%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW277+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n008.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 : Fri May 19 12:25:51 EDT 2023

% Result   : Theorem 144.57s 140.24s
% Output   : Proof 144.57s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SWW277+1 : TPTP v8.1.2. Released v5.2.0.
% 0.06/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n008.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Thu May 18 22:13:24 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 144.57/140.24  
% 144.57/140.24  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 144.57/140.24  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 144.57/140.24  %-----------------------------------------------------
% 144.57/140.24  ncf(matrix, plain, [(12633 ^ _227627) ^ [] : [v_thesis____], (798 ^ _227627) ^ [_252362, _252364, _252366, _252368, _252370, _252372] : [-(c_Polynomial_Oorder(_252372, _252368, _252364) = c_Polynomial_Oorder(_252370, _252366, _252362)), _252372 = _252370, _252368 = _252366, _252364 = _252362], (812 ^ _227627) ^ [_252850, _252852, _252854, _252856] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_252856, _252852) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_252854, _252850)), _252856 = _252854, _252852 = _252850], (822 ^ _227627) ^ [_253237, _253239, _253241, _253243, _253245, _253247] : [-(c_Power_Opower_Opower(_253247, _253243, _253239) = c_Power_Opower_Opower(_253245, _253241, _253237)), _253247 = _253245, _253243 = _253241, _253239 = _253237], (836 ^ _227627) ^ [_253781, _253783, _253785, _253787, _253789, _253791, _253793, _253795] : [-(c_If(_253795, _253791, _253787, _253783) = c_If(_253793, _253789, _253785, _253781)), _253795 = _253793, _253791 = _253789, _253787 = _253785, _253783 = _253781], (854 ^ _227627) ^ [_254498, _254500, _254502, _254504, _254506, _254508, _254510, _254512, _254514, _254516] : [-(c_Polynomial_Opoly__rec(_254516, _254512, _254508, _254504, _254500) = c_Polynomial_Opoly__rec(_254514, _254510, _254506, _254502, _254498)), _254516 = _254514, _254512 = _254510, _254508 = _254506, _254504 = _254502, _254500 = _254498], (876 ^ _227627) ^ [_255320, _255322, _255324, _255326, _255328, _255330] : [-(c_Polynomial_Osynthetic__div(_255330, _255326, _255322) = c_Polynomial_Osynthetic__div(_255328, _255324, _255320)), _255330 = _255328, _255326 = _255324, _255322 = _255320], (890 ^ _227627) ^ [_255808, _255810, _255812, _255814] : [-(c_Polynomial_Opoly(_255814, _255810) = c_Polynomial_Opoly(_255812, _255808)), _255814 = _255812, _255810 = _255808], (900 ^ _227627) ^ [_256195, _256197, _256199, _256201, _256203, _256205] : [-(c_Polynomial_Opcompose(_256205, _256201, _256197) = c_Polynomial_Opcompose(_256203, _256199, _256195)), _256205 = _256203, _256201 = _256199, _256197 = _256195], (914 ^ _227627) ^ [_256711, _256713, _256715, _256717, _256719, _256721] : [-(c_Polynomial_Omonom(_256721, _256717, _256713) = c_Polynomial_Omonom(_256719, _256715, _256711)), _256721 = _256719, _256717 = _256715, _256713 = _256711], (928 ^ _227627) ^ [_257199, _257201, _257203, _257205] : [-(c_Nat__Transfer_Otsub(_257205, _257201) = c_Nat__Transfer_Otsub(_257203, _257199)), _257205 = _257203, _257201 = _257199], (938 ^ _227627) ^ [_257530, _257532] : [_257532 = _257530, -(c_Power_Opower__class_Opower(_257532) = c_Power_Opower__class_Opower(_257530))], (944 ^ _227627) ^ [_257776, _257778, _257780, _257782] : [-(c_SMT_Oz3div(_257782, _257778) = c_SMT_Oz3div(_257780, _257776)), _257782 = _257780, _257778 = _257776], (954 ^ _227627) ^ [_258135, _258137, _258139, _258141] : [-(c_Groups_Osgn__class_Osgn(_258141, _258137) = c_Groups_Osgn__class_Osgn(_258139, _258135)), _258141 = _258139, _258137 = _258135], (964 ^ _227627) ^ [_258466, _258468] : [_258468 = _258466, -(c_Nat_OSuc(_258468) = c_Nat_OSuc(_258466))], (970 ^ _227627) ^ [_258740, _258742, _258744, _258746, _258748, _258750] : [-(c_Groups_Ominus__class_Ominus(_258750, _258746, _258742) = c_Groups_Ominus__class_Ominus(_258748, _258744, _258740)), _258750 = _258748, _258746 = _258744, _258742 = _258740], (984 ^ _227627) ^ [_259200, _259202] : [_259202 = _259200, -(c_Rings_Odvd__class_Odvd(_259202) = c_Rings_Odvd__class_Odvd(_259200))], (990 ^ _227627) ^ [_259446, _259448, _259450, _259452] : [-(c_Polynomial_Ocoeff(_259452, _259448) = c_Polynomial_Ocoeff(_259450, _259446)), _259452 = _259450, _259448 = _259446], (1000 ^ _227627) ^ [_259805, _259807, _259809, _259811] : [-(c_Polynomial_Odegree(_259811, _259807) = c_Polynomial_Odegree(_259809, _259805)), _259811 = _259809, _259807 = _259805], (1010 ^ _227627) ^ [_260192, _260194, _260196, _260198, _260200, _260202] : [-(c_Polynomial_Opoly__gcd(_260202, _260198, _260194) = c_Polynomial_Opoly__gcd(_260200, _260196, _260192)), _260202 = _260200, _260198 = _260196, _260194 = _260192], (1024 ^ _227627) ^ [_260708, _260710, _260712, _260714, _260716, _260718] : [-(c_Divides_Odiv__class_Odiv(_260718, _260714, _260710) = c_Divides_Odiv__class_Odiv(_260716, _260712, _260708)), _260718 = _260716, _260714 = _260712, _260710 = _260708], (1038 ^ _227627) ^ [_261224, _261226, _261228, _261230, _261232, _261234] : [-(c_Divides_Odiv__class_Omod(_261234, _261230, _261226) = c_Divides_Odiv__class_Omod(_261232, _261228, _261224)), _261234 = _261232, _261230 = _261228, _261226 = _261224], (1052 ^ _227627) ^ [_261740, _261742, _261744, _261746, _261748, _261750] : [-(c_Groups_Oplus__class_Oplus(_261750, _261746, _261742) = c_Groups_Oplus__class_Oplus(_261748, _261744, _261740)), _261750 = _261748, _261746 = _261744, _261742 = _261740], (1066 ^ _227627) ^ [_262228, _262230, _262232, _262234] : [-(tc_fun(_262234, _262230) = tc_fun(_262232, _262228)), _262234 = _262232, _262230 = _262228], (1076 ^ _227627) ^ [_262587, _262589, _262591, _262593] : [-(c_fequal(_262593, _262589) = c_fequal(_262591, _262587)), _262593 = _262591, _262589 = _262587], (1086 ^ _227627) ^ [_262946, _262948, _262950, _262952] : [-(hAPP(_262952, _262948) = hAPP(_262950, _262946)), _262952 = _262950, _262948 = _262946], (1096 ^ _227627) ^ [_263277, _263279] : [_263279 = _263277, -(c_Groups_Otimes__class_Otimes(_263279) = c_Groups_Otimes__class_Otimes(_263277))], (1102 ^ _227627) ^ [_263523, _263525, _263527, _263529] : [-(c_Groups_Ouminus__class_Ouminus(_263529, _263525) = c_Groups_Ouminus__class_Ouminus(_263527, _263523)), _263529 = _263527, _263525 = _263523], (1112 ^ _227627) ^ [_263910, _263912, _263914, _263916, _263918, _263920] : [-(c_Polynomial_OpCons(_263920, _263916, _263912) = c_Polynomial_OpCons(_263918, _263914, _263910)), _263920 = _263918, _263916 = _263914, _263912 = _263910], (1126 ^ _227627) ^ [_264370, _264372] : [_264372 = _264370, -(c_Groups_Oone__class_Oone(_264372) = c_Groups_Oone__class_Oone(_264370))], (1132 ^ _227627) ^ [_264588, _264590] : [_264590 = _264588, -(c_Groups_Ozero__class_Ozero(_264590) = c_Groups_Ozero__class_Ozero(_264588))], (1138 ^ _227627) ^ [_264786, _264788] : [_264788 = _264786, -(tc_Polynomial_Opoly(_264788) = tc_Polynomial_Opoly(_264786))], (2 ^ _227627) ^ [_227771] : [-(_227771 = _227771)], (4 ^ _227627) ^ [_227878, _227880] : [_227880 = _227878, -(_227878 = _227880)], (10 ^ _227627) ^ [_228082, _228084, _228086] : [-(_228086 = _228082), _228086 = _228084, _228084 = _228082], (20 ^ _227627) ^ [_228395, _228397] : [-(class_Lattices_Oab__semigroup__idem__mult(_228395)), _228397 = _228395, class_Lattices_Oab__semigroup__idem__mult(_228397)], (30 ^ _227627) ^ [_228774, _228776, _228778, _228780, _228782, _228784, _228786, _228788] : [-(c_Orderings_Oorder_Omono(_228786, _228782, _228778, _228774)), c_Orderings_Oorder_Omono(_228788, _228784, _228780, _228776), _228788 = _228786, _228784 = _228782, _228780 = _228778, _228776 = _228774], (52 ^ _227627) ^ [_229508, _229510, _229512, _229514] : [-(c_Polynomial_Opos__poly(_229512, _229508)), c_Polynomial_Opos__poly(_229514, _229510), _229514 = _229512, _229510 = _229508], (66 ^ _227627) ^ [_230036, _230038, _230040, _230042, _230044, _230046, _230048, _230050, _230052, _230054] : [-(c_Polynomial_Opdivmod__rel(_230052, _230048, _230044, _230040, _230036)), c_Polynomial_Opdivmod__rel(_230054, _230050, _230046, _230042, _230038), _230054 = _230052, _230050 = _230048, _230046 = _230044, _230042 = _230040, _230038 = _230036], (92 ^ _227627) ^ [_230967, _230969, _230971, _230973, _230975, _230977] : [-(c_Orderings_Oord__class_Oless__eq(_230975, _230971, _230967)), c_Orderings_Oord__class_Oless__eq(_230977, _230973, _230969), _230977 = _230975, _230973 = _230971, _230969 = _230967], (110 ^ _227627) ^ [_231576, _231578, _231580, _231582, _231584, _231586] : [-(c_Orderings_Oord__class_Oless(_231584, _231580, _231576)), c_Orderings_Oord__class_Oless(_231586, _231582, _231578), _231586 = _231584, _231582 = _231580, _231578 = _231576], (128 ^ _227627) ^ [_232129, _232131] : [-(class_Lattices_Oboolean__algebra(_232129)), _232131 = _232129, class_Lattices_Oboolean__algebra(_232131)], (138 ^ _227627) ^ [_232424, _232426] : [-(class_RealVector_Oreal__normed__div__algebra(_232424)), _232426 = _232424, class_RealVector_Oreal__normed__div__algebra(_232426)], (148 ^ _227627) ^ [_232719, _232721] : [-(class_RealVector_Oreal__normed__algebra__1(_232719)), _232721 = _232719, class_RealVector_Oreal__normed__algebra__1(_232721)], (158 ^ _227627) ^ [_233014, _233016] : [-(class_RealVector_Oreal__normed__algebra(_233014)), _233016 = _233014, class_RealVector_Oreal__normed__algebra(_233016)], (168 ^ _227627) ^ [_233309, _233311] : [-(class_RealVector_Oreal__normed__vector(_233309)), _233311 = _233309, class_RealVector_Oreal__normed__vector(_233311)], (178 ^ _227627) ^ [_233604, _233606] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_233604)), _233606 = _233604, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_233606)], (188 ^ _227627) ^ [_233899, _233901] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_233899)), _233901 = _233899, class_Groups_Oordered__cancel__ab__semigroup__add(_233901)], (198 ^ _227627) ^ [_234194, _234196] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_234194)), _234196 = _234194, class_Groups_Oordered__ab__semigroup__add__imp__le(_234196)], (208 ^ _227627) ^ [_234489, _234491] : [-(class_Rings_Olinordered__comm__semiring__strict(_234489)), _234491 = _234489, class_Rings_Olinordered__comm__semiring__strict(_234491)], (218 ^ _227627) ^ [_234784, _234786] : [-(class_Rings_Olinordered__semiring__1__strict(_234784)), _234786 = _234784, class_Rings_Olinordered__semiring__1__strict(_234786)], (228 ^ _227627) ^ [_235079, _235081] : [-(class_Rings_Olinordered__semiring__strict(_235079)), _235081 = _235079, class_Rings_Olinordered__semiring__strict(_235081)], (238 ^ _227627) ^ [_235374, _235376] : [-(class_Groups_Oordered__ab__semigroup__add(_235374)), _235376 = _235374, class_Groups_Oordered__ab__semigroup__add(_235376)], (248 ^ _227627) ^ [_235669, _235671] : [-(class_Groups_Oordered__comm__monoid__add(_235669)), _235671 = _235669, class_Groups_Oordered__comm__monoid__add(_235671)], (258 ^ _227627) ^ [_235964, _235966] : [-(class_Groups_Olinordered__ab__group__add(_235964)), _235966 = _235964, class_Groups_Olinordered__ab__group__add(_235966)], (268 ^ _227627) ^ [_236259, _236261] : [-(class_Groups_Ocancel__ab__semigroup__add(_236259)), _236261 = _236259, class_Groups_Ocancel__ab__semigroup__add(_236261)], (278 ^ _227627) ^ [_236554, _236556] : [-(class_Rings_Oring__1__no__zero__divisors(_236554)), _236556 = _236554, class_Rings_Oring__1__no__zero__divisors(_236556)], (288 ^ _227627) ^ [_236849, _236851] : [-(class_Rings_Oordered__cancel__semiring(_236849)), _236851 = _236849, class_Rings_Oordered__cancel__semiring(_236851)], (298 ^ _227627) ^ [_237144, _237146] : [-(class_Rings_Olinordered__ring__strict(_237144)), _237146 = _237144, class_Rings_Olinordered__ring__strict(_237146)], (308 ^ _227627) ^ [_237439, _237441] : [-(class_Rings_Oring__no__zero__divisors(_237439)), _237441 = _237439, class_Rings_Oring__no__zero__divisors(_237441)], (318 ^ _227627) ^ [_237734, _237736] : [-(class_Rings_Oordered__comm__semiring(_237734)), _237736 = _237734, class_Rings_Oordered__comm__semiring(_237736)], (328 ^ _227627) ^ [_238029, _238031] : [-(class_Rings_Olinordered__semiring__1(_238029)), _238031 = _238029, class_Rings_Olinordered__semiring__1(_238031)], (338 ^ _227627) ^ [_238324, _238326] : [-(class_Groups_Oordered__ab__group__add(_238324)), _238326 = _238324, class_Groups_Oordered__ab__group__add(_238326)], (348 ^ _227627) ^ [_238619, _238621] : [-(class_Groups_Ocancel__comm__monoid__add(_238619)), _238621 = _238619, class_Groups_Ocancel__comm__monoid__add(_238621)], (358 ^ _227627) ^ [_238914, _238916] : [-(class_Groups_Ocancel__semigroup__add(_238914)), _238916 = _238914, class_Groups_Ocancel__semigroup__add(_238916)], (368 ^ _227627) ^ [_239209, _239211] : [-(class_Rings_Olinordered__semiring(_239209)), _239211 = _239209, class_Rings_Olinordered__semiring(_239211)], (378 ^ _227627) ^ [_239504, _239506] : [-(class_Rings_Olinordered__semidom(_239504)), _239506 = _239504, class_Rings_Olinordered__semidom(_239506)], (388 ^ _227627) ^ [_239799, _239801] : [-(class_Groups_Oab__semigroup__mult(_239799)), _239801 = _239799, class_Groups_Oab__semigroup__mult(_239801)], (398 ^ _227627) ^ [_240094, _240096] : [-(class_Groups_Ocomm__monoid__mult(_240094)), _240096 = _240094, class_Groups_Ocomm__monoid__mult(_240096)], (408 ^ _227627) ^ [_240389, _240391] : [-(class_Groups_Oab__semigroup__add(_240389)), _240391 = _240389, class_Groups_Oab__semigroup__add(_240391)], (418 ^ _227627) ^ [_240684, _240686] : [-(class_Rings_Oordered__semiring(_240684)), _240686 = _240684, class_Rings_Oordered__semiring(_240686)], (428 ^ _227627) ^ [_240979, _240981] : [-(class_Rings_Ono__zero__divisors(_240979)), _240981 = _240979, class_Rings_Ono__zero__divisors(_240981)], (438 ^ _227627) ^ [_241274, _241276] : [-(class_Rings_Olinordered__ring(_241274)), _241276 = _241274, class_Rings_Olinordered__ring(_241276)], (448 ^ _227627) ^ [_241569, _241571] : [-(class_Divides_Osemiring__div(_241569)), _241571 = _241569, class_Divides_Osemiring__div(_241571)], (458 ^ _227627) ^ [_241864, _241866] : [-(class_Rings_Ocomm__semiring(_241864)), _241866 = _241864, class_Rings_Ocomm__semiring(_241866)], (468 ^ _227627) ^ [_242159, _242161] : [-(class_Rings_Ozero__neq__one(_242159)), _242161 = _242159, class_Rings_Ozero__neq__one(_242161)], (478 ^ _227627) ^ [_242454, _242456] : [-(class_Rings_Oordered__ring(_242454)), _242456 = _242454, class_Rings_Oordered__ring(_242456)], (488 ^ _227627) ^ [_242749, _242751] : [-(class_Orderings_Opreorder(_242749)), _242751 = _242749, class_Orderings_Opreorder(_242751)], (498 ^ _227627) ^ [_243044, _243046] : [-(class_Orderings_Olinorder(_243044)), _243046 = _243044, class_Orderings_Olinorder(_243046)], (508 ^ _227627) ^ [_243339, _243341] : [-(class_Groups_Omonoid__mult(_243339)), _243341 = _243339, class_Groups_Omonoid__mult(_243341)], (518 ^ _227627) ^ [_243634, _243636] : [-(class_Groups_Ocomm__monoid__add(_243634)), _243636 = _243634, class_Groups_Ocomm__monoid__add(_243636)], (528 ^ _227627) ^ [_243929, _243931] : [-(class_Groups_Omonoid__add(_243929)), _243931 = _243929, class_Groups_Omonoid__add(_243931)], (538 ^ _227627) ^ [_244224, _244226] : [-(class_Rings_Osemiring__0(_244224)), _244226 = _244224, class_Rings_Osemiring__0(_244226)], (548 ^ _227627) ^ [_244519, _244521] : [-(class_Groups_Ogroup__add(_244519)), _244521 = _244519, class_Groups_Ogroup__add(_244521)], (558 ^ _227627) ^ [_244814, _244816] : [-(class_Fields_Ofield(_244814)), _244816 = _244814, class_Fields_Ofield(_244816)], (568 ^ _227627) ^ [_245109, _245111] : [-(class_Divides_Oring__div(_245109)), _245111 = _245109, class_Divides_Oring__div(_245111)], (578 ^ _227627) ^ [_245404, _245406] : [-(class_Rings_Omult__zero(_245404)), _245406 = _245404, class_Rings_Omult__zero(_245406)], (588 ^ _227627) ^ [_245699, _245701] : [-(class_Orderings_Oorder(_245699)), _245701 = _245699, class_Orderings_Oorder(_245701)], (598 ^ _227627) ^ [_245994, _245996] : [-(class_Int_Oring__char__0(_245994)), _245996 = _245994, class_Int_Oring__char__0(_245996)], (608 ^ _227627) ^ [_246289, _246291] : [-(class_Rings_Ocomm__semiring__0(_246289)), _246291 = _246289, class_Rings_Ocomm__semiring__0(_246291)], (618 ^ _227627) ^ [_246584, _246586] : [-(class_Rings_Osemiring(_246584)), _246586 = _246584, class_Rings_Osemiring(_246586)], (628 ^ _227627) ^ [_246879, _246881] : [-(class_Orderings_Oord(_246879)), _246881 = _246879, class_Orderings_Oord(_246881)], (638 ^ _227627) ^ [_247174, _247176] : [-(class_Groups_Ouminus(_247174)), _247176 = _247174, class_Groups_Ouminus(_247176)], (648 ^ _227627) ^ [_247469, _247471] : [-(class_Rings_Olinordered__idom(_247469)), _247471 = _247469, class_Rings_Olinordered__idom(_247471)], (658 ^ _227627) ^ [_247764, _247766] : [-(class_Groups_Osgn__if(_247764)), _247766 = _247764, class_Groups_Osgn__if(_247766)], (668 ^ _227627) ^ [_248059, _248061] : [-(class_Rings_Ocomm__ring__1(_248059)), _248061 = _248059, class_Rings_Ocomm__ring__1(_248061)], (678 ^ _227627) ^ [_248354, _248356] : [-(class_Rings_Oring__1(_248354)), _248356 = _248354, class_Rings_Oring__1(_248356)], (688 ^ _227627) ^ [_248649, _248651] : [-(class_Groups_Oab__group__add(_248649)), _248651 = _248649, class_Groups_Oab__group__add(_248651)], (698 ^ _227627) ^ [_248944, _248946] : [-(class_Groups_Ominus(_248944)), _248946 = _248944, class_Groups_Ominus(_248946)], (708 ^ _227627) ^ [_249239, _249241] : [-(class_Power_Opower(_249239)), _249241 = _249239, class_Power_Opower(_249241)], (718 ^ _227627) ^ [_249534, _249536] : [-(class_Groups_Ozero(_249534)), _249536 = _249534, class_Groups_Ozero(_249536)], (728 ^ _227627) ^ [_249829, _249831] : [-(class_Rings_Ocomm__ring(_249829)), _249831 = _249829, class_Rings_Ocomm__ring(_249831)], (738 ^ _227627) ^ [_250124, _250126] : [-(class_Rings_Oring(_250124)), _250126 = _250124, class_Rings_Oring(_250126)], (748 ^ _227627) ^ [_250419, _250421] : [-(class_Rings_Oidom(_250419)), _250421 = _250419, class_Rings_Oidom(_250421)], (758 ^ _227627) ^ [_250714, _250716] : [-(class_Groups_Oone(_250714)), _250716 = _250714, class_Groups_Oone(_250716)], (768 ^ _227627) ^ [_251009, _251011] : [-(class_Rings_Ocomm__semiring__1(_251009)), _251011 = _251009, class_Rings_Ocomm__semiring__1(_251011)], (778 ^ _227627) ^ [_251304, _251306] : [-(class_Rings_Odvd(_251304)), _251306 = _251304, class_Rings_Odvd(_251306)], (788 ^ _227627) ^ [_251579, _251581] : [-(hBOOL(_251579)), _251581 = _251579, hBOOL(_251581)], (1144 ^ _227627) ^ [_265202, _265204] : [hAPP(_265202, 1145 ^ [_265202, _265204]) = hAPP(_265204, 1145 ^ [_265202, _265204]), -(_265202 = _265204)], (1151 ^ _227627) ^ [] : [-(v_x____ = v_a____)], (1153 ^ _227627) ^ [] : [v_qa____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))], (1155 ^ _227627) ^ [] : [v_s____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))], (1157 ^ _227627) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), v_s____)))], (1159 ^ _227627) ^ [] : [-(v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), v_r____))], (1161 ^ _227627) ^ [_265743] : [class_Rings_Ocomm__semiring__1(_265743), -(c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_265743)) = c_Polynomial_OpCons(_265743, c_Groups_Oone__class_Oone(_265743), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_265743))))], (1167 ^ _227627) ^ [_265959] : [class_Groups_Ozero(_265959), -(c_Polynomial_OpCons(_265959, c_Groups_Ozero__class_Ozero(_265959), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_265959))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_265959)))], (1173 ^ _227627) ^ [_266203, _266205, _266207] : [class_Groups_Ozero(_266203), 1176 ^ _227627 : [(1177 ^ _227627) ^ [] : [c_Polynomial_OpCons(_266203, _266205, _266207) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_266203)), 1180 ^ _227627 : [(1181 ^ _227627) ^ [] : [-(_266205 = c_Groups_Ozero__class_Ozero(_266203))], (1183 ^ _227627) ^ [] : [-(_266207 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_266203)))]]], (1185 ^ _227627) ^ [] : [-(c_Polynomial_OpCons(_266203, _266205, _266207) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_266203))), _266205 = c_Groups_Ozero__class_Ozero(_266203), _266207 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_266203))]]], (1195 ^ _227627) ^ [_266883, _266885] : [class_Rings_Ocomm__ring__1(_266883), -(c_Groups_Ouminus__class_Ouminus(_266883, _266885) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_266883), c_Groups_Ouminus__class_Ouminus(_266883, c_Groups_Oone__class_Oone(_266883))), _266885))], (1201 ^ _227627) ^ [_267123, _267125] : [class_Rings_Oring__1__no__zero__divisors(_267123), 1204 ^ _227627 : [(1215 ^ _227627) ^ [] : [1216 ^ _227627 : [(1217 ^ _227627) ^ [] : [_267125 = c_Groups_Oone__class_Oone(_267123)], (1219 ^ _227627) ^ [] : [_267125 = c_Groups_Ouminus__class_Ouminus(_267123, c_Groups_Oone__class_Oone(_267123))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_267123), _267125), _267125) = c_Groups_Oone__class_Oone(_267123))], (1205 ^ _227627) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_267123), _267125), _267125) = c_Groups_Oone__class_Oone(_267123), -(_267125 = c_Groups_Oone__class_Oone(_267123)), -(_267125 = c_Groups_Ouminus__class_Ouminus(_267123, c_Groups_Oone__class_Oone(_267123)))]]], (1224 ^ _227627) ^ [] : [-(v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), 1222 ^ []))], (1226 ^ _227627) ^ [_267885, _267887] : [class_Rings_Ocomm__semiring__0(_267885), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_267885)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_267885))), _267887) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_267885)))], (1232 ^ _227627) ^ [_268129, _268131] : [class_Rings_Ocomm__semiring__0(_268129), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_268129)), _268131), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_268129))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_268129)))], (1238 ^ _227627) ^ [] : [-(v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____))), v_s____))], (1240 ^ _227627) ^ [_268440, _268442, _268444] : [class_Groups_Oab__group__add(_268440), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_268440), c_Polynomial_OpCons(_268440, _268442, _268444)) = c_Polynomial_OpCons(_268440, c_Groups_Ouminus__class_Ouminus(_268440, _268442), c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_268440), _268444)))], (1246 ^ _227627) ^ [_268710, _268712, _268714] : [class_Groups_Oab__group__add(_268710), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_268710), c_Polynomial_OpCons(_268710, _268712, _268714)) = c_Polynomial_OpCons(_268710, c_Groups_Ouminus__class_Ouminus(_268710, _268712), c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_268710), _268714)))], (1252 ^ _227627) ^ [_268980, _268982, _268984] : [class_Rings_Oring(_268980), -(c_Groups_Ouminus__class_Ouminus(_268980, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_268980), _268982), _268984)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_268980), _268982), c_Groups_Ouminus__class_Ouminus(_268980, _268984)))], (1258 ^ _227627) ^ [] : [v_na____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (1260 ^ _227627) ^ [] : [c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (1262 ^ _227627) ^ [] : [v_pa____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))], (1264 ^ _227627) ^ [_269394, _269396] : [class_Rings_Ocomm__semiring__1(_269394), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_269394), _269396), c_Groups_Ozero__class_Ozero(_269394))))], (1270 ^ _227627) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), v_qa____)))], (1272 ^ _227627) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____))), v_pa____)))], (1274 ^ _227627) ^ [] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____), v_a____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))], (1276 ^ _227627) ^ [_269765] : [hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____), _269765) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), -(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_qa____), _269765) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))], (1282 ^ _227627) ^ [] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_s____), v_x____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))], (1284 ^ _227627) ^ [] : [c_Polynