v2a_lthm = $true)) & ((? [X151 : subst,X152 : term] : ((comp @ sh @ (push @ X152 @ X151)) != X151) | ? [X149 : term,X150 : subst] : ((sub @ one @ (push @ X149 @ X150)) != X149) | ! [X153 : term,X154 : term > $o,X155 : subst,X156 : term,X157 : term > $o] : (((X157 @ (sub @ X153 @ (push @ X156 @ X155))) = $true) | ($true != (X154 @ X153)))) <=> (pushprop_lem1_lthm = $true)) & ((! [X90 : subst > term > subst > $o,X91 : term] : (? [X97 : term] : (($true = (X90 @ id @ X97 @ id)) & ($true != (X90 @ id @ (sub @ X91 @ (push @ X97 @ id)) @ id))) | ((X90 @ id @ (lam @ X91) @ id) = $true) | ? [X92 : subst > term > term] : (! [X94 : term,X95 : subst,X96 : subst] : ((sub @ (X92 @ X96 @ X94) @ X95) = (X92 @ (comp @ X96 @ X95) @ (sub @ X94 @ X95))) & ! [X93 : term] : (($true = (X90 @ id @ (X92 @ id @ X93) @ id)) | ($true != (X90 @ id @ X93 @ id))) & ($true != (X90 @ id @ (lam @ (X92 @ sh @ one)) @ id)))) | ? [X82 : subst > term > subst > $o,X83 : term] : (((X82 @ id @ (lam @ (sub @ X83 @ (push @ one @ sh))) @ id) != $true) & ! [X89 : term] : (($true = (X82 @ id @ (sub @ X83 @ (push @ X89 @ id)) @ id)) | ((X82 @ id @ X89 @ id) != $true)) & ! [X84 : subst > term > term] : (? [X85 : term,X86 : subst,X87 : subst] : ((sub @ (X84 @ X87 @ X85) @ X86) != (X84 @ (comp @ X87 @ X86) @ (sub @ X85 @ X86))) | ($true = (X82 @ id @ (lam @ (X84 @ sh @ one)) @ id)) | ? [X88 : term] : (((X82 @ id @ (X84 @ id @ X88) @ id) != $true) & ($true = (X82 @ id @ X88 @ id))))) | ? [X81 : term] : ((sub @ X81 @ id) != X81)) <=> (hoasinduction_lem3a_lthm = $true)) & (hoasinduction_lem1v2 = $true) & (! [X399 : subst,X400 : term > $o,X401 : term > $o,X402 : term] : (? [X403 : term] : ((X400 @ (sub @ X403 @ (push @ X402 @ X399))) != (X401 @ X403)) | ($true = (X401 @ one)) | ($true != (X400 @ X402))) <=> (pushprop_lem1v2 = $true)) & (lamnotap != $true) & (hoasapnotvar_gthm = $true) & (! [X449 : subst > term > subst > $o] : ? [X450 : term > $o] : ! [X451 : term] : ((X449 @ id @ X451 @ id) = (X450 @ X451)) <=> (hoasinduction_lem0_lthm = $true)) & ((d2subst @ d_id) = sh) & ((pushprop_lem1v2_lthm = $true) <=> (! [X286 : term,X287 : subst,X288 : term > $o,X289 : term > $o] : (? [X290 : term] : ((X288 @ (sub @ X290 @ (push @ X286 @ X287))) != (X289 @ X290)) | ((X289 @ one) = $true) | ($true != (X288 @ X286))) | ? [X284 : term,X285 : subst] : ((sub @ one @ (push @ X284 @ X285)) != X284))) & (hoasinduction_lem1_gthm = $true) & (pushprop_lem0_gthm = $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & ((axvarid = $true) <=> ! [X236 : term] : ((sub @ X236 @ id) = X236)) & (! [X158 : term > $o,X159 : subst > term > subst > $o,X160 : term] : (? [X167 : term] : (($true != (X158 @ (sub @ X160 @ (push @ X167 @ id)))) & ((X158 @ X167) = $true)) | ? [X161 : term] : ((X158 @ X161) != (X159 @ id @ X161 @ id)) | ($true = (X158 @ (lam @ X160))) | ? [X162 : subst > term > term] : (! [X163 : term] : (($true != (X159 @ id @ X163 @ id)) | ($true = (X159 @ id @ (X162 @ id @ X163) @ id))) & ((X159 @ id @ (lam @ (X162 @ sh @ one)) @ id) != $true) & ! [X164 : subst,X165 : term,X166 : subst] : ((sub @ (X162 @ X166 @ X165) @ X164) = (X162 @ (comp @ X166 @ X164) @ (sub @ X165 @ X164))))) <=> (hoasinduction_lem3v2a = $true)) & ((hoasapinj1 = $true) <=> ! [X486 : term,X487 : term,X488 : term,X489 : term] : (((ap @ (sub @ X489 @ id) @ X486) != (ap @ (sub @ X488 @ id) @ X487)) | (X488 = X489))) & (pushprop_gthm = $true) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & ((axscons = $true) <=> ! [X267 : subst] : ((push @ (sub @ one @ X267) @ (comp @ sh @ X267)) = X267)) & ((hoasinduction = $true) <=> ! [X292 : term,X293 : subst > term > subst > $o] : (? [X306 : term,X307 : subst,X308 : subst,X309 : subst] : (($true = (X293 @ (comp @ X308 @ X307) @ (sub @ X306 @ X307) @ X309)) & ((X293 @ X308 @ X306 @ (comp @ X307 @ X309)) != $true)) | ? [X303 : term] : (($true = (var @ (sub @ X303 @ id))) & ((X293 @ id @ X303 @ id) != $true)) | ((X293 @ id @ X292 @ id) = $true) | ? [X304 : term,X305 : term] : (($true != (X293 @ id @ (ap @ (sub @ X304 @ id) @ X305) @ id)) & ($true = (X293 @ id @ X305 @ id)) & ($true = (X293 @ id @ X304 @ id))) | ? [X294 : subst > term > term] : (($true != (X293 @ id @ (lam @ (X294 @ sh @ one)) @ id)) & ! [X298 : term] : (($true != (X293 @ id @ X298 @ id)) | ($true = (X293 @ id @ (X294 @ id @ X298) @ id))) & ! [X295 : subst,X296 : term,X297 : subst] : ((X294 @ (comp @ X295 @ X297) @ (sub @ X296 @ X297)) = (sub @ (X294 @ X295 @ X296) @ X297))) | ? [X299 : subst,X300 : subst,X301 : term,X302 : subst] : (($true != (X293 @ (comp @ X302 @ X300) @ (sub @ X301 @ X300) @ X299)) & ((X293 @ X302 @ X301 @ (comp @ X300 @ X299)) = $true)))) & (pushprop_lem2v2 = $true) & ((hoasinduction_no_psi_cond = $true) <=> ! [X330 : term,X331 : subst > term > subst > $o] : (((X331 @ id @ X330 @ id) = $true) | ? [X337 : term,X338 : term] : (((X331 @ id @ (ap @ (sub @ X337 @ id) @ X338) @ id) != $true) & ((X331 @ id @ X338 @ id) = $true) & ((X331 @ id @ X337 @ id) = $true)) | ? [X332 : subst > term > term] : (($true != (X331 @ id @ (lam @ (X332 @ sh @ one)) @ id)) & ! [X333 : term] : (((X331 @ id @ X333 @ id) != $true) | ((X331 @ id @ (X332 @ id @ X333) @ id) = $true)) & ! [X334 : subst,X335 : subst,X336 : term] : ((sub @ (X332 @ X335 @ X336) @ X334) = (X332 @ (comp @ X335 @ X334) @ (sub @ X336 @ X334)))))) & (hoasinduction_lem3_gthm = $true) & ((termmset = $true) <=> ! [X394 : term] : ((sub @ X394 @ id) = X394)) & ! [X531 : d_term] : (d_one = X531) & (ulamvarsh = $true) & (hoasapinj2_gthm = $true) & (axmap = $true) & (! [X32 : term,X33 : subst > term > subst > $o] : (? [X42 : subst > term > term] : (((X33 @ id @ (lam @ (X42 @ sh @ one)) @ id) != $true) & ! [X43 : term] : (($true != (X33 @ id @ X43 @ id)) | ((X33 @ id @ (X42 @ id @ X43) @ id) = $true)) & ! [X44 : term,X45 : subst,X46 : subst] : ((X42 @ (comp @ X46 @ X45) @ (sub @ X44 @ X45)) = (sub @ (X42 @ X46 @ X44) @ X45))) | ? [X38 : subst,X39 : subst,X40 : subst,X41 : term] : (($true != (X33 @ (comp @ X39 @ X40) @ (sub @ X41 @ X40) @ X38)) & ($true = (X33 @ X39 @ X41 @ (comp @ X40 @ X38)))) | ($true = (X33 @ id @ (lam @ X32) @ id)) | ? [X47 : term] : (((X33 @ id @ (sub @ X32 @ (push @ X47 @ id)) @ id) != $true) & ($true = (X33 @ id @ X47 @ id))) | ? [X34 : term,X35 : subst,X36 : subst,X37 : subst] : (((X33 @ X36 @ X34 @ (comp @ X37 @ X35)) != $true) & ((X33 @ (comp @ X36 @ X37) @ (sub @ X34 @ X37) @ X35) = $true))) <=> (hoasinduction_lem3 = $true)) & ((! [X254 : term] : ((sub @ X254 @ id) = X254) | ? [X253 : term] : ((sub @ X253 @ id) != X253)) <=> (termmset_lthm = $true)) & ((pushprop_lem1 = $true) <=> ! [X275 : term,X276 : term,X277 : term > $o,X278 : subst,X279 : term > $o] : (((X279 @ X276) != $true) | ((X277 @ (sub @ X276 @ (push @ X275 @ X278))) = $true))) & ((axvarcons = $true) <=> ! [X77 : subst,X78 : term] : ((sub @ one @ (push @ X78 @ X77)) = X78)) & ((hoasinduction_lthm_3 = $true) <=> (? [X350 : term,X351 : term > $o] : (($true != (X351 @ X350)) & ! [X353 : term,X354 : term] : (((X351 @ X353) != $true) | ($true = (X351 @ (ap @ X354 @ X353))) | ($true != (X351 @ X354))) & ! [X352 : term] : (((X351 @ X352) = $true) | ((var @ X352) != $true)) & ! [X355 : term] : (($true = (X351 @ (lam @ X355))) | ? [X356 : term] : (((X351 @ (sub @ X355 @ (push @ X356 @ id))) != $true) & ((X351 @ X356) = $true)))) | ! [X368 : term,X369 : subst > term > subst > $o] : (? [X374 : term,X375 : term] : (((X369 @ id @ X375 @ id) = $true) & ($true = (X369 @ id @ X374 @ id)) & ((X369 @ id @ (ap @ (sub @ X374 @ id) @ X375) @ id) != $true)) | ? [X376 : subst,X377 : subst,X378 : subst,X379 : term] : (((X369 @ X378 @ X379 @ (comp @ X376 @ X377)) = $true) & ((X369 @ (comp @ X378 @ X376) @ (sub @ X379 @ X376) @ X377) != $true)) | ? [X380 : subst > term > term] : (! [X381 : term] : (($true != (X369 @ id @ X381 @ id)) | ((X369 @ id @ (X380 @ id @ X381) @ id) = $true)) & ! [X382 : subst,X383 : term,X384 : subst] : ((X380 @ (comp @ X382 @ X384) @ (sub @ X383 @ X384)) = (sub @ (X380 @ X382 @ X383) @ X384)) & ($true != (X369 @ id @ (lam @ (X380 @ sh @ one)) @ id))) | ? [X370 : term,X371 : subst,X372 : subst,X373 : subst] : (($true != (X369 @ X373 @ X370 @ (comp @ X372 @ X371))) & ($true = (X369 @ (comp @ X373 @ X372) @ (sub @ X370 @ X372) @ X371))) | ($true = (X369 @ id @ X368 @ id)) | ? [X385 : term] : (($true != (X369 @ id @ X385 @ id)) & ($true = (var @ (sub @ X385 @ id))))) | ? [X357 : term] : ((sub @ X357 @ id) != X357) | ? [X347 : subst > term > subst > $o] : ! [X348 : term > $o] : ? [X349 : term] : ((X347 @ id @ X349 @ id) != (X348 @ X349)) | ? [X358 : subst > term > subst > $o,X359 : term,X360 : term > $o] : (($true != (X360 @ (lam @ X359))) & ! [X361 : term] : ((X360 @ X361) = (X358 @ id @ X361 @ id)) & ! [X367 : term] : (((X360 @ X367) != $true) | ($true = (X360 @ (sub @ X359 @ (push @ X367 @ id))))) & ! [X362 : subst > term > term] : (? [X363 : term] : (((X358 @ id @ (X362 @ id @ X363) @ id) != $true) & ((X358 @ id @ X363 @ id) = $true)) | ($true = (X358 @ id @ (lam @ (X362 @ sh @ one)) @ id)) | ? [X364 : subst,X365 : subst,X366 : term] : ((sub @ (X362 @ X364 @ X366) @ X365) != (X362 @ (comp @ X364 @ X365) @ (sub @ X366 @ X365))))))) & (pushprop_lthm = $true) & (! [X528 : subst] : ((comp @ id @ X528) = X528) <=> (axidl = $true)) & ((hoasinduction_lem3aa = $true) <=> ! [X498 : subst > term > subst > $o,X499 : term] : (? [X501 : subst > term > term] : (! [X505 : term] : (($true != (X498 @ id @ X505 @ id)) | ($true = (X498 @ id @ (X501 @ id @ X505) @ id))) & ($true != (X498 @ id @ (lam @ (X501 @ sh @ one)) @ id)) & ! [X502 : subst,X503 : subst,X504 : term] : ((X501 @ (comp @ X502 @ X503) @ (sub @ X504 @ X503)) = (sub @ (X501 @ X502 @ X504) @ X503))) | ? [X500 : term] : (($true != (X498 @ id @ (sub @ X499 @ (push @ X500 @ id)) @ id)) & ($true = (X498 @ id @ X500 @ id))) | ($true = (X498 @ id @ (lam @ (sub @ X499 @ (push @ one @ sh))) @ id)))) & (hoaslaminj_gthm = $true) & ((hoasinduction_lem0 = $true) <=> ! [X525 : subst > term > subst > $o] : ? [X526 : term > $o] : ! [X527 : term] : ((X525 @ id @ X527 @ id) = (X526 @ X527))) & ! [X484 : subst] : ? [X485 : d_subst] : ((d2subst @ X485) = X484)),
% 15.02/3.54 inference(flattening,[status(thm)],[f12])).
% 15.02/3.54 thf(f12,plain,(
% 15.02/3.54 ((pushprop_lem1 = $true) <=> ! [X275 : term,X276 : term,X277 : term > $o,X278 : subst,X279 : term > $o] : (((X279 @ X276) != $true) | ((X277 @ (sub @ X276 @ (push @ X275 @ X278))) = $true))) & (induction2_gthm = $true) & (! [X404 : subst,X405 : subst > term > term,X406 : term,X407 : subst > term > term] : (? [X411 : subst,X412 : subst,X413 : term] : ((X405 @ (comp @ X412 @ X411) @ (sub @ X413 @ X411)) != (sub @ (X405 @ X412 @ X413) @ X411)) | ((lam @ (X407 @ sh @ one)) != (lam @ (X405 @ sh @ one))) | ? [X408 : term,X409 : subst,X410 : subst] : ((X407 @ (comp @ X409 @ X410) @ (sub @ X408 @ X410)) != (sub @ (X407 @ X409 @ X408) @ X410)) | ((X407 @ X404 @ X406) = (X405 @ X404 @ X406))) <=> (hoaslaminj = $true)) & ((axshiftcons = $true) <=> ! [X117 : term,X118 : subst] : ((comp @ sh @ (push @ X117 @ X118)) = X118)) & ((hoasinduction_lem3a = $true) <=> ! [X490 : term,X491 : subst > term > subst > $o] : (? [X493 : subst > term > term] : (! [X497 : term] : (((X491 @ id @ (X493 @ id @ X497) @ id) = $true) | ((X491 @ id @ X497 @ id) != $true)) & ((X491 @ id @ (lam @ (X493 @ sh @ one)) @ id) != $true) & ! [X494 : subst,X495 : subst,X496 : term] : ((X493 @ (comp @ X494 @ X495) @ (sub @ X496 @ X495)) = (sub @ (X493 @ X494 @ X496) @ X495))) | ? [X492 : term] : (((X491 @ id @ (sub @ X490 @ (push @ X492 @ id)) @ id) != $true) & ((X491 @ id @ X492 @ id) = $true)) | ($true = (X491 @ id @ (lam @ X490) @ id)))) & (pushprop_lem2v2 = $true) & (! [X53 : term,X54 : term > $o,X55 : subst > term > subst > $o,X56 : term] : (? [X64 : subst,X65 : term,X66 : subst,X67 : subst] : (((X55 @ X66 @ X65 @ (comp @ X67 @ X64)) != $true) & ((X55 @ (comp @ X66 @ X67) @ (sub @ X65 @ X67) @ X64) = $true)) | ? [X61 : term,X62 : term] : (((X55 @ id @ X62 @ id) = $true) & ((X55 @ id @ (ap @ (sub @ X62 @ id) @ X61) @ id) != $true) & ($true = (X55 @ id @ X61 @ id))) | ((X54 @ (ap @ X53 @ X56)) = $true) | ((X54 @ X53) != $true) | ? [X63 : term] : ((X55 @ id @ X63 @ id) != (X54 @ X63)) | ((X54 @ X56) != $true) | ? [X57 : subst,X58 : term,X59 : subst,X60 : subst] : (((X55 @ (comp @ X60 @ X57) @ (sub @ X58 @ X57) @ X59) != $true) & ($true = (X55 @ X60 @ X58 @ (comp @ X57 @ X59))))) <=> (hoasinduction_lem2v2 = $true)) & (! [X386 : term,X387 : subst,X388 : term > $o] : (? [X392 : term] : (((X388 @ (lam @ X392)) != $true) & ! [X393 : term] : (($true != (X388 @ X393)) | ((X388 @ (sub @ X392 @ (push @ X393 @ id))) = $true))) | ($true = (X388 @ (sub @ X386 @ X387))) | ? [X389 : term] : (($true = (var @ X389)) & ((X388 @ (sub @ X389 @ X387)) != $true)) | ? [X390 : term,X391 : term] : (((X388 @ X390) = $true) & ((X388 @ (ap @ X391 @ X390)) != $true) & ($true = (X388 @ X391)))) <=> (induction2lem = $true)) & (((! [X470 : subst > term > subst > $o,X471 : term,X472 : term > $o] : (? [X473 : subst > term > term] : (! [X475 : subst,X476 : subst,X477 : term] : ((X473 @ (comp @ X476 @ X475) @ (sub @ X477 @ X475)) = (sub @ (X473 @ X476 @ X477) @ X475)) & ((X470 @ id @ (lam @ (X473 @ sh @ one)) @ id) != $true) & ! [X474 : term] : (((X470 @ id @ X474 @ id) != $true) | ((X470 @ id @ (X473 @ id @ X474) @ id) = $true))) | ? [X479 : term] : (((X472 @ (sub @ X471 @ (push @ X479 @ id))) != $true) & ($true = (X472 @ X479))) | ? [X478 : term] : ((X470 @ id @ X478 @ id) != (X472 @ X478)) | ((X472 @ (lam @ X471)) = $true)) | ? [X469 : term] : ((sub @ X469 @ id) != X469)) | ? [X465 : term] : ! [X466 : subst > term > term] : ? [X467 : subst,X468 : term] : ((sub @ X465 @ (push @ X468 @ X467)) != (X466 @ X467 @ X468))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (hoasapnotvar_gthm = $true) & (! [X144 : subst,X145 : term > $o,X146 : term] : ? [X147 : term > $o] : ! [X148 : term] : ((X145 @ (sub @ X148 @ (push @ X146 @ X144))) = (X147 @ X148)) <=> (pushprop_lem0_lthm = $true)) & (hoasinduction_lem3a_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X280 : term] : ? [X281 : subst > term > term] : ! [X282 : term,X283 : subst] : ((X281 @ X283 @ X282) = (sub @ X280 @ (push @ X282 @ X283)))) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (termmset_gthm = $true) & ((hoasinduction_lem3v2_f_lthm = $true) <=> ! [X124 : term] : ? [X125 : subst > term > term] : ! [X126 : term,X127 : subst] : ((sub @ X124 @ (push @ X126 @ X127)) = (X125 @ X127 @ X126))) & ((pushprop_lem1v2_lthm = $true) <=> (! [X286 : term,X287 : subst,X288 : term > $o,X289 : term > $o] : (? [X290 : term] : ((X288 @ (sub @ X290 @ (push @ X286 @ X287))) != (X289 @ X290)) | ((X289 @ one) = $true) | ($true != (X288 @ X286))) | ? [X284 : term,X285 : subst] : ((sub @ one @ (push @ X284 @ X285)) != X284))) & (! [X30 : term,X31 : term] : ((X30 = X31) | ((lam @ X30) != (lam @ X31))) <=> (laminj = $true)) & ((hoasinduction_lem0 = $true) <=> ! [X525 : subst > term > subst > $o] : ? [X526 : term > $o] : ! [X527 : term] : ((X525 @ id @ X527 @ id) = (X526 @ X527))) & (! [X399 : subst,X400 : term > $o,X401 : term > $o,X402 : term] : (? [X403 : term] : ((X400 @ (sub @ X403 @ (push @ X402 @ X399))) != (X401 @ X403)) | ($true = (X401 @ one)) | ($true != (X400 @ X402))) <=> (pushprop_lem1v2 = $true)) & ((apinj1 = $true) <=> ! [X261 : term,X262 : term,X263 : term,X264 : term] : ((X262 = X264) | ((ap @ X264 @ X263) != (ap @ X262 @ X261)))) & (one = (d2term @ d_one)) & (! [X528 : subst] : ((comp @ id @ X528) = X528) <=> (axidl = $true)) & ((hoasinduction_lem3_lthm = $true) <=> ((! [X433 : term,X434 : subst > term > subst > $o] : (? [X444 : subst > term > term] : (! [X445 : term] : (((X434 @ id @ (X444 @ id @ X445) @ id) = $true) | ((X434 @ id @ X445 @ id) != $true)) & ((X434 @ id @ (lam @ (X444 @ sh @ one)) @ id) != $true) & ! [X446 : subst,X447 : term,X448 : subst] : ((X444 @ (comp @ X448 @ X446) @ (sub @ X447 @ X446)) = (sub @ (X444 @ X448 @ X447) @ X446))) | ((X434 @ id @ (lam @ X433) @ id) = $true) | ? [X440 : subst,X441 : term,X442 : subst,X443 : subst] : (((X434 @ (comp @ X442 @ X440) @ (sub @ X441 @ X440) @ X443) = $true) & ((X434 @ X442 @ X441 @ (comp @ X440 @ X443)) != $true)) | ? [X436 : subst,X437 : term,X438 : subst,X439 : subst] : (($true != (X434 @ (comp @ X436 @ X439) @ (sub @ X437 @ X439) @ X438)) & ((X434 @ X436 @ X437 @ (comp @ X439 @ X438)) = $true)) | ? [X435 : term] : (($true = (X434 @ id @ X435 @ id)) & ((X434 @ id @ (sub @ X433 @ (push @ X435 @ id)) @ id) != $true))) | ? [X425 : subst > term > subst > $o,X426 : term] : (($true != (X425 @ id @ (lam @ (sub @ X426 @ (push @ one @ sh))) @ id)) & ! [X432 : term] : (($true = (X425 @ id @ (sub @ X426 @ (push @ X432 @ id)) @ id)) | ((X425 @ id @ X432 @ id) != $true)) & ! [X427 : subst > term > term] : (? [X428 : subst,X429 : term,X430 : subst] : ((X427 @ (comp @ X430 @ X428) @ (sub @ X429 @ X428)) != (sub @ (X427 @ X430 @ X429) @ X428)) | ($true = (X425 @ id @ (lam @ (X427 @ sh @ one)) @ id)) | ? [X431 : term] : (($true = (X425 @ id @ X431 @ id)) & ((X425 @ id @ (X427 @ id @ X431) @ id) != $true))))) | ? [X424 : term] : ((sub @ X424 @ id) != X424))) & (apnotvar = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ((hoasinduction = $true) <=> ! [X292 : term,X293 : subst > term > subst > $o] : (? [X306 : term,X307 : subst,X308 : subst,X309 : subst] : (($true = (X293 @ (comp @ X308 @ X307) @ (sub @ X306 @ X307) @ X309)) & ((X293 @ X308 @ X306 @ (comp @ X307 @ X309)) != $true)) | ? [X303 : term] : (($true = (var @ (sub @ X303 @ id))) & ((X293 @ id @ X303 @ id) != $true)) | ((X293 @ id @ X292 @ id) = $true) | ? [X304 : term,X305 : term] : (($true != (X293 @ id @ (ap @ (sub @ X304 @ id) @ X305) @ id)) & ($true = (X293 @ id @ X305 @ id)) & ($true = (X293 @ id @ X304 @ id))) | ? [X294 : subst > term > term] : (($true != (X293 @ id @ (lam @ (X294 @ sh @ one)) @ id)) & ! [X298 : term] : (($true != (X293 @ id @ X298 @ id)) | ($true = (X293 @ id @ (X294 @ id @ X298) @ id))) & ! [X295 : subst,X296 : term,X297 : subst] : ((X294 @ (comp @ X295 @ X297) @ (sub @ X296 @ X297)) = (sub @ (X294 @ X295 @ X296) @ X297))) | ? [X299 : subst,X300 : subst,X301 : term,X302 : subst] : (($true != (X293 @ (comp @ X302 @ X300) @ (sub @ X301 @ X300) @ X299)) & ((X293 @ X302 @ X301 @ (comp @ X300 @ X299)) = $true)))) & ((d2subst @ d_id) = sh) & (lamnotap != $true) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (((((! [X368 : term,X369 : subst > term > subst > $o] : (? [X374 : term,X375 : term] : (((X369 @ id @ X375 @ id) = $true) & ($true = (X369 @ id @ X374 @ id)) & ((X369 @ id @ (ap @ (sub @ X374 @ id) @ X375) @ id) != $true)) | ? [X376 : subst,X377 : subst,X378 : subst,X379 : term] : (((X369 @ X378 @ X379 @ (comp @ X376 @ X377)) = $true) & ((X369 @ (comp @ X378 @ X376) @ (sub @ X379 @ X376) @ X377) != $true)) | ? [X380 : subst > term > term] : (! [X381 : term] : (($true != (X369 @ id @ X381 @ id)) | ((X369 @ id @ (X380 @ id @ X381) @ id) = $true)) & ! [X382 : subst,X383 : term,X384 : subst] : ((X380 @ (comp @ X382 @ X384) @ (sub @ X383 @ X384)) = (sub @ (X380 @ X382 @ X383) @ X384)) & ($true != (X369 @ id @ (lam @ (X380 @ sh @ one)) @ id))) | ? [X370 : term,X371 : subst,X372 : subst,X373 : subst] : (($true != (X369 @ X373 @ X370 @ (comp @ X372 @ X371))) & ($true = (X369 @ (comp @ X373 @ X372) @ (sub @ X370 @ X372) @ X371))) | ($true = (X369 @ id @ X368 @ id)) | ? [X385 : term] : (($true != (X369 @ id @ X385 @ id)) & ($true = (var @ (sub @ X385 @ id))))) | ? [X358 : subst > term > subst > $o,X359 : term,X360 : term > $o] : (($true != (X360 @ (lam @ X359))) & ! [X361 : term] : ((X360 @ X361) = (X358 @ id @ X361 @ id)) & ! [X367 : term] : (((X360 @ X367) != $true) | ($true = (X360 @ (sub @ X359 @ (push @ X367 @ id))))) & ! [X362 : subst > term > term] : (? [X363 : term] : (((X358 @ id @ (X362 @ id @ X363) @ id) != $true) & ((X358 @ id @ X363 @ id) = $true)) | ($true = (X358 @ id @ (lam @ (X362 @ sh @ one)) @ id)) | ? [X364 : subst,X365 : subst,X366 : term] : ((sub @ (X362 @ X364 @ X366) @ X365) != (X362 @ (comp @ X364 @ X365) @ (sub @ X366 @ X365)))))) | ? [X357 : term] : ((sub @ X357 @ id) != X357)) | ? [X350 : term,X351 : term > $o] : (($true != (X351 @ X350)) & ! [X353 : term,X354 : term] : (((X351 @ X353) != $true) | ($true = (X351 @ (ap @ X354 @ X353))) | ($true != (X351 @ X354))) & ! [X352 : term] : (((X351 @ X352) = $true) | ((var @ X352) != $true)) & ! [X355 : term] : (($true = (X351 @ (lam @ X355))) | ? [X356 : term] : (((X351 @ (sub @ X355 @ (push @ X356 @ id))) != $true) & ((X351 @ X356) = $true))))) | ? [X347 : subst > term > subst > $o] : ! [X348 : term > $o] : ? [X349 : term] : ((X347 @ id @ X349 @ id) != (X348 @ X349))) <=> (hoasinduction_lthm_3 = $true)) & ((axvarcons = $true) <=> ! [X77 : subst,X78 : term] : ((sub @ one @ (push @ X78 @ X77)) = X78)) & (pushprop_lem1v2_gthm = $true) & (! [X48 : term,X49 : term,X50 : term,X51 : term] : (((ap @ X49 @ X48) != (ap @ X50 @ X51)) | (X48 = X51)) <=> (apinj2 = $true)) & (hoasinduction_lem2v2_gthm = $true) & (pushprop_lem3v2 = $true) & (hoasapinj1_gthm = $true) & (hoasapnotvar_lthm = $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> ((((! [X21 : subst > term > subst > $o,X22 : term] : (? [X23 : term,X24 : term] : (((X21 @ id @ X24 @ id) = $true) & ($true != (X21 @ id @ (ap @ (sub @ X23 @ id) @ X24) @ id)) & ($true = (X21 @ id @ X23 @ id))) | ($true = (X21 @ id @ X22 @ id)) | ? [X25 : subst > term > term] : (((X21 @ id @ (lam @ (X25 @ sh @ one)) @ id) != $true) & ! [X26 : term] : (((X21 @ id @ X26 @ id) != $true) | ((X21 @ id @ (X25 @ id @ X26) @ id) = $true)) & ! [X27 : term,X28 : subst,X29 : subst] : ((X25 @ (comp @ X28 @ X29) @ (sub @ X27 @ X29)) = (sub @ (X25 @ X28 @ X27) @ X29)))) | ? [X11 : term,X12 : subst > term > subst > $o,X13 : term > $o] : (! [X14 : term] : ((X13 @ X14) = (X12 @ id @ X14 @ id)) & ! [X20 : term] : (($true = (X13 @ (sub @ X11 @ (push @ X20 @ id)))) | ((X13 @ X20) != $true)) & ((X13 @ (lam @ X11)) != $true) & ! [X15 : subst > term > term] : (? [X16 : term] : (((X12 @ id @ (X15 @ id @ X16) @ id) != $true) & ($true = (X12 @ id @ X16 @ id))) | ($true = (X12 @ id @ (lam @ (X15 @ sh @ one)) @ id)) | ? [X17 : term,X18 : subst,X19 : subst] : ((sub @ (X15 @ X19 @ X17) @ X18) != (X15 @ (comp @ X19 @ X18) @ (sub @ X17 @ X18)))))) | ? [X10 : term] : ((sub @ X10 @ id) != X10)) | ? [X3 : term,X4 : term > $o] : (! [X8 : term] : (((X4 @ (lam @ X8)) = $true) | ? [X9 : term] : (($true != (X4 @ (sub @ X8 @ (push @ X9 @ id)))) & ($true = (X4 @ X9)))) & ! [X7 : term] : (($true != (var @ X7)) | ((X4 @ X7) = $true)) & ($true != (X4 @ X3)) & ! [X5 : term,X6 : term] : (((X4 @ X5) != $true) | ((X4 @ X6) != $true) | ($true = (X4 @ (ap @ X5 @ X6)))))) | ? [X0 : subst > term > subst > $o] : ! [X1 : term > $o] : ? [X2 : term] : ((X0 @ id @ X2 @ id) != (X1 @ X2)))) & (hoaslamnotap_gthm = $true) & (pushprop = $true) & (hoaslamnotvar_lthm = $true) & (! [X32 : term,X33 : subst > term > subst > $o] : (? [X42 : subst > term > term] : (((X33 @ id @ (lam @ (X42 @ sh @ one)) @ id) != $true) & ! [X43 : term] : (($true != (X33 @ id @ X43 @ id)) | ((X33 @ id @ (X42 @ id @ X43) @ id) = $true)) & ! [X44 : term,X45 : subst,X46 : subst] : ((X42 @ (comp @ X46 @ X45) @ (sub @ X44 @ X45)) = (sub @ (X42 @ X46 @ X44) @ X45))) | ? [X38 : subst,X39 : subst,X40 : subst,X41 : term] : (($true != (X33 @ (comp @ X39 @ X40) @ (sub @ X41 @ X40) @ X38)) & ($true = (X33 @ X39 @ X41 @ (comp @ X40 @ X38)))) | ($true = (X33 @ id @ (lam @ X32) @ id)) | ? [X47 : term] : (((X33 @ id @ (sub @ X32 @ (push @ X47 @ id)) @ id) != $true) & ($true = (X33 @ id @ X47 @ id))) | ? [X34 : term,X35 : subst,X36 : subst,X37 : subst] : (((X33 @ X36 @ X34 @ (comp @ X37 @ X35)) != $true) & ((X33 @ (comp @ X36 @ X37) @ (sub @ X34 @ X37) @ X35) = $true))) <=> (hoasinduction_lem3 = $true)) & ((axvarid = $true) <=> ! [X236 : term] : ((sub @ X236 @ id) = X236)) & ((! [X254 : term] : ((sub @ X254 @ id) = X254) | ? [X253 : term] : ((sub @ X253 @ id) != X253)) <=> (termmset_lthm = $true)) & (axapp = $true) & (lamnotvar = $true) & ((termmset = $true) <=> ! [X394 : term] : ((sub @ X394 @ id) = X394)) & (! [X158 : term > $o,X159 : subst > term > subst > $o,X160 : term] : (? [X167 : term] : (($true != (X158 @ (sub @ X160 @ (push @ X167 @ id)))) & ((X158 @ X167) = $true)) | ? [X161 : term] : ((X158 @ X161) != (X159 @ id @ X161 @ id)) | ($true = (X158 @ (lam @ X160))) | ? [X162 : subst > term > term] : (! [X163 : term] : (($true != (X159 @ id @ X163 @ id)) | ($true = (X159 @ id @ (X162 @ id @ X163) @ id))) & ((X159 @ id @ (lam @ (X162 @ sh @ one)) @ id) != $true) & ! [X164 : subst,X165 : term,X166 : subst] : ((sub @ (X162 @ X166 @ X165) @ X164) = (X162 @ (comp @ X166 @ X164) @ (sub @ X165 @ X164))))) <=> (hoasinduction_lem3v2a = $true)) & (hoaslamnotvar_gthm = $true) & ((hoasinduction_lem2 = $true) <=> ! [X452 : term,X453 : term,X454 : subst > term > subst > $o] : (((X454 @ id @ X453 @ id) != $true) | ? [X463 : term,X464 : term] : (($true = (X454 @ id @ X463 @ id)) & ($true != (X454 @ id @ (ap @ (sub @ X463 @ id) @ X464) @ id)) & ((X454 @ id @ X464 @ id) = $true)) | ((X454 @ id @ X452 @ id) != $true) | ? [X455 : subst,X456 : subst,X457 : term,X458 : subst] : (((X454 @ X458 @ X457 @ (comp @ X455 @ X456)) != $true) & ($true = (X454 @ (comp @ X458 @ X455) @ (sub @ X457 @ X455) @ X456))) | ((X454 @ id @ (ap @ X452 @ X453) @ id) = $true) | ? [X459 : subst,X460 : term,X461 : subst,X462 : subst] : (((X454 @ X461 @ X460 @ (comp @ X459 @ X462)) = $true) & ((X454 @ (comp @ X461 @ X459) @ (sub @ X460 @ X459) @ X462) != $true)))) & ((hoasinduction_lem3aa = $true) <=> ! [X498 : subst > term > subst > $o,X499 : term] : (? [X501 : subst > term > term] : (! [X505 : term] : (($true != (X498 @ id @ X505 @ id)) | ($true = (X498 @ id @ (X501 @ id @ X505) @ id))) & ($true != (X498 @ id @ (lam @ (X501 @ sh @ one)) @ id)) & ! [X502 : subst,X503 : subst,X504 : term] : ((X501 @ (comp @ X502 @ X503) @ (sub @ X504 @ X503)) = (sub @ (X501 @ X502 @ X504) @ X503))) | ? [X500 : term] : (($true != (X498 @ id @ (sub @ X499 @ (push @ X500 @ id)) @ id)) & ($true = (X498 @ id @ X500 @ id))) | ($true = (X498 @ id @ (lam @ (sub @ X499 @ (push @ one @ sh))) @ id)))) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (! [X480 : term,X481 : term,X482 : term,X483 : term] : (((ap @ (sub @ X482 @ id) @ X481) != (ap @ (sub @ X480 @ id) @ X483)) | (X481 = X483)) <=> (hoasapinj2 = $true)) & ! [X422 : term] : ? [X423 : d_term] : ((d2term @ X423) = X422) & (substmonoid_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)))))))))))) & (hoaslaminj_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (pushprop_lthm_orig = $true) & (pushprop_lthm = $true) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem1_gthm = $true) & ((induction2_lthm = $true) <=> ((! [X137 : term,X138 : term > $o] : (? [X139 : term] : (((var @ X139) = $true) & ((X138 @ X139) != $true)) | ? [X142 : term] : (! [X143 : term] : (((X138 @ X143) != $true) | ((X138 @ (sub @ X142 @ (push @ X143 @ id))) = $true)) & ($true != (X138 @ (lam @ X142)))) | ? [X140 : term,X141 : term] : (((X138 @ X140) = $true) & ((X138 @ (ap @ X140 @ X141)) != $true) & ($true = (X138 @ X141))) | ($true = (X138 @ X137))) | ? [X129 : subst,X130 : term > $o,X131 : term] : (! [X132 : term] : (? [X133 : term] : (($true != (X130 @ (sub @ X132 @ (push @ X133 @ id)))) & ((X130 @ X133) = $true)) | ((X130 @ (lam @ X132)) = $true)) & ! [X136 : term] : (((var @ X136) != $true) | ($true = (X130 @ (sub @ X136 @ X129)))) & ($true != (X130 @ (sub @ X131 @ X129))) & ! [X134 : term,X135 : term] : (((X130 @ X134) != $true) | ($true != (X130 @ X135)) | ((X130 @ (ap @ X134 @ X135)) = $true)))) | ? [X128 : term] : ((sub @ X128 @ id) != X128))) & (! [X529 : term] : ? [X530 : subst > term > term] : ((X530 @ sh @ one) = (sub @ X529 @ (push @ one @ sh))) <=> (hoasinduction_lem3b = $true)) & (pushprop_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (hoasinduction_lem1 = $true) & (hoasapinj2_gthm = $true) & ! [X265 : d_subst,X266 : d_subst] : ((X265 = X266) | ((d2subst @ X266) != (d2subst @ X265))) & (pushprop_lem0_gthm = $true) & (! [X341 : subst > term > term,X342 : term,X343 : term] : (((ap @ (sub @ X342 @ id) @ X343) != (lam @ (X341 @ sh @ one))) | ? [X344 : subst,X345 : term,X346 : subst] : ((sub @ (X341 @ X346 @ X345) @ X344) != (X341 @ (comp @ X346 @ X344) @ (sub @ X345 @ X344)))) <=> (hoaslamnotap = $true)) & (axvarshift = $true) & ((pushprop_lem0 = $true) <=> ! [X119 : term > $o,X120 : subst,X121 : term] : ? [X122 : term > $o] : ! [X123 : term] : ((X122 @ X123) = (X119 @ (sub @ X123 @ (push @ X121 @ X120))))) & (((! [X73 : term,X74 : term,X75 : term,X76 : term] : ((X73 = X74) | ((ap @ (sub @ X74 @ id) @ X76) != (ap @ (sub @ X73 @ id) @ X75))) | ? [X69 : term,X70 : term,X71 : term,X72 : term] : (((ap @ X69 @ X70) = (ap @ X71 @ X72)) & (X69 != X71))) | ? [X68 : term] : ((sub @ X68 @ id) != X68)) <=> (hoasapinj1_lthm = $true)) & ((axscons = $true) <=> ! [X267 : subst] : ((push @ (sub @ one @ X267) @ (comp @ sh @ X267)) = X267)) & (((((! [X517 : subst,X518 : term > $o,X519 : term] : (? [X522 : term,X523 : term] : (($true != (X518 @ (ap @ X523 @ X522))) & ((X518 @ X522) = $true) & ((X518 @ X523) = $true)) | ($true = (X518 @ (sub @ X519 @ X517))) | ? [X524 : term] : (($true != (X518 @ (sub @ X524 @ X517))) & ((var @ X524) = $true)) | ? [X520 : term] : (! [X521 : term] : (($true != (X518 @ X521)) | ($true = (X518 @ (sub @ X520 @ (push @ X521 @ id))))) & ((X518 @ (lam @ X520)) != $true))) | ? [X511 : term,X512 : term > $o] : (! [X515 : term,X516 : term] : (((X512 @ (ap @ X516 @ X515)) = $true) | ((X512 @ X515) != $true) | ($true != (X512 @ X516))) & ((X512 @ X511) != $true) & ! [X513 : term] : (($true != (X512 @ X513)) | ((X512 @ (lam @ X513)) = $true)) & ! [X514 : term] : (((X512 @ X514) = $true) | ((var @ X514) != $true)))) | ? [X510 : subst] : ((comp @ X510 @ id) != X510)) | ? [X508 : subst,X509 : term] : ((comp @ sh @ (push @ X509 @ X508)) != X508)) | ? [X506 : term,X507 : subst] : ((sub @ one @ (push @ X506 @ X507)) != X506)) <=> (induction2lem_lthm = $true)) & ((shinj = $true) <=> ! [X328 : term,X329 : term] : ((X328 = X329) | ((sub @ X329 @ sh) != (sub @ X328 @ sh)))) & (axassoc = $true) & (hoasinduction_lem1v2 = $true) & (! [X52 : subst] : ((comp @ X52 @ id) = X52) <=> (axidr = $true)) & (! [X414 : term,X415 : subst > term > subst > $o] : (? [X417 : subst > term > term] : (! [X421 : term] : (($true != (X415 @ id @ X421 @ id)) | ((X415 @ id @ (X417 @ id @ X421) @ id) = $true)) & ((X415 @ id @ (lam @ (X417 @ sh @ one)) @ id) != $true) & ! [X418 : subst,X419 : term,X420 : subst] : ((sub @ (X417 @ X418 @ X419) @ X420) = (X417 @ (comp @ X418 @ X420) @ (sub @ X419 @ X420)))) | ((X415 @ id @ (lam @ (sub @ X414 @ (push @ one @ sh))) @ id) = $true) | ? [X416 : term] : (((X415 @ id @ X416 @ id) = $true) & ((X415 @ id @ (sub @ X414 @ (push @ X416 @ id)) @ id) != $true))) <=> (hoasinduction_lem3aa_lthm = $true)) & ! [X234 : d_term,X235 : d_term] : (((d2term @ X234) != (d2term @ X235)) | (X234 = X235)) & ((var @ (d2term @ d_one)) != $true) & ((((! [X204 : subst > term > subst > $o,X205 : term] : (? [X216 : term] : (($true = (var @ (sub @ X216 @ id))) & ((X204 @ id @ X216 @ id) != $true)) | ? [X208 : subst,X209 : subst,X210 : subst,X211 : term] : (($true = (X204 @ (comp @ X210 @ X208) @ (sub @ X211 @ X208) @ X209)) & ((X204 @ X210 @ X211 @ (comp @ X208 @ X209)) != $true)) | ? [X217 : subst > term > term] : (! [X218 : subst,X219 : term,X220 : subst] : ((sub @ (X217 @ X220 @ X219) @ X218) = (X217 @ (comp @ X220 @ X218) @ (sub @ X219 @ X218))) & ! [X221 : term] : (($true != (X204 @ id @ X221 @ id)) | ((X204 @ id @ (X217 @ id @ X221) @ id) = $true)) & ((X204 @ id @ (lam @ (X217 @ sh @ one)) @ id) != $true)) | ? [X212 : subst,X213 : subst,X214 : term,X215 : subst] : (((X204 @ (comp @ X213 @ X212) @ (sub @ X214 @ X212) @ X215) != $true) & ($true = (X204 @ X213 @ X214 @ (comp @ X212 @ X215)))) | ($true = (X204 @ id @ X205 @ id)) | ? [X206 : term,X207 : term] : (($true = (X204 @ id @ X206 @ id)) & ($true != (X204 @ id @ (ap @ (sub @ X207 @ id) @ X206) @ id)) & ($true = (X204 @ id @ X207 @ id)))) | ? [X188 : term,X189 : subst > term > subst > $o] : (! [X198 : term] : (((X189 @ id @ (sub @ X188 @ (push @ X198 @ id)) @ id) = $true) | ($true != (X189 @ id @ X198 @ id))) & ! [X190 : subst,X191 : term,X192 : subst,X193 : subst] : (((X189 @ X193 @ X191 @ (comp @ X190 @ X192)) != $true) | ((X189 @ (comp @ X193 @ X190) @ (sub @ X191 @ X190) @ X192) = $true)) & ((X189 @ id @ (lam @ X188) @ id) != $true) & ! [X194 : subst,X195 : subst,X196 : term,X197 : subst] : (((X189 @ (comp @ X197 @ X195) @ (sub @ X196 @ X195) @ X194) != $true) | ((X189 @ X197 @ X196 @ (comp @ X195 @ X194)) = $true)) & ! [X199 : subst > term > term] : (? [X200 : term,X201 : subst,X202 : subst] : ((sub @ (X199 @ X201 @ X200) @ X202) != (X199 @ (comp @ X201 @ X202) @ (sub @ X200 @ X202))) | ? [X203 : term] : (((X189 @ id @ X203 @ id) = $true) & ((X189 @ id @ (X199 @ id @ X203) @ id) != $true)) | ((X189 @ id @ (lam @ (X199 @ sh @ one)) @ id) = $true)))) | ? [X175 : term,X176 : term,X177 : subst > term > subst > $o] : (($true = (X177 @ id @ X175 @ id)) & ! [X182 : subst,X183 : subst,X184 : term,X185 : subst] : (($true = (X177 @ X185 @ X184 @ (comp @ X183 @ X182))) | ($true != (X177 @ (comp @ X185 @ X183) @ (sub @ X184 @ X183) @ X182))) & ! [X186 : term,X187 : term] : (($true != (X177 @ id @ X187 @ id)) | ($true != (X177 @ id @ X186 @ id)) | ($true = (X177 @ id @ (ap @ (sub @ X187 @ id) @ X186) @ id))) & ($true = (X177 @ id @ X176 @ id)) & ! [X178 : subst,X179 : subst,X180 : term,X181 : subst] : (((X177 @ X179 @ X180 @ (comp @ X181 @ X178)) != $true) | ((X177 @ (comp @ X179 @ X181) @ (sub @ X180 @ X181) @ X178) = $true)) & ((X177 @ id @ (ap @ X175 @ X176) @ id) != $true))) | ? [X168 : term > $o,X169 : term] : (($true != (X168 @ X169)) & ! [X172 : term,X173 : term] : (((X168 @ X172) != $true) | ((X168 @ (ap @ X173 @ X172)) = $true) | ($true != (X168 @ X173))) & ! [X174 : term] : (((var @ X174) != $true) | ((X168 @ X174) = $true)) & ! [X170 : term] : (((X168 @ (lam @ X170)) = $true) | ? [X171 : term] : (((X168 @ X171) = $true) & ($true != (X168 @ (sub @ X170 @ (push @ X171 @ id)))))))) <=> (hoasinduction_lthm = $true)) & (axmap = $true) & ((hoasapinj1 = $true) <=> ! [X486 : term,X487 : term,X488 : term,X489 : term] : (((ap @ (sub @ X489 @ id) @ X486) != (ap @ (sub @ X488 @ id) @ X487)) | (X488 = X489))) & (hoaslamnotvar = $true) & (hoasinduction_lem1v2_gthm = $true) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & ((hoasinduction_lem3aaa = $true) <=> ! [X222 : term,X223 : subst > term > subst > $o] : (? [X225 : term,X226 : subst > term > term] : (! [X233 : term] : (((X223 @ id @ (X226 @ id @ X233) @ id) = $true) | ($true != (X223 @ id @ X233 @ id))) & ! [X227 : subst,X228 : term,X229 : subst] : ((sub @ (sub @ X225 @ (push @ X228 @ X229)) @ X227) = (sub @ (X226 @ X229 @ X228) @ X227)) & ($true != (X223 @ id @ (lam @ (X226 @ sh @ one)) @ id)) & ! [X230 : subst,X231 : term,X232 : subst] : ((sub @ X225 @ (push @ (sub @ X231 @ X232) @ (comp @ X230 @ X232))) = (X226 @ (comp @ X230 @ X232) @ (sub @ X231 @ X232)))) | ? [X224 : term] : (((X223 @ id @ X224 @ id) = $true) & ($true != (X223 @ id @ (sub @ X222 @ (push @ X224 @ id)) @ id))) | ($true = (X223 @ id @ (lam @ (sub @ X222 @ (push @ one @ sh))) @ id)))) & ((hoasinduction_lem3a_lthm = $true) <=> ((! [X90 : subst > term > subst > $o,X91 : term] : (? [X97 : term] : (($true = (X90 @ id @ X97 @ id)) & ($true != (X90 @ id @ (sub @ X91 @ (push @ X97 @ id)) @ id))) | ((X90 @ id @ (lam @ X91) @ id) = $true) | ? [X92 : subst > term > term] : (! [X94 : term,X95 : subst,X96 : subst] : ((sub @ (X92 @ X96 @ X94) @ X95) = (X92 @ (comp @ X96 @ X95) @ (sub @ X94 @ X95))) & ! [X93 : term] : (($true = (X90 @ id @ (X92 @ id @ X93) @ id)) | ($true != (X90 @ id @ X93 @ id))) & ($true != (X90 @ id @ (lam @ (X92 @ sh @ one)) @ id)))) | ? [X82 : subst > term > subst > $o,X83 : term] : (((X82 @ id @ (lam @ (sub @ X83 @ (push @ one @ sh))) @ id) != $true) & ! [X89 : term] : (($true = (X82 @ id @ (sub @ X83 @ (push @ X89 @ id)) @ id)) | ((X82 @ id @ X89 @ id) != $true)) & ! [X84 : subst > term > term] : (? [X85 : term,X86 : subst,X87 : subst] : ((sub @ (X84 @ X87 @ X85) @ X86) != (X84 @ (comp @ X87 @ X86) @ (sub @ X85 @ X86))) | ($true = (X82 @ id @ (lam @ (X84 @ sh @ one)) @ id)) | ? [X88 : term] : (((X82 @ id @ (X84 @ id @ X88) @ id) != $true) & ($true = (X82 @ id @ X88 @ id)))))) | ? [X81 : term] : ((sub @ X81 @ id) != X81))) & ! [X484 : subst] : ? [X485 : d_subst] : ((d2subst @ X485) = X484) & (pushprop_lem3v2_lthm = $true) & (hoasinduction_lem2_lthm = $true) & (axabs = $true) & (hoasapnotvar = $true) & ((hoaslaminj_lthm = $true) <=> (((! [X243 : subst,X244 : term,X245 : subst > term > term,X246 : subst > term > term] : (((lam @ (X246 @ sh @ one)) != (lam @ (X245 @ sh @ one))) | ((X246 @ X243 @ X244) = (X245 @ X243 @ X244)) | ? [X250 : subst,X251 : term,X252 : subst] : ((X245 @ (comp @ X250 @ X252) @ (sub @ X251 @ X252)) != (sub @ (X245 @ X250 @ X251) @ X252)) | ? [X247 : term,X248 : subst,X249 : subst] : ((sub @ (X246 @ X248 @ X247) @ X249) != (X246 @ (comp @ X248 @ X249) @ (sub @ X247 @ X249)))) | ? [X241 : term,X242 : term] : ((X241 != X242) & ((lam @ X241) = (lam @ X242)))) | ? [X239 : term,X240 : subst] : ((comp @ sh @ (push @ X239 @ X240)) != X240)) | ? [X237 : subst,X238 : term] : ((sub @ one @ (push @ X238 @ X237)) != X238))) & (ulamvarsh = $true) & (hoasinduction_lem2_gthm = $true) & ((induction = $true) <=> ! [X255 : term,X256 : term > $o] : (? [X258 : term,X259 : term] : (((X256 @ X258) = $true) & ((X256 @ (ap @ X259 @ X258)) != $true) & ($true = (X256 @ X259))) | ? [X257 : term] : (($true = (X256 @ X257)) & ((X256 @ (lam @ X257)) != $true)) | ((X256 @ X255) = $true) | ? [X260 : term] : (($true != (X256 @ X260)) & ((var @ X260) = $true)))) & ((hoasinduction_lem3v2_lthm = $true) <=> (? [X98 : term] : ((sub @ X98 @ id) != X98) | ! [X99 : term > $o,X100 : subst > term > subst > $o,X101 : term] : (((X99 @ (lam @ X101)) = $true) | ? [X102 : term] : (((X99 @ (sub @ X101 @ (push @ X102 @ id))) != $true) & ((X99 @ X102) = $true)) | ? [X103 : subst > term > term] : (! [X104 : subst,X105 : subst,X106 : term] : ((X103 @ (comp @ X105 @ X104) @ (sub @ X106 @ X104)) = (sub @ (X103 @ X105 @ X106) @ X104)) & ! [X107 : term] : (((X100 @ id @ X107 @ id) != $true) | ($true = (X100 @ id @ (X103 @ id @ X107) @ id))) & ($true != (X100 @ id @ (lam @ (X103 @ sh @ one)) @ id))) | ? [X113 : subst,X114 : subst,X115 : term,X116 : subst] : (($true = (X100 @ (comp @ X114 @ X113) @ (sub @ X115 @ X113) @ X116)) & ($true != (X100 @ X114 @ X115 @ (comp @ X113 @ X116)))) | ? [X112 : term] : ((X100 @ id @ X112 @ id) != (X99 @ X112)) | ? [X108 : subst,X109 : term,X110 : subst,X111 : subst] : (((X100 @ (comp @ X108 @ X110) @ (sub @ X109 @ X110) @ X111) != $true) & ((X100 @ X108 @ X109 @ (comp @ X110 @ X111)) = $true))))) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_lem3_gthm = $true) & (ulamvarind = $true) & (((! [X153 : term,X154 : term > $o,X155 : subst,X156 : term,X157 : term > $o] : (((X157 @ (sub @ X153 @ (push @ X156 @ X155))) = $true) | ($true != (X154 @ X153))) | ? [X151 : subst,X152 : term] : ((comp @ sh @ (push @ X152 @ X151)) != X151)) | ? [X149 : term,X150 : subst] : ((sub @ one @ (push @ X149 @ X150)) != X149)) <=> (pushprop_lem1_lthm = $true)) & (induction2lem_gthm = $true) & ((? [X532 : term,X533 : term,X534 : term,X535 : term] : (((ap @ X532 @ X534) = (ap @ X535 @ X533)) & (X533 != X534)) | ! [X536 : term,X537 : term,X538 : term,X539 : term] : (((ap @ (sub @ X536 @ id) @ X539) != (ap @ (sub @ X537 @ id) @ X538)) | (X538 = X539))) <=> (hoasapinj2_lthm = $true)) & ((hoasinduction_lem3b_lthm = $true) <=> ! [X339 : term] : ? [X340 : subst > term > term] : ((X340 @ sh @ one) = (sub @ X339 @ (push @ one @ sh)))) & ((hoasinduction_no_psi_cond = $true) <=> ! [X330 : term,X331 : subst > term > subst > $o] : (((X331 @ id @ X330 @ id) = $true) | ? [X337 : term,X338 : term] : (((X331 @ id @ (ap @ (sub @ X337 @ id) @ X338) @ id) != $true) & ((X331 @ id @ X338 @ id) = $true) & ((X331 @ id @ X337 @ id) = $true)) | ? [X332 : subst > term > term] : (($true != (X331 @ id @ (lam @ (X332 @ sh @ one)) @ id)) & ! [X333 : term] : (((X331 @ id @ X333 @ id) != $true) | ((X331 @ id @ (X332 @ id @ X333) @ id) = $true)) & ! [X334 : subst,X335 : subst,X336 : term] : ((sub @ (X332 @ X335 @ X336) @ X334) = (X332 @ (comp @ X335 @ X334) @ (sub @ X336 @ X334)))))) & ((substmonoid_lthm = $true) <=> (((! [X397 : subst] : ((comp @ id @ X397) = X397) & ! [X398 : subst] : ((comp @ X398 @ id) = X398)) | ? [X396 : subst] : ((comp @ X396 @ id) != X396)) | ? [X395 : subst] : ((comp @ id @ X395) != X395))) & ! [X291 : d_subst] : (d_id = X291) & ((induction2 = $true) <=> ! [X268 : term > $o,X269 : term] : (? [X274 : term] : (($true != (X268 @ X274)) & ((var @ X274) = $true)) | ? [X272 : term,X273 : term] : (($true = (X268 @ X272)) & ((X268 @ (ap @ X273 @ X272)) != $true) & ((X268 @ X273) = $true)) | ((X268 @ X269) = $true) | ? [X270 : term] : (! [X271 : term] : (($true = (X268 @ (sub @ X270 @ (push @ X271 @ id)))) | ($true != (X268 @ X271))) & ((X268 @ (lam @ X270)) != $true)))) & (hoasinduction_gthm = $true) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (pushprop_lem2v2_lthm = $true) & (! [X310 : term,X311 : subst > term > subst > $o,X312 : term > $o] : (? [X323 : subst > term > term] : (((X311 @ id @ (lam @ (X323 @ sh @ one)) @ id) != $true) & ! [X325 : term,X326 : subst,X327 : subst] : ((X323 @ (comp @ X327 @ X326) @ (sub @ X325 @ X326)) = (sub @ (X323 @ X327 @ X325) @ X326)) & ! [X324 : term] : (((X311 @ id @ (X323 @ id @ X324) @ id) = $true) | ($true != (X311 @ id @ X324 @ id)))) | ? [X315 : subst,X316 : subst,X317 : subst,X318 : term] : (($true != (X311 @ X316 @ X318 @ (comp @ X317 @ X315))) & ((X311 @ (comp @ X316 @ X317) @ (sub @ X318 @ X317) @ X315) = $true)) | ? [X314 : term] : (((X312 @ X314) = $true) & ((X312 @ (sub @ X310 @ (push @ X314 @ id))) != $true)) | ((X312 @ (lam @ X310)) = $true) | ? [X319 : subst,X320 : subst,X321 : term,X322 : subst] : (((X311 @ X322 @ X321 @ (comp @ X319 @ X320)) = $true) & ((X311 @ (comp @ X322 @ X319) @ (sub @ X321 @ X319) @ X320) != $true)) | ? [X313 : term] : ((X312 @ X313) != (X311 @ id @ X313 @ id))) <=> (hoasinduction_lem3v2 = $true)) & (hoaslamnotap_lthm = $true) & (axclos = $true) & (ulamvar1 != $true) & ((d2subst @ d_id) = id) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((! [X79 : subst] : ((comp @ id @ X79) = X79) & ! [X80 : subst] : ((comp @ X80 @ id) = X80)) <=> (substmonoid = $true)) & (! [X449 : subst > term > subst > $o] : ? [X450 : term > $o] : ! [X451 : term] : ((X449 @ id @ X451 @ id) = (X450 @ X451)) <=> (hoasinduction_lem0_lthm = $true)) & (hoasinduction_lem3b_gthm = $true) & ! [X531 : d_term] : (d_one = X531)),
% 15.02/3.54 inference(ennf_transformation,[status(thm)],[f11])).
% 15.02/3.54 thf(f11,plain,(
% 15.02/3.54 ((pushprop_lem1 = $true) <=> ! [X275 : term,X276 : term,X277 : term > $o,X278 : subst,X279 : term > $o] : (((X279 @ X276) != $true) | ((X277 @ (sub @ X276 @ (push @ X275 @ X278))) = $true))) & (induction2_gthm = $true) & ((hoaslaminj = $true) <=> ! [X404 : subst,X405 : subst > term > term,X406 : term,X407 : subst > term > term] : (~! [X408 : term,X409 : subst,X410 : subst] : ((X407 @ (comp @ X409 @ X410) @ (sub @ X408 @ X410)) = (sub @ (X407 @ X409 @ X408) @ X410)) | ((X407 @ X404 @ X406) = (X405 @ X404 @ X406)) | ~! [X411 : subst,X412 : subst,X413 : term] : ((X405 @ (comp @ X412 @ X411) @ (sub @ X413 @ X411)) = (sub @ (X405 @ X412 @ X413) @ X411)) | ((lam @ (X407 @ sh @ one)) != (lam @ (X405 @ sh @ one))))) & ((axshiftcons = $true) <=> ! [X117 : term,X118 : subst] : ((comp @ sh @ (push @ X117 @ X118)) = X118)) & (! [X490 : term,X491 : subst > term > subst > $o] : (~! [X492 : term] : (((X491 @ id @ X492 @ id) != $true) | ((X491 @ id @ (sub @ X490 @ (push @ X492 @ id)) @ id) = $true)) | ~! [X493 : subst > term > term] : (~! [X494 : subst,X495 : subst,X496 : term] : ((X493 @ (comp @ X494 @ X495) @ (sub @ X496 @ X495)) = (sub @ (X493 @ X494 @ X496) @ X495)) | ((X491 @ id @ (lam @ (X493 @ sh @ one)) @ id) = $true) | ~! [X497 : term] : (((X491 @ id @ (X493 @ id @ X497) @ id) = $true) | ((X491 @ id @ X497 @ id) != $true))) | ($true = (X491 @ id @ (lam @ X490) @ id))) <=> (hoasinduction_lem3a = $true)) & (pushprop_lem2v2 = $true) & (! [X53 : term,X54 : term > $o,X55 : subst > term > subst > $o,X56 : term] : (((X54 @ X56) != $true) | ((X54 @ (ap @ X53 @ X56)) = $true) | ~! [X64 : subst,X65 : term,X66 : subst,X67 : subst] : (((X55 @ X66 @ X65 @ (comp @ X67 @ X64)) = $true) | ((X55 @ (comp @ X66 @ X67) @ (sub @ X65 @ X67) @ X64) != $true)) | ~! [X61 : term,X62 : term] : (((X55 @ id @ X62 @ id) != $true) | ($true != (X55 @ id @ X61 @ id)) | ((X55 @ id @ (ap @ (sub @ X62 @ id) @ X61) @ id) = $true)) | ~! [X57 : subst,X58 : term,X59 : subst,X60 : subst] : (($true != (X55 @ X60 @ X58 @ (comp @ X57 @ X59))) | ((X55 @ (comp @ X60 @ X57) @ (sub @ X58 @ X57) @ X59) = $true)) | ~! [X63 : term] : ((X55 @ id @ X63 @ id) = (X54 @ X63)) | ((X54 @ X53) != $true)) <=> (hoasinduction_lem2v2 = $true)) & ((induction2lem = $true) <=> ! [X386 : term,X387 : subst,X388 : term > $o] : (~! [X389 : term] : (($true != (var @ X389)) | ((X388 @ (sub @ X389 @ X387)) = $true)) | ~! [X392 : term] : (((X388 @ (lam @ X392)) = $true) | ~! [X393 : term] : (($true != (X388 @ X393)) | ((X388 @ (sub @ X392 @ (push @ X393 @ id))) = $true))) | ($true = (X388 @ (sub @ X386 @ X387))) | ~! [X390 : term,X391 : term] : (((X388 @ X390) != $true) | ((X388 @ (ap @ X391 @ X390)) = $true) | ($true != (X388 @ X391))))) & ((! [X465 : term] : ~! [X466 : subst > term > term] : ~! [X467 : subst,X468 : term] : ((sub @ X465 @ (push @ X468 @ X467)) = (X466 @ X467 @ X468)) => (! [X469 : term] : ((sub @ X469 @ id) = X469) => ! [X470 : subst > term > subst > $o,X471 : term,X472 : term > $o] : (~! [X479 : term] : (($true != (X472 @ X479)) | ((X472 @ (sub @ X471 @ (push @ X479 @ id))) = $true)) | ~! [X473 : subst > term > term] : (~! [X475 : subst,X476 : subst,X477 : term] : ((X473 @ (comp @ X476 @ X475) @ (sub @ X477 @ X475)) = (sub @ (X473 @ X476 @ X477) @ X475)) | ((X470 @ id @ (lam @ (X473 @ sh @ one)) @ id) = $true) | ~! [X474 : term] : (((X470 @ id @ X474 @ id) != $true) | ((X470 @ id @ (X473 @ id @ X474) @ id) = $true))) | ~! [X478 : term] : ((X470 @ id @ X478 @ id) = (X472 @ X478)) | ((X472 @ (lam @ X471)) = $true)))) <=> (hoasinduction_lem3v2a_lthm = $true)) & (hoasapnotvar_gthm = $true) & (! [X144 : subst,X145 : term > $o,X146 : term] : ~! [X147 : term > $o] : ~! [X148 : term] : ((X145 @ (sub @ X148 @ (push @ X146 @ X144))) = (X147 @ X148)) <=> (pushprop_lem0_lthm = $true)) & (hoasinduction_lem3a_gthm = $true) & (hoasinduction_lem3v2_gthm = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X280 : term] : ~! [X281 : subst > term > term] : ~! [X282 : term,X283 : subst] : ((X281 @ X283 @ X282) = (sub @ X280 @ (push @ X282 @ X283)))) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (termmset_gthm = $true) & (! [X124 : term] : ~! [X125 : subst > term > term] : ~! [X126 : term,X127 : subst] : ((sub @ X124 @ (push @ X126 @ X127)) = (X125 @ X127 @ X126)) <=> (hoasinduction_lem3v2_f_lthm = $true)) & ((! [X284 : term,X285 : subst] : ((sub @ one @ (push @ X284 @ X285)) = X284) => ! [X286 : term,X287 : subst,X288 : term > $o,X289 : term > $o] : (~! [X290 : term] : ((X288 @ (sub @ X290 @ (push @ X286 @ X287))) = (X289 @ X290)) | ((X289 @ one) = $true) | ($true != (X288 @ X286)))) <=> (pushprop_lem1v2_lthm = $true)) & (! [X30 : term,X31 : term] : ((X30 = X31) | ((lam @ X30) != (lam @ X31))) <=> (laminj = $true)) & (! [X525 : subst > term > subst > $o] : ~! [X526 : term > $o] : ~! [X527 : term] : ((X525 @ id @ X527 @ id) = (X526 @ X527)) <=> (hoasinduction_lem0 = $true)) & (! [X399 : subst,X400 : term > $o,X401 : term > $o,X402 : term] : (($true != (X400 @ X402)) | ~! [X403 : term] : ((X400 @ (sub @ X403 @ (push @ X402 @ X399))) = (X401 @ X403)) | ($true = (X401 @ one))) <=> (pushprop_lem1v2 = $true)) & ((apinj1 = $true) <=> ! [X261 : term,X262 : term,X263 : term,X264 : term] : ((X262 = X264) | ((ap @ X264 @ X263) != (ap @ X262 @ X261)))) & (one = (d2term @ d_one)) & (! [X528 : subst] : ((comp @ id @ X528) = X528) <=> (axidl = $true)) & ((hoasinduction_lem3_lthm = $true) <=> (! [X424 : term] : ((sub @ X424 @ id) = X424) => (! [X425 : subst > term > subst > $o,X426 : term] : (~! [X432 : term] : (($true = (X425 @ id @ (sub @ X426 @ (push @ X432 @ id)) @ id)) | ((X425 @ id @ X432 @ id) != $true)) | ~! [X427 : subst > term > term] : (($true = (X425 @ id @ (lam @ (X427 @ sh @ one)) @ id)) | ~! [X428 : subst,X429 : term,X430 : subst] : ((X427 @ (comp @ X430 @ X428) @ (sub @ X429 @ X428)) = (sub @ (X427 @ X430 @ X429) @ X428)) | ~! [X431 : term] : (($true != (X425 @ id @ X431 @ id)) | ((X425 @ id @ (X427 @ id @ X431) @ id) = $true))) | ($true = (X425 @ id @ (lam @ (sub @ X426 @ (push @ one @ sh))) @ id))) => ! [X433 : term,X434 : subst > term > subst > $o] : (~! [X435 : term] : (($true != (X434 @ id @ X435 @ id)) | ((X434 @ id @ (sub @ X433 @ (push @ X435 @ id)) @ id) = $true)) | ~! [X440 : subst,X441 : term,X442 : subst,X443 : subst] : (((X434 @ X442 @ X441 @ (comp @ X440 @ X443)) = $true) | ((X434 @ (comp @ X442 @ X440) @ (sub @ X441 @ X440) @ X443) != $true)) | ~! [X444 : subst > term > term] : (((X434 @ id @ (lam @ (X444 @ sh @ one)) @ id) = $true) | ~! [X446 : subst,X447 : term,X448 : subst] : ((X444 @ (comp @ X448 @ X446) @ (sub @ X447 @ X446)) = (sub @ (X444 @ X448 @ X447) @ X446)) | ~! [X445 : term] : (((X434 @ id @ (X444 @ id @ X445) @ id) = $true) | ((X434 @ id @ X445 @ id) != $true))) | ~! [X436 : subst,X437 : term,X438 : subst,X439 : subst] : (((X434 @ X436 @ X437 @ (comp @ X439 @ X438)) != $true) | ($true = (X434 @ (comp @ X436 @ X439) @ (sub @ X437 @ X439) @ X438))) | ((X434 @ id @ (lam @ X433) @ id) = $true))))) & (apnotvar = $true) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (! [X292 : term,X293 : subst > term > subst > $o] : (~! [X299 : subst,X300 : subst,X301 : term,X302 : subst] : (((X293 @ X302 @ X301 @ (comp @ X300 @ X299)) != $true) | ($true = (X293 @ (comp @ X302 @ X300) @ (sub @ X301 @ X300) @ X299))) | ~! [X294 : subst > term > term] : (~! [X298 : term] : (($true != (X293 @ id @ X298 @ id)) | ($true = (X293 @ id @ (X294 @ id @ X298) @ id))) | ~! [X295 : subst,X296 : term,X297 : subst] : ((X294 @ (comp @ X295 @ X297) @ (sub @ X296 @ X297)) = (sub @ (X294 @ X295 @ X296) @ X297)) | ($true = (X293 @ id @ (lam @ (X294 @ sh @ one)) @ id))) | ~! [X304 : term,X305 : term] : (($true = (X293 @ id @ (ap @ (sub @ X304 @ id) @ X305) @ id)) | ($true != (X293 @ id @ X305 @ id)) | ($true != (X293 @ id @ X304 @ id))) | ((X293 @ id @ X292 @ id) = $true) | ~! [X306 : term,X307 : subst,X308 : subst,X309 : subst] : (((X293 @ X308 @ X306 @ (comp @ X307 @ X309)) = $true) | ($true != (X293 @ (comp @ X308 @ X307) @ (sub @ X306 @ X307) @ X309))) | ~! [X303 : term] : (($true != (var @ (sub @ X303 @ id))) | ((X293 @ id @ X303 @ id) = $true))) <=> (hoasinduction = $true)) & ((d2subst @ d_id) = sh) & (lamnotap != $true) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & ((! [X347 : subst > term > subst > $o] : ~! [X348 : term > $o] : ~! [X349 : term] : ((X347 @ id @ X349 @ id) = (X348 @ X349)) => (! [X350 : term,X351 : term > $o] : (~! [X355 : term] : (($true = (X351 @ (lam @ X355))) | ~! [X356 : term] : (((X351 @ (sub @ X355 @ (push @ X356 @ id))) = $true) | ((X351 @ X356) != $true))) | ($true = (X351 @ X350)) | ~! [X353 : term,X354 : term] : (((X351 @ X353) != $true) | ($true = (X351 @ (ap @ X354 @ X353))) | ($true != (X351 @ X354))) | ~! [X352 : term] : (((X351 @ X352) = $true) | ((var @ X352) != $true))) => (! [X357 : term] : ((sub @ X357 @ id) = X357) => (! [X358 : subst > term > subst > $o,X359 : term,X360 : term > $o] : (~! [X362 : subst > term > term] : (($true = (X358 @ id @ (lam @ (X362 @ sh @ one)) @ id)) | ~! [X364 : subst,X365 : subst,X366 : term] : ((sub @ (X362 @ X364 @ X366) @ X365) = (X362 @ (comp @ X364 @ X365) @ (sub @ X366 @ X365))) | ~! [X363 : term] : (((X358 @ id @ X363 @ id) != $true) | ((X358 @ id @ (X362 @ id @ X363) @ id) = $true))) | ~! [X361 : term] : ((X360 @ X361) = (X358 @ id @ X361 @ id)) | ($true = (X360 @ (lam @ X359))) | ~! [X367 : term] : (((X360 @ X367) != $true) | ($true = (X360 @ (sub @ X359 @ (push @ X367 @ id)))))) => ! [X368 : term,X369 : subst > term > subst > $o] : (~! [X380 : subst > term > term] : (($true = (X369 @ id @ (lam @ (X380 @ sh @ one)) @ id)) | ~! [X382 : subst,X383 : term,X384 : subst] : ((X380 @ (comp @ X382 @ X384) @ (sub @ X383 @ X384)) = (sub @ (X380 @ X382 @ X383) @ X384)) | ~! [X381 : term] : (($true != (X369 @ id @ X381 @ id)) | ((X369 @ id @ (X380 @ id @ X381) @ id) = $true))) | ~! [X374 : term,X375 : term] : (((X369 @ id @ (ap @ (sub @ X374 @ id) @ X375) @ id) = $true) | ((X369 @ id @ X375 @ id) != $true) | ($true != (X369 @ id @ X374 @ id))) | ~! [X376 : subst,X377 : subst,X378 : subst,X379 : term] : (((X369 @ (comp @ X378 @ X376) @ (sub @ X379 @ X376) @ X377) = $true) | ((X369 @ X378 @ X379 @ (comp @ X376 @ X377)) != $true)) | ~! [X370 : term,X371 : subst,X372 : subst,X373 : subst] : (($true = (X369 @ X373 @ X370 @ (comp @ X372 @ X371))) | ($true != (X369 @ (comp @ X373 @ X372) @ (sub @ X370 @ X372) @ X371))) | ~! [X385 : term] : (($true != (var @ (sub @ X385 @ id))) | ($true = (X369 @ id @ X385 @ id))) | ($true = (X369 @ id @ X368 @ id))))))) <=> (hoasinduction_lthm_3 = $true)) & ((axvarcons = $true) <=> ! [X77 : subst,X78 : term] : ((sub @ one @ (push @ X78 @ X77)) = X78)) & (pushprop_lem1v2_gthm = $true) & (! [X48 : term,X49 : term,X50 : term,X51 : term] : (((ap @ X49 @ X48) != (ap @ X50 @ X51)) | (X48 = X51)) <=> (apinj2 = $true)) & (hoasinduction_lem2v2_gthm = $true) & (pushprop_lem3v2 = $true) & (hoasapinj1_gthm = $true) & (hoasapnotvar_lthm = $true) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X0 : subst > term > subst > $o] : ~! [X1 : term > $o] : ~! [X2 : term] : ((X0 @ id @ X2 @ id) = (X1 @ X2)) => (! [X3 : term,X4 : term > $o] : (~! [X7 : term] : (($true != (var @ X7)) | ((X4 @ X7) = $true)) | ~! [X5 : term,X6 : term] : (((X4 @ X5) != $true) | ((X4 @ X6) != $true) | ($true = (X4 @ (ap @ X5 @ X6)))) | ~! [X8 : term] : (((X4 @ (lam @ X8)) = $true) | ~! [X9 : term] : (($true = (X4 @ (sub @ X8 @ (push @ X9 @ id)))) | ($true != (X4 @ X9)))) | ($true = (X4 @ X3))) => (! [X10 : term] : ((sub @ X10 @ id) = X10) => (! [X11 : term,X12 : subst > term > subst > $o,X13 : term > $o] : (~! [X15 : subst > term > term] : (~! [X17 : term,X18 : subst,X19 : subst] : ((sub @ (X15 @ X19 @ X17) @ X18) = (X15 @ (comp @ X19 @ X18) @ (sub @ X17 @ X18))) | ~! [X16 : term] : (((X12 @ id @ (X15 @ id @ X16) @ id) = $true) | ($true != (X12 @ id @ X16 @ id))) | ($true = (X12 @ id @ (lam @ (X15 @ sh @ one)) @ id))) | ~! [X14 : term] : ((X13 @ X14) = (X12 @ id @ X14 @ id)) | ~! [X20 : term] : (($true = (X13 @ (sub @ X11 @ (push @ X20 @ id)))) | ((X13 @ X20) != $true)) | ((X13 @ (lam @ X11)) = $true)) => ! [X21 : subst > term > subst > $o,X22 : term] : (($true = (X21 @ id @ X22 @ id)) | ~! [X25 : subst > term > term] : (((X21 @ id @ (lam @ (X25 @ sh @ one)) @ id) = $true) | ~! [X27 : term,X28 : subst,X29 : subst] : ((X25 @ (comp @ X28 @ X29) @ (sub @ X27 @ X29)) = (sub @ (X25 @ X28 @ X27) @ X29)) | ~! [X26 : term] : (((X21 @ id @ X26 @ id) != $true) | ((X21 @ id @ (X25 @ id @ X26) @ id) = $true))) | ~! [X23 : term,X24 : term] : (($true != (X21 @ id @ X23 @ id)) | ($true = (X21 @ id @ (ap @ (sub @ X23 @ id) @ X24) @ id)) | ((X21 @ id @ X24 @ id) != $true)))))))) & (hoaslamnotap_gthm = $true) & (pushprop = $true) & (hoaslamnotvar_lthm = $true) & ((hoasinduction_lem3 = $true) <=> ! [X32 : term,X33 : subst > term > subst > $o] : (~! [X34 : term,X35 : subst,X36 : subst,X37 : subst] : (((X33 @ (comp @ X36 @ X37) @ (sub @ X34 @ X37) @ X35) != $true) | ((X33 @ X36 @ X34 @ (comp @ X37 @ X35)) = $true)) | ~! [X42 : subst > term > term] : (~! [X44 : term,X45 : subst,X46 : subst] : ((X42 @ (comp @ X46 @ X45) @ (sub @ X44 @ X45)) = (sub @ (X42 @ X46 @ X44) @ X45)) | ~! [X43 : term] : (($true != (X33 @ id @ X43 @ id)) | ((X33 @ id @ (X42 @ id @ X43) @ id) = $true)) | ((X33 @ id @ (lam @ (X42 @ sh @ one)) @ id) = $true)) | ($true = (X33 @ id @ (lam @ X32) @ id)) | ~! [X38 : subst,X39 : subst,X40 : subst,X41 : term] : (($true = (X33 @ (comp @ X39 @ X40) @ (sub @ X41 @ X40) @ X38)) | ($true != (X33 @ X39 @ X41 @ (comp @ X40 @ X38)))) | ~! [X47 : term] : (($true != (X33 @ id @ X47 @ id)) | ((X33 @ id @ (sub @ X32 @ (push @ X47 @ id)) @ id) = $true)))) & ((axvarid = $true) <=> ! [X236 : term] : ((sub @ X236 @ id) = X236)) & ((! [X253 : term] : ((sub @ X253 @ id) = X253) => ! [X254 : term] : ((sub @ X254 @ id) = X254)) <=> (termmset_lthm = $true)) & (axapp = $true) & (lamnotvar = $true) & ((termmset = $true) <=> ! [X394 : term] : ((sub @ X394 @ id) = X394)) & (! [X158 : term > $o,X159 : subst > term > subst > $o,X160 : term] : (~! [X167 : term] : (((X158 @ X167) != $true) | ($true = (X158 @ (sub @ X160 @ (push @ X167 @ id))))) | ~! [X162 : subst > term > term] : (((X159 @ id @ (lam @ (X162 @ sh @ one)) @ id) = $true) | ~! [X163 : term] : (($true != (X159 @ id @ X163 @ id)) | ($true = (X159 @ id @ (X162 @ id @ X163) @ id))) | ~! [X164 : subst,X165 : term,X166 : subst] : ((sub @ (X162 @ X166 @ X165) @ X164) = (X162 @ (comp @ X166 @ X164) @ (sub @ X165 @ X164)))) | ($true = (X158 @ (lam @ X160))) | ~! [X161 : term] : ((X158 @ X161) = (X159 @ id @ X161 @ id))) <=> (hoasinduction_lem3v2a = $true)) & (hoaslamnotvar_gthm = $true) & (! [X452 : term,X453 : term,X454 : subst > term > subst > $o] : (((X454 @ id @ X453 @ id) != $true) | ~! [X463 : term,X464 : term] : (($true = (X454 @ id @ (ap @ (sub @ X463 @ id) @ X464) @ id)) | ($true != (X454 @ id @ X463 @ id)) | ((X454 @ id @ X464 @ id) != $true)) | ~! [X459 : subst,X460 : term,X461 : subst,X462 : subst] : (((X454 @ (comp @ X461 @ X459) @ (sub @ X460 @ X459) @ X462) = $true) | ((X454 @ X461 @ X460 @ (comp @ X459 @ X462)) != $true)) | ~! [X455 : subst,X456 : subst,X457 : term,X458 : subst] : (((X454 @ X458 @ X457 @ (comp @ X455 @ X456)) = $true) | ($true != (X454 @ (comp @ X458 @ X455) @ (sub @ X457 @ X455) @ X456))) | ((X454 @ id @ X452 @ id) != $true) | ((X454 @ id @ (ap @ X452 @ X453) @ id) = $true)) <=> (hoasinduction_lem2 = $true)) & ((hoasinduction_lem3aa = $true) <=> ! [X498 : subst > term > subst > $o,X499 : term] : (~! [X500 : term] : (($true = (X498 @ id @ (sub @ X499 @ (push @ X500 @ id)) @ id)) | ($true != (X498 @ id @ X500 @ id))) | ~! [X501 : subst > term > term] : (~! [X502 : subst,X503 : subst,X504 : term] : ((X501 @ (comp @ X502 @ X503) @ (sub @ X504 @ X503)) = (sub @ (X501 @ X502 @ X504) @ X503)) | ~! [X505 : term] : (($true != (X498 @ id @ X505 @ id)) | ($true = (X498 @ id @ (X501 @ id @ X505) @ id))) | ($true = (X498 @ id @ (lam @ (X501 @ sh @ one)) @ id))) | ($true = (X498 @ id @ (lam @ (sub @ X499 @ (push @ one @ sh))) @ id)))) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (! [X480 : term,X481 : term,X482 : term,X483 : term] : (((ap @ (sub @ X482 @ id) @ X481) != (ap @ (sub @ X480 @ id) @ X483)) | (X481 = X483)) <=> (hoasapinj2 = $true)) & ! [X422 : term] : ? [X423 : d_term] : ((d2term @ X423) = X422) & (substmonoid_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)))))))))))) & (hoaslaminj_gthm = $true) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (pushprop_lthm_orig = $true) & (pushprop_lthm = $true) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem1_gthm = $true) & ((induction2_lthm = $true) <=> (! [X128 : term] : ((sub @ X128 @ id) = X128) => (! [X129 : subst,X130 : term > $o,X131 : term] : (~! [X134 : term,X135 : term] : (((X130 @ X134) != $true) | ($true != (X130 @ X135)) | ((X130 @ (ap @ X134 @ X135)) = $true)) | ~! [X136 : term] : (((var @ X136) != $true) | ($true = (X130 @ (sub @ X136 @ X129)))) | ($true = (X130 @ (sub @ X131 @ X129))) | ~! [X132 : term] : (~! [X133 : term] : (((X130 @ X133) != $true) | ($true = (X130 @ (sub @ X132 @ (push @ X133 @ id))))) | ((X130 @ (lam @ X132)) = $true))) => ! [X137 : term,X138 : term > $o] : (~! [X142 : term] : (($true = (X138 @ (lam @ X142))) | ~! [X143 : term] : (((X138 @ X143) != $true) | ((X138 @ (sub @ X142 @ (push @ X143 @ id))) = $true))) | ~! [X140 : term,X141 : term] : (((X138 @ (ap @ X140 @ X141)) = $true) | ((X138 @ X140) != $true) | ($true != (X138 @ X141))) | ($true = (X138 @ X137)) | ~! [X139 : term] : (((var @ X139) != $true) | ((X138 @ X139) = $true)))))) & (! [X529 : term] : ~! [X530 : subst > term > term] : ((X530 @ sh @ one) != (sub @ X529 @ (push @ one @ sh))) <=> (hoasinduction_lem3b = $true)) & (pushprop_gthm = $true) & (pushprop_lem2v2_gthm = $true) & (hoasinduction_lem1 = $true) & (hoasapinj2_gthm = $true) & ! [X265 : d_subst,X266 : d_subst] : (((d2subst @ X266) = (d2subst @ X265)) => (X265 = X266)) & (pushprop_lem0_gthm = $true) & ((hoaslamnotap = $true) <=> ! [X341 : subst > term > term,X342 : term,X343 : term] : (((ap @ (sub @ X342 @ id) @ X343) != (lam @ (X341 @ sh @ one))) | ~! [X344 : subst,X345 : term,X346 : subst] : ((sub @ (X341 @ X346 @ X345) @ X344) = (X341 @ (comp @ X346 @ X344) @ (sub @ X345 @ X344))))) & (axvarshift = $true) & ((pushprop_lem0 = $true) <=> ! [X119 : term > $o,X120 : subst,X121 : term] : ~! [X122 : term > $o] : ~! [X123 : term] : ((X122 @ X123) = (X119 @ (sub @ X123 @ (push @ X121 @ X120))))) & ((! [X68 : term] : ((sub @ X68 @ id) = X68) => (! [X69 : term,X70 : term,X71 : term,X72 : term] : ((X69 = X71) | ((ap @ X69 @ X70) != (ap @ X71 @ X72))) => ! [X73 : term,X74 : term,X75 : term,X76 : term] : ((X73 = X74) | ((ap @ (sub @ X74 @ id) @ X76) != (ap @ (sub @ X73 @ id) @ X75))))) <=> (hoasapinj1_lthm = $true)) & ((axscons = $true) <=> ! [X267 : subst] : ((push @ (sub @ one @ X267) @ (comp @ sh @ X267)) = X267)) & ((! [X506 : term,X507 : subst] : ((sub @ one @ (push @ X506 @ X507)) = X506) => (! [X508 : subst,X509 : term] : ((comp @ sh @ (push @ X509 @ X508)) = X508) => (! [X510 : subst] : ((comp @ X510 @ id) = X510) => (! [X511 : term,X512 : term > $o] : (~! [X513 : term] : (($true != (X512 @ X513)) | ((X512 @ (lam @ X513)) = $true)) | ~! [X515 : term,X516 : term] : (((X512 @ (ap @ X516 @ X515)) = $true) | ((X512 @ X515) != $true) | ($true != (X512 @ X516))) | ~! [X514 : term] : (((X512 @ X514) = $true) | ((var @ X514) != $true)) | ((X512 @ X511) = $true)) => ! [X517 : subst,X518 : term > $o,X519 : term] : (~! [X522 : term,X523 : term] : (((X518 @ X523) != $true) | ((X518 @ X522) != $true) | ($true = (X518 @ (ap @ X523 @ X522)))) | ($true = (X518 @ (sub @ X519 @ X517))) | ~! [X520 : term] : (~! [X521 : term] : (($true != (X518 @ X521)) | ($true = (X518 @ (sub @ X520 @ (push @ X521 @ id))))) | ((X518 @ (lam @ X520)) = $true)) | ~! [X524 : term] : (((var @ X524) != $true) | ($true = (X518 @ (sub @ X524 @ X517))))))))) <=> (induction2lem_lthm = $true)) & ((shinj = $true) <=> ! [X328 : term,X329 : term] : ((X328 = X329) | ((sub @ X329 @ sh) != (sub @ X328 @ sh)))) & (axassoc = $true) & (hoasinduction_lem1v2 = $true) & (! [X52 : subst] : ((comp @ X52 @ id) = X52) <=> (axidr = $true)) & (! [X414 : term,X415 : subst > term > subst > $o] : (~! [X417 : subst > term > term] : (~! [X421 : term] : (($true != (X415 @ id @ X421 @ id)) | ((X415 @ id @ (X417 @ id @ X421) @ id) = $true)) | ~! [X418 : subst,X419 : term,X420 : subst] : ((sub @ (X417 @ X418 @ X419) @ X420) = (X417 @ (comp @ X418 @ X420) @ (sub @ X419 @ X420))) | ((X415 @ id @ (lam @ (X417 @ sh @ one)) @ id) = $true)) | ((X415 @ id @ (lam @ (sub @ X414 @ (push @ one @ sh))) @ id) = $true) | ~! [X416 : term] : (((X415 @ id @ X416 @ id) != $true) | ((X415 @ id @ (sub @ X414 @ (push @ X416 @ id)) @ id) = $true))) <=> (hoasinduction_lem3aa_lthm = $true)) & ! [X234 : d_term,X235 : d_term] : (((d2term @ X234) = (d2term @ X235)) => (X234 = X235)) & ((var @ (d2term @ d_one)) != $true) & ((! [X168 : term > $o,X169 : term] : (~! [X170 : term] : (~! [X171 : term] : (((X168 @ X171) != $true) | ($true = (X168 @ (sub @ X170 @ (push @ X171 @ id))))) | ((X168 @ (lam @ X170)) = $true)) | ~! [X172 : term,X173 : term] : (((X168 @ X172) != $true) | ((X168 @ (ap @ X173 @ X172)) = $true) | ($true != (X168 @ X173))) | ~! [X174 : term] : (((var @ X174) != $true) | ((X168 @ X174) = $true)) | ($true = (X168 @ X169))) => (! [X175 : term,X176 : term,X177 : subst > term > subst > $o] : (($true != (X177 @ id @ X176 @ id)) | ~! [X186 : term,X187 : term] : (($true != (X177 @ id @ X187 @ id)) | ($true != (X177 @ id @ X186 @ id)) | ($true = (X177 @ id @ (ap @ (sub @ X187 @ id) @ X186) @ id))) | ~! [X178 : subst,X179 : subst,X180 : term,X181 : subst] : (((X177 @ X179 @ X180 @ (comp @ X181 @ X178)) != $true) | ((X177 @ (comp @ X179 @ X181) @ (sub @ X180 @ X181) @ X178) = $true)) | ~! [X182 : subst,X183 : subst,X184 : term,X185 : subst] : (($true = (X177 @ X185 @ X184 @ (comp @ X183 @ X182))) | ($true != (X177 @ (comp @ X185 @ X183) @ (sub @ X184 @ X183) @ X182))) | ((X177 @ id @ (ap @ X175 @ X176) @ id) = $true) | ($true != (X177 @ id @ X175 @ id))) => (! [X188 : term,X189 : subst > term > subst > $o] : (~! [X198 : term] : (((X189 @ id @ (sub @ X188 @ (push @ X198 @ id)) @ id) = $true) | ($true != (X189 @ id @ X198 @ id))) | ~! [X194 : subst,X195 : subst,X196 : term,X197 : subst] : (((X189 @ (comp @ X197 @ X195) @ (sub @ X196 @ X195) @ X194) != $true) | ((X189 @ X197 @ X196 @ (comp @ X195 @ X194)) = $true)) | ~! [X199 : subst > term > term] : (((X189 @ id @ (lam @ (X199 @ sh @ one)) @ id) = $true) | ~! [X203 : term] : (((X189 @ id @ X203 @ id) != $true) | ((X189 @ id @ (X199 @ id @ X203) @ id) = $true)) | ~! [X200 : term,X201 : subst,X202 : subst] : ((sub @ (X199 @ X201 @ X200) @ X202) = (X199 @ (comp @ X201 @ X202) @ (sub @ X200 @ X202)))) | ~! [X190 : subst,X191 : term,X192 : subst,X193 : subst] : (((X189 @ X193 @ X191 @ (comp @ X190 @ X192)) != $true) | ((X189 @ (comp @ X193 @ X190) @ (sub @ X191 @ X190) @ X192) = $true)) | ((X189 @ id @ (lam @ X188) @ id) = $true)) => ! [X204 : subst > term > subst > $o,X205 : term] : (~! [X216 : term] : (((X204 @ id @ X216 @ id) = $true) | ($true != (var @ (sub @ X216 @ id)))) | ~! [X206 : term,X207 : term] : (($true != (X204 @ id @ X206 @ id)) | ($true != (X204 @ id @ X207 @ id)) | ($true = (X204 @ id @ (ap @ (sub @ X207 @ id) @ X206) @ id))) | ~! [X217 : subst > term > term] : (~! [X221 : term] : (($true != (X204 @ id @ X221 @ id)) | ((X204 @ id @ (X217 @ id @ X221) @ id) = $true)) | ((X204 @ id @ (lam @ (X217 @ sh @ one)) @ id) = $true) | ~! [X218 : subst,X219 : term,X220 : subst] : ((sub @ (X217 @ X220 @ X219) @ X218) = (X217 @ (comp @ X220 @ X218) @ (sub @ X219 @ X218)))) | ($true = (X204 @ id @ X205 @ id)) | ~! [X208 : subst,X209 : subst,X210 : subst,X211 : term] : (((X204 @ X210 @ X211 @ (comp @ X208 @ X209)) = $true) | ($true != (X204 @ (comp @ X210 @ X208) @ (sub @ X211 @ X208) @ X209))) | ~! [X212 : subst,X213 : subst,X214 : term,X215 : subst] : (((X204 @ (comp @ X213 @ X212) @ (sub @ X214 @ X212) @ X215) = $true) | ($true != (X204 @ X213 @ X214 @ (comp @ X212 @ X215)))))))) <=> (hoasinduction_lthm = $true)) & (axmap = $true) & ((hoasapinj1 = $true) <=> ! [X486 : term,X487 : term,X488 : term,X489 : term] : (((ap @ (sub @ X489 @ id) @ X486) != (ap @ (sub @ X488 @ id) @ X487)) | (X488 = X489))) & (hoaslamnotvar = $true) & (hoasinduction_lem1v2_gthm = $true) & ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (! [X222 : term,X223 : subst > term > subst > $o] : (~! [X224 : term] : (($true = (X223 @ id @ (sub @ X222 @ (push @ X224 @ id)) @ id)) | ((X223 @ id @ X224 @ id) != $true)) | ($true = (X223 @ id @ (lam @ (sub @ X222 @ (push @ one @ sh))) @ id)) | ~! [X225 : term,X226 : subst > term > term] : (~! [X227 : subst,X228 : term,X229 : subst] : ((sub @ (sub @ X225 @ (push @ X228 @ X229)) @ X227) = (sub @ (X226 @ X229 @ X228) @ X227)) | ~! [X233 : term] : (((X223 @ id @ (X226 @ id @ X233) @ id) = $true) | ($true != (X223 @ id @ X233 @ id))) | ($true = (X223 @ id @ (lam @ (X226 @ sh @ one)) @ id)) | ~! [X230 : subst,X231 : term,X232 : subst] : ((sub @ X225 @ (push @ (sub @ X231 @ X232) @ (comp @ X230 @ X232))) = (X226 @ (comp @ X230 @ X232) @ (sub @ X231 @ X232))))) <=> (hoasinduction_lem3aaa = $true)) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X81 : term] : ((sub @ X81 @ id) = X81) => (! [X82 : subst > term > subst > $o,X83 : term] : (~! [X84 : subst > term > term] : (~! [X85 : term,X86 : subst,X87 : subst] : ((sub @ (X84 @ X87 @ X85) @ X86) = (X84 @ (comp @ X87 @ X86) @ (sub @ X85 @ X86))) | ~! [X88 : term] : (($true != (X82 @ id @ X88 @ id)) | ((X82 @ id @ (X84 @ id @ X88) @ id) = $true)) | ($true = (X82 @ id @ (lam @ (X84 @ sh @ one)) @ id))) | ((X82 @ id @ (lam @ (sub @ X83 @ (push @ one @ sh))) @ id) = $true) | ~! [X89 : term] : (($true = (X82 @ id @ (sub @ X83 @ (push @ X89 @ id)) @ id)) | ((X82 @ id @ X89 @ id) != $true))) => ! [X90 : subst > term > subst > $o,X91 : term] : (~! [X97 : term] : (($true != (X90 @ id @ X97 @ id)) | ($true = (X90 @ id @ (sub @ X91 @ (push @ X97 @ id)) @ id))) | ~! [X92 : subst > term > term] : (($true = (X90 @ id @ (lam @ (X92 @ sh @ one)) @ id)) | ~! [X94 : term,X95 : subst,X96 : subst] : ((sub @ (X92 @ X96 @ X94) @ X95) = (X92 @ (comp @ X96 @ X95) @ (sub @ X94 @ X95))) | ~! [X93 : term] : (($true = (X90 @ id @ (X92 @ id @ X93) @ id)) | ($true != (X90 @ id @ X93 @ id)))) | ((X90 @ id @ (lam @ X91) @ id) = $true))))) & ! [X484 : subst] : ? [X485 : d_subst] : ((d2subst @ X485) = X484) & (pushprop_lem3v2_lthm = $true) & (hoasinduction_lem2_lthm = $true) & (axabs = $true) & (hoasapnotvar = $true) & ((hoaslaminj_lthm = $true) <=> (! [X237 : subst,X238 : term] : ((sub @ one @ (push @ X238 @ X237)) = X238) => (! [X239 : term,X240 : subst] : ((comp @ sh @ (push @ X239 @ X240)) = X240) => (! [X241 : term,X242 : term] : ((X241 = X242) | ((lam @ X241) != (lam @ X242))) => ! [X243 : subst,X244 : term,X245 : subst > term > term,X246 : subst > term > term] : (((lam @ (X246 @ sh @ one)) != (lam @ (X245 @ sh @ one))) | ~! [X247 : term,X248 : subst,X249 : subst] : ((sub @ (X246 @ X248 @ X247) @ X249) = (X246 @ (comp @ X248 @ X249) @ (sub @ X247 @ X249))) | ~! [X250 : subst,X251 : term,X252 : subst] : ((X245 @ (comp @ X250 @ X252) @ (sub @ X251 @ X252)) = (sub @ (X245 @ X250 @ X251) @ X252)) | ((X246 @ X243 @ X244) = (X245 @ X243 @ X244))))))) & (ulamvarsh = $true) & (hoasinduction_lem2_gthm = $true) & (! [X255 : term,X256 : term > $o] : (~! [X260 : term] : (((var @ X260) != $true) | ($true = (X256 @ X260))) | ~! [X257 : term] : (((X256 @ (lam @ X257)) = $true) | ($true != (X256 @ X257))) | ~! [X258 : term,X259 : term] : (((X256 @ (ap @ X259 @ X258)) = $true) | ($true != (X256 @ X259)) | ((X256 @ X258) != $true)) | ((X256 @ X255) = $true)) <=> (induction = $true)) & ((! [X98 : term] : ((sub @ X98 @ id) = X98) => ! [X99 : term > $o,X100 : subst > term > subst > $o,X101 : term] : (~! [X108 : subst,X109 : term,X110 : subst,X111 : subst] : (((X100 @ (comp @ X108 @ X110) @ (sub @ X109 @ X110) @ X111) = $true) | ((X100 @ X108 @ X109 @ (comp @ X110 @ X111)) != $true)) | ~! [X112 : term] : ((X100 @ id @ X112 @ id) = (X99 @ X112)) | ((X99 @ (lam @ X101)) = $true) | ~! [X103 : subst > term > term] : (~! [X104 : subst,X105 : subst,X106 : term] : ((X103 @ (comp @ X105 @ X104) @ (sub @ X106 @ X104)) = (sub @ (X103 @ X105 @ X106) @ X104)) | ~! [X107 : term] : (((X100 @ id @ X107 @ id) != $true) | ($true = (X100 @ id @ (X103 @ id @ X107) @ id))) | ($true = (X100 @ id @ (lam @ (X103 @ sh @ one)) @ id))) | ~! [X113 : subst,X114 : subst,X115 : term,X116 : subst] : (($true = (X100 @ X114 @ X115 @ (comp @ X113 @ X116))) | ($true != (X100 @ (comp @ X114 @ X113) @ (sub @ X115 @ X113) @ X116))) | ~! [X102 : term] : (((X99 @ (sub @ X101 @ (push @ X102 @ id))) = $true) | ((X99 @ X102) != $true)))) <=> (hoasinduction_lem3v2_lthm = $true)) & (hoasinduction_lem1_lthm = $true) & (hoasinduction_lem3_gthm = $true) & (ulamvarind = $true) & ((! [X149 : term,X150 : subst] : ((sub @ one @ (push @ X149 @ X150)) = X149) => (! [X151 : subst,X152 : term] : ((comp @ sh @ (push @ X152 @ X151)) = X151) => ! [X153 : term,X154 : term > $o,X155 : subst,X156 : term,X157 : term > $o] : (((X157 @ (sub @ X153 @ (push @ X156 @ X155))) = $true) | ($true != (X154 @ X153))))) <=> (pushprop_lem1_lthm = $true)) & (induction2lem_gthm = $true) & ((hoasapinj2_lthm = $true) <=> (! [X532 : term,X533 : term,X534 : term,X535 : term] : ((X533 = X534) | ((ap @ X532 @ X534) != (ap @ X535 @ X533))) => ! [X536 : term,X537 : term,X538 : term,X539 : term] : (((ap @ (sub @ X536 @ id) @ X539) != (ap @ (sub @ X537 @ id) @ X538)) | (X538 = X539)))) & (! [X339 : term] : ~! [X340 : subst > term > term] : ((X340 @ sh @ one) != (sub @ X339 @ (push @ one @ sh))) <=> (hoasinduction_lem3b_lthm = $true)) & ((hoasinduction_no_psi_cond = $true) <=> ! [X330 : term,X331 : subst > term > subst > $o] : (~! [X337 : term,X338 : term] : (((X331 @ id @ (ap @ (sub @ X337 @ id) @ X338) @ id) = $true) | ((X331 @ id @ X337 @ id) != $true) | ((X331 @ id @ X338 @ id) != $true)) | ((X331 @ id @ X330 @ id) = $true) | ~! [X332 : subst > term > term] : (~! [X334 : subst,X335 : subst,X336 : term] : ((sub @ (X332 @ X335 @ X336) @ X334) = (X332 @ (comp @ X335 @ X334) @ (sub @ X336 @ X334))) | ~! [X333 : term] : (((X331 @ id @ X333 @ id) != $true) | ((X331 @ id @ (X332 @ id @ X333) @ id) = $true)) | ($true = (X331 @ id @ (lam @ (X332 @ sh @ one)) @ id))))) & ((substmonoid_lthm = $true) <=> (! [X395 : subst] : ((comp @ id @ X395) = X395) => (! [X396 : subst] : ((comp @ X396 @ id) = X396) => (! [X397 : subst] : ((comp @ id @ X397) = X397) & ! [X398 : subst] : ((comp @ X398 @ id) = X398))))) & ! [X291 : d_subst] : (d_id = X291) & (! [X268 : term > $o,X269 : term] : (~! [X270 : term] : (((X268 @ (lam @ X270)) = $true) | ~! [X271 : term] : (($true = (X268 @ (sub @ X270 @ (push @ X271 @ id)))) | ($true != (X268 @ X271)))) | ~! [X274 : term] : (((var @ X274) != $true) | ($true = (X268 @ X274))) | ((X268 @ X269) = $true) | ~! [X272 : term,X273 : term] : (((X268 @ (ap @ X273 @ X272)) = $true) | ((X268 @ X273) != $true) | ($true != (X268 @ X272)))) <=> (induction2 = $true)) & (hoasinduction_gthm = $true) & ((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (pushprop_lem2v2_lthm = $true) & (! [X310 : term,X311 : subst > term > subst > $o,X312 : term > $o] : (~! [X315 : subst,X316 : subst,X317 : subst,X318 : term] : (((X311 @ (comp @ X316 @ X317) @ (sub @ X318 @ X317) @ X315) != $true) | ($true = (X311 @ X316 @ X318 @ (comp @ X317 @ X315)))) | ~! [X319 : subst,X320 : subst,X321 : term,X322 : subst] : (((X311 @ X322 @ X321 @ (comp @ X319 @ X320)) != $true) | ((X311 @ (comp @ X322 @ X319) @ (sub @ X321 @ X319) @ X320) = $true)) | ((X312 @ (lam @ X310)) = $true) | ~! [X313 : term] : ((X312 @ X313) = (X311 @ id @ X313 @ id)) | ~! [X314 : term] : (((X312 @ X314) != $true) | ((X312 @ (sub @ X310 @ (push @ X314 @ id))) = $true)) | ~! [X323 : subst > term > term] : (~! [X325 : term,X326 : subst,X327 : subst] : ((X323 @ (comp @ X327 @ X326) @ (sub @ X325 @ X326)) = (sub @ (X323 @ X327 @ X325) @ X326)) | ((X311 @ id @ (lam @ (X323 @ sh @ one)) @ id) = $true) | ~! [X324 : term] : (((X311 @ id @ (X323 @ id @ X324) @ id) = $true) | ($true != (X311 @ id @ X324 @ id))))) <=> (hoasinduction_lem3v2 = $true)) & (hoaslamnotap_lthm = $true) & (axclos = $true) & (ulamvar1 != $true) & ((d2subst @ d_id) = id) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & ((! [X79 : subst] : ((comp @ id @ X79) = X79) & ! [X80 : subst] : ((comp @ X80 @ id) = X80)) <=> (substmonoid = $true)) & (! [X449 : subst > term > subst > $o] : ~! [X450 : term > $o] : ~! [X451 : term] : ((X449 @ id @ X451 @ id) = (X450 @ X451)) <=> (hoasinduction_lem0_lthm = $true)) & (hoasinduction_lem3b_gthm = $true) & ! [X531 : d_term] : (d_one = X531)),
% 15.02/3.54 inference(flattening,[status(thm)],[f10])).
% 15.02/3.54 thf(f10,plain,(
% 15.02/3.54 ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X0 : subst > term > subst > $o] : ~! [X1 : term > $o] : ~! [X2 : term] : ((X0 @ id @ X2 @ id) = (X1 @ X2)) => (! [X3 : term,X4 : term > $o] : (($true = (X4 @ X3)) | ~! [X5 : term,X6 : term] : (~((X4 @ X5) = $true) | ($true = (X4 @ (ap @ X5 @ X6))) | ~((X4 @ X6) = $true)) | ~! [X7 : term] : (((X4 @ X7) = $true) | ~($true = (var @ X7))) | ~! [X8 : term] : (((X4 @ (lam @ X8)) = $true) | ~! [X9 : term] : (~($true = (X4 @ X9)) | ($true = (X4 @ (sub @ X8 @ (push @ X9 @ id))))))) => (! [X10 : term] : ((sub @ X10 @ id) = X10) => (! [X11 : term,X12 : subst > term > subst > $o,X13 : term > $o] : (~! [X14 : term] : ((X13 @ X14) = (X12 @ id @ X14 @ id)) | ~! [X15 : subst > term > term] : (~! [X16 : term] : (~($true = (X12 @ id @ X16 @ id)) | ((X12 @ id @ (X15 @ id @ X16) @ id) = $true)) | ~! [X17 : term,X18 : subst,X19 : subst] : ((sub @ (X15 @ X19 @ X17) @ X18) = (X15 @ (comp @ X19 @ X18) @ (sub @ X17 @ X18))) | ($true = (X12 @ id @ (lam @ (X15 @ sh @ one)) @ id))) | ((X13 @ (lam @ X11)) = $true) | ~! [X20 : term] : (~((X13 @ X20) = $true) | ($true = (X13 @ (sub @ X11 @ (push @ X20 @ id)))))) => ! [X21 : subst > term > subst > $o,X22 : term] : (~! [X23 : term,X24 : term] : (~((X21 @ id @ X24 @ id) = $true) | ($true = (X21 @ id @ (ap @ (sub @ X23 @ id) @ X24) @ id)) | ~($true = (X21 @ id @ X23 @ id))) | ~! [X25 : subst > term > term] : (~! [X26 : term] : (~((X21 @ id @ X26 @ id) = $true) | ((X21 @ id @ (X25 @ id @ X26) @ id) = $true)) | ((X21 @ id @ (lam @ (X25 @ sh @ one)) @ id) = $true) | ~! [X27 : term,X28 : subst,X29 : subst] : ((X25 @ (comp @ X28 @ X29) @ (sub @ X27 @ X29)) = (sub @ (X25 @ X28 @ X27) @ X29))) | ($true = (X21 @ id @ X22 @ id)))))))) & (! [X30 : term,X31 : term] : ((X30 = X31) | ((lam @ X30) != (lam @ X31))) <=> (laminj = $true)) & ((hoasinduction_lem3 = $true) <=> ! [X32 : term,X33 : subst > term > subst > $o] : (($true = (X33 @ id @ (lam @ X32) @ id)) | ~! [X34 : term,X35 : subst,X36 : subst,X37 : subst] : (((X33 @ X36 @ X34 @ (comp @ X37 @ X35)) = $true) | ~((X33 @ (comp @ X36 @ X37) @ (sub @ X34 @ X37) @ X35) = $true)) | ~! [X38 : subst,X39 : subst,X40 : subst,X41 : term] : (~($true = (X33 @ X39 @ X41 @ (comp @ X40 @ X38))) | ($true = (X33 @ (comp @ X39 @ X40) @ (sub @ X41 @ X40) @ X38))) | ~! [X42 : subst > term > term] : (~! [X43 : term] : (((X33 @ id @ (X42 @ id @ X43) @ id) = $true) | ~($true = (X33 @ id @ X43 @ id))) | ((X33 @ id @ (lam @ (X42 @ sh @ one)) @ id) = $true) | ~! [X44 : term,X45 : subst,X46 : subst] : ((X42 @ (comp @ X46 @ X45) @ (sub @ X44 @ X45)) = (sub @ (X42 @ X46 @ X44) @ X45))) | ~! [X47 : term] : (((X33 @ id @ (sub @ X32 @ (push @ X47 @ id)) @ id) = $true) | ~($true = (X33 @ id @ X47 @ id))))) & (! [X48 : term,X49 : term,X50 : term,X51 : term] : (((ap @ X49 @ X48) != (ap @ X50 @ X51)) | (X48 = X51)) <=> (apinj2 = $true)) & (ulamvarsh = $true) & (axclos = $true) & (hoasinduction_lem1v2 = $true) & (! [X52 : subst] : ((comp @ X52 @ id) = X52) <=> (axidr = $true)) & ((hoasinduction_lem2v2 = $true) <=> ! [X53 : term,X54 : term > $o,X55 : subst > term > subst > $o,X56 : term] : (~((X54 @ X53) = $true) | ~! [X57 : subst,X58 : term,X59 : subst,X60 : subst] : (((X55 @ (comp @ X60 @ X57) @ (sub @ X58 @ X57) @ X59) = $true) | ~($true = (X55 @ X60 @ X58 @ (comp @ X57 @ X59)))) | ~! [X61 : term,X62 : term] : (~((X55 @ id @ X62 @ id) = $true) | ((X55 @ id @ (ap @ (sub @ X62 @ id) @ X61) @ id) = $true) | ~($true = (X55 @ id @ X61 @ id))) | ((X54 @ (ap @ X53 @ X56)) = $true) | ~((X54 @ X56) = $true) | ~! [X63 : term] : ((X55 @ id @ X63 @ id) = (X54 @ X63)) | ~! [X64 : subst,X65 : term,X66 : subst,X67 : subst] : (~((X55 @ (comp @ X66 @ X67) @ (sub @ X65 @ X67) @ X64) = $true) | ((X55 @ X66 @ X65 @ (comp @ X67 @ X64)) = $true)))) & ((! [X68 : term] : ((sub @ X68 @ id) = X68) => (! [X69 : term,X70 : term,X71 : term,X72 : term] : ((X69 = X71) | ((ap @ X69 @ X70) != (ap @ X71 @ X72))) => ! [X73 : term,X74 : term,X75 : term,X76 : term] : ((X73 = X74) | ((ap @ (sub @ X74 @ id) @ X76) != (ap @ (sub @ X73 @ id) @ X75))))) <=> (hoasapinj1_lthm = $true)) & ((axvarcons = $true) <=> ! [X77 : subst,X78 : term] : ((sub @ one @ (push @ X78 @ X77)) = X78)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (pushprop_lem2v2 = $true) & (axassoc = $true) & ~((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) & ((! [X79 : subst] : ((comp @ id @ X79) = X79) & ! [X80 : subst] : ((comp @ X80 @ id) = X80)) <=> (substmonoid = $true)) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X81 : term] : ((sub @ X81 @ id) = X81) => (! [X82 : subst > term > subst > $o,X83 : term] : (((X82 @ id @ (lam @ (sub @ X83 @ (push @ one @ sh))) @ id) = $true) | ~! [X84 : subst > term > term] : (~! [X85 : term,X86 : subst,X87 : subst] : ((sub @ (X84 @ X87 @ X85) @ X86) = (X84 @ (comp @ X87 @ X86) @ (sub @ X85 @ X86))) | ~! [X88 : term] : (((X82 @ id @ (X84 @ id @ X88) @ id) = $true) | ~($true = (X82 @ id @ X88 @ id))) | ($true = (X82 @ id @ (lam @ (X84 @ sh @ one)) @ id))) | ~! [X89 : term] : (~((X82 @ id @ X89 @ id) = $true) | ($true = (X82 @ id @ (sub @ X83 @ (push @ X89 @ id)) @ id)))) => ! [X90 : subst > term > subst > $o,X91 : term] : (((X90 @ id @ (lam @ X91) @ id) = $true) | ~! [X92 : subst > term > term] : (~! [X93 : term] : (($true = (X90 @ id @ (X92 @ id @ X93) @ id)) | ~($true = (X90 @ id @ X93 @ id))) | ~! [X94 : term,X95 : subst,X96 : subst] : ((sub @ (X92 @ X96 @ X94) @ X95) = (X92 @ (comp @ X96 @ X95) @ (sub @ X94 @ X95))) | ($true = (X90 @ id @ (lam @ (X92 @ sh @ one)) @ id))) | ~! [X97 : term] : (~($true = (X90 @ id @ X97 @ id)) | ($true = (X90 @ id @ (sub @ X91 @ (push @ X97 @ id)) @ id))))))) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X98 : term] : ((sub @ X98 @ id) = X98) => ! [X99 : term > $o,X100 : subst > term > subst > $o,X101 : term] : (~! [X102 : term] : (~((X99 @ X102) = $true) | ((X99 @ (sub @ X101 @ (push @ X102 @ id))) = $true)) | ~! [X103 : subst > term > term] : (~! [X104 : subst,X105 : subst,X106 : term] : ((X103 @ (comp @ X105 @ X104) @ (sub @ X106 @ X104)) = (sub @ (X103 @ X105 @ X106) @ X104)) | ~! [X107 : term] : (~((X100 @ id @ X107 @ id) = $true) | ($true = (X100 @ id @ (X103 @ id @ X107) @ id))) | ($true = (X100 @ id @ (lam @ (X103 @ sh @ one)) @ id))) | ~! [X108 : subst,X109 : term,X110 : subst,X111 : subst] : (((X100 @ (comp @ X108 @ X110) @ (sub @ X109 @ X110) @ X111) = $true) | ~((X100 @ X108 @ X109 @ (comp @ X110 @ X111)) = $true)) | ~! [X112 : term] : ((X100 @ id @ X112 @ id) = (X99 @ X112)) | ((X99 @ (lam @ X101)) = $true) | ~! [X113 : subst,X114 : subst,X115 : term,X116 : subst] : (~($true = (X100 @ (comp @ X114 @ X113) @ (sub @ X115 @ X113) @ X116)) | ($true = (X100 @ X114 @ X115 @ (comp @ X113 @ X116))))))) & ((axshiftcons = $true) <=> ! [X117 : term,X118 : subst] : ((comp @ sh @ (push @ X117 @ X118)) = X118)) & ((pushprop_lem0 = $true) <=> ! [X119 : term > $o,X120 : subst,X121 : term] : ~! [X122 : term > $o] : ~! [X123 : term] : ((X122 @ X123) = (X119 @ (sub @ X123 @ (push @ X121 @ X120))))) & ~(lamnotap = $true) & (! [X124 : term] : ~! [X125 : subst > term > term] : ~! [X126 : term,X127 : subst] : ((sub @ X124 @ (push @ X126 @ X127)) = (X125 @ X127 @ X126)) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (axmap = $true) & (hoasinduction_lem2v2_gthm = $true) & ((induction2_lthm = $true) <=> (! [X128 : term] : ((sub @ X128 @ id) = X128) => (! [X129 : subst,X130 : term > $o,X131 : term] : (~! [X132 : term] : (((X130 @ (lam @ X132)) = $true) | ~! [X133 : term] : (($true = (X130 @ (sub @ X132 @ (push @ X133 @ id)))) | ~((X130 @ X133) = $true))) | ~! [X134 : term,X135 : term] : (((X130 @ (ap @ X134 @ X135)) = $true) | ~($true = (X130 @ X135)) | ~((X130 @ X134) = $true)) | ~! [X136 : term] : (($true = (X130 @ (sub @ X136 @ X129))) | ~((var @ X136) = $true)) | ($true = (X130 @ (sub @ X131 @ X129)))) => ! [X137 : term,X138 : term > $o] : (~! [X139 : term] : (~((var @ X139) = $true) | ((X138 @ X139) = $true)) | ~! [X140 : term,X141 : term] : (~($true = (X138 @ X141)) | ((X138 @ (ap @ X140 @ X141)) = $true) | ~((X138 @ X140) = $true)) | ~! [X142 : term] : (~! [X143 : term] : (~((X138 @ X143) = $true) | ((X138 @ (sub @ X142 @ (push @ X143 @ id))) = $true)) | ($true = (X138 @ (lam @ X142)))) | ($true = (X138 @ X137)))))) & (! [X144 : subst,X145 : term > $o,X146 : term] : ~! [X147 : term > $o] : ~! [X148 : term] : ((X145 @ (sub @ X148 @ (push @ X146 @ X144))) = (X147 @ X148)) <=> (pushprop_lem0_lthm = $true)) & (induction2lem_gthm = $true) & ((pushprop_lem1_lthm = $true) <=> (! [X149 : term,X150 : subst] : ((sub @ one @ (push @ X149 @ X150)) = X149) => (! [X151 : subst,X152 : term] : ((comp @ sh @ (push @ X152 @ X151)) = X151) => ! [X153 : term,X154 : term > $o,X155 : subst,X156 : term,X157 : term > $o] : (~($true = (X154 @ X153)) | ((X157 @ (sub @ X153 @ (push @ X156 @ X155))) = $true))))) & ((hoasinduction_lem3v2a = $true) <=> ! [X158 : term > $o,X159 : subst > term > subst > $o,X160 : term] : (~! [X161 : term] : ((X158 @ X161) = (X159 @ id @ X161 @ id)) | ~! [X162 : subst > term > term] : (~! [X163 : term] : (($true = (X159 @ id @ (X162 @ id @ X163) @ id)) | ~($true = (X159 @ id @ X163 @ id))) | ((X159 @ id @ (lam @ (X162 @ sh @ one)) @ id) = $true) | ~! [X164 : subst,X165 : term,X166 : subst] : ((sub @ (X162 @ X166 @ X165) @ X164) = (X162 @ (comp @ X166 @ X164) @ (sub @ X165 @ X164)))) | ~! [X167 : term] : (~((X158 @ X167) = $true) | ($true = (X158 @ (sub @ X160 @ (push @ X167 @ id))))) | ($true = (X158 @ (lam @ X160))))) & ((hoasinduction_lthm = $true) <=> (! [X168 : term > $o,X169 : term] : (($true = (X168 @ X169)) | ~! [X170 : term] : (~! [X171 : term] : (($true = (X168 @ (sub @ X170 @ (push @ X171 @ id)))) | ~((X168 @ X171) = $true)) | ((X168 @ (lam @ X170)) = $true)) | ~! [X172 : term,X173 : term] : (~($true = (X168 @ X173)) | ((X168 @ (ap @ X173 @ X172)) = $true) | ~((X168 @ X172) = $true)) | ~! [X174 : term] : (~((var @ X174) = $true) | ((X168 @ X174) = $true))) => (! [X175 : term,X176 : term,X177 : subst > term > subst > $o] : (~($true = (X177 @ id @ X176 @ id)) | ((X177 @ id @ (ap @ X175 @ X176) @ id) = $true) | ~! [X178 : subst,X179 : subst,X180 : term,X181 : subst] : (~((X177 @ X179 @ X180 @ (comp @ X181 @ X178)) = $true) | ((X177 @ (comp @ X179 @ X181) @ (sub @ X180 @ X181) @ X178) = $true)) | ~($true = (X177 @ id @ X175 @ id)) | ~! [X182 : subst,X183 : subst,X184 : term,X185 : subst] : (($true = (X177 @ X185 @ X184 @ (comp @ X183 @ X182))) | ~($true = (X177 @ (comp @ X185 @ X183) @ (sub @ X184 @ X183) @ X182))) | ~! [X186 : term,X187 : term] : (~($true = (X177 @ id @ X187 @ id)) | ($true = (X177 @ id @ (ap @ (sub @ X187 @ id) @ X186) @ id)) | ~($true = (X177 @ id @ X186 @ id)))) => (! [X188 : term,X189 : subst > term > subst > $o] : (~! [X190 : subst,X191 : term,X192 : subst,X193 : subst] : (~((X189 @ X193 @ X191 @ (comp @ X190 @ X192)) = $true) | ((X189 @ (comp @ X193 @ X190) @ (sub @ X191 @ X190) @ X192) = $true)) | ~! [X194 : subst,X195 : subst,X196 : term,X197 : subst] : (~((X189 @ (comp @ X197 @ X195) @ (sub @ X196 @ X195) @ X194) = $true) | ((X189 @ X197 @ X196 @ (comp @ X195 @ X194)) = $true)) | ~! [X198 : term] : (~($true = (X189 @ id @ X198 @ id)) | ((X189 @ id @ (sub @ X188 @ (push @ X198 @ id)) @ id) = $true)) | ((X189 @ id @ (lam @ X188) @ id) = $true) | ~! [X199 : subst > term > term] : (~! [X200 : term,X201 : subst,X202 : subst] : ((sub @ (X199 @ X201 @ X200) @ X202) = (X199 @ (comp @ X201 @ X202) @ (sub @ X200 @ X202))) | ~! [X203 : term] : (~((X189 @ id @ X203 @ id) = $true) | ((X189 @ id @ (X199 @ id @ X203) @ id) = $true)) | ((X189 @ id @ (lam @ (X199 @ sh @ one)) @ id) = $true))) => ! [X204 : subst > term > subst > $o,X205 : term] : (~! [X206 : term,X207 : term] : (($true = (X204 @ id @ (ap @ (sub @ X207 @ id) @ X206) @ id)) | ~($true = (X204 @ id @ X206 @ id)) | ~($true = (X204 @ id @ X207 @ id))) | ~! [X208 : subst,X209 : subst,X210 : subst,X211 : term] : (((X204 @ X210 @ X211 @ (comp @ X208 @ X209)) = $true) | ~($true = (X204 @ (comp @ X210 @ X208) @ (sub @ X211 @ X208) @ X209))) | ~! [X212 : subst,X213 : subst,X214 : term,X215 : subst] : (~($true = (X204 @ X213 @ X214 @ (comp @ X212 @ X215))) | ((X204 @ (comp @ X213 @ X212) @ (sub @ X214 @ X212) @ X215) = $true)) | ~! [X216 : term] : (((X204 @ id @ X216 @ id) = $true) | ~($true = (var @ (sub @ X216 @ id)))) | ~! [X217 : subst > term > term] : (~! [X218 : subst,X219 : term,X220 : subst] : ((sub @ (X217 @ X220 @ X219) @ X218) = (X217 @ (comp @ X220 @ X218) @ (sub @ X219 @ X218))) | ((X204 @ id @ (lam @ (X217 @ sh @ one)) @ id) = $true) | ~! [X221 : term] : (~($true = (X204 @ id @ X221 @ id)) | ((X204 @ id @ (X217 @ id @ X221) @ id) = $true))) | ($true = (X204 @ id @ X205 @ id))))))) & (hoaslaminj_gthm = $true) & (! [X222 : term,X223 : subst > term > subst > $o] : (~! [X224 : term] : (~((X223 @ id @ X224 @ id) = $true) | ($true = (X223 @ id @ (sub @ X222 @ (push @ X224 @ id)) @ id))) | ($true = (X223 @ id @ (lam @ (sub @ X222 @ (push @ one @ sh))) @ id)) | ~! [X225 : term,X226 : subst > term > term] : (~! [X227 : subst,X228 : term,X229 : subst] : ((sub @ (sub @ X225 @ (push @ X228 @ X229)) @ X227) = (sub @ (X226 @ X229 @ X228) @ X227)) | ~! [X230 : subst,X231 : term,X232 : subst] : ((sub @ X225 @ (push @ (sub @ X231 @ X232) @ (comp @ X230 @ X232))) = (X226 @ (comp @ X230 @ X232) @ (sub @ X231 @ X232))) | ~! [X233 : term] : (~($true = (X223 @ id @ X233 @ id)) | ((X223 @ id @ (X226 @ id @ X233) @ id) = $true)) | ($true = (X223 @ id @ (lam @ (X226 @ sh @ one)) @ id)))) <=> (hoasinduction_lem3aaa = $true)) & (hoasapnotvar = $true) & ! [X234 : d_term,X235 : d_term] : (((d2term @ X234) = (d2term @ X235)) => (X234 = X235)) & ((d2subst @ d_id) = sh) & (hoaslamnotvar_gthm = $true) & ((axvarid = $true) <=> ! [X236 : term] : ((sub @ X236 @ id) = X236)) & ((hoaslaminj_lthm = $true) <=> (! [X237 : subst,X238 : term] : ((sub @ one @ (push @ X238 @ X237)) = X238) => (! [X239 : term,X240 : subst] : ((comp @ sh @ (push @ X239 @ X240)) = X240) => (! [X241 : term,X242 : term] : ((X241 = X242) | ((lam @ X241) != (lam @ X242))) => ! [X243 : subst,X244 : term,X245 : subst > term > term,X246 : subst > term > term] : (((lam @ (X246 @ sh @ one)) != (lam @ (X245 @ sh @ one))) | ~! [X247 : term,X248 : subst,X249 : subst] : ((sub @ (X246 @ X248 @ X247) @ X249) = (X246 @ (comp @ X248 @ X249) @ (sub @ X247 @ X249))) | ~! [X250 : subst,X251 : term,X252 : subst] : ((X245 @ (comp @ X250 @ X252) @ (sub @ X251 @ X252)) = (sub @ (X245 @ X250 @ X251) @ X252)) | ((X246 @ X243 @ X244) = (X245 @ X243 @ X244))))))) & (hoaslamnotvar = $true) & ((! [X253 : term] : ((sub @ X253 @ id) = X253) => ! [X254 : term] : ((sub @ X254 @ id) = X254)) <=> (termmset_lthm = $true)) & (substmonoid_gthm = $true) & ((induction = $true) <=> ! [X255 : term,X256 : term > $o] : (~! [X257 : term] : (~($true = (X256 @ X257)) | ((X256 @ (lam @ X257)) = $true)) | ((X256 @ X255) = $true) | ~! [X258 : term,X259 : term] : (~((X256 @ X258) = $true) | ~($true = (X256 @ X259)) | ((X256 @ (ap @ X259 @ X258)) = $true)) | ~! [X260 : term] : (($true = (X256 @ X260)) | ~((var @ X260) = $true)))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (pushprop_lem2v2_lthm = $true) & ((apinj1 = $true) <=> ! [X261 : term,X262 : term,X263 : term,X264 : term] : ((X262 = X264) | ((ap @ X264 @ X263) != (ap @ X262 @ X261)))) & ~((var @ (d2term @ d_one)) = $true) & (hoasinduction_lem2_gthm = $true) & ((d2subst @ d_id) = id) & ! [X265 : d_subst,X266 : d_subst] : (((d2subst @ X266) = (d2subst @ X265)) => (X265 = X266)) & ((axscons = $true) <=> ! [X267 : subst] : ((push @ (sub @ one @ X267) @ (comp @ sh @ X267)) = X267)) & (pushprop_lthm = $true) & ((induction2 = $true) <=> ! [X268 : term > $o,X269 : term] : (~! [X270 : term] : (~! [X271 : term] : (~($true = (X268 @ X271)) | ($true = (X268 @ (sub @ X270 @ (push @ X271 @ id))))) | ((X268 @ (lam @ X270)) = $true)) | ~! [X272 : term,X273 : term] : (~($true = (X268 @ X272)) | ~((X268 @ X273) = $true) | ((X268 @ (ap @ X273 @ X272)) = $true)) | ((X268 @ X269) = $true) | ~! [X274 : term] : (~((var @ X274) = $true) | ($true = (X268 @ X274))))) & (! [X275 : term,X276 : term,X277 : term > $o,X278 : subst,X279 : term > $o] : (((X277 @ (sub @ X276 @ (push @ X275 @ X278))) = $true) | ~((X279 @ X276) = $true)) <=> (pushprop_lem1 = $true)) & (hoasinduction_lem1_gthm = $true) & ((hoasinduction_lem3v2_f = $true) <=> ! [X280 : term] : ~! [X281 : subst > term > term] : ~! [X282 : term,X283 : subst] : ((X281 @ X283 @ X282) = (sub @ X280 @ (push @ X282 @ X283)))) & (hoasinduction_gthm = $true) & ((! [X284 : term,X285 : subst] : ((sub @ one @ (push @ X284 @ X285)) = X284) => ! [X286 : term,X287 : subst,X288 : term > $o,X289 : term > $o] : (((X289 @ one) = $true) | ~($true = (X288 @ X286)) | ~! [X290 : term] : ((X288 @ (sub @ X290 @ (push @ X286 @ X287))) = (X289 @ X290)))) <=> (pushprop_lem1v2_lthm = $true)) & (one = (d2term @ d_one)) & ! [X291 : d_subst] : (d_id = X291) & (! [X292 : term,X293 : subst > term > subst > $o] : (~! [X294 : subst > term > term] : (~! [X295 : subst,X296 : term,X297 : subst] : ((X294 @ (comp @ X295 @ X297) @ (sub @ X296 @ X297)) = (sub @ (X294 @ X295 @ X296) @ X297)) | ($true = (X293 @ id @ (lam @ (X294 @ sh @ one)) @ id)) | ~! [X298 : term] : (($true = (X293 @ id @ (X294 @ id @ X298) @ id)) | ~($true = (X293 @ id @ X298 @ id)))) | ~! [X299 : subst,X300 : subst,X301 : term,X302 : subst] : (~((X293 @ X302 @ X301 @ (comp @ X300 @ X299)) = $true) | ($true = (X293 @ (comp @ X302 @ X300) @ (sub @ X301 @ X300) @ X299))) | ((X293 @ id @ X292 @ id) = $true) | ~! [X303 : term] : (((X293 @ id @ X303 @ id) = $true) | ~($true = (var @ (sub @ X303 @ id)))) | ~! [X304 : term,X305 : term] : (~($true = (X293 @ id @ X305 @ id)) | ($true = (X293 @ id @ (ap @ (sub @ X304 @ id) @ X305) @ id)) | ~($true = (X293 @ id @ X304 @ id))) | ~! [X306 : term,X307 : subst,X308 : subst,X309 : subst] : (((X293 @ X308 @ X306 @ (comp @ X307 @ X309)) = $true) | ~($true = (X293 @ (comp @ X308 @ X307) @ (sub @ X306 @ X307) @ X309)))) <=> (hoasinduction = $true)) & (pushprop = $true) & ~(ulamvar1 = $true) & (hoasapinj1_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoaslamnotvar_lthm = $true) & ((hoasinduction_lem3v2 = $true) <=> ! [X310 : term,X311 : subst > term > subst > $o,X312 : term > $o] : (~! [X313 : term] : ((X312 @ X313) = (X311 @ id @ X313 @ id)) | ~! [X314 : term] : (~((X312 @ X314) = $true) | ((X312 @ (sub @ X310 @ (push @ X314 @ id))) = $true)) | ((X312 @ (lam @ X310)) = $true) | ~! [X315 : subst,X316 : subst,X317 : subst,X318 : term] : (~((X311 @ (comp @ X316 @ X317) @ (sub @ X318 @ X317) @ X315) = $true) | ($true = (X311 @ X316 @ X318 @ (comp @ X317 @ X315)))) | ~! [X319 : subst,X320 : subst,X321 : term,X322 : subst] : (~((X311 @ X322 @ X321 @ (comp @ X319 @ X320)) = $true) | ((X311 @ (comp @ X322 @ X319) @ (sub @ X321 @ X319) @ X320) = $true)) | ~! [X323 : subst > term > term] : (~! [X324 : term] : (~($true = (X311 @ id @ X324 @ id)) | ((X311 @ id @ (X323 @ id @ X324) @ id) = $true)) | ((X311 @ id @ (lam @ (X323 @ sh @ one)) @ id) = $true) | ~! [X325 : term,X326 : subst,X327 : subst] : ((X323 @ (comp @ X327 @ X326) @ (sub @ X325 @ X326)) = (sub @ (X323 @ X327 @ X325) @ X326))))) & (pushprop_gthm = $true) & (apnotvar = $true) & (hoasinduction_lem2_lthm = $true) & ((shinj = $true) <=> ! [X328 : term,X329 : term] : ((X328 = X329) | ((sub @ X329 @ sh) != (sub @ X328 @ sh)))) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (! [X330 : term,X331 : subst > term > subst > $o] : (~! [X332 : subst > term > term] : (($true = (X331 @ id @ (lam @ (X332 @ sh @ one)) @ id)) | ~! [X333 : term] : (((X331 @ id @ (X332 @ id @ X333) @ id) = $true) | ~((X331 @ id @ X333 @ id) = $true)) | ~! [X334 : subst,X335 : subst,X336 : term] : ((sub @ (X332 @ X335 @ X336) @ X334) = (X332 @ (comp @ X335 @ X334) @ (sub @ X336 @ X334)))) | ((X331 @ id @ X330 @ id) = $true) | ~! [X337 : term,X338 : term] : (((X331 @ id @ (ap @ (sub @ X337 @ id) @ X338) @ id) = $true) | ~((X331 @ id @ X337 @ id) = $true) | ~((X331 @ id @ X338 @ id) = $true))) <=> (hoasinduction_no_psi_cond = $true)) & (! [X339 : term] : ~! [X340 : subst > term > term] : ((X340 @ sh @ one) != (sub @ X339 @ (push @ one @ sh))) <=> (hoasinduction_lem3b_lthm = $true)) & (hoasinduction_lem3_gthm = $true) & (hoasapnotvar_lthm = $true) & ((hoaslamnotap = $true) <=> ! [X341 : subst > term > term,X342 : term,X343 : term] : (((ap @ (sub @ X342 @ id) @ X343) != (lam @ (X341 @ sh @ one))) | ~! [X344 : subst,X345 : term,X346 : subst] : ((sub @ (X341 @ X346 @ X345) @ X344) = (X341 @ (comp @ X346 @ X344) @ (sub @ X345 @ X344))))) & (hoaslamnotap_lthm = $true) & (pushprop_lem0_gthm = $true) & (axabs = $true) & (axapp = $true) & ((hoasinduction_lthm_3 = $true) <=> (! [X347 : subst > term > subst > $o] : ~! [X348 : term > $o] : ~! [X349 : term] : ((X347 @ id @ X349 @ id) = (X348 @ X349)) => (! [X350 : term,X351 : term > $o] : (~! [X352 : term] : (((X351 @ X352) = $true) | ~((var @ X352) = $true)) | ~! [X353 : term,X354 : term] : (($true = (X351 @ (ap @ X354 @ X353))) | ~((X351 @ X353) = $true) | ~($true = (X351 @ X354))) | ($true = (X351 @ X350)) | ~! [X355 : term] : (($true = (X351 @ (lam @ X355))) | ~! [X356 : term] : (~((X351 @ X356) = $true) | ((X351 @ (sub @ X355 @ (push @ X356 @ id))) = $true)))) => (! [X357 : term] : ((sub @ X357 @ id) = X357) => (! [X358 : subst > term > subst > $o,X359 : term,X360 : term > $o] : (~! [X361 : term] : ((X360 @ X361) = (X358 @ id @ X361 @ id)) | ~! [X362 : subst > term > term] : (~! [X363 : term] : (~((X358 @ id @ X363 @ id) = $true) | ((X358 @ id @ (X362 @ id @ X363) @ id) = $true)) | ~! [X364 : subst,X365 : subst,X366 : term] : ((sub @ (X362 @ X364 @ X366) @ X365) = (X362 @ (comp @ X364 @ X365) @ (sub @ X366 @ X365))) | ($true = (X358 @ id @ (lam @ (X362 @ sh @ one)) @ id))) | ($true = (X360 @ (lam @ X359))) | ~! [X367 : term] : (($true = (X360 @ (sub @ X359 @ (push @ X367 @ id)))) | ~((X360 @ X367) = $true))) => ! [X368 : term,X369 : subst > term > subst > $o] : (~! [X370 : term,X371 : subst,X372 : subst,X373 : subst] : (($true = (X369 @ X373 @ X370 @ (comp @ X372 @ X371))) | ~($true = (X369 @ (comp @ X373 @ X372) @ (sub @ X370 @ X372) @ X371))) | ~! [X374 : term,X375 : term] : (~((X369 @ id @ X375 @ id) = $true) | ~($true = (X369 @ id @ X374 @ id)) | ((X369 @ id @ (ap @ (sub @ X374 @ id) @ X375) @ id) = $true)) | ~! [X376 : subst,X377 : subst,X378 : subst,X379 : term] : (((X369 @ (comp @ X378 @ X376) @ (sub @ X379 @ X376) @ X377) = $true) | ~((X369 @ X378 @ X379 @ (comp @ X376 @ X377)) = $true)) | ~! [X380 : subst > term > term] : (~! [X381 : term] : (~($true = (X369 @ id @ X381 @ id)) | ((X369 @ id @ (X380 @ id @ X381) @ id) = $true)) | ~! [X382 : subst,X383 : term,X384 : subst] : ((X380 @ (comp @ X382 @ X384) @ (sub @ X383 @ X384)) = (sub @ (X380 @ X382 @ X383) @ X384)) | ($true = (X369 @ id @ (lam @ (X380 @ sh @ one)) @ id))) | ~! [X385 : term] : (~($true = (var @ (sub @ X385 @ id))) | ($true = (X369 @ id @ X385 @ id))) | ($true = (X369 @ id @ X368 @ id)))))))) & ((induction2lem = $true) <=> ! [X386 : term,X387 : subst,X388 : term > $o] : (~! [X389 : term] : (((X388 @ (sub @ X389 @ X387)) = $true) | ~($true = (var @ X389))) | ~! [X390 : term,X391 : term] : (~($true = (X388 @ X391)) | ~((X388 @ X390) = $true) | ((X388 @ (ap @ X391 @ X390)) = $true)) | ($true = (X388 @ (sub @ X386 @ X387))) | ~! [X392 : term] : (((X388 @ (lam @ X392)) = $true) | ~! [X393 : term] : (~($true = (X388 @ X393)) | ((X388 @ (sub @ X392 @ (push @ X393 @ id))) = $true))))) & ((termmset = $true) <=> ! [X394 : term] : ((sub @ X394 @ id) = X394)) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (pushprop_lthm_orig = $true) & ((substmonoid_lthm = $true) <=> (! [X395 : subst] : ((comp @ id @ X395) = X395) => (! [X396 : subst] : ((comp @ X396 @ id) = X396) => (! [X397 : subst] : ((comp @ id @ X397) = X397) & ! [X398 : subst] : ((comp @ X398 @ id) = X398))))) & (hoasinduction_lem3v2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (! [X399 : subst,X400 : term > $o,X401 : term > $o,X402 : term] : (~! [X403 : term] : ((X400 @ (sub @ X403 @ (push @ X402 @ X399))) = (X401 @ X403)) | ($true = (X401 @ one)) | ~($true = (X400 @ X402))) <=> (pushprop_lem1v2 = $true)) & ((hoaslaminj = $true) <=> ! [X404 : subst,X405 : subst > term > term,X406 : term,X407 : subst > term > term] : (~! [X408 : term,X409 : subst,X410 : subst] : ((X407 @ (comp @ X409 @ X410) @ (sub @ X408 @ X410)) = (sub @ (X407 @ X409 @ X408) @ X410)) | ((X407 @ X404 @ X406) = (X405 @ X404 @ X406)) | ~! [X411 : subst,X412 : subst,X413 : term] : ((X405 @ (comp @ X412 @ X411) @ (sub @ X413 @ X411)) = (sub @ (X405 @ X412 @ X413) @ X411)) | ((lam @ (X407 @ sh @ one)) != (lam @ (X405 @ sh @ one))))) & (axvarshift = $true) & (! [X414 : term,X415 : subst > term > subst > $o] : (~! [X416 : term] : (((X415 @ id @ (sub @ X414 @ (push @ X416 @ id)) @ id) = $true) | ~((X415 @ id @ X416 @ id) = $true)) | ((X415 @ id @ (lam @ (sub @ X414 @ (push @ one @ sh))) @ id) = $true) | ~! [X417 : subst > term > term] : (~! [X418 : subst,X419 : term,X420 : subst] : ((sub @ (X417 @ X418 @ X419) @ X420) = (X417 @ (comp @ X418 @ X420) @ (sub @ X419 @ X420))) | ~! [X421 : term] : (((X415 @ id @ (X417 @ id @ X421) @ id) = $true) | ~($true = (X415 @ id @ X421 @ id))) | ((X415 @ id @ (lam @ (X417 @ sh @ one)) @ id) = $true))) <=> (hoasinduction_lem3aa_lthm = $true)) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem3v2_lthm = $true) & (lamnotvar = $true) & (induction2_gthm = $true) & (pushprop_lem3v2 = $true) & ! [X422 : term] : ? [X423 : d_term] : ((d2term @ X423) = X422) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ((hoasinduction_lem3_lthm = $true) <=> (! [X424 : term] : ((sub @ X424 @ id) = X424) => (! [X425 : subst > term > subst > $o,X426 : term] : (~! [X427 : subst > term > term] : (~! [X428 : subst,X429 : term,X430 : subst] : ((X427 @ (comp @ X430 @ X428) @ (sub @ X429 @ X428)) = (sub @ (X427 @ X430 @ X429) @ X428)) | ($true = (X425 @ id @ (lam @ (X427 @ sh @ one)) @ id)) | ~! [X431 : term] : (~($true = (X425 @ id @ X431 @ id)) | ((X425 @ id @ (X427 @ id @ X431) @ id) = $true))) | ($true = (X425 @ id @ (lam @ (sub @ X426 @ (push @ one @ sh))) @ id)) | ~! [X432 : term] : (($true = (X425 @ id @ (sub @ X426 @ (push @ X432 @ id)) @ id)) | ~((X425 @ id @ X432 @ id) = $true))) => ! [X433 : term,X434 : subst > term > subst > $o] : (~! [X435 : term] : (~($true = (X434 @ id @ X435 @ id)) | ((X434 @ id @ (sub @ X433 @ (push @ X435 @ id)) @ id) = $true)) | ((X434 @ id @ (lam @ X433) @ id) = $true) | ~! [X436 : subst,X437 : term,X438 : subst,X439 : subst] : (~((X434 @ X436 @ X437 @ (comp @ X439 @ X438)) = $true) | ($true = (X434 @ (comp @ X436 @ X439) @ (sub @ X437 @ X439) @ X438))) | ~! [X440 : subst,X441 : term,X442 : subst,X443 : subst] : (((X434 @ X442 @ X441 @ (comp @ X440 @ X443)) = $true) | ~((X434 @ (comp @ X442 @ X440) @ (sub @ X441 @ X440) @ X443) = $true)) | ~! [X444 : subst > term > term] : (((X434 @ id @ (lam @ (X444 @ sh @ one)) @ id) = $true) | ~! [X445 : term] : (((X434 @ id @ (X444 @ id @ X445) @ id) = $true) | ~((X434 @ id @ X445 @ id) = $true)) | ~! [X446 : subst,X447 : term,X448 : subst] : ((X444 @ (comp @ X448 @ X446) @ (sub @ X447 @ X446)) = (sub @ (X444 @ X448 @ X447) @ X446))))))) & (! [X449 : subst > term > subst > $o] : ~! [X450 : term > $o] : ~! [X451 : term] : ((X449 @ id @ X451 @ id) = (X450 @ X451)) <=> (hoasinduction_lem0_lthm = $true)) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem1 = $true) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (hoasapnotvar_gthm = $true) & (hoaslamnotap_gthm = $true) & ((hoasinduction_lem2 = $true) <=> ! [X452 : term,X453 : term,X454 : subst > term > subst > $o] : (~((X454 @ id @ X453 @ id) = $true) | ~! [X455 : subst,X456 : subst,X457 : term,X458 : subst] : (((X454 @ X458 @ X457 @ (comp @ X455 @ X456)) = $true) | ~($true = (X454 @ (comp @ X458 @ X455) @ (sub @ X457 @ X455) @ X456))) | ((X454 @ id @ (ap @ X452 @ X453) @ id) = $true) | ~! [X459 : subst,X460 : term,X461 : subst,X462 : subst] : (~((X454 @ X461 @ X460 @ (comp @ X459 @ X462)) = $true) | ((X454 @ (comp @ X461 @ X459) @ (sub @ X460 @ X459) @ X462) = $true)) | ~((X454 @ id @ X452 @ id) = $true) | ~! [X463 : term,X464 : term] : (~($true = (X454 @ id @ X463 @ id)) | ($true = (X454 @ id @ (ap @ (sub @ X463 @ id) @ X464) @ id)) | ~((X454 @ id @ X464 @ id) = $true)))) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X465 : term] : ~! [X466 : subst > term > term] : ~! [X467 : subst,X468 : term] : ((sub @ X465 @ (push @ X468 @ X467)) = (X466 @ X467 @ X468)) => (! [X469 : term] : ((sub @ X469 @ id) = X469) => ! [X470 : subst > term > subst > $o,X471 : term,X472 : term > $o] : (~! [X473 : subst > term > term] : (((X470 @ id @ (lam @ (X473 @ sh @ one)) @ id) = $true) | ~! [X474 : term] : (~((X470 @ id @ X474 @ id) = $true) | ((X470 @ id @ (X473 @ id @ X474) @ id) = $true)) | ~! [X475 : subst,X476 : subst,X477 : term] : ((X473 @ (comp @ X476 @ X475) @ (sub @ X477 @ X475)) = (sub @ (X473 @ X476 @ X477) @ X475))) | ~! [X478 : term] : ((X470 @ id @ X478 @ id) = (X472 @ X478)) | ((X472 @ (lam @ X471)) = $true) | ~! [X479 : term] : (~($true = (X472 @ X479)) | ((X472 @ (sub @ X471 @ (push @ X479 @ id))) = $true)))))) & (! [X480 : term,X481 : term,X482 : term,X483 : term] : (((ap @ (sub @ X482 @ id) @ X481) != (ap @ (sub @ X480 @ id) @ X483)) | (X481 = X483)) <=> (hoasapinj2 = $true)) & ! [X484 : subst] : ? [X485 : d_subst] : ((d2subst @ X485) = X484) & ((hoasapinj1 = $true) <=> ! [X486 : term,X487 : term,X488 : term,X489 : term] : (((ap @ (sub @ X489 @ id) @ X486) != (ap @ (sub @ X488 @ id) @ X487)) | (X488 = X489))) & ((hoasinduction_lem3a = $true) <=> ! [X490 : term,X491 : subst > term > subst > $o] : (~! [X492 : term] : (((X491 @ id @ (sub @ X490 @ (push @ X492 @ id)) @ id) = $true) | ~((X491 @ id @ X492 @ id) = $true)) | ($true = (X491 @ id @ (lam @ X490) @ id)) | ~! [X493 : subst > term > term] : (~! [X494 : subst,X495 : subst,X496 : term] : ((X493 @ (comp @ X494 @ X495) @ (sub @ X496 @ X495)) = (sub @ (X493 @ X494 @ X496) @ X495)) | ((X491 @ id @ (lam @ (X493 @ sh @ one)) @ id) = $true) | ~! [X497 : term] : (~((X491 @ id @ X497 @ id) = $true) | ((X491 @ id @ (X493 @ id @ X497) @ id) = $true))))) & ((hoasinduction_lem3aa = $true) <=> ! [X498 : subst > term > subst > $o,X499 : term] : (($true = (X498 @ id @ (lam @ (sub @ X499 @ (push @ one @ sh))) @ id)) | ~! [X500 : term] : (($true = (X498 @ id @ (sub @ X499 @ (push @ X500 @ id)) @ id)) | ~($true = (X498 @ id @ X500 @ id))) | ~! [X501 : subst > term > term] : (($true = (X498 @ id @ (lam @ (X501 @ sh @ one)) @ id)) | ~! [X502 : subst,X503 : subst,X504 : term] : ((X501 @ (comp @ X502 @ X503) @ (sub @ X504 @ X503)) = (sub @ (X501 @ X502 @ X504) @ X503)) | ~! [X505 : term] : (~($true = (X498 @ id @ X505 @ id)) | ($true = (X498 @ id @ (X501 @ id @ X505) @ id)))))) & (ulamvarind = $true) & ((! [X506 : term,X507 : subst] : ((sub @ one @ (push @ X506 @ X507)) = X506) => (! [X508 : subst,X509 : term] : ((comp @ sh @ (push @ X509 @ X508)) = X508) => (! [X510 : subst] : ((comp @ X510 @ id) = X510) => (! [X511 : term,X512 : term > $o] : (~! [X513 : term] : (~($true = (X512 @ X513)) | ((X512 @ (lam @ X513)) = $true)) | ~! [X514 : term] : (~((var @ X514) = $true) | ((X512 @ X514) = $true)) | ((X512 @ X511) = $true) | ~! [X515 : term,X516 : term] : (((X512 @ (ap @ X516 @ X515)) = $true) | ~($true = (X512 @ X516)) | ~((X512 @ X515) = $true))) => ! [X517 : subst,X518 : term > $o,X519 : term] : (~! [X520 : term] : (((X518 @ (lam @ X520)) = $true) | ~! [X521 : term] : (($true = (X518 @ (sub @ X520 @ (push @ X521 @ id)))) | ~($true = (X518 @ X521)))) | ~! [X522 : term,X523 : term] : (($true = (X518 @ (ap @ X523 @ X522))) | ~((X518 @ X523) = $true) | ~((X518 @ X522) = $true)) | ($true = (X518 @ (sub @ X519 @ X517))) | ~! [X524 : term] : (($true = (X518 @ (sub @ X524 @ X517))) | ~((var @ X524) = $true))))))) <=> (induction2lem_lthm = $true)) & (hoasinduction_lem1_lthm = $true) & (! [X525 : subst > term > subst > $o] : ~! [X526 : term > $o] : ~! [X527 : term] : ((X525 @ id @ X527 @ id) = (X526 @ X527)) <=> (hoasinduction_lem0 = $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)))))))))))) & (! [X528 : subst] : ((comp @ id @ X528) = X528) <=> (axidl = $true)) & (termmset_gthm = $true) & (hoasapinj2_gthm = $true) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (! [X529 : term] : ~! [X530 : subst > term > term] : ((X530 @ sh @ one) != (sub @ X529 @ (push @ one @ sh))) <=> (hoasinduction_lem3b = $true)) & ! [X531 : d_term] : (d_one = X531) & (hoasinduction_lem3a_gthm = $true) & ((hoasapinj2_lthm = $true) <=> (! [X532 : term,X533 : term,X534 : term,X535 : term] : ((X533 = X534) | ((ap @ X532 @ X534) != (ap @ X535 @ X533))) => ! [X536 : term,X537 : term,X538 : term,X539 : term] : (((ap @ (sub @ X536 @ id) @ X539) != (ap @ (sub @ X537 @ id) @ X538)) | (X538 = X539)))) & (hoasinduction_lem3b_gthm = $true)),
% 15.02/3.54 inference(rectify,[status(thm)],[f8])).
% 15.02/3.54 thf(f8,plain,(
% 15.02/3.54 ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & ((hoasinduction_no_psi_cond_lthm = $true) <=> (! [X0 : subst > term > subst > $o] : ~! [X1 : term > $o] : ~! [X2 : term] : ((X0 @ id @ X2 @ id) = (X1 @ X2)) => (! [X3 : term,X4 : term > $o] : (($true = (X4 @ X3)) | ~! [X5 : term,X6 : term] : (~((X4 @ X5) = $true) | ($true = (X4 @ (ap @ X5 @ X6))) | ~((X4 @ X6) = $true)) | ~! [X7 : term] : (((X4 @ X7) = $true) | ~($true = (var @ X7))) | ~! [X8 : term] : (((X4 @ (lam @ X8)) = $true) | ~! [X9 : term] : (~($true = (X4 @ X9)) | ($true = (X4 @ (sub @ X8 @ (push @ X9 @ id))))))) => (! [X10 : term] : ((sub @ X10 @ id) = X10) => (! [X11 : term,X12 : subst > term > subst > $o,X13 : term > $o] : (~! [X14 : term] : ((X13 @ X14) = (X12 @ id @ X14 @ id)) | ~! [X15 : subst > term > term] : (~! [X16 : term] : (~($true = (X12 @ id @ X16 @ id)) | ((X12 @ id @ (X15 @ id @ X16) @ id) = $true)) | ~! [X17 : term,X18 : subst,X19 : subst] : ((sub @ (X15 @ X19 @ X17) @ X18) = (X15 @ (comp @ X19 @ X18) @ (sub @ X17 @ X18))) | ($true = (X12 @ id @ (lam @ (X15 @ sh @ one)) @ id))) | ((X13 @ (lam @ X11)) = $true) | ~! [X20 : term] : (~((X13 @ X20) = $true) | ($true = (X13 @ (sub @ X11 @ (push @ X20 @ id)))))) => ! [X21 : subst > term > subst > $o,X22 : term] : (~! [X23 : term,X24 : term] : (~((X21 @ id @ X24 @ id) = $true) | ($true = (X21 @ id @ (ap @ (sub @ X23 @ id) @ X24) @ id)) | ~($true = (X21 @ id @ X23 @ id))) | ~! [X25 : subst > term > term] : (~! [X26 : term] : (~((X21 @ id @ X26 @ id) = $true) | ((X21 @ id @ (X25 @ id @ X26) @ id) = $true)) | ((X21 @ id @ (lam @ (X25 @ sh @ one)) @ id) = $true) | ~! [X27 : term,X28 : subst,X29 : subst] : ((X25 @ (comp @ X28 @ X29) @ (sub @ X27 @ X29)) = (sub @ (X25 @ X28 @ X27) @ X29))) | ($true = (X21 @ id @ X22 @ id)))))))) & (! [X30 : term,X31 : term] : ((X30 = X31) | ((lam @ X30) != (lam @ X31))) <=> (laminj = $true)) & ((hoasinduction_lem3 = $true) <=> ! [X32 : term,X33 : subst > term > subst > $o] : (($true = (X33 @ id @ (lam @ X32) @ id)) | ~! [X34 : term,X35 : subst,X36 : subst,X37 : subst] : (((X33 @ X36 @ X34 @ (comp @ X37 @ X35)) = $true) | ~((X33 @ (comp @ X36 @ X37) @ (sub @ X34 @ X37) @ X35) = $true)) | ~! [X38 : subst,X39 : subst,X40 : subst,X41 : term] : (~($true = (X33 @ X39 @ X41 @ (comp @ X40 @ X38))) | ($true = (X33 @ (comp @ X39 @ X40) @ (sub @ X41 @ X40) @ X38))) | ~! [X42 : subst > term > term] : (~! [X43 : term] : (((X33 @ id @ (X42 @ id @ X43) @ id) = $true) | ~($true = (X33 @ id @ X43 @ id))) | ((X33 @ id @ (lam @ (X42 @ sh @ one)) @ id) = $true) | ~! [X44 : term,X45 : subst,X46 : subst] : ((X42 @ (comp @ X46 @ X45) @ (sub @ X44 @ X45)) = (sub @ (X42 @ X46 @ X44) @ X45))) | ~! [X47 : term] : (((X33 @ id @ (sub @ X32 @ (push @ X47 @ id)) @ id) = $true) | ~($true = (X33 @ id @ X47 @ id))))) & (! [X48 : term,X49 : term,X50 : term,X51 : term] : (((ap @ X49 @ X48) != (ap @ X50 @ X51)) | (X48 = X51)) <=> (apinj2 = $true)) & (ulamvarsh = $true) & (axclos = $true) & (hoasinduction_lem1v2 = $true) & (! [X52 : subst] : ((comp @ X52 @ id) = X52) <=> (axidr = $true)) & ((hoasinduction_lem2v2 = $true) <=> ! [X53 : term,X54 : term > $o,X55 : subst > term > subst > $o,X56 : term] : (~((X54 @ X53) = $true) | ~! [X57 : subst,X58 : term,X59 : subst,X60 : subst] : (((X55 @ (comp @ X60 @ X57) @ (sub @ X58 @ X57) @ X59) = $true) | ~($true = (X55 @ X60 @ X58 @ (comp @ X57 @ X59)))) | ~! [X61 : term,X62 : term] : (~((X55 @ id @ X62 @ id) = $true) | ((X55 @ id @ (ap @ (sub @ X62 @ id) @ X61) @ id) = $true) | ~($true = (X55 @ id @ X61 @ id))) | ((X54 @ (ap @ X53 @ X56)) = $true) | ~((X54 @ X56) = $true) | ~! [X63 : term] : ((X55 @ id @ X63 @ id) = (X54 @ X63)) | ~! [X64 : subst,X65 : term,X66 : subst,X67 : subst] : (~((X55 @ (comp @ X66 @ X67) @ (sub @ X65 @ X67) @ X64) = $true) | ((X55 @ X66 @ X65 @ (comp @ X67 @ X64)) = $true)))) & ((! [X68 : term] : ((sub @ X68 @ id) = X68) => (! [X69 : term,X70 : term,X71 : term,X72 : term] : ((X69 = X71) | ((ap @ X69 @ X70) != (ap @ X71 @ X72))) => ! [X73 : term,X74 : term,X75 : term,X76 : term] : ((X73 = X74) | ((ap @ (sub @ X74 @ id) @ X76) != (ap @ (sub @ X73 @ id) @ X75))))) <=> (hoasapinj1_lthm = $true)) & ((axvarcons = $true) <=> ! [X77 : subst,X78 : term] : ((sub @ one @ (push @ X78 @ X77)) = X78)) & (hoasinduction_p_and_p_prime = (^[Y0 : subst > term > subst > $o]: ((^[Y1 : term > $o]: (!! @ term @ (^[Y2 : term]: ((Y1 @ Y2) = (Y0 @ id @ Y2 @ id)))))))) & (pushprop_lem2v2 = $true) & (axassoc = $true) & ~((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) & ((! [X82 : subst] : ((comp @ id @ X82) = X82) & ! [X83 : subst] : ((comp @ X83 @ id) = X83)) <=> (substmonoid = $true)) & ((hoasinduction_lem3a_lthm = $true) <=> (! [X84 : term] : ((sub @ X84 @ id) = X84) => (! [X85 : subst > term > subst > $o,X86 : term] : (((X85 @ id @ (lam @ (sub @ X86 @ (push @ one @ sh))) @ id) = $true) | ~! [X87 : subst > term > term] : (~! [X88 : term,X89 : subst,X90 : subst] : ((X87 @ (comp @ X90 @ X89) @ (sub @ X88 @ X89)) = (sub @ (X87 @ X90 @ X88) @ X89)) | ~! [X91 : term] : (($true = (X85 @ id @ (X87 @ id @ X91) @ id)) | ~($true = (X85 @ id @ X91 @ id))) | ($true = (X85 @ id @ (lam @ (X87 @ sh @ one)) @ id))) | ~! [X92 : term] : (~($true = (X85 @ id @ X92 @ id)) | ((X85 @ id @ (sub @ X86 @ (push @ X92 @ id)) @ id) = $true))) => ! [X93 : subst > term > subst > $o,X94 : term] : (($true = (X93 @ id @ (lam @ X94) @ id)) | ~! [X95 : subst > term > term] : (~! [X96 : term] : (($true = (X93 @ id @ (X95 @ id @ X96) @ id)) | ~($true = (X93 @ id @ X96 @ id))) | ~! [X97 : term,X98 : subst,X99 : subst] : ((X95 @ (comp @ X99 @ X98) @ (sub @ X97 @ X98)) = (sub @ (X95 @ X99 @ X97) @ X98)) | ((X93 @ id @ (lam @ (X95 @ sh @ one)) @ id) = $true)) | ~! [X100 : term] : (~($true = (X93 @ id @ X100 @ id)) | ($true = (X93 @ id @ (sub @ X94 @ (push @ X100 @ id)) @ id))))))) & ((hoasinduction_lem3v2_lthm = $true) <=> (! [X101 : term] : ((sub @ X101 @ id) = X101) => ! [X102 : term > $o,X103 : subst > term > subst > $o,X104 : term] : (~! [X105 : term] : (~((X102 @ X105) = $true) | ((X102 @ (sub @ X104 @ (push @ X105 @ id))) = $true)) | ~! [X106 : subst > term > term] : (~! [X107 : subst,X108 : subst,X109 : term] : ((X106 @ (comp @ X108 @ X107) @ (sub @ X109 @ X107)) = (sub @ (X106 @ X108 @ X109) @ X107)) | ~! [X110 : term] : (~($true = (X103 @ id @ X110 @ id)) | ($true = (X103 @ id @ (X106 @ id @ X110) @ id))) | ((X103 @ id @ (lam @ (X106 @ sh @ one)) @ id) = $true)) | ~! [X111 : subst,X112 : term,X113 : subst,X114 : subst] : (((X103 @ (comp @ X111 @ X113) @ (sub @ X112 @ X113) @ X114) = $true) | ~($true = (X103 @ X111 @ X112 @ (comp @ X113 @ X114)))) | ~! [X115 : term] : ((X103 @ id @ X115 @ id) = (X102 @ X115)) | ((X102 @ (lam @ X104)) = $true) | ~! [X116 : subst,X117 : subst,X118 : term,X119 : subst] : (~((X103 @ (comp @ X117 @ X116) @ (sub @ X118 @ X116) @ X119) = $true) | ((X103 @ X117 @ X118 @ (comp @ X116 @ X119)) = $true))))) & (! [X120 : term,X121 : subst] : ((comp @ sh @ (push @ X120 @ X121)) = X121) <=> (axshiftcons = $true)) & ((pushprop_lem0 = $true) <=> ! [X122 : term > $o,X123 : subst,X124 : term] : ~! [X125 : term > $o] : ~! [X126 : term] : ((X125 @ X126) = (X122 @ (sub @ X126 @ (push @ X124 @ X123))))) & ~(lamnotap = $true) & (! [X127 : term] : ~! [X128 : subst > term > term] : ~! [X129 : term,X130 : subst] : ((sub @ X127 @ (push @ X129 @ X130)) = (X128 @ X130 @ X129)) <=> (hoasinduction_lem3v2_f_lthm = $true)) & (axmap = $true) & (hoasinduction_lem2v2_gthm = $true) & ((induction2_lthm = $true) <=> (! [X131 : term] : ((sub @ X131 @ id) = X131) => (! [X132 : subst,X133 : term > $o,X134 : term] : (~! [X135 : term] : (((X133 @ (lam @ X135)) = $true) | ~! [X136 : term] : (((X133 @ (sub @ X135 @ (push @ X136 @ id))) = $true) | ~((X133 @ X136) = $true))) | ~! [X137 : term,X138 : term] : (((X133 @ (ap @ X137 @ X138)) = $true) | ~($true = (X133 @ X138)) | ~($true = (X133 @ X137))) | ~! [X139 : term] : (($true = (X133 @ (sub @ X139 @ X132))) | ~((var @ X139) = $true)) | ((X133 @ (sub @ X134 @ X132)) = $true)) => ! [X140 : term,X141 : term > $o] : (~! [X142 : term] : (~($true = (var @ X142)) | ($true = (X141 @ X142))) | ~! [X143 : term,X144 : term] : (~((X141 @ X144) = $true) | ((X141 @ (ap @ X143 @ X144)) = $true) | ~((X141 @ X143) = $true)) | ~! [X145 : term] : (~! [X146 : term] : (~((X141 @ X146) = $true) | ((X141 @ (sub @ X145 @ (push @ X146 @ id))) = $true)) | ((X141 @ (lam @ X145)) = $true)) | ($true = (X141 @ X140)))))) & ((pushprop_lem0_lthm = $true) <=> ! [X147 : subst,X148 : term > $o,X149 : term] : ~! [X150 : term > $o] : ~! [X151 : term] : ((X148 @ (sub @ X151 @ (push @ X149 @ X147))) = (X150 @ X151))) & (induction2lem_gthm = $true) & ((pushprop_lem1_lthm = $true) <=> (! [X152 : term,X153 : subst] : ((sub @ one @ (push @ X152 @ X153)) = X152) => (! [X154 : subst,X155 : term] : ((comp @ sh @ (push @ X155 @ X154)) = X154) => ! [X156 : term,X157 : term > $o,X158 : subst,X159 : term,X160 : term > $o] : (~($true = (X157 @ X156)) | ($true = (X160 @ (sub @ X156 @ (push @ X159 @ X158)))))))) & ((hoasinduction_lem3v2a = $true) <=> ! [X161 : term > $o,X162 : subst > term > subst > $o,X163 : term] : (~! [X164 : term] : ((X162 @ id @ X164 @ id) = (X161 @ X164)) | ~! [X165 : subst > term > term] : (~! [X166 : term] : (($true = (X162 @ id @ (X165 @ id @ X166) @ id)) | ~((X162 @ id @ X166 @ id) = $true)) | ((X162 @ id @ (lam @ (X165 @ sh @ one)) @ id) = $true) | ~! [X167 : subst,X168 : term,X169 : subst] : ((X165 @ (comp @ X169 @ X167) @ (sub @ X168 @ X167)) = (sub @ (X165 @ X169 @ X168) @ X167))) | ~! [X170 : term] : (~((X161 @ X170) = $true) | ((X161 @ (sub @ X163 @ (push @ X170 @ id))) = $true)) | ($true = (X161 @ (lam @ X163))))) & ((hoasinduction_lthm = $true) <=> (! [X171 : term > $o,X172 : term] : (((X171 @ X172) = $true) | ~! [X173 : term] : (~! [X174 : term] : (($true = (X171 @ (sub @ X173 @ (push @ X174 @ id)))) | ~((X171 @ X174) = $true)) | ($true = (X171 @ (lam @ X173)))) | ~! [X175 : term,X176 : term] : (~((X171 @ X176) = $true) | ((X171 @ (ap @ X176 @ X175)) = $true) | ~($true = (X171 @ X175))) | ~! [X177 : term] : (~((var @ X177) = $true) | ((X171 @ X177) = $true))) => (! [X178 : term,X179 : term,X180 : subst > term > subst > $o] : (~($true = (X180 @ id @ X179 @ id)) | ((X180 @ id @ (ap @ X178 @ X179) @ id) = $true) | ~! [X181 : subst,X182 : subst,X183 : term,X184 : subst] : (~((X180 @ X182 @ X183 @ (comp @ X184 @ X181)) = $true) | ($true = (X180 @ (comp @ X182 @ X184) @ (sub @ X183 @ X184) @ X181))) | ~($true = (X180 @ id @ X178 @ id)) | ~! [X185 : subst,X186 : subst,X187 : term,X188 : subst] : (((X180 @ X188 @ X187 @ (comp @ X186 @ X185)) = $true) | ~($true = (X180 @ (comp @ X188 @ X186) @ (sub @ X187 @ X186) @ X185))) | ~! [X189 : term,X190 : term] : (~((X180 @ id @ X190 @ id) = $true) | ($true = (X180 @ id @ (ap @ (sub @ X190 @ id) @ X189) @ id)) | ~($true = (X180 @ id @ X189 @ id)))) => (! [X191 : term,X192 : subst > term > subst > $o] : (~! [X193 : subst,X194 : term,X195 : subst,X196 : subst] : (~((X192 @ X196 @ X194 @ (comp @ X193 @ X195)) = $true) | ((X192 @ (comp @ X196 @ X193) @ (sub @ X194 @ X193) @ X195) = $true)) | ~! [X197 : subst,X198 : subst,X199 : term,X200 : subst] : (~((X192 @ (comp @ X200 @ X198) @ (sub @ X199 @ X198) @ X197) = $true) | ($true = (X192 @ X200 @ X199 @ (comp @ X198 @ X197)))) | ~! [X201 : term] : (~($true = (X192 @ id @ X201 @ id)) | ($true = (X192 @ id @ (sub @ X191 @ (push @ X201 @ id)) @ id))) | ((X192 @ id @ (lam @ X191) @ id) = $true) | ~! [X202 : subst > term > term] : (~! [X203 : term,X204 : subst,X205 : subst] : ((X202 @ (comp @ X204 @ X205) @ (sub @ X203 @ X205)) = (sub @ (X202 @ X204 @ X203) @ X205)) | ~! [X206 : term] : (~((X192 @ id @ X206 @ id) = $true) | ((X192 @ id @ (X202 @ id @ X206) @ id) = $true)) | ($true = (X192 @ id @ (lam @ (X202 @ sh @ one)) @ id)))) => ! [X207 : subst > term > subst > $o,X208 : term] : (~! [X209 : term,X210 : term] : (((X207 @ id @ (ap @ (sub @ X210 @ id) @ X209) @ id) = $true) | ~((X207 @ id @ X209 @ id) = $true) | ~((X207 @ id @ X210 @ id) = $true)) | ~! [X211 : subst,X212 : subst,X213 : subst,X214 : term] : (((X207 @ X213 @ X214 @ (comp @ X211 @ X212)) = $true) | ~($true = (X207 @ (comp @ X213 @ X211) @ (sub @ X214 @ X211) @ X212))) | ~! [X215 : subst,X216 : subst,X217 : term,X218 : subst] : (~($true = (X207 @ X216 @ X217 @ (comp @ X215 @ X218))) | ((X207 @ (comp @ X216 @ X215) @ (sub @ X217 @ X215) @ X218) = $true)) | ~! [X219 : term] : (((X207 @ id @ X219 @ id) = $true) | ~($true = (var @ (sub @ X219 @ id)))) | ~! [X220 : subst > term > term] : (~! [X221 : subst,X222 : term,X223 : subst] : ((sub @ (X220 @ X223 @ X222) @ X221) = (X220 @ (comp @ X223 @ X221) @ (sub @ X222 @ X221))) | ($true = (X207 @ id @ (lam @ (X220 @ sh @ one)) @ id)) | ~! [X224 : term] : (~((X207 @ id @ X224 @ id) = $true) | ((X207 @ id @ (X220 @ id @ X224) @ id) = $true))) | ($true = (X207 @ id @ X208 @ id))))))) & (hoaslaminj_gthm = $true) & (! [X225 : term,X226 : subst > term > subst > $o] : (~! [X227 : term] : (~($true = (X226 @ id @ X227 @ id)) | ($true = (X226 @ id @ (sub @ X225 @ (push @ X227 @ id)) @ id))) | ((X226 @ id @ (lam @ (sub @ X225 @ (push @ one @ sh))) @ id) = $true) | ~! [X228 : term,X229 : subst > term > term] : (~! [X230 : subst,X231 : term,X232 : subst] : ((sub @ (X229 @ X232 @ X231) @ X230) = (sub @ (sub @ X228 @ (push @ X231 @ X232)) @ X230)) | ~! [X233 : subst,X234 : term,X235 : subst] : ((sub @ X228 @ (push @ (sub @ X234 @ X235) @ (comp @ X233 @ X235))) = (X229 @ (comp @ X233 @ X235) @ (sub @ X234 @ X235))) | ~! [X236 : term] : (~((X226 @ id @ X236 @ id) = $true) | ((X226 @ id @ (X229 @ id @ X236) @ id) = $true)) | ($true = (X226 @ id @ (lam @ (X229 @ sh @ one)) @ id)))) <=> (hoasinduction_lem3aaa = $true)) & (hoasapnotvar = $true) & ! [X237 : d_term,X238 : d_term] : (((d2term @ X237) = (d2term @ X238)) => (X237 = X238)) & ((d2subst @ d_id) = sh) & (hoaslamnotvar_gthm = $true) & (! [X239 : term] : ((sub @ X239 @ id) = X239) <=> (axvarid = $true)) & ((hoaslaminj_lthm = $true) <=> (! [X240 : subst,X241 : term] : ((sub @ one @ (push @ X241 @ X240)) = X241) => (! [X242 : term,X243 : subst] : ((comp @ sh @ (push @ X242 @ X243)) = X243) => (! [X244 : term,X245 : term] : (((lam @ X244) != (lam @ X245)) | (X244 = X245)) => ! [X246 : subst,X247 : term,X248 : subst > term > term,X249 : subst > term > term] : (((X249 @ X246 @ X247) = (X248 @ X246 @ X247)) | ~! [X250 : term,X251 : subst,X252 : subst] : ((X249 @ (comp @ X251 @ X252) @ (sub @ X250 @ X252)) = (sub @ (X249 @ X251 @ X250) @ X252)) | ((lam @ (X248 @ sh @ one)) != (lam @ (X249 @ sh @ one))) | ~! [X253 : subst,X254 : term,X255 : subst] : ((sub @ (X248 @ X253 @ X254) @ X255) = (X248 @ (comp @ X253 @ X255) @ (sub @ X254 @ X255)))))))) & (hoaslamnotvar = $true) & ((termmset_lthm = $true) <=> (! [X256 : term] : ((sub @ X256 @ id) = X256) => ! [X257 : term] : ((sub @ X257 @ id) = X257))) & (substmonoid_gthm = $true) & ((induction = $true) <=> ! [X258 : term,X259 : term > $o] : (~! [X260 : term] : (~($true = (X259 @ X260)) | ((X259 @ (lam @ X260)) = $true)) | ((X259 @ X258) = $true) | ~! [X261 : term,X262 : term] : (~((X259 @ X261) = $true) | ~((X259 @ X262) = $true) | ((X259 @ (ap @ X262 @ X261)) = $true)) | ~! [X263 : term] : (((X259 @ X263) = $true) | ~((var @ X263) = $true)))) & (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one))))) & (pushprop_lem2v2_lthm = $true) & (! [X266 : term,X267 : term,X268 : term,X269 : term] : (((ap @ X267 @ X266) != (ap @ X269 @ X268)) | (X267 = X269)) <=> (apinj1 = $true)) & ~((var @ (d2term @ d_one)) = $true) & (hoasinduction_lem2_gthm = $true) & ((d2subst @ d_id) = id) & ! [X270 : d_subst,X271 : d_subst] : (((d2subst @ X271) = (d2subst @ X270)) => (X270 = X271)) & ((axscons = $true) <=> ! [X272 : subst] : ((push @ (sub @ one @ X272) @ (comp @ sh @ X272)) = X272)) & (pushprop_lthm = $true) & ((induction2 = $true) <=> ! [X273 : term > $o,X274 : term] : (~! [X275 : term] : (~! [X276 : term] : (~($true = (X273 @ X276)) | ($true = (X273 @ (sub @ X275 @ (push @ X276 @ id))))) | ((X273 @ (lam @ X275)) = $true)) | ~! [X277 : term,X278 : term] : (~((X273 @ X277) = $true) | ~($true = (X273 @ X278)) | ((X273 @ (ap @ X278 @ X277)) = $true)) | ((X273 @ X274) = $true) | ~! [X279 : term] : (~($true = (var @ X279)) | ((X273 @ X279) = $true)))) & (! [X280 : term,X281 : term,X282 : term > $o,X283 : subst,X284 : term > $o] : (($true = (X282 @ (sub @ X281 @ (push @ X280 @ X283)))) | ~((X284 @ X281) = $true)) <=> (pushprop_lem1 = $true)) & (hoasinduction_lem1_gthm = $true) & (! [X285 : term] : ~! [X286 : subst > term > term] : ~! [X287 : term,X288 : subst] : ((X286 @ X288 @ X287) = (sub @ X285 @ (push @ X287 @ X288))) <=> (hoasinduction_lem3v2_f = $true)) & (hoasinduction_gthm = $true) & ((! [X289 : term,X290 : subst] : ((sub @ one @ (push @ X289 @ X290)) = X289) => ! [X291 : term,X292 : subst,X293 : term > $o,X294 : term > $o] : (((X294 @ one) = $true) | ~($true = (X293 @ X291)) | ~! [X295 : term] : ((X294 @ X295) = (X293 @ (sub @ X295 @ (push @ X291 @ X292)))))) <=> (pushprop_lem1v2_lthm = $true)) & (one = (d2term @ d_one)) & ! [X296 : d_subst] : (d_id = X296) & (! [X297 : term,X298 : subst > term > subst > $o] : (~! [X299 : subst > term > term] : (~! [X300 : subst,X301 : term,X302 : subst] : ((X299 @ (comp @ X300 @ X302) @ (sub @ X301 @ X302)) = (sub @ (X299 @ X300 @ X301) @ X302)) | ($true = (X298 @ id @ (lam @ (X299 @ sh @ one)) @ id)) | ~! [X303 : term] : (($true = (X298 @ id @ (X299 @ id @ X303) @ id)) | ~((X298 @ id @ X303 @ id) = $true))) | ~! [X304 : subst,X305 : subst,X306 : term,X307 : subst] : (~((X298 @ X307 @ X306 @ (comp @ X305 @ X304)) = $true) | ((X298 @ (comp @ X307 @ X305) @ (sub @ X306 @ X305) @ X304) = $true)) | ($true = (X298 @ id @ X297 @ id)) | ~! [X308 : term] : (($true = (X298 @ id @ X308 @ id)) | ~($true = (var @ (sub @ X308 @ id)))) | ~! [X309 : term,X310 : term] : (~((X298 @ id @ X310 @ id) = $true) | ((X298 @ id @ (ap @ (sub @ X309 @ id) @ X310) @ id) = $true) | ~($true = (X298 @ id @ X309 @ id))) | ~! [X311 : term,X312 : subst,X313 : subst,X314 : subst] : (($true = (X298 @ X313 @ X311 @ (comp @ X312 @ X314))) | ~((X298 @ (comp @ X313 @ X312) @ (sub @ X311 @ X312) @ X314) = $true))) <=> (hoasinduction = $true)) & (pushprop = $true) & ~(ulamvar1 = $true) & (hoasapinj1_gthm = $true) & (hoasinduction_lem1v2_gthm = $true) & (hoaslamnotvar_lthm = $true) & ((hoasinduction_lem3v2 = $true) <=> ! [X315 : term,X316 : subst > term > subst > $o,X317 : term > $o] : (~! [X318 : term] : ((X316 @ id @ X318 @ id) = (X317 @ X318)) | ~! [X319 : term] : (~((X317 @ X319) = $true) | ((X317 @ (sub @ X315 @ (push @ X319 @ id))) = $true)) | ((X317 @ (lam @ X315)) = $true) | ~! [X320 : subst,X321 : subst,X322 : subst,X323 : term] : (~((X316 @ (comp @ X321 @ X322) @ (sub @ X323 @ X322) @ X320) = $true) | ($true = (X316 @ X321 @ X323 @ (comp @ X322 @ X320)))) | ~! [X324 : subst,X325 : subst,X326 : term,X327 : subst] : (~((X316 @ X327 @ X326 @ (comp @ X324 @ X325)) = $true) | ((X316 @ (comp @ X327 @ X324) @ (sub @ X326 @ X324) @ X325) = $true)) | ~! [X328 : subst > term > term] : (~! [X329 : term] : (~((X316 @ id @ X329 @ id) = $true) | ((X316 @ id @ (X328 @ id @ X329) @ id) = $true)) | ($true = (X316 @ id @ (lam @ (X328 @ sh @ one)) @ id)) | ~! [X330 : term,X331 : subst,X332 : subst] : ((X328 @ (comp @ X332 @ X331) @ (sub @ X330 @ X331)) = (sub @ (X328 @ X332 @ X330) @ X331))))) & (pushprop_gthm = $true) & (apnotvar = $true) & (hoasinduction_lem2_lthm = $true) & ((shinj = $true) <=> ! [X333 : term,X334 : term] : ((X333 = X334) | ((sub @ X333 @ sh) != (sub @ X334 @ sh)))) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (! [X335 : term,X336 : subst > term > subst > $o] : (~! [X337 : subst > term > term] : (((X336 @ id @ (lam @ (X337 @ sh @ one)) @ id) = $true) | ~! [X338 : term] : (($true = (X336 @ id @ (X337 @ id @ X338) @ id)) | ~((X336 @ id @ X338 @ id) = $true)) | ~! [X339 : subst,X340 : subst,X341 : term] : ((X337 @ (comp @ X340 @ X339) @ (sub @ X341 @ X339)) = (sub @ (X337 @ X340 @ X341) @ X339))) | ($true = (X336 @ id @ X335 @ id)) | ~! [X342 : term,X343 : term] : (((X336 @ id @ (ap @ (sub @ X342 @ id) @ X343) @ id) = $true) | ~((X336 @ id @ X342 @ id) = $true) | ~((X336 @ id @ X343 @ id) = $true))) <=> (hoasinduction_no_psi_cond = $true)) & (! [X344 : term] : ~! [X345 : subst > term > term] : ((sub @ X344 @ (push @ one @ sh)) != (X345 @ sh @ one)) <=> (hoasinduction_lem3b_lthm = $true)) & (hoasinduction_lem3_gthm = $true) & (hoasapnotvar_lthm = $true) & ((hoaslamnotap = $true) <=> ! [X346 : subst > term > term,X347 : term,X348 : term] : (~! [X349 : subst,X350 : term,X351 : subst] : ((X346 @ (comp @ X351 @ X349) @ (sub @ X350 @ X349)) = (sub @ (X346 @ X351 @ X350) @ X349)) | ((lam @ (X346 @ sh @ one)) != (ap @ (sub @ X347 @ id) @ X348)))) & (hoaslamnotap_lthm = $true) & (pushprop_lem0_gthm = $true) & (axabs = $true) & (axapp = $true) & ((hoasinduction_lthm_3 = $true) <=> (! [X352 : subst > term > subst > $o] : ~! [X353 : term > $o] : ~! [X354 : term] : ((X352 @ id @ X354 @ id) = (X353 @ X354)) => (! [X355 : term,X356 : term > $o] : (~! [X357 : term] : (($true = (X356 @ X357)) | ~($true = (var @ X357))) | ~! [X358 : term,X359 : term] : (($true = (X356 @ (ap @ X359 @ X358))) | ~((X356 @ X358) = $true) | ~((X356 @ X359) = $true)) | ($true = (X356 @ X355)) | ~! [X360 : term] : (((X356 @ (lam @ X360)) = $true) | ~! [X361 : term] : (~($true = (X356 @ X361)) | ($true = (X356 @ (sub @ X360 @ (push @ X361 @ id))))))) => (! [X362 : term] : ((sub @ X362 @ id) = X362) => (! [X363 : subst > term > subst > $o,X364 : term,X365 : term > $o] : (~! [X366 : term] : ((X363 @ id @ X366 @ id) = (X365 @ X366)) | ~! [X367 : subst > term > term] : (~! [X368 : term] : (~((X363 @ id @ X368 @ id) = $true) | ((X363 @ id @ (X367 @ id @ X368) @ id) = $true)) | ~! [X369 : subst,X370 : subst,X371 : term] : ((X367 @ (comp @ X369 @ X370) @ (sub @ X371 @ X370)) = (sub @ (X367 @ X369 @ X371) @ X370)) | ((X363 @ id @ (lam @ (X367 @ sh @ one)) @ id) = $true)) | ((X365 @ (lam @ X364)) = $true) | ~! [X372 : term] : (($true = (X365 @ (sub @ X364 @ (push @ X372 @ id)))) | ~($true = (X365 @ X372)))) => ! [X373 : term,X374 : subst > term > subst > $o] : (~! [X375 : term,X376 : subst,X377 : subst,X378 : subst] : (((X374 @ X378 @ X375 @ (comp @ X377 @ X376)) = $true) | ~((X374 @ (comp @ X378 @ X377) @ (sub @ X375 @ X377) @ X376) = $true)) | ~! [X379 : term,X380 : term] : (~((X374 @ id @ X380 @ id) = $true) | ~($true = (X374 @ id @ X379 @ id)) | ($true = (X374 @ id @ (ap @ (sub @ X379 @ id) @ X380) @ id))) | ~! [X381 : subst,X382 : subst,X383 : subst,X384 : term] : (((X374 @ (comp @ X383 @ X381) @ (sub @ X384 @ X381) @ X382) = $true) | ~($true = (X374 @ X383 @ X384 @ (comp @ X381 @ X382)))) | ~! [X385 : subst > term > term] : (~! [X386 : term] : (~((X374 @ id @ X386 @ id) = $true) | ((X374 @ id @ (X385 @ id @ X386) @ id) = $true)) | ~! [X387 : subst,X388 : term,X389 : subst] : ((X385 @ (comp @ X387 @ X389) @ (sub @ X388 @ X389)) = (sub @ (X385 @ X387 @ X388) @ X389)) | ($true = (X374 @ id @ (lam @ (X385 @ sh @ one)) @ id))) | ~! [X390 : term] : (~((var @ (sub @ X390 @ id)) = $true) | ((X374 @ id @ X390 @ id) = $true)) | ((X374 @ id @ X373 @ id) = $true))))))) & ((induction2lem = $true) <=> ! [X391 : term,X392 : subst,X393 : term > $o] : (~! [X394 : term] : (($true = (X393 @ (sub @ X394 @ X392))) | ~($true = (var @ X394))) | ~! [X395 : term,X396 : term] : (~((X393 @ X396) = $true) | ~((X393 @ X395) = $true) | ($true = (X393 @ (ap @ X396 @ X395)))) | ($true = (X393 @ (sub @ X391 @ X392))) | ~! [X397 : term] : (($true = (X393 @ (lam @ X397))) | ~! [X398 : term] : (~($true = (X393 @ X398)) | ($true = (X393 @ (sub @ X397 @ (push @ X398 @ id)))))))) & (! [X399 : term] : ((sub @ X399 @ id) = X399) <=> (termmset = $true)) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & (pushprop_lthm_orig = $true) & ((! [X400 : subst] : ((comp @ id @ X400) = X400) => (! [X401 : subst] : ((comp @ X401 @ id) = X401) => (! [X402 : subst] : ((comp @ id @ X402) = X402) & ! [X403 : subst] : ((comp @ X403 @ id) = X403)))) <=> (substmonoid_lthm = $true)) & (hoasinduction_lem3v2_gthm = $true) & (pushprop_lem1v2_gthm = $true) & (! [X404 : subst,X405 : term > $o,X406 : term > $o,X407 : term] : (~! [X408 : term] : ((X405 @ (sub @ X408 @ (push @ X407 @ X404))) = (X406 @ X408)) | ((X406 @ one) = $true) | ~((X405 @ X407) = $true)) <=> (pushprop_lem1v2 = $true)) & ((hoaslaminj = $true) <=> ! [X409 : subst,X410 : subst > term > term,X411 : term,X412 : subst > term > term] : (((lam @ (X412 @ sh @ one)) != (lam @ (X410 @ sh @ one))) | ~! [X413 : term,X414 : subst,X415 : subst] : ((sub @ (X412 @ X414 @ X413) @ X415) = (X412 @ (comp @ X414 @ X415) @ (sub @ X413 @ X415))) | ((X410 @ X409 @ X411) = (X412 @ X409 @ X411)) | ~! [X416 : subst,X417 : subst,X418 : term] : ((sub @ (X410 @ X417 @ X418) @ X416) = (X410 @ (comp @ X417 @ X416) @ (sub @ X418 @ X416))))) & (axvarshift = $true) & (! [X419 : term,X420 : subst > term > subst > $o] : (~! [X421 : term] : (((X420 @ id @ (sub @ X419 @ (push @ X421 @ id)) @ id) = $true) | ~($true = (X420 @ id @ X421 @ id))) | ($true = (X420 @ id @ (lam @ (sub @ X419 @ (push @ one @ sh))) @ id)) | ~! [X422 : subst > term > term] : (~! [X423 : subst,X424 : term,X425 : subst] : ((X422 @ (comp @ X423 @ X425) @ (sub @ X424 @ X425)) = (sub @ (X422 @ X423 @ X424) @ X425)) | ~! [X426 : term] : (((X420 @ id @ (X422 @ id @ X426) @ id) = $true) | ~((X420 @ id @ X426 @ id) = $true)) | ((X420 @ id @ (lam @ (X422 @ sh @ one)) @ id) = $true))) <=> (hoasinduction_lem3aa_lthm = $true)) & (pushprop_lem2v2_gthm = $true) & (pushprop_lem3v2_lthm = $true) & (lamnotvar = $true) & (induction2_gthm = $true) & (pushprop_lem3v2 = $true) & ! [X427 : term] : ? [X428 : d_term] : ((d2term @ X428) = X427) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & ((hoasinduction_lem3_lthm = $true) <=> (! [X429 : term] : ((sub @ X429 @ id) = X429) => (! [X430 : subst > term > subst > $o,X431 : term] : (~! [X432 : subst > term > term] : (~! [X433 : subst,X434 : term,X435 : subst] : ((sub @ (X432 @ X435 @ X434) @ X433) = (X432 @ (comp @ X435 @ X433) @ (sub @ X434 @ X433))) | ((X430 @ id @ (lam @ (X432 @ sh @ one)) @ id) = $true) | ~! [X436 : term] : (~((X430 @ id @ X436 @ id) = $true) | ($true = (X430 @ id @ (X432 @ id @ X436) @ id)))) | ((X430 @ id @ (lam @ (sub @ X431 @ (push @ one @ sh))) @ id) = $true) | ~! [X437 : term] : (($true = (X430 @ id @ (sub @ X431 @ (push @ X437 @ id)) @ id)) | ~($true = (X430 @ id @ X437 @ id)))) => ! [X438 : term,X439 : subst > term > subst > $o] : (~! [X440 : term] : (~((X439 @ id @ X440 @ id) = $true) | ((X439 @ id @ (sub @ X438 @ (push @ X440 @ id)) @ id) = $true)) | ($true = (X439 @ id @ (lam @ X438) @ id)) | ~! [X441 : subst,X442 : term,X443 : subst,X444 : subst] : (~($true = (X439 @ X441 @ X442 @ (comp @ X444 @ X443))) | ((X439 @ (comp @ X441 @ X444) @ (sub @ X442 @ X444) @ X443) = $true)) | ~! [X445 : subst,X446 : term,X447 : subst,X448 : subst] : (($true = (X439 @ X447 @ X446 @ (comp @ X445 @ X448))) | ~((X439 @ (comp @ X447 @ X445) @ (sub @ X446 @ X445) @ X448) = $true)) | ~! [X449 : subst > term > term] : (((X439 @ id @ (lam @ (X449 @ sh @ one)) @ id) = $true) | ~! [X450 : term] : (((X439 @ id @ (X449 @ id @ X450) @ id) = $true) | ~((X439 @ id @ X450 @ id) = $true)) | ~! [X451 : subst,X452 : term,X453 : subst] : ((X449 @ (comp @ X453 @ X451) @ (sub @ X452 @ X451)) = (sub @ (X449 @ X453 @ X452) @ X451))))))) & ((hoasinduction_lem0_lthm = $true) <=> ! [X454 : subst > term > subst > $o] : ~! [X455 : term > $o] : ~! [X456 : term] : ((X454 @ id @ X456 @ id) = (X455 @ X456))) & (pushprop_lem1_gthm = $true) & (hoasinduction_lem1 = $true) & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & (hoasapnotvar_gthm = $true) & (hoaslamnotap_gthm = $true) & ((hoasinduction_lem2 = $true) <=> ! [X457 : term,X458 : term,X459 : subst > term > subst > $o] : (~((X459 @ id @ X458 @ id) = $true) | ~! [X460 : subst,X461 : subst,X462 : term,X463 : subst] : (((X459 @ X463 @ X462 @ (comp @ X460 @ X461)) = $true) | ~((X459 @ (comp @ X463 @ X460) @ (sub @ X462 @ X460) @ X461) = $true)) | ($true = (X459 @ id @ (ap @ X457 @ X458) @ id)) | ~! [X464 : subst,X465 : term,X466 : subst,X467 : subst] : (~($true = (X459 @ X466 @ X465 @ (comp @ X464 @ X467))) | ($true = (X459 @ (comp @ X466 @ X464) @ (sub @ X465 @ X464) @ X467))) | ~((X459 @ id @ X457 @ id) = $true) | ~! [X468 : term,X469 : term] : (~($true = (X459 @ id @ X468 @ id)) | ((X459 @ id @ (ap @ (sub @ X468 @ id) @ X469) @ id) = $true) | ~($true = (X459 @ id @ X469 @ id))))) & ((hoasinduction_lem3v2a_lthm = $true) <=> (! [X470 : term] : ~! [X471 : subst > term > term] : ~! [X472 : subst,X473 : term] : ((X471 @ X472 @ X473) = (sub @ X470 @ (push @ X473 @ X472))) => (! [X474 : term] : ((sub @ X474 @ id) = X474) => ! [X475 : subst > term > subst > $o,X476 : term,X477 : term > $o] : (~! [X478 : subst > term > term] : (((X475 @ id @ (lam @ (X478 @ sh @ one)) @ id) = $true) | ~! [X479 : term] : (~($true = (X475 @ id @ X479 @ id)) | ($true = (X475 @ id @ (X478 @ id @ X479) @ id))) | ~! [X480 : subst,X481 : subst,X482 : term] : ((X478 @ (comp @ X481 @ X480) @ (sub @ X482 @ X480)) = (sub @ (X478 @ X481 @ X482) @ X480))) | ~! [X483 : term] : ((X475 @ id @ X483 @ id) = (X477 @ X483)) | ((X477 @ (lam @ X476)) = $true) | ~! [X484 : term] : (~($true = (X477 @ X484)) | ($true = (X477 @ (sub @ X476 @ (push @ X484 @ id))))))))) & ((hoasapinj2 = $true) <=> ! [X485 : term,X486 : term,X487 : term,X488 : term] : (((ap @ (sub @ X487 @ id) @ X486) != (ap @ (sub @ X485 @ id) @ X488)) | (X486 = X488))) & ! [X489 : subst] : ? [X490 : d_subst] : ((d2subst @ X490) = X489) & ((hoasapinj1 = $true) <=> ! [X491 : term,X492 : term,X493 : term,X494 : term] : (((ap @ (sub @ X493 @ id) @ X492) != (ap @ (sub @ X494 @ id) @ X491)) | (X493 = X494))) & ((hoasinduction_lem3a = $true) <=> ! [X495 : term,X496 : subst > term > subst > $o] : (~! [X497 : term] : (((X496 @ id @ (sub @ X495 @ (push @ X497 @ id)) @ id) = $true) | ~((X496 @ id @ X497 @ id) = $true)) | ($true = (X496 @ id @ (lam @ X495) @ id)) | ~! [X498 : subst > term > term] : (~! [X499 : subst,X500 : subst,X501 : term] : ((sub @ (X498 @ X499 @ X501) @ X500) = (X498 @ (comp @ X499 @ X500) @ (sub @ X501 @ X500))) | ((X496 @ id @ (lam @ (X498 @ sh @ one)) @ id) = $true) | ~! [X502 : term] : (~((X496 @ id @ X502 @ id) = $true) | ($true = (X496 @ id @ (X498 @ id @ X502) @ id)))))) & ((hoasinduction_lem3aa = $true) <=> ! [X503 : subst > term > subst > $o,X504 : term] : (($true = (X503 @ id @ (lam @ (sub @ X504 @ (push @ one @ sh))) @ id)) | ~! [X505 : term] : (((X503 @ id @ (sub @ X504 @ (push @ X505 @ id)) @ id) = $true) | ~((X503 @ id @ X505 @ id) = $true)) | ~! [X506 : subst > term > term] : (((X503 @ id @ (lam @ (X506 @ sh @ one)) @ id) = $true) | ~! [X507 : subst,X508 : subst,X509 : term] : ((X506 @ (comp @ X507 @ X508) @ (sub @ X509 @ X508)) = (sub @ (X506 @ X507 @ X509) @ X508)) | ~! [X510 : term] : (~($true = (X503 @ id @ X510 @ id)) | ($true = (X503 @ id @ (X506 @ id @ X510) @ id)))))) & (ulamvarind = $true) & ((! [X511 : term,X512 : subst] : ((sub @ one @ (push @ X511 @ X512)) = X511) => (! [X513 : subst,X514 : term] : ((comp @ sh @ (push @ X514 @ X513)) = X513) => (! [X515 : subst] : ((comp @ X515 @ id) = X515) => (! [X516 : term,X517 : term > $o] : (~! [X518 : term] : (~($true = (X517 @ X518)) | ((X517 @ (lam @ X518)) = $true)) | ~! [X519 : term] : (~($true = (var @ X519)) | ($true = (X517 @ X519))) | ($true = (X517 @ X516)) | ~! [X520 : term,X521 : term] : (((X517 @ (ap @ X521 @ X520)) = $true) | ~($true = (X517 @ X521)) | ~((X517 @ X520) = $true))) => ! [X522 : subst,X523 : term > $o,X524 : term] : (~! [X525 : term] : (((X523 @ (lam @ X525)) = $true) | ~! [X526 : term] : (((X523 @ (sub @ X525 @ (push @ X526 @ id))) = $true) | ~($true = (X523 @ X526)))) | ~! [X527 : term,X528 : term] : (((X523 @ (ap @ X528 @ X527)) = $true) | ~((X523 @ X528) = $true) | ~((X523 @ X527) = $true)) | ($true = (X523 @ (sub @ X524 @ X522))) | ~! [X529 : term] : (((X523 @ (sub @ X529 @ X522)) = $true) | ~((var @ X529) = $true))))))) <=> (induction2lem_lthm = $true)) & (hoasinduction_lem1_lthm = $true) & (! [X530 : subst > term > subst > $o] : ~! [X531 : term > $o] : ~! [X532 : term] : ((X530 @ id @ X532 @ id) = (X531 @ X532)) <=> (hoasinduction_lem0 = $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)))))))))))) & (! [X538 : subst] : ((comp @ id @ X538) = X538) <=> (axidl = $true)) & (termmset_gthm = $true) & (hoasapinj2_gthm = $true) & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (! [X539 : term] : ~! [X540 : subst > term > term] : ((X540 @ sh @ one) != (sub @ X539 @ (push @ one @ sh))) <=> (hoasinduction_lem3b = $true)) & ! [X541 : d_term] : (d_one = X541) & (hoasinduction_lem3a_gthm = $true) & ((! [X542 : term,X543 : term,X544 : term,X545 : term] : (((ap @ X542 @ X544) != (ap @ X545 @ X543)) | (X543 = X544)) => ! [X546 : term,X547 : term,X548 : term,X549 : term] : (((ap @ (sub @ X546 @ id) @ X549) != (ap @ (sub @ X547 @ id) @ X548)) | (X548 = X549))) <=> (hoasapinj2_lthm = $true)) & (hoasinduction_lem3b_gthm = $true)),
% 15.02/3.54 inference(fool_elimination,[status(thm)],[f7])).
% 15.02/3.54 thf(f7,plain,(
% 15.02/3.54 ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (hoasinduction_no_psi_cond_lthm <=> (! [X0 : subst > term > subst > $o] : ~! [X1 : term > $o] : ~! [X2 : term] : ((X0 @ id @ X2 @ id) = (X1 @ X2)) => (! [X3 : term,X4 : term > $o] : ((X4 @ X3) | ~! [X5 : term,X6 : term] : (~(X4 @ X5) | (X4 @ (ap @ X5 @ X6)) | ~(X4 @ X6)) | ~! [X7 : term] : ((X4 @ X7) | ~(var @ X7)) | ~! [X8 : term] : ((X4 @ (lam @ X8)) | ~! [X9 : term] : (~(X4 @ X9) | (X4 @ (sub @ X8 @ (push @ X9 @ id)))))) => (! [X10 : term] : ((sub @ X10 @ id) = X10) => (! [X11 : term,X12 : subst > term > subst > $o,X13 : term > $o] : (~! [X14 : term] : ((X13 @ X14) = (X12 @ id @ X14 @ id)) | ~! [X15 : subst > term > term] : (~! [X16 : term] : (~(X12 @ id @ X16 @ id) | (X12 @ id @ (X15 @ id @ X16) @ id)) | ~! [X17 : term,X18 : subst,X19 : subst] : ((sub @ (X15 @ X19 @ X17) @ X18) = (X15 @ (comp @ X19 @ X18) @ (sub @ X17 @ X18))) | (X12 @ id @ (lam @ (X15 @ sh @ one)) @ id)) | (X13 @ (lam @ X11)) | ~! [X20 : term] : (~(X13 @ X20) | (X13 @ (sub @ X11 @ (push @ X20 @ id))))) => ! [X21 : subst > term > subst > $o,X22 : term] : (~! [X23 : term,X24 : term] : (~(X21 @ id @ X24 @ id) | (X21 @ id @ (ap @ (sub @ X23 @ id) @ X24) @ id) | ~(X21 @ id @ X23 @ id)) | ~! [X25 : subst > term > term] : (~! [X26 : term] : (~(X21 @ id @ X26 @ id) | (X21 @ id @ (X25 @ id @ X26) @ id)) | (X21 @ id @ (lam @ (X25 @ sh @ one)) @ id) | ~! [X27 : term,X28 : subst,X29 : subst] : ((X25 @ (comp @ X28 @ X29) @ (sub @ X27 @ X29)) = (sub @ (X25 @ X28 @ X27) @ X29))) | (X21 @ id @ X22 @ id))))))) & (! [X30 : term,X31 : term] : (((lam @ X30) != (lam @ X31)) | (X30 = X31)) <=> laminj) & (hoasinduction_lem3 <=> ! [X32 : term,X33 : subst > term > subst > $o] : ((X33 @ id @ (lam @ X32) @ id) | ~! [X34 : term,X35 : subst,X36 : subst,X37 : subst] : ((X33 @ X36 @ X34 @ (comp @ X37 @ X35)) | ~(X33 @ (comp @ X36 @ X37) @ (sub @ X34 @ X37) @ X35)) | ~! [X38 : subst,X39 : subst,X40 : subst,X41 : term] : (~(X33 @ X39 @ X41 @ (comp @ X40 @ X38)) | (X33 @ (comp @ X39 @ X40) @ (sub @ X41 @ X40) @ X38)) | ~! [X42 : subst > term > term] : (~! [X43 : term] : ((X33 @ id @ (X42 @ id @ X43) @ id) | ~(X33 @ id @ X43 @ id)) | (X33 @ id @ (lam @ (X42 @ sh @ one)) @ id) | ~! [X44 : term,X45 : subst,X46 : subst] : ((X42 @ (comp @ X46 @ X45) @ (sub @ X44 @ X45)) = (sub @ (X42 @ X46 @ X44) @ X45))) | ~! [X47 : term] : ((X33 @ id @ (sub @ X32 @ (push @ X47 @ id)) @ id) | ~(X33 @ id @ X47 @ id)))) & (apinj2 <=> ! [X48 : term,X49 : term,X50 : term,X51 : term] : ((X48 = X51) | ((ap @ X49 @ X48) != (ap @ X50 @ X51)))) & ulamvarsh & axclos & hoasinduction_lem1v2 & (axidr <=> ! [X52 : subst] : ((comp @ X52 @ id) = X52)) & (hoasinduction_lem2v2 <=> ! [X53 : term,X54 : term > $o,X55 : subst > term > subst > $o,X56 : term] : (~(X54 @ X53) | ~! [X57 : subst,X58 : term,X59 : subst,X60 : subst] : ((X55 @ (comp @ X60 @ X57) @ (sub @ X58 @ X57) @ X59) | ~(X55 @ X60 @ X58 @ (comp @ X57 @ X59))) | ~! [X61 : term,X62 : term] : (~(X55 @ id @ X62 @ id) | (X55 @ id @ (ap @ (sub @ X62 @ id) @ X61) @ id) | ~(X55 @ id @ X61 @ id)) | (X54 @ (ap @ X53 @ X56)) | ~(X54 @ X56) | ~! [X63 : term] : ((X55 @ id @ X63 @ id) = (X54 @ X63)) | ~! [X64 : subst,X65 : term,X66 : subst,X67 : subst] : (~(X55 @ (comp @ X66 @ X67) @ (sub @ X65 @ X67) @ X64) | (X55 @ X66 @ X65 @ (comp @ X67 @ X64))))) & (hoasapinj1_lthm <=> (! [X68 : term] : ((sub @ X68 @ id) = X68) => (! [X69 : term,X70 : term,X71 : term,X72 : term] : (((ap @ X69 @ X70) != (ap @ X71 @ X72)) | (X69 = X71)) => ! [X73 : term,X74 : term,X75 : term,X76 : term] : (((ap @ (sub @ X74 @ id) @ X76) != (ap @ (sub @ X73 @ id) @ X75)) | (X73 = X74))))) & (! [X77 : subst,X78 : term] : ((sub @ one @ (push @ X78 @ X77)) = X78) <=> axvarcons) & ((^[X79 : subst > term > subst > $o, X80 : term > $o] : (! [X81 : term] : ((X80 @ X81) = (X79 @ id @ X81 @ id)))) = hoasinduction_p_and_p_prime) & pushprop_lem2v2 & axassoc & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & ((! [X82 : subst] : ((comp @ id @ X82) = X82) & ! [X83 : subst] : ((comp @ X83 @ id) = X83)) <=> substmonoid) & (hoasinduction_lem3a_lthm <=> (! [X84 : term] : ((sub @ X84 @ id) = X84) => (! [X85 : subst > term > subst > $o,X86 : term] : ((X85 @ id @ (lam @ (sub @ X86 @ (push @ one @ sh))) @ id) | ~! [X87 : subst > term > term] : (~! [X88 : term,X89 : subst,X90 : subst] : ((X87 @ (comp @ X90 @ X89) @ (sub @ X88 @ X89)) = (sub @ (X87 @ X90 @ X88) @ X89)) | ~! [X91 : term] : ((X85 @ id @ (X87 @ id @ X91) @ id) | ~(X85 @ id @ X91 @ id)) | (X85 @ id @ (lam @ (X87 @ sh @ one)) @ id)) | ~! [X92 : term] : (~(X85 @ id @ X92 @ id) | (X85 @ id @ (sub @ X86 @ (push @ X92 @ id)) @ id))) => ! [X93 : subst > term > subst > $o,X94 : term] : ((X93 @ id @ (lam @ X94) @ id) | ~! [X95 : subst > term > term] : (~! [X96 : term] : ((X93 @ id @ (X95 @ id @ X96) @ id) | ~(X93 @ id @ X96 @ id)) | ~! [X97 : term,X98 : subst,X99 : subst] : ((X95 @ (comp @ X99 @ X98) @ (sub @ X97 @ X98)) = (sub @ (X95 @ X99 @ X97) @ X98)) | (X93 @ id @ (lam @ (X95 @ sh @ one)) @ id)) | ~! [X100 : term] : (~(X93 @ id @ X100 @ id) | (X93 @ id @ (sub @ X94 @ (push @ X100 @ id)) @ id)))))) & (hoasinduction_lem3v2_lthm <=> (! [X101 : term] : ((sub @ X101 @ id) = X101) => ! [X102 : term > $o,X103 : subst > term > subst > $o,X104 : term] : (~! [X105 : term] : (~(X102 @ X105) | (X102 @ (sub @ X104 @ (push @ X105 @ id)))) | ~! [X106 : subst > term > term] : (~! [X107 : subst,X108 : subst,X109 : term] : ((X106 @ (comp @ X108 @ X107) @ (sub @ X109 @ X107)) = (sub @ (X106 @ X108 @ X109) @ X107)) | ~! [X110 : term] : (~(X103 @ id @ X110 @ id) | (X103 @ id @ (X106 @ id @ X110) @ id)) | (X103 @ id @ (lam @ (X106 @ sh @ one)) @ id)) | ~! [X111 : subst,X112 : term,X113 : subst,X114 : subst] : ((X103 @ (comp @ X111 @ X113) @ (sub @ X112 @ X113) @ X114) | ~(X103 @ X111 @ X112 @ (comp @ X113 @ X114))) | ~! [X115 : term] : ((X103 @ id @ X115 @ id) = (X102 @ X115)) | (X102 @ (lam @ X104)) | ~! [X116 : subst,X117 : subst,X118 : term,X119 : subst] : (~(X103 @ (comp @ X117 @ X116) @ (sub @ X118 @ X116) @ X119) | (X103 @ X117 @ X118 @ (comp @ X116 @ X119)))))) & (! [X120 : term,X121 : subst] : ((comp @ sh @ (push @ X120 @ X121)) = X121) <=> axshiftcons) & (pushprop_lem0 <=> ! [X122 : term > $o,X123 : subst,X124 : term] : ~! [X125 : term > $o] : ~! [X126 : term] : ((X125 @ X126) = (X122 @ (sub @ X126 @ (push @ X124 @ X123))))) & ~lamnotap & (! [X127 : term] : ~! [X128 : subst > term > term] : ~! [X129 : term,X130 : subst] : ((sub @ X127 @ (push @ X129 @ X130)) = (X128 @ X130 @ X129)) <=> hoasinduction_lem3v2_f_lthm) & axmap & hoasinduction_lem2v2_gthm & (induction2_lthm <=> (! [X131 : term] : ((sub @ X131 @ id) = X131) => (! [X132 : subst,X133 : term > $o,X134 : term] : (~! [X135 : term] : ((X133 @ (lam @ X135)) | ~! [X136 : term] : ((X133 @ (sub @ X135 @ (push @ X136 @ id))) | ~(X133 @ X136))) | ~! [X137 : term,X138 : term] : ((X133 @ (ap @ X137 @ X138)) | ~(X133 @ X138) | ~(X133 @ X137)) | ~! [X139 : term] : ((X133 @ (sub @ X139 @ X132)) | ~(var @ X139)) | (X133 @ (sub @ X134 @ X132))) => ! [X140 : term,X141 : term > $o] : (~! [X142 : term] : (~(var @ X142) | (X141 @ X142)) | ~! [X143 : term,X144 : term] : (~(X141 @ X144) | (X141 @ (ap @ X143 @ X144)) | ~(X141 @ X143)) | ~! [X145 : term] : (~! [X146 : term] : (~(X141 @ X146) | (X141 @ (sub @ X145 @ (push @ X146 @ id)))) | (X141 @ (lam @ X145))) | (X141 @ X140))))) & (pushprop_lem0_lthm <=> ! [X147 : subst,X148 : term > $o,X149 : term] : ~! [X150 : term > $o] : ~! [X151 : term] : ((X148 @ (sub @ X151 @ (push @ X149 @ X147))) = (X150 @ X151))) & induction2lem_gthm & (pushprop_lem1_lthm <=> (! [X152 : term,X153 : subst] : ((sub @ one @ (push @ X152 @ X153)) = X152) => (! [X154 : subst,X155 : term] : ((comp @ sh @ (push @ X155 @ X154)) = X154) => ! [X156 : term,X157 : term > $o,X158 : subst,X159 : term,X160 : term > $o] : (~(X157 @ X156) | (X160 @ (sub @ X156 @ (push @ X159 @ X158))))))) & (hoasinduction_lem3v2a <=> ! [X161 : term > $o,X162 : subst > term > subst > $o,X163 : term] : (~! [X164 : term] : ((X162 @ id @ X164 @ id) = (X161 @ X164)) | ~! [X165 : subst > term > term] : (~! [X166 : term] : ((X162 @ id @ (X165 @ id @ X166) @ id) | ~(X162 @ id @ X166 @ id)) | (X162 @ id @ (lam @ (X165 @ sh @ one)) @ id) | ~! [X167 : subst,X168 : term,X169 : subst] : ((X165 @ (comp @ X169 @ X167) @ (sub @ X168 @ X167)) = (sub @ (X165 @ X169 @ X168) @ X167))) | ~! [X170 : term] : (~(X161 @ X170) | (X161 @ (sub @ X163 @ (push @ X170 @ id)))) | (X161 @ (lam @ X163)))) & (hoasinduction_lthm <=> (! [X171 : term > $o,X172 : term] : ((X171 @ X172) | ~! [X173 : term] : (~! [X174 : term] : ((X171 @ (sub @ X173 @ (push @ X174 @ id))) | ~(X171 @ X174)) | (X171 @ (lam @ X173))) | ~! [X175 : term,X176 : term] : (~(X171 @ X176) | (X171 @ (ap @ X176 @ X175)) | ~(X171 @ X175)) | ~! [X177 : term] : (~(var @ X177) | (X171 @ X177))) => (! [X178 : term,X179 : term,X180 : subst > term > subst > $o] : (~(X180 @ id @ X179 @ id) | (X180 @ id @ (ap @ X178 @ X179) @ id) | ~! [X181 : subst,X182 : subst,X183 : term,X184 : subst] : (~(X180 @ X182 @ X183 @ (comp @ X184 @ X181)) | (X180 @ (comp @ X182 @ X184) @ (sub @ X183 @ X184) @ X181)) | ~(X180 @ id @ X178 @ id) | ~! [X185 : subst,X186 : subst,X187 : term,X188 : subst] : ((X180 @ X188 @ X187 @ (comp @ X186 @ X185)) | ~(X180 @ (comp @ X188 @ X186) @ (sub @ X187 @ X186) @ X185)) | ~! [X189 : term,X190 : term] : (~(X180 @ id @ X190 @ id) | (X180 @ id @ (ap @ (sub @ X190 @ id) @ X189) @ id) | ~(X180 @ id @ X189 @ id))) => (! [X191 : term,X192 : subst > term > subst > $o] : (~! [X193 : subst,X194 : term,X195 : subst,X196 : subst] : (~(X192 @ X196 @ X194 @ (comp @ X193 @ X195)) | (X192 @ (comp @ X196 @ X193) @ (sub @ X194 @ X193) @ X195)) | ~! [X197 : subst,X198 : subst,X199 : term,X200 : subst] : (~(X192 @ (comp @ X200 @ X198) @ (sub @ X199 @ X198) @ X197) | (X192 @ X200 @ X199 @ (comp @ X198 @ X197))) | ~! [X201 : term] : (~(X192 @ id @ X201 @ id) | (X192 @ id @ (sub @ X191 @ (push @ X201 @ id)) @ id)) | (X192 @ id @ (lam @ X191) @ id) | ~! [X202 : subst > term > term] : (~! [X203 : term,X204 : subst,X205 : subst] : ((X202 @ (comp @ X204 @ X205) @ (sub @ X203 @ X205)) = (sub @ (X202 @ X204 @ X203) @ X205)) | ~! [X206 : term] : (~(X192 @ id @ X206 @ id) | (X192 @ id @ (X202 @ id @ X206) @ id)) | (X192 @ id @ (lam @ (X202 @ sh @ one)) @ id))) => ! [X207 : subst > term > subst > $o,X208 : term] : (~! [X209 : term,X210 : term] : ((X207 @ id @ (ap @ (sub @ X210 @ id) @ X209) @ id) | ~(X207 @ id @ X209 @ id) | ~(X207 @ id @ X210 @ id)) | ~! [X211 : subst,X212 : subst,X213 : subst,X214 : term] : ((X207 @ X213 @ X214 @ (comp @ X211 @ X212)) | ~(X207 @ (comp @ X213 @ X211) @ (sub @ X214 @ X211) @ X212)) | ~! [X215 : subst,X216 : subst,X217 : term,X218 : subst] : (~(X207 @ X216 @ X217 @ (comp @ X215 @ X218)) | (X207 @ (comp @ X216 @ X215) @ (sub @ X217 @ X215) @ X218)) | ~! [X219 : term] : ((X207 @ id @ X219 @ id) | ~(var @ (sub @ X219 @ id))) | ~! [X220 : subst > term > term] : (~! [X221 : subst,X222 : term,X223 : subst] : ((sub @ (X220 @ X223 @ X222) @ X221) = (X220 @ (comp @ X223 @ X221) @ (sub @ X222 @ X221))) | (X207 @ id @ (lam @ (X220 @ sh @ one)) @ id) | ~! [X224 : term] : (~(X207 @ id @ X224 @ id) | (X207 @ id @ (X220 @ id @ X224) @ id))) | (X207 @ id @ X208 @ id)))))) & hoaslaminj_gthm & (! [X225 : term,X226 : subst > term > subst > $o] : (~! [X227 : term] : (~(X226 @ id @ X227 @ id) | (X226 @ id @ (sub @ X225 @ (push @ X227 @ id)) @ id)) | (X226 @ id @ (lam @ (sub @ X225 @ (push @ one @ sh))) @ id) | ~! [X228 : term,X229 : subst > term > term] : (~! [X230 : subst,X231 : term,X232 : subst] : ((sub @ (X229 @ X232 @ X231) @ X230) = (sub @ (sub @ X228 @ (push @ X231 @ X232)) @ X230)) | ~! [X233 : subst,X234 : term,X235 : subst] : ((sub @ X228 @ (push @ (sub @ X234 @ X235) @ (comp @ X233 @ X235))) = (X229 @ (comp @ X233 @ X235) @ (sub @ X234 @ X235))) | ~! [X236 : term] : (~(X226 @ id @ X236 @ id) | (X226 @ id @ (X229 @ id @ X236) @ id)) | (X226 @ id @ (lam @ (X229 @ sh @ one)) @ id))) <=> hoasinduction_lem3aaa) & hoasapnotvar & ! [X237 : d_term,X238 : d_term] : (((d2term @ X237) = (d2term @ X238)) => (X237 = X238)) & ((d2subst @ d_id) = sh) & hoaslamnotvar_gthm & (! [X239 : term] : ((sub @ X239 @ id) = X239) <=> axvarid) & (hoaslaminj_lthm <=> (! [X240 : subst,X241 : term] : ((sub @ one @ (push @ X241 @ X240)) = X241) => (! [X242 : term,X243 : subst] : ((comp @ sh @ (push @ X242 @ X243)) = X243) => (! [X244 : term,X245 : term] : (((lam @ X244) != (lam @ X245)) | (X244 = X245)) => ! [X246 : subst,X247 : term,X248 : subst > term > term,X249 : subst > term > term] : (((X249 @ X246 @ X247) = (X248 @ X246 @ X247)) | ~! [X250 : term,X251 : subst,X252 : subst] : ((X249 @ (comp @ X251 @ X252) @ (sub @ X250 @ X252)) = (sub @ (X249 @ X251 @ X250) @ X252)) | ((lam @ (X248 @ sh @ one)) != (lam @ (X249 @ sh @ one))) | ~! [X253 : subst,X254 : term,X255 : subst] : ((sub @ (X248 @ X253 @ X254) @ X255) = (X248 @ (comp @ X253 @ X255) @ (sub @ X254 @ X255)))))))) & hoaslamnotvar & (termmset_lthm <=> (! [X256 : term] : ((sub @ X256 @ id) = X256) => ! [X257 : term] : ((sub @ X257 @ id) = X257))) & substmonoid_gthm & (induction <=> ! [X258 : term,X259 : term > $o] : (~! [X260 : term] : (~(X259 @ X260) | (X259 @ (lam @ X260))) | (X259 @ X258) | ~! [X261 : term,X262 : term] : (~(X259 @ X261) | ~(X259 @ X262) | (X259 @ (ap @ X262 @ X261))) | ~! [X263 : term] : ((X259 @ X263) | ~(var @ X263)))) & (hoaslam = (^[X264 : subst, X265 : subst > term > term] : (d2term @ d_one))) & pushprop_lem2v2_lthm & (! [X266 : term,X267 : term,X268 : term,X269 : term] : (((ap @ X267 @ X266) != (ap @ X269 @ X268)) | (X267 = X269)) <=> apinj1) & ~(var @ (d2term @ d_one)) & hoasinduction_lem2_gthm & ((d2subst @ d_id) = id) & ! [X270 : d_subst,X271 : d_subst] : (((d2subst @ X271) = (d2subst @ X270)) => (X270 = X271)) & (axscons <=> ! [X272 : subst] : ((push @ (sub @ one @ X272) @ (comp @ sh @ X272)) = X272)) & pushprop_lthm & (induction2 <=> ! [X273 : term > $o,X274 : term] : (~! [X275 : term] : (~! [X276 : term] : (~(X273 @ X276) | (X273 @ (sub @ X275 @ (push @ X276 @ id)))) | (X273 @ (lam @ X275))) | ~! [X277 : term,X278 : term] : (~(X273 @ X277) | ~(X273 @ X278) | (X273 @ (ap @ X278 @ X277))) | (X273 @ X274) | ~! [X279 : term] : (~(var @ X279) | (X273 @ X279)))) & (! [X280 : term,X281 : term,X282 : term > $o,X283 : subst,X284 : term > $o] : ((X282 @ (sub @ X281 @ (push @ X280 @ X283))) | ~(X284 @ X281)) <=> pushprop_lem1) & hoasinduction_lem1_gthm & (! [X285 : term] : ~! [X286 : subst > term > term] : ~! [X287 : term,X288 : subst] : ((X286 @ X288 @ X287) = (sub @ X285 @ (push @ X287 @ X288))) <=> hoasinduction_lem3v2_f) & hoasinduction_gthm & ((! [X289 : term,X290 : subst] : ((sub @ one @ (push @ X289 @ X290)) = X289) => ! [X291 : term,X292 : subst,X293 : term > $o,X294 : term > $o] : ((X294 @ one) | ~(X293 @ X291) | ~! [X295 : term] : ((X294 @ X295) = (X293 @ (sub @ X295 @ (push @ X291 @ X292)))))) <=> pushprop_lem1v2_lthm) & (one = (d2term @ d_one)) & ! [X296 : d_subst] : (d_id = X296) & (! [X297 : term,X298 : subst > term > subst > $o] : (~! [X299 : subst > term > term] : (~! [X300 : subst,X301 : term,X302 : subst] : ((X299 @ (comp @ X300 @ X302) @ (sub @ X301 @ X302)) = (sub @ (X299 @ X300 @ X301) @ X302)) | (X298 @ id @ (lam @ (X299 @ sh @ one)) @ id) | ~! [X303 : term] : ((X298 @ id @ (X299 @ id @ X303) @ id) | ~(X298 @ id @ X303 @ id))) | ~! [X304 : subst,X305 : subst,X306 : term,X307 : subst] : (~(X298 @ X307 @ X306 @ (comp @ X305 @ X304)) | (X298 @ (comp @ X307 @ X305) @ (sub @ X306 @ X305) @ X304)) | (X298 @ id @ X297 @ id) | ~! [X308 : term] : ((X298 @ id @ X308 @ id) | ~(var @ (sub @ X308 @ id))) | ~! [X309 : term,X310 : term] : (~(X298 @ id @ X310 @ id) | (X298 @ id @ (ap @ (sub @ X309 @ id) @ X310) @ id) | ~(X298 @ id @ X309 @ id)) | ~! [X311 : term,X312 : subst,X313 : subst,X314 : subst] : ((X298 @ X313 @ X311 @ (comp @ X312 @ X314)) | ~(X298 @ (comp @ X313 @ X312) @ (sub @ X311 @ X312) @ X314))) <=> hoasinduction) & pushprop & ~ulamvar1 & hoasapinj1_gthm & hoasinduction_lem1v2_gthm & hoaslamnotvar_lthm & (hoasinduction_lem3v2 <=> ! [X315 : term,X316 : subst > term > subst > $o,X317 : term > $o] : (~! [X318 : term] : ((X316 @ id @ X318 @ id) = (X317 @ X318)) | ~! [X319 : term] : (~(X317 @ X319) | (X317 @ (sub @ X315 @ (push @ X319 @ id)))) | (X317 @ (lam @ X315)) | ~! [X320 : subst,X321 : subst,X322 : subst,X323 : term] : (~(X316 @ (comp @ X321 @ X322) @ (sub @ X323 @ X322) @ X320) | (X316 @ X321 @ X323 @ (comp @ X322 @ X320))) | ~! [X324 : subst,X325 : subst,X326 : term,X327 : subst] : (~(X316 @ X327 @ X326 @ (comp @ X324 @ X325)) | (X316 @ (comp @ X327 @ X324) @ (sub @ X326 @ X324) @ X325)) | ~! [X328 : subst > term > term] : (~! [X329 : term] : (~(X316 @ id @ X329 @ id) | (X316 @ id @ (X328 @ id @ X329) @ id)) | (X316 @ id @ (lam @ (X328 @ sh @ one)) @ id) | ~! [X330 : term,X331 : subst,X332 : subst] : ((X328 @ (comp @ X332 @ X331) @ (sub @ X330 @ X331)) = (sub @ (X328 @ X332 @ X330) @ X331))))) & pushprop_gthm & apnotvar & hoasinduction_lem2_lthm & (shinj <=> ! [X333 : term,X334 : term] : ((X333 = X334) | ((sub @ X333 @ sh) != (sub @ X334 @ sh)))) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (! [X335 : term,X336 : subst > term > subst > $o] : (~! [X337 : subst > term > term] : ((X336 @ id @ (lam @ (X337 @ sh @ one)) @ id) | ~! [X338 : term] : ((X336 @ id @ (X337 @ id @ X338) @ id) | ~(X336 @ id @ X338 @ id)) | ~! [X339 : subst,X340 : subst,X341 : term] : ((X337 @ (comp @ X340 @ X339) @ (sub @ X341 @ X339)) = (sub @ (X337 @ X340 @ X341) @ X339))) | (X336 @ id @ X335 @ id) | ~! [X342 : term,X343 : term] : ((X336 @ id @ (ap @ (sub @ X342 @ id) @ X343) @ id) | ~(X336 @ id @ X342 @ id) | ~(X336 @ id @ X343 @ id))) <=> hoasinduction_no_psi_cond) & (! [X344 : term] : ~! [X345 : subst > term > term] : ((sub @ X344 @ (push @ one @ sh)) != (X345 @ sh @ one)) <=> hoasinduction_lem3b_lthm) & hoasinduction_lem3_gthm & hoasapnotvar_lthm & (hoaslamnotap <=> ! [X346 : subst > term > term,X347 : term,X348 : term] : (~! [X349 : subst,X350 : term,X351 : subst] : ((X346 @ (comp @ X351 @ X349) @ (sub @ X350 @ X349)) = (sub @ (X346 @ X351 @ X350) @ X349)) | ((lam @ (X346 @ sh @ one)) != (ap @ (sub @ X347 @ id) @ X348)))) & hoaslamnotap_lthm & pushprop_lem0_gthm & axabs & axapp & (hoasinduction_lthm_3 <=> (! [X352 : subst > term > subst > $o] : ~! [X353 : term > $o] : ~! [X354 : term] : ((X352 @ id @ X354 @ id) = (X353 @ X354)) => (! [X355 : term,X356 : term > $o] : (~! [X357 : term] : ((X356 @ X357) | ~(var @ X357)) | ~! [X358 : term,X359 : term] : ((X356 @ (ap @ X359 @ X358)) | ~(X356 @ X358) | ~(X356 @ X359)) | (X356 @ X355) | ~! [X360 : term] : ((X356 @ (lam @ X360)) | ~! [X361 : term] : (~(X356 @ X361) | (X356 @ (sub @ X360 @ (push @ X361 @ id)))))) => (! [X362 : term] : ((sub @ X362 @ id) = X362) => (! [X363 : subst > term > subst > $o,X364 : term,X365 : term > $o] : (~! [X366 : term] : ((X363 @ id @ X366 @ id) = (X365 @ X366)) | ~! [X367 : subst > term > term] : (~! [X368 : term] : (~(X363 @ id @ X368 @ id) | (X363 @ id @ (X367 @ id @ X368) @ id)) | ~! [X369 : subst,X370 : subst,X371 : term] : ((X367 @ (comp @ X369 @ X370) @ (sub @ X371 @ X370)) = (sub @ (X367 @ X369 @ X371) @ X370)) | (X363 @ id @ (lam @ (X367 @ sh @ one)) @ id)) | (X365 @ (lam @ X364)) | ~! [X372 : term] : ((X365 @ (sub @ X364 @ (push @ X372 @ id))) | ~(X365 @ X372))) => ! [X373 : term,X374 : subst > term > subst > $o] : (~! [X375 : term,X376 : subst,X377 : subst,X378 : subst] : ((X374 @ X378 @ X375 @ (comp @ X377 @ X376)) | ~(X374 @ (comp @ X378 @ X377) @ (sub @ X375 @ X377) @ X376)) | ~! [X379 : term,X380 : term] : (~(X374 @ id @ X380 @ id) | ~(X374 @ id @ X379 @ id) | (X374 @ id @ (ap @ (sub @ X379 @ id) @ X380) @ id)) | ~! [X381 : subst,X382 : subst,X383 : subst,X384 : term] : ((X374 @ (comp @ X383 @ X381) @ (sub @ X384 @ X381) @ X382) | ~(X374 @ X383 @ X384 @ (comp @ X381 @ X382))) | ~! [X385 : subst > term > term] : (~! [X386 : term] : (~(X374 @ id @ X386 @ id) | (X374 @ id @ (X385 @ id @ X386) @ id)) | ~! [X387 : subst,X388 : term,X389 : subst] : ((X385 @ (comp @ X387 @ X389) @ (sub @ X388 @ X389)) = (sub @ (X385 @ X387 @ X388) @ X389)) | (X374 @ id @ (lam @ (X385 @ sh @ one)) @ id)) | ~! [X390 : term] : (~(var @ (sub @ X390 @ id)) | (X374 @ id @ X390 @ id)) | (X374 @ id @ X373 @ id))))))) & (induction2lem <=> ! [X391 : term,X392 : subst,X393 : term > $o] : (~! [X394 : term] : ((X393 @ (sub @ X394 @ X392)) | ~(var @ X394)) | ~! [X395 : term,X396 : term] : (~(X393 @ X396) | ~(X393 @ X395) | (X393 @ (ap @ X396 @ X395))) | (X393 @ (sub @ X391 @ X392)) | ~! [X397 : term] : ((X393 @ (lam @ X397)) | ~! [X398 : term] : (~(X393 @ X398) | (X393 @ (sub @ X397 @ (push @ X398 @ id))))))) & (! [X399 : term] : ((sub @ X399 @ id) = X399) <=> termmset) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & pushprop_lthm_orig & ((! [X400 : subst] : ((comp @ id @ X400) = X400) => (! [X401 : subst] : ((comp @ X401 @ id) = X401) => (! [X402 : subst] : ((comp @ id @ X402) = X402) & ! [X403 : subst] : ((comp @ X403 @ id) = X403)))) <=> substmonoid_lthm) & hoasinduction_lem3v2_gthm & pushprop_lem1v2_gthm & (! [X404 : subst,X405 : term > $o,X406 : term > $o,X407 : term] : (~! [X408 : term] : ((X405 @ (sub @ X408 @ (push @ X407 @ X404))) = (X406 @ X408)) | (X406 @ one) | ~(X405 @ X407)) <=> pushprop_lem1v2) & (hoaslaminj <=> ! [X409 : subst,X410 : subst > term > term,X411 : term,X412 : subst > term > term] : (((lam @ (X412 @ sh @ one)) != (lam @ (X410 @ sh @ one))) | ~! [X413 : term,X414 : subst,X415 : subst] : ((sub @ (X412 @ X414 @ X413) @ X415) = (X412 @ (comp @ X414 @ X415) @ (sub @ X413 @ X415))) | ((X410 @ X409 @ X411) = (X412 @ X409 @ X411)) | ~! [X416 : subst,X417 : subst,X418 : term] : ((sub @ (X410 @ X417 @ X418) @ X416) = (X410 @ (comp @ X417 @ X416) @ (sub @ X418 @ X416))))) & axvarshift & (! [X419 : term,X420 : subst > term > subst > $o] : (~! [X421 : term] : ((X420 @ id @ (sub @ X419 @ (push @ X421 @ id)) @ id) | ~(X420 @ id @ X421 @ id)) | (X420 @ id @ (lam @ (sub @ X419 @ (push @ one @ sh))) @ id) | ~! [X422 : subst > term > term] : (~! [X423 : subst,X424 : term,X425 : subst] : ((X422 @ (comp @ X423 @ X425) @ (sub @ X424 @ X425)) = (sub @ (X422 @ X423 @ X424) @ X425)) | ~! [X426 : term] : ((X420 @ id @ (X422 @ id @ X426) @ id) | ~(X420 @ id @ X426 @ id)) | (X420 @ id @ (lam @ (X422 @ sh @ one)) @ id))) <=> hoasinduction_lem3aa_lthm) & pushprop_lem2v2_gthm & pushprop_lem3v2_lthm & lamnotvar & induction2_gthm & pushprop_lem3v2 & ! [X427 : term] : ? [X428 : d_term] : ((d2term @ X428) = X427) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (hoasinduction_lem3_lthm <=> (! [X429 : term] : ((sub @ X429 @ id) = X429) => (! [X430 : subst > term > subst > $o,X431 : term] : (~! [X432 : subst > term > term] : (~! [X433 : subst,X434 : term,X435 : subst] : ((sub @ (X432 @ X435 @ X434) @ X433) = (X432 @ (comp @ X435 @ X433) @ (sub @ X434 @ X433))) | (X430 @ id @ (lam @ (X432 @ sh @ one)) @ id) | ~! [X436 : term] : (~(X430 @ id @ X436 @ id) | (X430 @ id @ (X432 @ id @ X436) @ id))) | (X430 @ id @ (lam @ (sub @ X431 @ (push @ one @ sh))) @ id) | ~! [X437 : term] : ((X430 @ id @ (sub @ X431 @ (push @ X437 @ id)) @ id) | ~(X430 @ id @ X437 @ id))) => ! [X438 : term,X439 : subst > term > subst > $o] : (~! [X440 : term] : (~(X439 @ id @ X440 @ id) | (X439 @ id @ (sub @ X438 @ (push @ X440 @ id)) @ id)) | (X439 @ id @ (lam @ X438) @ id) | ~! [X441 : subst,X442 : term,X443 : subst,X444 : subst] : (~(X439 @ X441 @ X442 @ (comp @ X444 @ X443)) | (X439 @ (comp @ X441 @ X444) @ (sub @ X442 @ X444) @ X443)) | ~! [X445 : subst,X446 : term,X447 : subst,X448 : subst] : ((X439 @ X447 @ X446 @ (comp @ X445 @ X448)) | ~(X439 @ (comp @ X447 @ X445) @ (sub @ X446 @ X445) @ X448)) | ~! [X449 : subst > term > term] : ((X439 @ id @ (lam @ (X449 @ sh @ one)) @ id) | ~! [X450 : term] : ((X439 @ id @ (X449 @ id @ X450) @ id) | ~(X439 @ id @ X450 @ id)) | ~! [X451 : subst,X452 : term,X453 : subst] : ((X449 @ (comp @ X453 @ X451) @ (sub @ X452 @ X451)) = (sub @ (X449 @ X453 @ X452) @ X451))))))) & (hoasinduction_lem0_lthm <=> ! [X454 : subst > term > subst > $o] : ~! [X455 : term > $o] : ~! [X456 : term] : ((X454 @ id @ X456 @ id) = (X455 @ X456))) & pushprop_lem1_gthm & hoasinduction_lem1 & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & hoasapnotvar_gthm & hoaslamnotap_gthm & (hoasinduction_lem2 <=> ! [X457 : term,X458 : term,X459 : subst > term > subst > $o] : (~(X459 @ id @ X458 @ id) | ~! [X460 : subst,X461 : subst,X462 : term,X463 : subst] : ((X459 @ X463 @ X462 @ (comp @ X460 @ X461)) | ~(X459 @ (comp @ X463 @ X460) @ (sub @ X462 @ X460) @ X461)) | (X459 @ id @ (ap @ X457 @ X458) @ id) | ~! [X464 : subst,X465 : term,X466 : subst,X467 : subst] : (~(X459 @ X466 @ X465 @ (comp @ X464 @ X467)) | (X459 @ (comp @ X466 @ X464) @ (sub @ X465 @ X464) @ X467)) | ~(X459 @ id @ X457 @ id) | ~! [X468 : term,X469 : term] : (~(X459 @ id @ X468 @ id) | (X459 @ id @ (ap @ (sub @ X468 @ id) @ X469) @ id) | ~(X459 @ id @ X469 @ id)))) & (hoasinduction_lem3v2a_lthm <=> (! [X470 : term] : ~! [X471 : subst > term > term] : ~! [X472 : subst,X473 : term] : ((X471 @ X472 @ X473) = (sub @ X470 @ (push @ X473 @ X472))) => (! [X474 : term] : ((sub @ X474 @ id) = X474) => ! [X475 : subst > term > subst > $o,X476 : term,X477 : term > $o] : (~! [X478 : subst > term > term] : ((X475 @ id @ (lam @ (X478 @ sh @ one)) @ id) | ~! [X479 : term] : (~(X475 @ id @ X479 @ id) | (X475 @ id @ (X478 @ id @ X479) @ id)) | ~! [X480 : subst,X481 : subst,X482 : term] : ((X478 @ (comp @ X481 @ X480) @ (sub @ X482 @ X480)) = (sub @ (X478 @ X481 @ X482) @ X480))) | ~! [X483 : term] : ((X475 @ id @ X483 @ id) = (X477 @ X483)) | (X477 @ (lam @ X476)) | ~! [X484 : term] : (~(X477 @ X484) | (X477 @ (sub @ X476 @ (push @ X484 @ id)))))))) & (hoasapinj2 <=> ! [X485 : term,X486 : term,X487 : term,X488 : term] : (((ap @ (sub @ X487 @ id) @ X486) != (ap @ (sub @ X485 @ id) @ X488)) | (X486 = X488))) & ! [X489 : subst] : ? [X490 : d_subst] : ((d2subst @ X490) = X489) & (hoasapinj1 <=> ! [X491 : term,X492 : term,X493 : term,X494 : term] : (((ap @ (sub @ X493 @ id) @ X492) != (ap @ (sub @ X494 @ id) @ X491)) | (X493 = X494))) & (hoasinduction_lem3a <=> ! [X495 : term,X496 : subst > term > subst > $o] : (~! [X497 : term] : ((X496 @ id @ (sub @ X495 @ (push @ X497 @ id)) @ id) | ~(X496 @ id @ X497 @ id)) | (X496 @ id @ (lam @ X495) @ id) | ~! [X498 : subst > term > term] : (~! [X499 : subst,X500 : subst,X501 : term] : ((sub @ (X498 @ X499 @ X501) @ X500) = (X498 @ (comp @ X499 @ X500) @ (sub @ X501 @ X500))) | (X496 @ id @ (lam @ (X498 @ sh @ one)) @ id) | ~! [X502 : term] : (~(X496 @ id @ X502 @ id) | (X496 @ id @ (X498 @ id @ X502) @ id))))) & (hoasinduction_lem3aa <=> ! [X503 : subst > term > subst > $o,X504 : term] : ((X503 @ id @ (lam @ (sub @ X504 @ (push @ one @ sh))) @ id) | ~! [X505 : term] : ((X503 @ id @ (sub @ X504 @ (push @ X505 @ id)) @ id) | ~(X503 @ id @ X505 @ id)) | ~! [X506 : subst > term > term] : ((X503 @ id @ (lam @ (X506 @ sh @ one)) @ id) | ~! [X507 : subst,X508 : subst,X509 : term] : ((X506 @ (comp @ X507 @ X508) @ (sub @ X509 @ X508)) = (sub @ (X506 @ X507 @ X509) @ X508)) | ~! [X510 : term] : (~(X503 @ id @ X510 @ id) | (X503 @ id @ (X506 @ id @ X510) @ id))))) & ulamvarind & ((! [X511 : term,X512 : subst] : ((sub @ one @ (push @ X511 @ X512)) = X511) => (! [X513 : subst,X514 : term] : ((comp @ sh @ (push @ X514 @ X513)) = X513) => (! [X515 : subst] : ((comp @ X515 @ id) = X515) => (! [X516 : term,X517 : term > $o] : (~! [X518 : term] : (~(X517 @ X518) | (X517 @ (lam @ X518))) | ~! [X519 : term] : (~(var @ X519) | (X517 @ X519)) | (X517 @ X516) | ~! [X520 : term,X521 : term] : ((X517 @ (ap @ X521 @ X520)) | ~(X517 @ X521) | ~(X517 @ X520))) => ! [X522 : subst,X523 : term > $o,X524 : term] : (~! [X525 : term] : ((X523 @ (lam @ X525)) | ~! [X526 : term] : ((X523 @ (sub @ X525 @ (push @ X526 @ id))) | ~(X523 @ X526))) | ~! [X527 : term,X528 : term] : ((X523 @ (ap @ X528 @ X527)) | ~(X523 @ X528) | ~(X523 @ X527)) | (X523 @ (sub @ X524 @ X522)) | ~! [X529 : term] : ((X523 @ (sub @ X529 @ X522)) | ~(var @ X529))))))) <=> induction2lem_lthm) & hoasinduction_lem1_lthm & (! [X530 : subst > term > subst > $o] : ~! [X531 : term > $o] : ~! [X532 : term] : ((X530 @ id @ X532 @ id) = (X531 @ X532)) <=> hoasinduction_lem0) & ((^[X533 : term, X534 : subst, X535 : term > $o, X536 : term > $o] : (! [X537 : term] : ((X535 @ (sub @ X537 @ (push @ X533 @ X534))) = (X536 @ X537)))) = pushprop_p_and_p_prime) & (! [X538 : subst] : ((comp @ id @ X538) = X538) <=> axidl) & termmset_gthm & hoasapinj2_gthm & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (! [X539 : term] : ~! [X540 : subst > term > term] : ((X540 @ sh @ one) != (sub @ X539 @ (push @ one @ sh))) <=> hoasinduction_lem3b) & ! [X541 : d_term] : (d_one = X541) & hoasinduction_lem3a_gthm & ((! [X542 : term,X543 : term,X544 : term,X545 : term] : (((ap @ X542 @ X544) != (ap @ X545 @ X543)) | (X543 = X544)) => ! [X546 : term,X547 : term,X548 : term,X549 : term] : (((ap @ (sub @ X546 @ id) @ X549) != (ap @ (sub @ X547 @ id) @ X548)) | (X548 = X549))) <=> hoasapinj2_lthm) & hoasinduction_lem3b_gthm),
% 15.02/3.54 inference(rectify,[status(thm)],[f1])).
% 15.02/3.54 thf(f1,axiom,(
% 15.02/3.54 ((d2subst @ d_id) = (push @ (d2term @ d_one) @ (d2subst @ d_id))) & (hoasinduction_no_psi_cond_lthm <=> (! [X10 : subst > term > subst > $o] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) => (! [X22 : term,X10 : term > $o] : ((X10 @ X22) | ~! [X13 : term,X15 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | ~! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~! [X13 : term] : ((X10 @ (lam @ X13)) | ~! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))))) => (! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X29 : term,X10 : subst > term > subst > $o,X11 : term > $o] : (~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | ~! [X18 : subst > term > term] : (~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~! [X13 : term,X25 : subst,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X11 @ (lam @ X29)) | ~! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id))))) => ! [X10 : subst > term > subst > $o,X30 : term] : (~! [X13 : term,X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id)) | ~! [X18 : subst > term > term] : (~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term,X14 : subst,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | (X10 @ id @ X30 @ id))))))) & (! [X13 : term,X15 : term] : (((lam @ X13) != (lam @ X15)) | (X13 = X15)) <=> laminj) & (hoasinduction_lem3 <=> ! [X27 : term,X10 : subst > term > subst > $o] : ((X10 @ id @ (lam @ X27) @ id) | ~! [X13 : term,X25 : subst,X14 : subst,X26 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X25 : subst,X14 : subst,X26 : subst,X13 : term] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X18 : subst > term > term] : (~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term,X25 : subst,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~! [X15 : term] : ((X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)))) & (apinj2 <=> ! [X20 : term,X15 : term,X13 : term,X19 : term] : ((X19 = X20) | ((ap @ X13 @ X19) != (ap @ X15 @ X20)))) & ulamvarsh & axclos & hoasinduction_lem1v2 & (axidr <=> ! [X14 : subst] : ((comp @ X14 @ id) = X14)) & (hoasinduction_lem2v2 <=> ! [X44 : term,X11 : term > $o,X10 : subst > term > subst > $o,X45 : term] : (~(X11 @ X44) | ~! [X26 : subst,X13 : term,X25 : subst,X14 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X15 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id)) | (X11 @ (ap @ X44 @ X45)) | ~(X11 @ X45) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | ~! [X25 : subst,X13 : term,X14 : subst,X26 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))))) & (hoasapinj1_lthm <=> (! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X15 : term,X20 : term,X13 : term,X19 : term] : (((ap @ X13 @ X19) != (ap @ X15 @ X20)) | (X13 = X15)) => ! [X15 : term,X13 : term,X20 : term,X19 : term] : (((ap @ (sub @ X13 @ id) @ X19) != (ap @ (sub @ X15 @ id) @ X20)) | (X13 = X15))))) & (! [X14 : subst,X13 : term] : ((sub @ one @ (push @ X13 @ X14)) = X13) <=> axvarcons) & ((^[X10 : subst > term > subst > $o, X11 : term > $o] : (! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)))) = hoasinduction_p_and_p_prime) & pushprop_lem2v2 & axassoc & ~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) & ((! [X14 : subst] : ((comp @ id @ X14) = X14) & ! [X14 : subst] : ((comp @ X14 @ id) = X14)) <=> substmonoid) & (hoasinduction_lem3a_lthm <=> (! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X10 : subst > term > subst > $o,X42 : term] : ((X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~! [X18 : subst > term > term] : (~! [X13 : term,X25 : subst,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ 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)) | ~! [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)) | ~! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id)))))) & (hoasinduction_lem3v2_lthm <=> (! [X13 : term] : ((sub @ X13 @ id) = X13) => ! [X11 : term > $o,X10 : subst > term > subst > $o,X48 : term] : (~! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X48 @ (push @ X15 @ id)))) | ~! [X18 : subst > term > term] : (~! [X25 : subst,X14 : subst,X13 : term] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~! [X14 : subst,X13 : term,X26 : subst,X25 : subst] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | (X11 @ (lam @ X48)) | ~! [X26 : subst,X14 : subst,X13 : term,X25 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25)))))) & (! [X13 : term,X14 : subst] : ((comp @ sh @ (push @ X13 @ X14)) = X14) <=> axshiftcons) & (pushprop_lem0 <=> ! [X10 : term > $o,X14 : subst,X13 : term] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ (sub @ X12 @ (push @ X13 @ X14))))) & ~lamnotap & (! [X15 : term] : ~! [X18 : subst > term > term] : ~! [X13 : term,X14 : subst] : ((sub @ X15 @ (push @ X13 @ X14)) = (X18 @ X14 @ X13)) <=> hoasinduction_lem3v2_f_lthm) & axmap & hoasinduction_lem2v2_gthm & (induction2_lthm <=> (! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X17 : subst,X10 : term > $o,X16 : term] : (~! [X13 : term] : ((X10 @ (lam @ X13)) | ~! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~! [X13 : term,X15 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | ~! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)) | (X10 @ (sub @ X16 @ X17))) => ! [X22 : term,X10 : term > $o] : (~! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | ~! [X13 : term,X15 : term] : (~(X10 @ X15) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13)) | ~! [X13 : term] : (~! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | (X10 @ X22))))) & (pushprop_lem0_lthm <=> ! [X14 : subst,X10 : term > $o,X13 : term] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ (sub @ X12 @ (push @ X13 @ X14))))) & induction2lem_gthm & (pushprop_lem1_lthm <=> (! [X13 : term,X14 : subst] : ((sub @ one @ (push @ X13 @ X14)) = X13) => (! [X14 : subst,X13 : term] : ((comp @ sh @ (push @ X13 @ X14)) = X14) => ! [X13 : term,X10 : term > $o,X14 : subst,X15 : term,X26 : term > $o] : (~(X10 @ X13) | (X26 @ (sub @ X13 @ (push @ X15 @ X14))))))) & (hoasinduction_lem3v2a <=> ! [X11 : term > $o,X10 : subst > term > subst > $o,X29 : term] : (~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | ~! [X18 : subst > term > term] : (~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X25 : subst,X13 : term,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id)))) | (X11 @ (lam @ X29)))) & (hoasinduction_lthm <=> (! [X10 : term > $o,X22 : term] : ((X10 @ X22) | ~! [X13 : term] : (~! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15)) | (X10 @ (lam @ X13))) | ~! [X15 : term,X13 : term] : (~(X10 @ X13) | (X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15)) | ~! [X13 : term] : (~(var @ X13) | (X10 @ X13))) => (! [X23 : term,X24 : term,X10 : subst > term > subst > $o] : (~(X10 @ id @ X24 @ id) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~! [X25 : subst,X14 : subst,X13 : term,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~(X10 @ id @ X23 @ id) | ~! [X25 : subst,X26 : subst,X13 : term,X14 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X15 : term,X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id))) => (! [X27 : term,X10 : subst > term > subst > $o] : (~! [X26 : subst,X13 : term,X25 : subst,X14 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X25 : subst,X26 : subst,X13 : term,X14 : subst] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)) | (X10 @ id @ (lam @ X27) @ id) | ~! [X18 : subst > term > term] : (~! [X13 : term,X14 : subst,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id))) => ! [X10 : subst > term > subst > $o,X28 : term] : (~! [X15 : term,X13 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id)) | ~! [X26 : subst,X25 : subst,X14 : subst,X13 : term] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X26 : subst,X14 : subst,X13 : term,X25 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | ~! [X18 : subst > term > term] : (~! [X25 : subst,X13 : term,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | (X10 @ id @ X28 @ id)))))) & hoaslaminj_gthm & (! [X34 : term,X10 : subst > term > subst > $o] : (~! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X34 @ (push @ X15 @ id)) @ id)) | (X10 @ id @ (lam @ (sub @ X34 @ (push @ one @ sh))) @ id) | ~! [X35 : term,X18 : subst > term > term] : (~! [X38 : subst,X37 : term,X36 : subst] : ((sub @ (X18 @ X36 @ X37) @ X38) = (sub @ (sub @ X35 @ (push @ X37 @ X36)) @ X38)) | ~! [X39 : subst,X40 : term,X41 : subst] : ((X18 @ (comp @ X39 @ X41) @ (sub @ X40 @ X41)) = (sub @ X35 @ (push @ (sub @ X40 @ X41) @ (comp @ X39 @ X41)))) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id))) <=> hoasinduction_lem3aaa) & hoasapnotvar & ! [X2 : d_term,X3 : d_term] : (((d2term @ X2) = (d2term @ X3)) => (X2 = X3)) & ((d2subst @ d_id) = sh) & hoaslamnotvar_gthm & (! [X13 : term] : ((sub @ X13 @ id) = X13) <=> axvarid) & (hoaslaminj_lthm <=> (! [X14 : subst,X13 : term] : ((sub @ one @ (push @ X13 @ X14)) = X13) => (! [X13 : term,X14 : subst] : ((comp @ sh @ (push @ X13 @ X14)) = X14) => (! [X13 : term,X15 : term] : (((lam @ X13) != (lam @ X15)) | (X13 = X15)) => ! [X32 : subst,X33 : term,X18 : subst > term > term,X31 : subst > term > term] : (((X18 @ X32 @ X33) = (X31 @ X32 @ X33)) | ~! [X13 : term,X14 : subst,X25 : subst] : ((sub @ (X31 @ X14 @ X13) @ X25) = (X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ((lam @ (X18 @ sh @ one)) != (lam @ (X31 @ sh @ one))) | ~! [X14 : subst,X13 : term,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))))) & hoaslamnotvar & (termmset_lthm <=> (! [X13 : term] : ((sub @ X13 @ id) = X13) => ! [X13 : term] : ((sub @ X13 @ id) = X13))) & substmonoid_gthm & (induction <=> ! [X21 : term,X10 : term > $o] : (~! [X13 : term] : (~(X10 @ X13) | (X10 @ (lam @ X13))) | (X10 @ X21) | ~! [X15 : term,X13 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))) | ~! [X13 : term] : ((X10 @ X13) | ~(var @ X13)))) & (hoaslam = (^[X8 : subst, X9 : subst > term > term] : (d2term @ d_one))) & pushprop_lem2v2_lthm & (! [X20 : term,X15 : term,X19 : term,X13 : term] : (((ap @ X13 @ X19) != (ap @ X15 @ X20)) | (X13 = X15)) <=> apinj1) & ~(var @ (d2term @ d_one)) & hoasinduction_lem2_gthm & ((d2subst @ d_id) = id) & ! [X6 : d_subst,X7 : d_subst] : (((d2subst @ X6) = (d2subst @ X7)) => (X6 = X7)) & (axscons <=> ! [X14 : subst] : ((push @ (sub @ one @ X14) @ (comp @ sh @ X14)) = X14)) & pushprop_lthm & (induction2 <=> ! [X10 : term > $o,X22 : term] : (~! [X13 : term] : (~! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))) | (X10 @ (lam @ X13))) | ~! [X15 : term,X13 : term] : (~(X10 @ X15) | ~(X10 @ X13) | (X10 @ (ap @ X13 @ X15))) | (X10 @ X22) | ~! [X13 : term] : (~(var @ X13) | (X10 @ X13)))) & (! [X15 : term,X13 : term,X26 : term > $o,X14 : subst,X10 : term > $o] : ((X26 @ (sub @ X13 @ (push @ X15 @ X14))) | ~(X10 @ X13)) <=> pushprop_lem1) & hoasinduction_lem1_gthm & (! [X15 : term] : ~! [X18 : subst > term > term] : ~! [X13 : term,X14 : subst] : ((sub @ X15 @ (push @ X13 @ X14)) = (X18 @ X14 @ X13)) <=> hoasinduction_lem3v2_f) & hoasinduction_gthm & ((! [X13 : term,X14 : subst] : ((sub @ one @ (push @ X13 @ X14)) = X13) => ! [X13 : term,X14 : subst,X10 : term > $o,X11 : term > $o] : ((X11 @ one) | ~(X10 @ X13) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ (sub @ X12 @ (push @ X13 @ X14)))))) <=> pushprop_lem1v2_lthm) & (one = (d2term @ d_one)) & ! [X5 : d_subst] : (d_id = X5) & (! [X28 : term,X10 : subst > term > subst > $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 @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id))) | ~! [X25 : subst,X26 : subst,X13 : term,X14 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X10 @ id @ X28 @ id) | ~! [X13 : term] : ((X10 @ id @ X13 @ id) | ~(var @ (sub @ X13 @ id))) | ~! [X13 : term,X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id)) | ~! [X13 : term,X26 : subst,X14 : subst,X25 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25))) <=> hoasinduction) & pushprop & ~ulamvar1 & hoasapinj1_gthm & hoasinduction_lem1v2_gthm & hoaslamnotvar_lthm & (hoasinduction_lem3v2 <=> ! [X48 : term,X10 : subst > term > subst > $o,X11 : term > $o] : (~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | ~! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X48 @ (push @ X15 @ id)))) | (X11 @ (lam @ X48)) | ~! [X25 : subst,X14 : subst,X26 : subst,X13 : term] : (~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | (X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X26 : subst,X25 : subst,X13 : term,X14 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X18 : subst > term > term] : (~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | (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)))))) & pushprop_gthm & apnotvar & hoasinduction_lem2_lthm & (shinj <=> ! [X15 : term,X13 : term] : ((X13 = X15) | ((sub @ X13 @ sh) != (sub @ X15 @ sh)))) & ((d2term @ d_one) = (lam @ (d2term @ d_one))) & (! [X30 : term,X10 : subst > term > subst > $o] : (~! [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 @ X30 @ id) | ~! [X13 : term,X15 : term] : ((X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X13 @ id) | ~(X10 @ id @ X15 @ id))) <=> hoasinduction_no_psi_cond) & (! [X15 : term] : ~! [X18 : subst > term > term] : ((X18 @ sh @ one) != (sub @ X15 @ (push @ one @ sh))) <=> hoasinduction_lem3b_lthm) & hoasinduction_lem3_gthm & hoasapnotvar_lthm & (hoaslamnotap <=> ! [X18 : subst > term > term,X46 : term,X47 : term] : (~! [X25 : subst,X13 : term,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ((lam @ (X18 @ sh @ one)) != (ap @ (sub @ X46 @ id) @ X47)))) & hoaslamnotap_lthm & pushprop_lem0_gthm & axabs & axapp & (hoasinduction_lthm_3 <=> (! [X10 : subst > term > subst > $o] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) => (! [X22 : term,X10 : term > $o] : (~! [X13 : term] : ((X10 @ X13) | ~(var @ X13)) | ~! [X15 : term,X13 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X15) | ~(X10 @ X13)) | (X10 @ X22) | ~! [X13 : term] : ((X10 @ (lam @ X13)) | ~! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id)))))) => (! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X10 : subst > term > subst > $o,X29 : term,X11 : term > $o] : (~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | ~! [X18 : subst > term > term] : (~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~! [X14 : subst,X25 : subst,X13 : term] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | (X11 @ (lam @ X29)) | ~! [X15 : term] : ((X11 @ (sub @ X29 @ (push @ X15 @ id))) | ~(X11 @ X15))) => ! [X28 : term,X10 : subst > term > subst > $o] : (~! [X13 : term,X25 : subst,X26 : subst,X14 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X13 : term,X15 : term] : (~(X10 @ id @ X15 @ id) | ~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id)) | ~! [X26 : subst,X25 : subst,X14 : subst,X13 : term] : ((X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25) | ~(X10 @ X14 @ X13 @ (comp @ X26 @ X25))) | ~! [X18 : subst > term > term] : (~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~! [X14 : subst,X13 : term,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id)) | ~! [X13 : term] : (~(var @ (sub @ X13 @ id)) | (X10 @ id @ X13 @ id)) | (X10 @ id @ X28 @ id))))))) & (induction2lem <=> ! [X16 : term,X17 : subst,X10 : term > $o] : (~! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15)) | ~! [X15 : term,X13 : term] : (~(X10 @ X13) | ~(X10 @ X15) | (X10 @ (ap @ X13 @ X15))) | (X10 @ (sub @ X16 @ X17)) | ~! [X13 : term] : ((X10 @ (lam @ X13)) | ~! [X15 : term] : (~(X10 @ X15) | (X10 @ (sub @ X13 @ (push @ X15 @ id))))))) & (! [X13 : term] : ((sub @ X13 @ id) = X13) <=> termmset) & ((d2term @ d_one) = (hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))) & pushprop_lthm_orig & ((! [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) & hoasinduction_lem3v2_gthm & pushprop_lem1v2_gthm & (! [X14 : subst,X10 : term > $o,X11 : term > $o,X13 : term] : (~! [X12 : term] : ((X11 @ X12) = (X10 @ (sub @ X12 @ (push @ X13 @ X14)))) | (X11 @ one) | ~(X10 @ X13)) <=> pushprop_lem1v2) & (hoaslaminj <=> ! [X32 : subst,X31 : subst > term > term,X33 : term,X18 : subst > term > term] : (((lam @ (X18 @ sh @ one)) != (lam @ (X31 @ sh @ one))) | ~! [X13 : term,X14 : subst,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ((X18 @ X32 @ X33) = (X31 @ X32 @ X33)) | ~! [X25 : subst,X14 : subst,X13 : term] : ((sub @ (X31 @ X14 @ X13) @ X25) = (X31 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))))) & axvarshift & (! [X42 : term,X10 : subst > term > subst > $o] : (~! [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,X13 : term,X25 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | ~! [X13 : term] : ((X10 @ id @ (X18 @ id @ X13) @ id) | ~(X10 @ id @ X13 @ id)) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id))) <=> hoasinduction_lem3aa_lthm) & pushprop_lem2v2_gthm & pushprop_lem3v2_lthm & lamnotvar & induction2_gthm & pushprop_lem3v2 & ! [X0 : term] : ? [X1 : d_term] : ((d2term @ X1) = X0) & ((d2subst @ d_id) = (comp @ (d2subst @ d_id) @ (d2subst @ d_id))) & (hoasinduction_lem3_lthm <=> (! [X13 : term] : ((sub @ X13 @ id) = X13) => (! [X10 : subst > term > subst > $o,X42 : term] : (~! [X18 : subst > term > term] : (~! [X25 : subst,X13 : term,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))) | (X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~! [X15 : term] : ((X10 @ id @ (sub @ X42 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id))) => ! [X27 : term,X10 : subst > term > subst > $o] : (~! [X15 : term] : (~(X10 @ id @ X15 @ id) | (X10 @ id @ (sub @ X27 @ (push @ X15 @ id)) @ id)) | (X10 @ id @ (lam @ X27) @ id) | ~! [X14 : subst,X13 : term,X25 : subst,X26 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [X26 : subst,X13 : term,X14 : subst,X25 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~! [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,X13 : term,X14 : subst] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))))))) & (hoasinduction_lem0_lthm <=> ! [X10 : subst > term > subst > $o] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id))) & pushprop_lem1_gthm & hoasinduction_lem1 & ((d2term @ d_one) = (sub @ (d2term @ d_one) @ (d2subst @ d_id))) & hoasapnotvar_gthm & hoaslamnotap_gthm & (hoasinduction_lem2 <=> ! [X23 : term,X24 : term,X10 : subst > term > subst > $o] : (~(X10 @ id @ X24 @ id) | ~! [X26 : subst,X25 : subst,X13 : term,X14 : subst] : ((X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | ~(X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | (X10 @ id @ (ap @ X23 @ X24) @ id) | ~! [X26 : subst,X13 : term,X14 : subst,X25 : subst] : (~(X10 @ X14 @ X13 @ (comp @ X26 @ X25)) | (X10 @ (comp @ X14 @ X26) @ (sub @ X13 @ X26) @ X25)) | ~(X10 @ id @ X23 @ id) | ~! [X13 : term,X15 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (ap @ (sub @ X13 @ id) @ X15) @ id) | ~(X10 @ id @ X15 @ id)))) & (hoasinduction_lem3v2a_lthm <=> (! [X15 : term] : ~! [X18 : subst > term > term] : ~! [X14 : subst,X13 : term] : ((sub @ X15 @ (push @ X13 @ X14)) = (X18 @ X14 @ X13)) => (! [X13 : term] : ((sub @ X13 @ id) = X13) => ! [X10 : subst > term > subst > $o,X29 : term,X11 : term > $o] : (~! [X18 : subst > term > term] : ((X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id)) | ~! [X25 : subst,X14 : subst,X13 : term] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)))) | ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) | (X11 @ (lam @ X29)) | ~! [X15 : term] : (~(X11 @ X15) | (X11 @ (sub @ X29 @ (push @ X15 @ id)))))))) & (hoasapinj2 <=> ! [X13 : term,X20 : term,X15 : term,X19 : term] : (((ap @ (sub @ X13 @ id) @ X19) != (ap @ (sub @ X15 @ id) @ X20)) | (X19 = X20))) & ! [X4 : subst] : ? [X5 : d_subst] : ((d2subst @ X5) = X4) & (hoasapinj1 <=> ! [X19 : term,X20 : term,X15 : term,X13 : term] : (((ap @ (sub @ X13 @ id) @ X19) != (ap @ (sub @ X15 @ id) @ X20)) | (X13 = X15))) & (hoasinduction_lem3a <=> ! [X43 : term,X10 : subst > term > subst > $o] : (~! [X15 : term] : ((X10 @ id @ (sub @ X43 @ (push @ X15 @ id)) @ id) | ~(X10 @ id @ X15 @ id)) | (X10 @ id @ (lam @ X43) @ id) | ~! [X18 : subst > term > term] : (~! [X14 : subst,X25 : subst,X13 : term] : ((sub @ (X18 @ X14 @ X13) @ X25) = (X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25))) | (X10 @ id @ (lam @ (X18 @ sh @ one)) @ id) | ~! [X13 : term] : (~(X10 @ id @ X13 @ id) | (X10 @ id @ (X18 @ id @ X13) @ id))))) & (hoasinduction_lem3aa <=> ! [X10 : subst > term > subst > $o,X42 : term] : ((X10 @ id @ (lam @ (sub @ X42 @ (push @ one @ sh))) @ id) | ~! [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) | ~! [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))))) & ulamvarind & ((! [X13 : term,X14 : subst] : ((sub @ one @ (push @ X13 @ X14)) = X13) => (! [X14 : subst,X13 : term] : ((comp @ sh @ (push @ X13 @ X14)) = X14) => (! [X14 : subst] : ((comp @ X14 @ id) = X14) => (! [X21 : term,X10 : term > $o] : (~! [X13 : term] : (~(X10 @ X13) | (X10 @ (lam @ X13))) | ~! [X13 : term] : (~(var @ X13) | (X10 @ X13)) | (X10 @ X21) | ~! [X15 : term,X13 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15))) => ! [X17 : subst,X10 : term > $o,X16 : term] : (~! [X13 : term] : ((X10 @ (lam @ X13)) | ~! [X15 : term] : ((X10 @ (sub @ X13 @ (push @ X15 @ id))) | ~(X10 @ X15))) | ~! [X15 : term,X13 : term] : ((X10 @ (ap @ X13 @ X15)) | ~(X10 @ X13) | ~(X10 @ X15)) | (X10 @ (sub @ X16 @ X17)) | ~! [X15 : term] : ((X10 @ (sub @ X15 @ X17)) | ~(var @ X15))))))) <=> induction2lem_lthm) & hoasinduction_lem1_lthm & (! [X10 : subst > term > subst > $o] : ~! [X11 : term > $o] : ~! [X12 : term] : ((X11 @ X12) = (X10 @ id @ X12 @ id)) <=> hoasinduction_lem0) & ((^[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] : ((comp @ id @ X14) = X14) <=> axidl) & termmset_gthm & hoasapinj2_gthm & ((d2term @ d_one) = (ap @ (d2term @ d_one) @ (d2term @ d_one))) & (! [X15 : term] : ~! [X18 : subst > term > term] : ((X18 @ sh @ one) != (sub @ X15 @ (push @ one @ sh))) <=> hoasinduction_lem3b) & ! [X1 : d_term] : (d_one = X1) & hoasinduction_lem3a_gthm & ((! [X13 : term,X20 : term,X19 : term,X15 : term] : (((ap @ X13 @ X19) != (ap @ X15 @ X20)) | (X19 = X20)) => ! [X15 : term,X13 : term,X19 : term,X20 : term] : (((ap @ (sub @ X13 @ id) @ X19) != (ap @ (sub @ X15 @ id) @ X20)) | (X19 = X20))) <=> hoasapinj2_lthm) & hoasinduction_lem3b_gthm),
% 15.02/3.54 file('/export/starexec/sandbox2/tmp/tmp.xoR6yAHn1s/DTF2THF_17021.p',alg444_1)).
% 15.02/3.54 thf(f1412,plain,(
% 15.02/3.54 ( ! [X97 : term] : (((d2term @ (sK563 @ X97)) = X97)) )),
% 15.02/3.54 inference(cnf_transformation,[status(thm)],[f749])).
% 15.02/3.54 thf(f3463,plain,(
% 15.02/3.54 ((sK322 @ (d2subst @ d_id) @ (lam @ (sub @ sK321 @ (push @ (d2term @ d_one) @ (d2subst @ d_id)))) @ (d2subst @ d_id)) != $true) | spl654_371),
% 15.02/3.54 inference(avatar_component_clause,[status(thm)],[f3462])).
% 15.02/3.54 thf(f3462,definition,(
% 15.02/3.54 spl654_371 <=> ((sK322 @ (d2subst @ d_id) @ (lam @ (sub @ sK321 @ (push @ (d2term @ d_one) @ (d2subst @ d_id)))) @ (d2subst @ d_id)) = $true)),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[spl654_371])],[avatar_definition])).
% 15.02/3.54 thf(f14981,plain,(
% 15.02/3.54 spl654_294 | ~spl654_488),
% 15.02/3.54 inference(avatar_contradiction_clause,[status(thm)],[f14980])).
% 15.02/3.54 thf(f14980,plain,(
% 15.02/3.54 $false | (spl654_294 | ~spl654_488)),
% 15.02/3.54 inference(subsumption_resolution,[status(thm)],[f14979,f3127])).
% 15.02/3.54 thf(f3127,plain,(
% 15.02/3.54 ($true != (sP44 @ sK322)) | spl654_294),
% 15.02/3.54 inference(avatar_component_clause,[status(thm)],[f3126])).
% 15.02/3.54 thf(f3126,definition,(
% 15.02/3.54 spl654_294 <=> ($true = (sP44 @ sK322))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[spl654_294])],[avatar_definition])).
% 15.02/3.54 thf(f14979,plain,(
% 15.02/3.54 ($true = (sP44 @ sK322)) | ~spl654_488),
% 15.02/3.54 inference(trivial_inequality_removal,[status(thm)],[f14923])).
% 15.02/3.54 thf(f14923,plain,(
% 15.02/3.54 ($true = (sP44 @ sK322)) | ($true != $true) | ~spl654_488),
% 15.02/3.54 inference(superposition,[status(thm)],[f8836,f14864])).
% 15.02/3.54 thf(f14864,plain,(
% 15.02/3.54 ( ! [X0 : subst > term > subst > $o] : (((X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) | ((sP44 @ X0) = $true)) )),
% 15.02/3.54 inference(subsumption_resolution,[status(thm)],[f14863,f11205])).
% 15.02/3.54 thf(f11205,plain,(
% 15.02/3.54 ( ! [X0 : subst > term > subst > $o,X8 : subst,X6 : term,X7 : subst] : (((X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ X7) = $true) | ((X0 @ X8 @ X6 @ (d2subst @ d_id)) != $true)) )),
% 15.02/3.54 inference(trivial_inequality_removal,[status(thm)],[f11204])).
% 15.02/3.54 thf(f11204,plain,(
% 15.02/3.54 ( ! [X0 : subst > term > subst > $o,X8 : subst,X6 : term,X7 : subst] : (($true != $true) | ((X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ X7) = $true) | ((X0 @ X8 @ X6 @ (d2subst @ d_id)) != $true)) )),
% 15.02/3.54 inference(backward_demodulation,[status(thm)],[f9346,f11203])).
% 15.02/3.54 thf(f11203,plain,(
% 15.02/3.54 ( ! [X0 : subst > term > subst > $o] : (($true = (sP67 @ X0))) )),
% 15.02/3.54 inference(subsumption_resolution,[status(thm)],[f11202,f7764])).
% 15.02/3.54 thf(f7764,plain,(
% 15.02/3.54 ( ! [X0 : subst > term > subst > $o] : (((X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) | ($true = (sP67 @ X0))) )),
% 15.02/3.54 inference(forward_demodulation,[status(thm)],[f7763,f3855])).
% 15.02/3.54 thf(f3855,plain,(
% 15.02/3.54 ( ! [X262 : subst] : (((d2subst @ d_id) = X262)) )),
% 15.02/3.54 inference(forward_demodulation,[status(thm)],[f1286,f1499])).
% 15.02/3.54 thf(f1499,plain,(
% 15.02/3.54 ( ! [X18 : d_subst] : ((d_id = X18)) )),
% 15.02/3.54 inference(cnf_transformation,[status(thm)],[f749])).
% 15.02/3.54 thf(f1286,plain,(
% 15.02/3.54 ( ! [X262 : subst] : (((d2subst @ (sK644 @ X262)) = X262)) )),
% 15.02/3.54 inference(cnf_transformation,[status(thm)],[f749])).
% 15.02/3.54 thf(f7763,plain,(
% 15.02/3.54 ( ! [X0 : subst > term > subst > $o] : (((X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (comp @ (sK245 @ X0) @ (sK247 @ X0))) = $true) | ($true = (sP67 @ X0))) )),
% 15.02/3.54 inference(forward_demodulation,[status(thm)],[f7762,f3865])).
% 15.02/3.54 thf(f7762,plain,(
% 15.02/3.54 ( ! [X0 : subst > term > subst > $o] : (($true = (sP67 @ X0)) | ($true = (X0 @ (d2subst @ d_id) @ (sK246 @ X0) @ (comp @ (sK245 @ X0) @ (sK247 @ X0))))) )),
% 15.02/3.54 inference(forward_demodulation,[status(thm)],[f970,f3855])).
% 15.02/3.54 thf(f970,plain,(
% 15.02/3.54 ( ! [X0 : subst > term > subst > $o] : (((X0 @ (sK248 @ X0) @ (sK246 @ X0) @ (comp @ (sK245 @ X0) @ (sK247 @ X0))) = $true) | ($true = (sP67 @ X0))) )),
% 15.02/3.54 inference(cnf_transformation,[status(thm)],[f331])).
% 15.02/3.54 thf(f331,plain,(
% 15.02/3.54 ! [X0 : subst > term > subst > $o] : ((($true = (sP67 @ X0)) | (((X0 @ (sK248 @ X0) @ (sK246 @ X0) @ (comp @ (sK245 @ X0) @ (sK247 @ X0))) = $true) & ($true != (X0 @ (comp @ (sK248 @ X0) @ (sK245 @ X0)) @ (sub @ (sK246 @ X0) @ (sK245 @ X0)) @ (sK247 @ X0))))) & (! [X5 : subst,X6 : term,X7 : subst,X8 : subst] : (($true != (X0 @ X8 @ X6 @ (comp @ X5 @ X7))) | ((X0 @ (comp @ X8 @ X5) @ (sub @ X6 @ X5) @ X7) = $true)) | ($true != (sP67 @ X0))))),
% 15.02/3.54 inference(skolemisation,[status(esa),new_symbols(skolem,[sK245,sK246,sK247,sK248])],[f329,f330])).
% 15.02/3.54 thf(f330,plain,(
% 15.02/3.54 ! [X0 : subst > term > subst > $o] : (? [X1 : subst,X2 : term,X3 : subst,X4 : subst] : (((X0 @ X4 @ X2 @ (comp @ X1 @ X3)) = $true) & ($true != (X0 @ (comp @ X4 @ X1) @ (sub @ X2 @ X1) @ X3))) => (((X0 @ (sK248 @ X0) @ (sK246 @ X0) @ (comp @ (sK245 @ X0) @ (sK247 @ X0))) = $true) & ($true != (X0 @ (comp @ (sK248 @ X0) @ (sK245 @ X0)) @ (sub @ (sK246 @ X0) @ (sK245 @ X0)) @ (sK247 @ X0)))))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f329,plain,(
% 15.02/3.54 ! [X0 : subst > term > subst > $o] : ((($true = (sP67 @ X0)) | ? [X1 : subst,X2 : term,X3 : subst,X4 : subst] : (((X0 @ X4 @ X2 @ (comp @ X1 @ X3)) = $true) & ($true != (X0 @ (comp @ X4 @ X1) @ (sub @ X2 @ X1) @ X3)))) & (! [X5 : subst,X6 : term,X7 : subst,X8 : subst] : (($true != (X0 @ X8 @ X6 @ (comp @ X5 @ X7))) | ((X0 @ (comp @ X8 @ X5) @ (sub @ X6 @ X5) @ X7) = $true)) | ($true != (sP67 @ X0))))),
% 15.02/3.54 inference(rectify,[status(thm)],[f328])).
% 15.02/3.54 thf(f328,plain,(
% 15.02/3.54 ! [X189 : subst > term > subst > $o] : ((($true = (sP67 @ X189)) | ? [X190 : subst,X191 : term,X192 : subst,X193 : subst] : (((X189 @ X193 @ X191 @ (comp @ X190 @ X192)) = $true) & ((X189 @ (comp @ X193 @ X190) @ (sub @ X191 @ X190) @ X192) != $true))) & (! [X190 : subst,X191 : term,X192 : subst,X193 : subst] : (((X189 @ X193 @ X191 @ (comp @ X190 @ X192)) != $true) | ((X189 @ (comp @ X193 @ X190) @ (sub @ X191 @ X190) @ X192) = $true)) | ($true != (sP67 @ X189))))),
% 15.02/3.54 inference(nnf_transformation,[status(thm)],[f83])).
% 15.02/3.54 thf(f11202,plain,(
% 15.02/3.54 ( ! [X0 : subst > term > subst > $o] : (($true = (sP67 @ X0)) | ((X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true)) )),
% 15.02/3.54 inference(forward_demodulation,[status(thm)],[f11201,f3855])).
% 15.02/3.54 thf(f11201,plain,(
% 15.02/3.54 ( ! [X0 : subst > term > subst > $o] : (((X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (sK247 @ X0)) != $true) | ($true = (sP67 @ X0))) )),
% 15.02/3.54 inference(forward_demodulation,[status(thm)],[f11200,f3865])).
% 15.02/3.54 thf(f11200,plain,(
% 15.02/3.54 ( ! [X0 : subst > term > subst > $o] : (($true = (sP67 @ X0)) | ($true != (X0 @ (d2subst @ d_id) @ (sub @ (sK246 @ X0) @ (sK245 @ X0)) @ (sK247 @ X0)))) )),
% 15.02/3.54 inference(forward_demodulation,[status(thm)],[f969,f3855])).
% 15.02/3.54 thf(f969,plain,(
% 15.02/3.54 ( ! [X0 : subst > term > subst > $o] : (($true != (X0 @ (comp @ (sK248 @ X0) @ (sK245 @ X0)) @ (sub @ (sK246 @ X0) @ (sK245 @ X0)) @ (sK247 @ X0))) | ($true = (sP67 @ X0))) )),
% 15.02/3.54 inference(cnf_transformation,[status(thm)],[f331])).
% 15.02/3.54 thf(f9346,plain,(
% 15.02/3.54 ( ! [X0 : subst > term > subst > $o,X8 : subst,X6 : term,X7 : subst] : (((X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ X7) = $true) | ((X0 @ X8 @ X6 @ (d2subst @ d_id)) != $true) | ($true != (sP67 @ X0))) )),
% 15.02/3.54 inference(forward_demodulation,[status(thm)],[f9345,f3855])).
% 15.02/3.54 thf(f9345,plain,(
% 15.02/3.54 ( ! [X0 : subst > term > subst > $o,X8 : subst,X6 : term,X7 : subst,X5 : subst] : (($true != (sP67 @ X0)) | ((X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ X7) = $true) | ($true != (X0 @ X8 @ X6 @ (comp @ X5 @ X7)))) )),
% 15.02/3.54 inference(forward_demodulation,[status(thm)],[f9344,f3865])).
% 15.02/3.54 thf(f9344,plain,(
% 15.02/3.54 ( ! [X0 : subst > term > subst > $o,X8 : subst,X6 : term,X7 : subst,X5 : subst] : (($true != (sP67 @ X0)) | ($true = (X0 @ (d2subst @ d_id) @ (sub @ X6 @ X5) @ X7)) | ($true != (X0 @ X8 @ X6 @ (comp @ X5 @ X7)))) )),
% 15.02/3.54 inference(forward_demodulation,[status(thm)],[f968,f3855])).
% 15.02/3.54 thf(f968,plain,(
% 15.02/3.54 ( ! [X0 : subst > term > subst > $o,X8 : subst,X6 : term,X7 : subst,X5 : subst] : (((X0 @ (comp @ X8 @ X5) @ (sub @ X6 @ X5) @ X7) = $true) | ($true != (X0 @ X8 @ X6 @ (comp @ X5 @ X7))) | ($true != (sP67 @ X0))) )),
% 15.02/3.54 inference(cnf_transformation,[status(thm)],[f331])).
% 15.02/3.54 thf(f14863,plain,(
% 15.02/3.54 ( ! [X2 : subst > term > term,X0 : subst > term > subst > $o] : (((X0 @ (d2subst @ d_id) @ (lam @ (X2 @ (d2subst @ d_id) @ (d2term @ d_one))) @ (d2subst @ d_id)) = $true) | ((X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) | ((sP44 @ X0) = $true)) )),
% 15.02/3.54 inference(forward_demodulation,[status(thm)],[f14862,f3865])).
% 15.02/3.54 thf(f14862,plain,(
% 15.02/3.54 ( ! [X2 : subst > term > term,X0 : subst > term > subst > $o] : (($true = (X0 @ (d2subst @ d_id) @ (sK324 @ X2 @ X0) @ (d2subst @ d_id))) | ((X0 @ (d2subst @ d_id) @ (lam @ (X2 @ (d2subst @ d_id) @ (d2term @ d_one))) @ (d2subst @ d_id)) = $true) | ((sP44 @ X0) = $true)) )),
% 15.02/3.54 inference(subsumption_resolution,[status(thm)],[f14861,f3869])).
% 15.02/3.54 thf(f3869,plain,(
% 15.02/3.54 ( ! [X0 : term,X1 : term] : ((X0 = X1)) )),
% 15.02/3.54 inference(superposition,[status(thm)],[f3865,f3865])).
% 15.02/3.54 thf(f14861,plain,(
% 15.02/3.54 ( ! [X2 : subst > term > term,X0 : subst > term > subst > $o,X1 : term] : (((sP44 @ X0) = $true) | ((X0 @ (d2subst @ d_id) @ (lam @ (X2 @ (d2subst @ d_id) @ (d2term @ d_one))) @ (d2subst @ d_id)) = $true) | ($true = (X0 @ (d2subst @ d_id) @ (sK324 @ X2 @ X0) @ (d2subst @ d_id))) | ((sub @ X1 @ (push @ (sub @ (sK329 @ X2 @ X1) @ (sK330 @ X2 @ X1)) @ (comp @ (sK328 @ X2 @ X1) @ (sK330 @ X2 @ X1)))) != (X2 @ (comp @ (sK328 @ X2 @ X1) @ (sK330 @ X2 @ X1)) @ (sub @ (sK329 @ X2 @ X1) @ (sK330 @ X2 @ X1))))) )),
% 15.02/3.54 inference(subsumption_resolution,[status(thm)],[f1649,f3869])).
% 15.02/3.54 thf(f1649,plain,(
% 15.02/3.54 ( ! [X2 : subst > term > term,X0 : subst > term > subst > $o,X1 : term] : (((sub @ (X2 @ (sK327 @ X2 @ X1) @ (sK326 @ X2 @ X1)) @ (sK325 @ X2 @ X1)) != (sub @ (sub @ X1 @ (push @ (sK326 @ X2 @ X1) @ (sK327 @ X2 @ X1))) @ (sK325 @ X2 @ X1))) | ((sP44 @ X0) = $true) | ((X0 @ (d2subst @ d_id) @ (lam @ (X2 @ (d2subst @ d_id) @ (d2term @ d_one))) @ (d2subst @ d_id)) = $true) | ((sub @ X1 @ (push @ (sub @ (sK329 @ X2 @ X1) @ (sK330 @ X2 @ X1)) @ (comp @ (sK328 @ X2 @ X1) @ (sK330 @ X2 @ X1)))) != (X2 @ (comp @ (sK328 @ X2 @ X1) @ (sK330 @ X2 @ X1)) @ (sub @ (sK329 @ X2 @ X1) @ (sK330 @ X2 @ X1)))) | ($true = (X0 @ (d2subst @ d_id) @ (sK324 @ X2 @ X0) @ (d2subst @ d_id)))) )),
% 15.02/3.54 inference(definition_unfolding,[status(thm)],[f1074,f1388,f1388,f1388,f1344,f1494,f1388])).
% 15.02/3.54 thf(f1494,plain,(
% 15.02/3.54 (one = (d2term @ d_one))),
% 15.02/3.54 inference(cnf_transformation,[status(thm)],[f749])).
% 15.02/3.54 thf(f1344,plain,(
% 15.02/3.54 ((d2subst @ d_id) = sh)),
% 15.02/3.54 inference(cnf_transformation,[status(thm)],[f749])).
% 15.02/3.54 thf(f1388,plain,(
% 15.02/3.54 ((d2subst @ d_id) = id)),
% 15.02/3.54 inference(cnf_transformation,[status(thm)],[f749])).
% 15.02/3.54 thf(f1074,plain,(
% 15.02/3.54 ( ! [X2 : subst > term > term,X0 : subst > term > subst > $o,X1 : term] : (((sP44 @ X0) = $true) | ((X0 @ id @ (sK324 @ X2 @ X0) @ id) = $true) | ((sub @ (X2 @ (sK327 @ X2 @ X1) @ (sK326 @ X2 @ X1)) @ (sK325 @ X2 @ X1)) != (sub @ (sub @ X1 @ (push @ (sK326 @ X2 @ X1) @ (sK327 @ X2 @ X1))) @ (sK325 @ X2 @ X1))) | ($true = (X0 @ id @ (lam @ (X2 @ sh @ one)) @ id)) | ((sub @ X1 @ (push @ (sub @ (sK329 @ X2 @ X1) @ (sK330 @ X2 @ X1)) @ (comp @ (sK328 @ X2 @ X1) @ (sK330 @ X2 @ X1)))) != (X2 @ (comp @ (sK328 @ X2 @ X1) @ (sK330 @ X2 @ X1)) @ (sub @ (sK329 @ X2 @ X1) @ (sK330 @ X2 @ X1))))) )),
% 15.02/3.54 inference(cnf_transformation,[status(thm)],[f441])).
% 15.02/3.54 thf(f441,plain,(
% 15.02/3.54 ! [X0 : subst > term > subst > $o] : ((((sP44 @ X0) = $true) | ! [X1 : term,X2 : subst > term > term] : ((((X0 @ id @ (X2 @ id @ (sK324 @ X2 @ X0)) @ id) != $true) & ((X0 @ id @ (sK324 @ X2 @ X0) @ id) = $true)) | ((sub @ (X2 @ (sK327 @ X2 @ X1) @ (sK326 @ X2 @ X1)) @ (sK325 @ X2 @ X1)) != (sub @ (sub @ X1 @ (push @ (sK326 @ X2 @ X1) @ (sK327 @ X2 @ X1))) @ (sK325 @ X2 @ X1))) | ($true = (X0 @ id @ (lam @ (X2 @ sh @ one)) @ id)) | ((sub @ X1 @ (push @ (sub @ (sK329 @ X2 @ X1) @ (sK330 @ X2 @ X1)) @ (comp @ (sK328 @ X2 @ X1) @ (sK330 @ X2 @ X1)))) != (X2 @ (comp @ (sK328 @ X2 @ X1) @ (sK330 @ X2 @ X1)) @ (sub @ (sK329 @ X2 @ X1) @ (sK330 @ X2 @ X1)))))) & ((! [X12 : term] : (($true = (X0 @ id @ (sK332 @ X0 @ id @ X12) @ id)) | ($true != (X0 @ id @ X12 @ id))) & ! [X13 : subst,X14 : term,X15 : subst] : ((sub @ (sub @ (sK331 @ X0) @ (push @ X14 @ X15)) @ X13) = (sub @ (sK332 @ X0 @ X15 @ X14) @ X13)) & ((X0 @ id @ (lam @ (sK332 @ X0 @ sh @ one)) @ id) != $true) & ! [X16 : subst,X17 : term,X18 : subst] : ((sK332 @ X0 @ (comp @ X16 @ X18) @ (sub @ X17 @ X18)) = (sub @ (sK331 @ X0) @ (push @ (sub @ X17 @ X18) @ (comp @ X16 @ X18))))) | ((sP44 @ X0) != $true)))),
% 15.02/3.54 inference(skolemisation,[status(esa),new_symbols(skolem,[sK324,sK325,sK326,sK327,sK328,sK329,sK330,sK331,sK332])],[f436,f440,f439,f438,f437])).
% 15.02/3.54 thf(f437,plain,(
% 15.02/3.54 ! [X0 : subst > term > subst > $o,X2 : subst > term > term] : (? [X3 : term] : (((X0 @ id @ (X2 @ id @ X3) @ id) != $true) & ((X0 @ id @ X3 @ id) = $true)) => (((X0 @ id @ (X2 @ id @ (sK324 @ X2 @ X0)) @ id) != $true) & ((X0 @ id @ (sK324 @ X2 @ X0) @ id) = $true)))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f438,plain,(
% 15.02/3.54 ! [X1 : term,X2 : subst > term > term] : (? [X4 : subst,X5 : term,X6 : subst] : ((sub @ (sub @ X1 @ (push @ X5 @ X6)) @ X4) != (sub @ (X2 @ X6 @ X5) @ X4)) => ((sub @ (X2 @ (sK327 @ X2 @ X1) @ (sK326 @ X2 @ X1)) @ (sK325 @ X2 @ X1)) != (sub @ (sub @ X1 @ (push @ (sK326 @ X2 @ X1) @ (sK327 @ X2 @ X1))) @ (sK325 @ X2 @ X1))))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f439,plain,(
% 15.02/3.54 ! [X1 : term,X2 : subst > term > term] : (? [X7 : subst,X8 : term,X9 : subst] : ((sub @ X1 @ (push @ (sub @ X8 @ X9) @ (comp @ X7 @ X9))) != (X2 @ (comp @ X7 @ X9) @ (sub @ X8 @ X9))) => ((sub @ X1 @ (push @ (sub @ (sK329 @ X2 @ X1) @ (sK330 @ X2 @ X1)) @ (comp @ (sK328 @ X2 @ X1) @ (sK330 @ X2 @ X1)))) != (X2 @ (comp @ (sK328 @ X2 @ X1) @ (sK330 @ X2 @ X1)) @ (sub @ (sK329 @ X2 @ X1) @ (sK330 @ X2 @ X1)))))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f440,plain,(
% 15.02/3.54 ! [X0 : subst > term > subst > $o] : (? [X10 : term,X11 : subst > term > term] : (! [X12 : term] : (((X0 @ id @ (X11 @ id @ X12) @ id) = $true) | ($true != (X0 @ id @ X12 @ id))) & ! [X13 : subst,X14 : term,X15 : subst] : ((sub @ (X11 @ X15 @ X14) @ X13) = (sub @ (sub @ X10 @ (push @ X14 @ X15)) @ X13)) & ((X0 @ id @ (lam @ (X11 @ sh @ one)) @ id) != $true) & ! [X16 : subst,X17 : term,X18 : subst] : ((sub @ X10 @ (push @ (sub @ X17 @ X18) @ (comp @ X16 @ X18))) = (X11 @ (comp @ X16 @ X18) @ (sub @ X17 @ X18)))) => (! [X12 : term] : (($true = (X0 @ id @ (sK332 @ X0 @ id @ X12) @ id)) | ($true != (X0 @ id @ X12 @ id))) & ! [X15 : subst,X14 : term,X13 : subst] : ((sub @ (sub @ (sK331 @ X0) @ (push @ X14 @ X15)) @ X13) = (sub @ (sK332 @ X0 @ X15 @ X14) @ X13)) & ((X0 @ id @ (lam @ (sK332 @ X0 @ sh @ one)) @ id) != $true) & ! [X18 : subst,X17 : term,X16 : subst] : ((sK332 @ X0 @ (comp @ X16 @ X18) @ (sub @ X17 @ X18)) = (sub @ (sK331 @ X0) @ (push @ (sub @ X17 @ X18) @ (comp @ X16 @ X18))))))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f436,plain,(
% 15.02/3.54 ! [X0 : subst > term > subst > $o] : ((((sP44 @ X0) = $true) | ! [X1 : term,X2 : subst > term > term] : (? [X3 : term] : (((X0 @ id @ (X2 @ id @ X3) @ id) != $true) & ((X0 @ id @ X3 @ id) = $true)) | ? [X4 : subst,X5 : term,X6 : subst] : ((sub @ (sub @ X1 @ (push @ X5 @ X6)) @ X4) != (sub @ (X2 @ X6 @ X5) @ X4)) | ($true = (X0 @ id @ (lam @ (X2 @ sh @ one)) @ id)) | ? [X7 : subst,X8 : term,X9 : subst] : ((sub @ X1 @ (push @ (sub @ X8 @ X9) @ (comp @ X7 @ X9))) != (X2 @ (comp @ X7 @ X9) @ (sub @ X8 @ X9))))) & (? [X10 : term,X11 : subst > term > term] : (! [X12 : term] : (((X0 @ id @ (X11 @ id @ X12) @ id) = $true) | ($true != (X0 @ id @ X12 @ id))) & ! [X13 : subst,X14 : term,X15 : subst] : ((sub @ (X11 @ X15 @ X14) @ X13) = (sub @ (sub @ X10 @ (push @ X14 @ X15)) @ X13)) & ((X0 @ id @ (lam @ (X11 @ sh @ one)) @ id) != $true) & ! [X16 : subst,X17 : term,X18 : subst] : ((sub @ X10 @ (push @ (sub @ X17 @ X18) @ (comp @ X16 @ X18))) = (X11 @ (comp @ X16 @ X18) @ (sub @ X17 @ X18)))) | ((sP44 @ X0) != $true)))),
% 15.02/3.54 inference(rectify,[status(thm)],[f435])).
% 15.02/3.54 thf(f435,plain,(
% 15.02/3.54 ! [X223 : subst > term > subst > $o] : ((((sP44 @ X223) = $true) | ! [X225 : term,X226 : subst > term > term] : (? [X233 : term] : (((X223 @ id @ (X226 @ id @ X233) @ id) != $true) & ($true = (X223 @ id @ X233 @ id))) | ? [X227 : subst,X228 : term,X229 : subst] : ((sub @ (sub @ X225 @ (push @ X228 @ X229)) @ X227) != (sub @ (X226 @ X229 @ X228) @ X227)) | ($true = (X223 @ id @ (lam @ (X226 @ sh @ one)) @ id)) | ? [X230 : subst,X231 : term,X232 : subst] : ((sub @ X225 @ (push @ (sub @ X231 @ X232) @ (comp @ X230 @ X232))) != (X226 @ (comp @ X230 @ X232) @ (sub @ X231 @ X232))))) & (? [X225 : term,X226 : subst > term > term] : (! [X233 : term] : (((X223 @ id @ (X226 @ id @ X233) @ id) = $true) | ($true != (X223 @ id @ X233 @ id))) & ! [X227 : subst,X228 : term,X229 : subst] : ((sub @ (sub @ X225 @ (push @ X228 @ X229)) @ X227) = (sub @ (X226 @ X229 @ X228) @ X227)) & ($true != (X223 @ id @ (lam @ (X226 @ sh @ one)) @ id)) & ! [X230 : subst,X231 : term,X232 : subst] : ((sub @ X225 @ (push @ (sub @ X231 @ X232) @ (comp @ X230 @ X232))) = (X226 @ (comp @ X230 @ X232) @ (sub @ X231 @ X232)))) | ((sP44 @ X223) != $true)))),
% 15.02/3.54 inference(nnf_transformation,[status(thm)],[f60])).
% 15.02/3.54 thf(f8836,plain,(
% 15.02/3.54 ( ! [X2 : term] : (((sK322 @ (d2subst @ d_id) @ X2 @ (d2subst @ d_id)) != $true)) ) | ~spl654_488),
% 15.02/3.54 inference(avatar_component_clause,[status(thm)],[f8835])).
% 15.02/3.54 thf(f8835,definition,(
% 15.02/3.54 spl654_488 <=> ! [X2 : term] : ((sK322 @ (d2subst @ d_id) @ X2 @ (d2subst @ d_id)) != $true)),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[spl654_488])],[avatar_definition])).
% 15.02/3.54 thf(f14490,plain,(
% 15.02/3.54 spl654_344 | ~spl654_521),
% 15.02/3.54 inference(avatar_split_clause,[status(thm)],[f14442,f11472,f3345])).
% 15.02/3.54 thf(f3345,definition,(
% 15.02/3.54 spl654_344 <=> ! [X1 : subst > term > subst > $o] : (($true = (sP111 @ X1)) | ((sP112 @ X1) = $true))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[spl654_344])],[avatar_definition])).
% 15.02/3.54 thf(f11472,definition,(
% 15.02/3.54 spl654_521 <=> ! [X0 : subst > term > subst > $o] : (((X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) | ((sP112 @ X0) = $true))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[spl654_521])],[avatar_definition])).
% 15.02/3.54 thf(f14442,plain,(
% 15.02/3.54 ( ! [X0 : subst > term > subst > $o] : (($true = (sP111 @ X0)) | ((sP112 @ X0) = $true)) ) | ~spl654_521),
% 15.02/3.54 inference(trivial_inequality_removal,[status(thm)],[f14417])).
% 15.02/3.54 thf(f14417,plain,(
% 15.02/3.54 ( ! [X0 : subst > term > subst > $o] : (($true != $true) | ((sP112 @ X0) = $true) | ($true = (sP111 @ X0))) ) | ~spl654_521),
% 15.02/3.54 inference(superposition,[status(thm)],[f8545,f11473])).
% 15.02/3.54 thf(f11473,plain,(
% 15.02/3.54 ( ! [X0 : subst > term > subst > $o] : (((X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) | ((sP112 @ X0) = $true)) ) | ~spl654_521),
% 15.02/3.54 inference(avatar_component_clause,[status(thm)],[f11472])).
% 15.02/3.54 thf(f8545,plain,(
% 15.02/3.54 ( ! [X0 : subst > term > subst > $o] : (((X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) != $true) | ($true = (sP111 @ X0))) )),
% 15.02/3.54 inference(forward_demodulation,[status(thm)],[f1855,f3865])).
% 15.02/3.54 thf(f1855,plain,(
% 15.02/3.54 ( ! [X0 : subst > term > subst > $o] : (($true = (sP111 @ X0)) | ((X0 @ (d2subst @ d_id) @ (lam @ (sub @ (sK647 @ X0) @ (push @ (d2term @ d_one) @ (d2subst @ d_id)))) @ (d2subst @ d_id)) != $true)) )),
% 15.02/3.54 inference(definition_unfolding,[status(thm)],[f1525,f1388,f1494,f1344,f1388])).
% 15.02/3.54 thf(f1525,plain,(
% 15.02/3.54 ( ! [X0 : subst > term > subst > $o] : (($true = (sP111 @ X0)) | ($true != (X0 @ id @ (lam @ (sub @ (sK647 @ X0) @ (push @ one @ sh))) @ id))) )),
% 15.02/3.54 inference(cnf_transformation,[status(thm)],[f759])).
% 15.02/3.54 thf(f759,plain,(
% 15.02/3.54 ! [X0 : subst > term > subst > $o] : ((($true = (sP111 @ X0)) | (($true != (X0 @ id @ (lam @ (sub @ (sK647 @ X0) @ (push @ one @ sh))) @ id)) & ! [X2 : term] : (((X0 @ id @ X2 @ id) != $true) | ($true = (X0 @ id @ (sub @ (sK647 @ X0) @ (push @ X2 @ id)) @ id))))) & (! [X3 : term] : (($true = (X0 @ id @ (lam @ (sub @ X3 @ (push @ one @ sh))) @ id)) | (($true = (X0 @ id @ (sK648 @ X3 @ X0) @ id)) & ((X0 @ id @ (sub @ X3 @ (push @ (sK648 @ X3 @ X0) @ id)) @ id) != $true))) | ($true != (sP111 @ X0))))),
% 15.02/3.54 inference(skolemisation,[status(esa),new_symbols(skolem,[sK647,sK648])],[f756,f758,f757])).
% 15.02/3.54 thf(f757,plain,(
% 15.02/3.54 ! [X0 : subst > term > subst > $o] : (? [X1 : term] : (((X0 @ id @ (lam @ (sub @ X1 @ (push @ one @ sh))) @ id) != $true) & ! [X2 : term] : (((X0 @ id @ X2 @ id) != $true) | ((X0 @ id @ (sub @ X1 @ (push @ X2 @ id)) @ id) = $true))) => (($true != (X0 @ id @ (lam @ (sub @ (sK647 @ X0) @ (push @ one @ sh))) @ id)) & ! [X2 : term] : (((X0 @ id @ X2 @ id) != $true) | ($true = (X0 @ id @ (sub @ (sK647 @ X0) @ (push @ X2 @ id)) @ id)))))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f758,plain,(
% 15.02/3.54 ! [X0 : subst > term > subst > $o,X3 : term] : (? [X4 : term] : (((X0 @ id @ X4 @ id) = $true) & ((X0 @ id @ (sub @ X3 @ (push @ X4 @ id)) @ id) != $true)) => (($true = (X0 @ id @ (sK648 @ X3 @ X0) @ id)) & ((X0 @ id @ (sub @ X3 @ (push @ (sK648 @ X3 @ X0) @ id)) @ id) != $true)))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f756,plain,(
% 15.02/3.54 ! [X0 : subst > term > subst > $o] : ((($true = (sP111 @ X0)) | ? [X1 : term] : (((X0 @ id @ (lam @ (sub @ X1 @ (push @ one @ sh))) @ id) != $true) & ! [X2 : term] : (((X0 @ id @ X2 @ id) != $true) | ((X0 @ id @ (sub @ X1 @ (push @ X2 @ id)) @ id) = $true)))) & (! [X3 : term] : (($true = (X0 @ id @ (lam @ (sub @ X3 @ (push @ one @ sh))) @ id)) | ? [X4 : term] : (((X0 @ id @ X4 @ id) = $true) & ((X0 @ id @ (sub @ X3 @ (push @ X4 @ id)) @ id) != $true))) | ($true != (sP111 @ X0))))),
% 15.02/3.54 inference(rectify,[status(thm)],[f755])).
% 15.02/3.54 thf(f755,plain,(
% 15.02/3.54 ! [X0 : subst > term > subst > $o] : ((($true = (sP111 @ X0)) | ? [X7 : term] : (($true != (X0 @ id @ (lam @ (sub @ X7 @ (push @ one @ sh))) @ id)) & ! [X8 : term] : (($true != (X0 @ id @ X8 @ id)) | ($true = (X0 @ id @ (sub @ X7 @ (push @ X8 @ id)) @ id))))) & (! [X7 : term] : (($true = (X0 @ id @ (lam @ (sub @ X7 @ (push @ one @ sh))) @ id)) | ? [X8 : term] : (($true = (X0 @ id @ X8 @ id)) & ($true != (X0 @ id @ (sub @ X7 @ (push @ X8 @ id)) @ id)))) | ($true != (sP111 @ X0))))),
% 15.02/3.54 inference(nnf_transformation,[status(thm)],[f128])).
% 15.02/3.54 thf(f128,plain,(
% 15.02/3.54 ! [X0 : subst > term > subst > $o] : (($true = (sP111 @ X0)) <=> ! [X7 : term] : (($true = (X0 @ id @ (lam @ (sub @ X7 @ (push @ one @ sh))) @ id)) | ? [X8 : term] : (($true = (X0 @ id @ X8 @ id)) & ($true != (X0 @ id @ (sub @ X7 @ (push @ X8 @ id)) @ id)))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f14373,plain,(
% 15.02/3.54 ~spl654_520),
% 15.02/3.54 inference(avatar_contradiction_clause,[status(thm)],[f14372])).
% 15.02/3.54 thf(f14372,plain,(
% 15.02/3.54 $false | ~spl654_520),
% 15.02/3.54 inference(subsumption_resolution,[status(thm)],[f14371,f11470])).
% 15.02/3.54 thf(f11470,plain,(
% 15.02/3.54 ( ! [X1 : subst > term > term] : (((sP110 @ X1) != $true)) ) | ~spl654_520),
% 15.02/3.54 inference(avatar_component_clause,[status(thm)],[f11469])).
% 15.02/3.54 thf(f11469,definition,(
% 15.02/3.54 spl654_520 <=> ! [X1 : subst > term > term] : ((sP110 @ X1) != $true)),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[spl654_520])],[avatar_definition])).
% 15.02/3.54 thf(f14371,plain,(
% 15.02/3.54 ( ! [X0 : subst > term > term] : (($true = (sP110 @ X0))) )),
% 15.02/3.54 inference(subsumption_resolution,[status(thm)],[f14370,f3869])).
% 15.02/3.54 thf(f14370,plain,(
% 15.02/3.54 ( ! [X0 : subst > term > term,X1 : term] : (((sub @ (X0 @ (sK651 @ X1 @ X0) @ (sK650 @ X1 @ X0)) @ (sK649 @ X1 @ X0)) != (sub @ (sub @ X1 @ (push @ (sK650 @ X1 @ X0) @ (sK651 @ X1 @ X0))) @ (sK649 @ X1 @ X0))) | ($true = (sP110 @ X0))) )),
% 15.02/3.54 inference(subsumption_resolution,[status(thm)],[f1528,f3869])).
% 15.02/3.54 thf(f1528,plain,(
% 15.02/3.54 ( ! [X0 : subst > term > term,X1 : term] : (((sub @ X1 @ (push @ (sub @ (sK650 @ X1 @ X0) @ (sK649 @ X1 @ X0)) @ (comp @ (sK651 @ X1 @ X0) @ (sK649 @ X1 @ X0)))) != (X0 @ (comp @ (sK651 @ X1 @ X0) @ (sK649 @ X1 @ X0)) @ (sub @ (sK650 @ X1 @ X0) @ (sK649 @ X1 @ X0)))) | ($true = (sP110 @ X0)) | ((sub @ (X0 @ (sK651 @ X1 @ X0) @ (sK650 @ X1 @ X0)) @ (sK649 @ X1 @ X0)) != (sub @ (sub @ X1 @ (push @ (sK650 @ X1 @ X0) @ (sK651 @ X1 @ X0))) @ (sK649 @ X1 @ X0)))) )),
% 15.02/3.54 inference(cnf_transformation,[status(thm)],[f764])).
% 15.02/3.54 thf(f764,plain,(
% 15.02/3.54 ! [X0 : subst > term > term] : ((($true = (sP110 @ X0)) | ! [X1 : term] : (((sub @ X1 @ (push @ (sub @ (sK650 @ X1 @ X0) @ (sK649 @ X1 @ X0)) @ (comp @ (sK651 @ X1 @ X0) @ (sK649 @ X1 @ X0)))) != (X0 @ (comp @ (sK651 @ X1 @ X0) @ (sK649 @ X1 @ X0)) @ (sub @ (sK650 @ X1 @ X0) @ (sK649 @ X1 @ X0)))) | ((sub @ (X0 @ (sK651 @ X1 @ X0) @ (sK650 @ X1 @ X0)) @ (sK649 @ X1 @ X0)) != (sub @ (sub @ X1 @ (push @ (sK650 @ X1 @ X0) @ (sK651 @ X1 @ X0))) @ (sK649 @ X1 @ X0))))) & (! [X6 : subst,X7 : term,X8 : subst] : (((sub @ (sK652 @ X0) @ (push @ (sub @ X7 @ X6) @ (comp @ X8 @ X6))) = (X0 @ (comp @ X8 @ X6) @ (sub @ X7 @ X6))) & ((sub @ (sub @ (sK652 @ X0) @ (push @ X7 @ X8)) @ X6) = (sub @ (X0 @ X8 @ X7) @ X6))) | ($true != (sP110 @ X0))))),
% 15.02/3.54 inference(skolemisation,[status(esa),new_symbols(skolem,[sK649,sK650,sK651,sK652])],[f761,f763,f762])).
% 15.02/3.54 thf(f762,plain,(
% 15.02/3.54 ! [X0 : subst > term > term,X1 : term] : (? [X2 : subst,X3 : term,X4 : subst] : (((sub @ X1 @ (push @ (sub @ X3 @ X2) @ (comp @ X4 @ X2))) != (X0 @ (comp @ X4 @ X2) @ (sub @ X3 @ X2))) | ((sub @ (sub @ X1 @ (push @ X3 @ X4)) @ X2) != (sub @ (X0 @ X4 @ X3) @ X2))) => (((sub @ X1 @ (push @ (sub @ (sK650 @ X1 @ X0) @ (sK649 @ X1 @ X0)) @ (comp @ (sK651 @ X1 @ X0) @ (sK649 @ X1 @ X0)))) != (X0 @ (comp @ (sK651 @ X1 @ X0) @ (sK649 @ X1 @ X0)) @ (sub @ (sK650 @ X1 @ X0) @ (sK649 @ X1 @ X0)))) | ((sub @ (X0 @ (sK651 @ X1 @ X0) @ (sK650 @ X1 @ X0)) @ (sK649 @ X1 @ X0)) != (sub @ (sub @ X1 @ (push @ (sK650 @ X1 @ X0) @ (sK651 @ X1 @ X0))) @ (sK649 @ X1 @ X0)))))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f763,plain,(
% 15.02/3.54 ! [X0 : subst > term > term] : (? [X5 : term] : ! [X6 : subst,X7 : term,X8 : subst] : (((sub @ X5 @ (push @ (sub @ X7 @ X6) @ (comp @ X8 @ X6))) = (X0 @ (comp @ X8 @ X6) @ (sub @ X7 @ X6))) & ((sub @ (sub @ X5 @ (push @ X7 @ X8)) @ X6) = (sub @ (X0 @ X8 @ X7) @ X6))) => ! [X8 : subst,X7 : term,X6 : subst] : (((sub @ (sK652 @ X0) @ (push @ (sub @ X7 @ X6) @ (comp @ X8 @ X6))) = (X0 @ (comp @ X8 @ X6) @ (sub @ X7 @ X6))) & ((sub @ (sub @ (sK652 @ X0) @ (push @ X7 @ X8)) @ X6) = (sub @ (X0 @ X8 @ X7) @ X6))))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f761,plain,(
% 15.02/3.54 ! [X0 : subst > term > term] : ((($true = (sP110 @ X0)) | ! [X1 : term] : ? [X2 : subst,X3 : term,X4 : subst] : (((sub @ X1 @ (push @ (sub @ X3 @ X2) @ (comp @ X4 @ X2))) != (X0 @ (comp @ X4 @ X2) @ (sub @ X3 @ X2))) | ((sub @ (sub @ X1 @ (push @ X3 @ X4)) @ X2) != (sub @ (X0 @ X4 @ X3) @ X2)))) & (? [X5 : term] : ! [X6 : subst,X7 : term,X8 : subst] : (((sub @ X5 @ (push @ (sub @ X7 @ X6) @ (comp @ X8 @ X6))) = (X0 @ (comp @ X8 @ X6) @ (sub @ X7 @ X6))) & ((sub @ (sub @ X5 @ (push @ X7 @ X8)) @ X6) = (sub @ (X0 @ X8 @ X7) @ X6))) | ($true != (sP110 @ X0))))),
% 15.02/3.54 inference(rectify,[status(thm)],[f760])).
% 15.02/3.54 thf(f760,plain,(
% 15.02/3.54 ! [X1 : subst > term > term] : ((((sP110 @ X1) = $true) | ! [X2 : term] : ? [X3 : subst,X4 : term,X5 : subst] : (((sub @ X2 @ (push @ (sub @ X4 @ X3) @ (comp @ X5 @ X3))) != (X1 @ (comp @ X5 @ X3) @ (sub @ X4 @ X3))) | ((sub @ (sub @ X2 @ (push @ X4 @ X5)) @ X3) != (sub @ (X1 @ X5 @ X4) @ X3)))) & (? [X2 : term] : ! [X3 : subst,X4 : term,X5 : subst] : (((sub @ X2 @ (push @ (sub @ X4 @ X3) @ (comp @ X5 @ X3))) = (X1 @ (comp @ X5 @ X3) @ (sub @ X4 @ X3))) & ((sub @ (sub @ X2 @ (push @ X4 @ X5)) @ X3) = (sub @ (X1 @ X5 @ X4) @ X3))) | ((sP110 @ X1) != $true)))),
% 15.02/3.54 inference(nnf_transformation,[status(thm)],[f127])).
% 15.02/3.54 thf(f127,plain,(
% 15.02/3.54 ! [X1 : subst > term > term] : (((sP110 @ X1) = $true) <=> ? [X2 : term] : ! [X3 : subst,X4 : term,X5 : subst] : (((sub @ X2 @ (push @ (sub @ X4 @ X3) @ (comp @ X5 @ X3))) = (X1 @ (comp @ X5 @ X3) @ (sub @ X4 @ X3))) & ((sub @ (sub @ X2 @ (push @ X4 @ X5)) @ X3) = (sub @ (X1 @ X5 @ X4) @ X3))))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f11474,plain,(
% 15.02/3.54 spl654_520 | spl654_521),
% 15.02/3.54 inference(avatar_split_clause,[status(thm)],[f11467,f11472,f11469])).
% 15.02/3.54 thf(f11467,plain,(
% 15.02/3.54 ( ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (((X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) | ((sP110 @ X1) != $true) | ((sP112 @ X0) = $true)) )),
% 15.02/3.54 inference(subsumption_resolution,[status(thm)],[f1859,f11205])).
% 15.02/3.54 thf(f1859,plain,(
% 15.02/3.54 ( ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (((sP112 @ X0) = $true) | ($true = (X0 @ (d2subst @ d_id) @ (sK645 @ X1 @ X0) @ (d2subst @ d_id))) | ((X0 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)) = $true) | ((sP110 @ X1) != $true)) )),
% 15.02/3.54 inference(beta_eta_normalization,[status(thm)],[f1852])).
% 15.02/3.54 thf(f1852,plain,(
% 15.02/3.54 ( ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (((sP112 @ X0) = $true) | ($true = (X0 @ (d2subst @ d_id) @ ((^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one)))) @ (d2subst @ d_id) @ (^[Y0 : subst]: ((^[Y1 : term]: (X1 @ Y0 @ Y1))))) @ (d2subst @ d_id))) | ((sP110 @ X1) != $true) | ($true = (X0 @ (d2subst @ d_id) @ (sK645 @ X1 @ X0) @ (d2subst @ d_id)))) )),
% 15.02/3.54 inference(definition_unfolding,[status(thm)],[f1520,f1388,f1388,f1388,f1420,f1388,f1388])).
% 15.02/3.54 thf(f1420,plain,(
% 15.02/3.54 (hoaslam = (^[Y0 : subst]: ((^[Y1 : subst > term > term]: (d2term @ d_one)))))),
% 15.02/3.54 inference(cnf_transformation,[status(thm)],[f749])).
% 15.02/3.54 thf(f1520,plain,(
% 15.02/3.54 ( ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (((sP112 @ X0) = $true) | ($true = (X0 @ id @ (sK645 @ X1 @ X0) @ id)) | ((sP110 @ X1) != $true) | ((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X1 @ Y0 @ Y1))))) @ id) = $true)) )),
% 15.02/3.54 inference(cnf_transformation,[status(thm)],[f754])).
% 15.02/3.54 thf(f754,plain,(
% 15.02/3.54 ! [X0 : subst > term > subst > $o] : ((((sP112 @ X0) = $true) | ! [X1 : subst > term > term] : ((((X0 @ id @ (X1 @ id @ (sK645 @ X1 @ X0)) @ id) != $true) & ($true = (X0 @ id @ (sK645 @ X1 @ X0) @ id))) | ((sP110 @ X1) != $true) | ((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X1 @ Y0 @ Y1))))) @ id) = $true))) & ((! [X4 : term] : (((X0 @ id @ (sK646 @ X0 @ id @ X4) @ id) = $true) | ((X0 @ id @ X4 @ id) != $true)) & ($true = (sP110 @ (sK646 @ X0))) & ((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (sK646 @ X0 @ Y0 @ Y1))))) @ id) != $true)) | ((sP112 @ X0) != $true)))),
% 15.02/3.54 inference(skolemisation,[status(esa),new_symbols(skolem,[sK645,sK646])],[f751,f753,f752])).
% 15.02/3.54 thf(f752,plain,(
% 15.02/3.54 ! [X0 : subst > term > subst > $o,X1 : subst > term > term] : (? [X2 : term] : (((X0 @ id @ (X1 @ id @ X2) @ id) != $true) & ((X0 @ id @ X2 @ id) = $true)) => (((X0 @ id @ (X1 @ id @ (sK645 @ X1 @ X0)) @ id) != $true) & ($true = (X0 @ id @ (sK645 @ X1 @ X0) @ id))))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f753,plain,(
% 15.02/3.54 ! [X0 : subst > term > subst > $o] : (? [X3 : subst > term > term] : (! [X4 : term] : (($true = (X0 @ id @ (X3 @ id @ X4) @ id)) | ((X0 @ id @ X4 @ id) != $true)) & ($true = (sP110 @ X3)) & ($true != (X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X3 @ Y0 @ Y1))))) @ id))) => (! [X4 : term] : (((X0 @ id @ (sK646 @ X0 @ id @ X4) @ id) = $true) | ((X0 @ id @ X4 @ id) != $true)) & ($true = (sP110 @ (sK646 @ X0))) & ((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (sK646 @ X0 @ Y0 @ Y1))))) @ id) != $true)))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f751,plain,(
% 15.02/3.54 ! [X0 : subst > term > subst > $o] : ((((sP112 @ X0) = $true) | ! [X1 : subst > term > term] : (? [X2 : term] : (((X0 @ id @ (X1 @ id @ X2) @ id) != $true) & ((X0 @ id @ X2 @ id) = $true)) | ((sP110 @ X1) != $true) | ((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X1 @ Y0 @ Y1))))) @ id) = $true))) & (? [X3 : subst > term > term] : (! [X4 : term] : (($true = (X0 @ id @ (X3 @ id @ X4) @ id)) | ((X0 @ id @ X4 @ id) != $true)) & ($true = (sP110 @ X3)) & ($true != (X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X3 @ Y0 @ Y1))))) @ id))) | ((sP112 @ X0) != $true)))),
% 15.02/3.54 inference(rectify,[status(thm)],[f750])).
% 15.02/3.54 thf(f750,plain,(
% 15.02/3.54 ! [X0 : subst > term > subst > $o] : ((((sP112 @ X0) = $true) | ! [X1 : subst > term > term] : (? [X6 : term] : (((X0 @ id @ (X1 @ id @ X6) @ id) != $true) & ((X0 @ id @ X6 @ id) = $true)) | ((sP110 @ X1) != $true) | ((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X1 @ Y0 @ Y1))))) @ id) = $true))) & (? [X1 : subst > term > term] : (! [X6 : term] : (((X0 @ id @ (X1 @ id @ X6) @ id) = $true) | ((X0 @ id @ X6 @ id) != $true)) & ((sP110 @ X1) = $true) & ((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X1 @ Y0 @ Y1))))) @ id) != $true)) | ((sP112 @ X0) != $true)))),
% 15.02/3.54 inference(nnf_transformation,[status(thm)],[f129])).
% 15.02/3.54 thf(f129,plain,(
% 15.02/3.54 ! [X0 : subst > term > subst > $o] : (((sP112 @ X0) = $true) <=> ? [X1 : subst > term > term] : (! [X6 : term] : (((X0 @ id @ (X1 @ id @ X6) @ id) = $true) | ((X0 @ id @ X6 @ id) != $true)) & ((sP110 @ X1) = $true) & ((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X1 @ Y0 @ Y1))))) @ id) != $true)))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 15.02/3.54 thf(f8846,plain,(
% 15.02/3.54 spl654_242 | spl654_250 | ~spl654_344),
% 15.02/3.54 inference(avatar_contradiction_clause,[status(thm)],[f8845])).
% 15.02/3.54 thf(f8845,plain,(
% 15.02/3.54 $false | (spl654_242 | spl654_250 | ~spl654_344)),
% 15.02/3.54 inference(subsumption_resolution,[status(thm)],[f8844,f2933])).
% 15.02/3.54 thf(f2933,plain,(
% 15.02/3.54 ((sP112 @ sK653) != $true) | spl654_250),
% 15.02/3.54 inference(avatar_component_clause,[status(thm)],[f2932])).
% 15.02/3.54 thf(f2932,definition,(
% 15.02/3.54 spl654_250 <=> ((sP112 @ sK653) = $true)),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[spl654_250])],[avatar_definition])).
% 15.02/3.54 thf(f8844,plain,(
% 15.02/3.54 ((sP112 @ sK653) = $true) | (spl654_242 | ~spl654_344)),
% 15.02/3.54 inference(trivial_inequality_removal,[status(thm)],[f8843])).
% 15.02/3.54 thf(f8843,plain,(
% 15.02/3.54 ($true != $true) | ((sP112 @ sK653) = $true) | (spl654_242 | ~spl654_344)),
% 15.02/3.54 inference(superposition,[status(thm)],[f2902,f3346])).
% 15.02/3.54 thf(f3346,plain,(
% 15.02/3.54 ( ! [X1 : subst > term > subst > $o] : (($true = (sP111 @ X1)) | ((sP112 @ X1) = $true)) ) | ~spl654_344),
% 15.02/3.54 inference(avatar_component_clause,[status(thm)],[f3345])).
% 15.02/3.54 thf(f2902,plain,(
% 15.02/3.54 ($true != (sP111 @ sK653)) | spl654_242),
% 15.02/3.54 inference(avatar_component_clause,[status(thm)],[f2901])).
% 15.02/3.54 thf(f2901,definition,(
% 15.02/3.54 spl654_242 <=> ($true = (sP111 @ sK653))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[spl654_242])],[avatar_definition])).
% 15.02/3.54 thf(f8837,plain,(
% 15.02/3.54 spl654_487 | spl654_488 | ~spl654_74),
% 15.02/3.54 inference(avatar_split_clause,[status(thm)],[f7236,f2200,f8835,f8832])).
% 15.02/3.54 thf(f2200,definition,(
% 15.02/3.54 spl654_74 <=> ! [X2 : term] : (((sK322 @ (d2subst @ d_id) @ X2 @ (d2subst @ d_id)) != $true) | ((sK322 @ (d2subst @ d_id) @ (sub @ sK321 @ (push @ X2 @ (d2subst @ d_id))) @ (d2subst @ d_id)) = $true))),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[spl654_74])],[avatar_definition])).
% 15.02/3.54 thf(f7236,plain,(
% 15.02/3.54 ( ! [X2 : term] : (((sK322 @ (d2subst @ d_id) @ X2 @ (d2subst @ d_id)) != $true) | ($true = (sK322 @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))) ) | ~spl654_74),
% 15.02/3.54 inference(forward_demodulation,[status(thm)],[f2201,f3865])).
% 15.02/3.54 thf(f2201,plain,(
% 15.02/3.54 ( ! [X2 : term] : (((sK322 @ (d2subst @ d_id) @ (sub @ sK321 @ (push @ X2 @ (d2subst @ d_id))) @ (d2subst @ d_id)) = $true) | ((sK322 @ (d2subst @ d_id) @ X2 @ (d2subst @ d_id)) != $true)) ) | ~spl654_74),
% 15.02/3.54 inference(avatar_component_clause,[status(thm)],[f2200])).
% 15.02/3.54 thf(f3464,plain,(
% 15.02/3.54 spl654_73 | ~spl654_371),
% 15.02/3.54 inference(avatar_split_clause,[status(thm)],[f1645,f3462,f2197])).
% 15.02/3.54 thf(f2197,definition,(
% 15.02/3.54 spl654_73 <=> ($true = sP45)),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[spl654_73])],[avatar_definition])).
% 15.02/3.54 thf(f1645,plain,(
% 15.02/3.54 ($true = sP45) | ((sK322 @ (d2subst @ d_id) @ (lam @ (sub @ sK321 @ (push @ (d2term @ d_one) @ (d2subst @ d_id)))) @ (d2subst @ d_id)) != $true)),
% 15.02/3.54 inference(definition_unfolding,[status(thm)],[f1067,f1388,f1494,f1344,f1388])).
% 15.02/3.54 thf(f1067,plain,(
% 15.02/3.54 ($true = sP45) | ((sK322 @ id @ (lam @ (sub @ sK321 @ (push @ one @ sh))) @ id) != $true)),
% 15.02/3.54 inference(cnf_transformation,[status(thm)],[f434])).
% 15.02/3.54 thf(f434,plain,(
% 15.02/3.54 (($true = sP45) | (($true != (sP44 @ sK322)) & ! [X2 : term] : (((sK322 @ id @ X2 @ id) != $true) | ($true = (sK322 @ id @ (sub @ sK321 @ (push @ X2 @ id)) @ id))) & ((sK322 @ id @ (lam @ (sub @ sK321 @ (push @ one @ sh))) @ id) != $true))) & (! [X3 : term,X4 : subst > term > subst > $o] : (($true = (sP44 @ X4)) | (($true = (X4 @ id @ (sK323 @ X4 @ X3) @ id)) & ((X4 @ id @ (sub @ X3 @ (push @ (sK323 @ X4 @ X3) @ id)) @ id) != $true)) | ((X4 @ id @ (lam @ (sub @ X3 @ (push @ one @ sh))) @ id) = $true)) | ($true != sP45))),
% 15.02/3.54 inference(skolemisation,[status(esa),new_symbols(skolem,[sK321,sK322,sK323])],[f431,f433,f432])).
% 15.02/3.54 thf(f432,plain,(
% 15.02/3.54 ? [X0 : term,X1 : subst > term > subst > $o] : (($true != (sP44 @ X1)) & ! [X2 : term] : (($true != (X1 @ id @ X2 @ id)) | ($true = (X1 @ id @ (sub @ X0 @ (push @ X2 @ id)) @ id))) & ((X1 @ id @ (lam @ (sub @ X0 @ (push @ one @ sh))) @ id) != $true)) => (($true != (sP44 @ sK322)) & ! [X2 : term] : (((sK322 @ id @ X2 @ id) != $true) | ($true = (sK322 @ id @ (sub @ sK321 @ (push @ X2 @ id)) @ id))) & ((sK322 @ id @ (lam @ (sub @ sK321 @ (push @ one @ sh))) @ id) != $true))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f433,plain,(
% 15.02/3.54 ! [X3 : term,X4 : subst > term > subst > $o] : (? [X5 : term] : (((X4 @ id @ X5 @ id) = $true) & ((X4 @ id @ (sub @ X3 @ (push @ X5 @ id)) @ id) != $true)) => (($true = (X4 @ id @ (sK323 @ X4 @ X3) @ id)) & ((X4 @ id @ (sub @ X3 @ (push @ (sK323 @ X4 @ X3) @ id)) @ id) != $true)))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f431,plain,(
% 15.02/3.54 (($true = sP45) | ? [X0 : term,X1 : subst > term > subst > $o] : (($true != (sP44 @ X1)) & ! [X2 : term] : (($true != (X1 @ id @ X2 @ id)) | ($true = (X1 @ id @ (sub @ X0 @ (push @ X2 @ id)) @ id))) & ((X1 @ id @ (lam @ (sub @ X0 @ (push @ one @ sh))) @ id) != $true))) & (! [X3 : term,X4 : subst > term > subst > $o] : (($true = (sP44 @ X4)) | ? [X5 : term] : (((X4 @ id @ X5 @ id) = $true) & ((X4 @ id @ (sub @ X3 @ (push @ X5 @ id)) @ id) != $true)) | ((X4 @ id @ (lam @ (sub @ X3 @ (push @ one @ sh))) @ id) = $true)) | ($true != sP45))),
% 15.02/3.54 inference(rectify,[status(thm)],[f430])).
% 15.02/3.54 thf(f430,plain,(
% 15.02/3.54 (($true = sP45) | ? [X222 : term,X223 : subst > term > subst > $o] : (((sP44 @ X223) != $true) & ! [X224 : term] : (((X223 @ id @ X224 @ id) != $true) | ($true = (X223 @ id @ (sub @ X222 @ (push @ X224 @ id)) @ id))) & ($true != (X223 @ id @ (lam @ (sub @ X222 @ (push @ one @ sh))) @ id)))) & (! [X222 : term,X223 : subst > term > subst > $o] : (((sP44 @ X223) = $true) | ? [X224 : term] : (((X223 @ id @ X224 @ id) = $true) & ($true != (X223 @ id @ (sub @ X222 @ (push @ X224 @ id)) @ id))) | ($true = (X223 @ id @ (lam @ (sub @ X222 @ (push @ one @ sh))) @ id))) | ($true != sP45))),
% 15.02/3.54 inference(nnf_transformation,[status(thm)],[f61])).
% 15.02/3.54 thf(f3268,plain,(
% 15.02/3.54 spl654_241 | ~spl654_73),
% 15.02/3.54 inference(avatar_split_clause,[status(thm)],[f1422,f2197,f2898])).
% 15.02/3.54 thf(f2898,definition,(
% 15.02/3.54 spl654_241 <=> (hoasinduction_lem3aaa = $true)),
% 15.02/3.54 introduced(definition,[new_symbols(naming,[spl654_241])],[avatar_definition])).
% 15.02/3.54 thf(f1422,plain,(
% 15.02/3.54 (hoasinduction_lem3aaa = $true) | ($true != sP45)),
% 15.02/3.54 inference(cnf_transformation,[status(thm)],[f749])).
% 15.02/3.54 thf(f3128,plain,(
% 15.02/3.54 ~spl654_294 | spl654_73),
% 15.02/3.54 inference(avatar_split_clause,[status(thm)],[f1069,f2197,f3126])).
% 15.02/3.54 thf(f1069,plain,(
% 15.02/3.54 ($true != (sP44 @ sK322)) | ($true = sP45)),
% 15.02/3.54 inference(cnf_transformation,[status(thm)],[f434])).
% 15.02/3.54 thf(f2934,plain,(
% 15.02/3.54 ~spl654_250 | ~spl654_241),
% 15.02/3.54 inference(avatar_split_clause,[status(thm)],[f1531,f2898,f2932])).
% 15.02/3.54 thf(f1531,plain,(
% 15.02/3.54 ((sP112 @ sK653) != $true) | (hoasinduction_lem3aaa != $true)),
% 15.02/3.54 inference(cnf_transformation,[status(thm)],[f768])).
% 15.02/3.54 thf(f768,plain,(
% 15.02/3.54 ((hoasinduction_lem3aaa != $true) | (((sP112 @ sK653) != $true) & ($true != (sP111 @ sK653)))) & ((hoasinduction_lem3aaa = $true) | ! [X1 : subst > term > subst > $o] : (((sP112 @ X1) = $true) | ($true = (sP111 @ X1))))),
% 15.02/3.54 inference(skolemisation,[status(esa),new_symbols(skolem,[sK653])],[f766,f767])).
% 15.02/3.54 thf(f767,plain,(
% 15.02/3.54 ? [X0 : subst > term > subst > $o] : (((sP112 @ X0) != $true) & ($true != (sP111 @ X0))) => (((sP112 @ sK653) != $true) & ($true != (sP111 @ sK653)))),
% 15.02/3.54 introduced(definition,[],[choice_axiom])).
% 15.02/3.54 thf(f766,plain,(
% 15.02/3.54 ((hoasinduction_lem3aaa != $true) | ? [X0 : subst > term > subst > $o] : (((sP112 @ X0) != $true) & ($true != (sP111 @ X0)))) & ((hoasinduction_lem3aaa = $true) | ! [X1 : subst > term > subst > $o] : (((sP112 @ X1) = $true) | ($true = (sP111 @ X1))))),
% 15.02/3.54 inference(rectify,[status(thm)],[f765])).
% 15.02/3.54 thf(f765,plain,(
% 15.02/3.54 ((hoasinduction_lem3aaa != $true) | ? [X0 : subst > term > subst > $o] : (((sP112 @ X0) != $true) & ($true != (sP111 @ X0)))) & ((hoasinduction_lem3aaa = $true) | ! [X0 : subst > term > subst > $o] : (((sP112 @ X0) = $true) | ($true = (sP111 @ X0))))),
% 15.02/3.54 inference(nnf_transformation,[status(thm)],[f130])).
% 15.02/3.54 thf(f130,plain,(
% 15.02/3.54 ! [X0 : subst > term > subst > $o] : (((sP112 @ X0) = $true) | ($true = (sP111 @ X0))) <~> (hoasinduction_lem3aaa = $true)),
% 15.02/3.54 inference(definition_folding,[status(thm)],[f15,f129,f128,f127])).
% 15.02/3.54 thf(f15,plain,(
% 15.02/3.54 ! [X0 : subst > term > subst > $o] : (? [X1 : subst > term > term] : (! [X6 : term] : (((X0 @ id @ (X1 @ id @ X6) @ id) = $true) | ((X0 @ id @ X6 @ id) != $true)) & ? [X2 : term] : ! [X3 : subst,X4 : term,X5 : subst] : (((sub @ X2 @ (push @ (sub @ X4 @ X3) @ (comp @ X5 @ X3))) = (X1 @ (comp @ X5 @ X3) @ (sub @ X4 @ X3))) & ((sub @ (sub @ X2 @ (push @ X4 @ X5)) @ X3) = (sub @ (X1 @ X5 @ X4) @ X3))) & ((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X1 @ Y0 @ Y1))))) @ id) != $true)) | ! [X7 : term] : (($true = (X0 @ id @ (lam @ (sub @ X7 @ (push @ one @ sh))) @ id)) | ? [X8 : term] : (($true = (X0 @ id @ X8 @ id)) & ($true != (X0 @ id @ (sub @ X7 @ (push @ X8 @ id)) @ id))))) <~> (hoasinduction_lem3aaa = $true)),
% 15.02/3.54 inference(flattening,[status(thm)],[f14])).
% 15.02/3.54 thf(f14,plain,(
% 15.02/3.54 (hoasinduction_lem3aaa = $true) <~> ! [X0 : subst > term > subst > $o] : (! [X7 : term] : (($true = (X0 @ id @ (lam @ (sub @ X7 @ (push @ one @ sh))) @ id)) | ? [X8 : term] : (($true = (X0 @ id @ X8 @ id)) & ($true != (X0 @ id @ (sub @ X7 @ (push @ X8 @ id)) @ id)))) | ? [X1 : subst > term > term] : ((((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X1 @ Y0 @ Y1))))) @ id) != $true) & ! [X6 : term] : (((X0 @ id @ (X1 @ id @ X6) @ id) = $true) | ((X0 @ id @ X6 @ id) != $true))) & ? [X2 : term] : ! [X3 : subst,X4 : term,X5 : subst] : (((sub @ X2 @ (push @ (sub @ X4 @ X3) @ (comp @ X5 @ X3))) = (X1 @ (comp @ X5 @ X3) @ (sub @ X4 @ X3))) & ((sub @ (sub @ X2 @ (push @ X4 @ X5)) @ X3) = (sub @ (X1 @ X5 @ X4) @ X3)))))),
% 15.02/3.54 inference(ennf_transformation,[status(thm)],[f9])).
% 15.02/3.54 thf(f9,plain,(
% 15.02/3.54 ~((hoasinduction_lem3aaa = $true) <=> ! [X0 : subst > term > subst > $o] : (! [X1 : subst > term > term] : (? [X2 : term] : ! [X3 : subst,X4 : term,X5 : subst] : (((sub @ X2 @ (push @ (sub @ X4 @ X3) @ (comp @ X5 @ X3))) = (X1 @ (comp @ X5 @ X3) @ (sub @ X4 @ X3))) & ((sub @ (sub @ X2 @ (push @ X4 @ X5)) @ X3) = (sub @ (X1 @ X5 @ X4) @ X3))) => (! [X6 : term] : (((X0 @ id @ X6 @ id) = $true) => ((X0 @ id @ (X1 @ id @ X6) @ id) = $true)) => ((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X1 @ Y0 @ Y1))))) @ id) = $true))) => ! [X7 : term] : (! [X8 : term] : (($true = (X0 @ id @ X8 @ id)) => ($true = (X0 @ id @ (sub @ X7 @ (push @ X8 @ id)) @ id))) => ($true = (X0 @ id @ (lam @ (sub @ X7 @ (push @ one @ sh))) @ id)))))),
% 15.02/3.54 inference(rectify,[status(thm)],[f6])).
% 15.02/3.54 thf(f6,plain,(
% 15.02/3.54 ~(! [X0 : subst > term > subst > $o] : (! [X1 : subst > term > term] : (? [X2 : term] : ! [X3 : subst,X4 : term,X5 : subst] : (((sub @ X2 @ (push @ (sub @ X4 @ X3) @ (comp @ X5 @ X3))) = (X1 @ (comp @ X5 @ X3) @ (sub @ X4 @ X3))) & ((sub @ (sub @ X2 @ (push @ X4 @ X5)) @ X3) = (sub @ (X1 @ X5 @ X4) @ X3))) => (! [X6 : term] : (((X0 @ id @ X6 @ id) = $true) => ((X0 @ id @ (X1 @ id @ X6) @ id) = $true)) => ((X0 @ id @ (hoaslam @ id @ (^[Y0 : subst]: ((^[Y1 : term]: (X1 @ Y0 @ Y1))))) @ id) = $true))) => ! [X9 : term] : (! [X10 : term] : (((X0 @ id @ X10 @ id) = $true) => ((X0 @ id @ (sub @ X9 @ (push @ X10 @ id)) @ id) = $true)) => ($true = (X0 @ id @ (lam @ (sub @ X9 @ (push @ one @ sh))) @ id)))) <=> (hoasinduction_lem3aaa = $true))),
% 15.02/3.54 inference(fool_elimination,[status(thm)],[f5])).
% 15.02/3.54 thf(f5,plain,(
% 15.02/3.54 ~(! [X0 : subst > term > subst > $o] : (! [X1 : subst > term > term] : (? [X2 : term] : ! [X3 : subst,X4 : term,X5 : subst] : (((sub @ X2 @ (push @ (sub @ X4 @ X3) @ (comp @ X5 @ X3))) = (X1 @ (comp @ X5 @ X3) @ (sub @ X4 @ X3))) & ((sub @ (sub @ X2 @ (push @ X4 @ X5)) @ X3) = (sub @ (X1 @ X5 @ X4) @ X3))) => (! [X6 : term] : ((X0 @ id @ X6 @ id) => (X0 @ id @ (X1 @ id @ X6) @ id)) => (X0 @ id @ (hoaslam @ id @ (^[X7 : subst, X8 : term] : (X1 @ X7 @ X8))) @ id))) => ! [X9 : term] : (! [X10 : term] : ((X0 @ id @ X10 @ id) => (X0 @ id @ (sub @ X9 @ (push @ X10 @ id)) @ id)) => (X0 @ id @ (lam @ (sub @ X9 @ (push @ one @ sh))) @ id))) = hoasinduction_lem3aaa)),
% 15.02/3.54 inference(rectify,[status(thm)],[f3])).
% 15.02/3.54 thf(f3,negated_conjecture,(
% 15.02/3.54 ~(! [X10 : subst > term > subst > $o] : (! [X18 : subst > term > term] : (? [X19 : term] : ! [X25 : subst,X13 : term,X14 : subst] : (((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)) = (sub @ X19 @ (push @ (sub @ X13 @ X25) @ (comp @ X14 @ X25)))) & ((sub @ (X18 @ X14 @ X13) @ X25) = (sub @ (sub @ X19 @ (push @ X13 @ X14)) @ X25))) => (! [X13 : term] : ((X10 @ id @ X13 @ id) => (X10 @ id @ (X18 @ id @ X13) @ id)) => (X10 @ id @ (hoaslam @ id @ (^[X14 : subst, X13 : term] : (X18 @ X14 @ X13))) @ id))) => ! [X13 : term] : (! [X15 : term] : ((X10 @ id @ X15 @ id) => (X10 @ id @ (sub @ X13 @ (push @ X15 @ id)) @ id)) => (X10 @ id @ (lam @ (sub @ X13 @ (push @ one @ sh))) @ id))) = hoasinduction_lem3aaa)),
% 15.02/3.54 inference(negated_conjecture,[status(cth)],[f2])).
% 15.02/3.54 thf(f2,conjecture,(
% 15.02/3.54 (! [X10 : subst > term > subst > $o] : (! [X18 : subst > term > term] : (? [X19 : term] : ! [X25 : subst,X13 : term,X14 : subst] : (((X18 @ (comp @ X14 @ X25) @ (sub @ X13 @ X25)) = (sub @ X19 @ (push @ (sub @ X13 @ X25) @ (comp @ X14 @ X25)))) & ((sub @ (X18 @ X14 @ X13) @ X25) = (sub @ (sub @ X19 @ (push @ X13 @ X14)) @ X25))) => (! [X13 : term] : ((X10 @ id @ X13 @ id) => (X10 @ id @ (X18 @ id @ X13) @ id)) => (X10 @ id @ (hoaslam @ id @ (^[X14 : subst, X13 : term] : (X18 @ X14 @ X13))) @ id))) => ! [X13 : term] : (! [X15 : term] : ((X10 @ id @ X15 @ id) => (X10 @ id @ (sub @ X13 @ (push @ X15 @ id)) @ id)) => (X10 @ id @ (lam @ (sub @ X13 @ (push @ one @ sh))) @ id))) = hoasinduction_lem3aaa)),
% 15.02/3.54 file('/export/starexec/sandbox2/tmp/tmp.xoR6yAHn1s/DTF2THF_17021.p',hoasinduction_lem3aaa)).
% 15.02/3.54 thf(f2903,plain,(
% 15.02/3.54 ~spl654_241 | ~spl654_242),
% 15.02/3.54 inference(avatar_split_clause,[status(thm)],[f1530,f2901,f2898])).
% 15.02/3.54 thf(f1530,plain,(
% 15.02/3.54 (hoasinduction_lem3aaa != $true) | ($true != (sP111 @ sK653))),
% 15.02/3.54 inference(cnf_transformation,[status(thm)],[f768])).
% 15.02/3.54 thf(f2202,plain,(
% 15.02/3.54 spl654_73 | spl654_74),
% 15.02/3.54 inference(avatar_split_clause,[status(thm)],[f1644,f2200,f2197])).
% 15.02/3.54 thf(f1644,plain,(
% 15.02/3.54 ( ! [X2 : term] : (((sK322 @ (d2subst @ d_id) @ X2 @ (d2subst @ d_id)) != $true) | ($true = sP45) | ((sK322 @ (d2subst @ d_id) @ (sub @ sK321 @ (push @ X2 @ (d2subst @ d_id))) @ (d2subst @ d_id)) = $true)) )),
% 15.02/3.54 inference(definition_unfolding,[status(thm)],[f1068,f1388,f1388,f1388,f1388,f1388])).
% 15.02/3.54 thf(f1068,plain,(
% 15.02/3.54 ( ! [X2 : term] : (($true = sP45) | ((sK322 @ id @ X2 @ id) != $true) | ($true = (sK322 @ id @ (sub @ sK321 @ (push @ X2 @ id)) @ id))) )),
% 15.02/3.54 inference(cnf_transformation,[status(thm)],[f434])).
% 15.02/3.54 % SZS output end Proof for DTF2THF_17021
% 15.02/3.54 % (17454)------------------------------
% 15.02/3.54 % (17454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.02/3.54 % (17454)Termination reason: Refutation
% 15.02/3.54
% 15.02/3.54 % (17454)Memory used [KB]: 15351
% 15.02/3.54 % (17454)Time elapsed: 1.189 s
% 15.02/3.54 % (17454)Instructions burned: 3461 (million)
% 15.02/3.54 % (17454)------------------------------
% 15.02/3.54 % (17454)------------------------------
% 15.02/3.54 % (17358)Success in time 2.018 s
%------------------------------------------------------------------------------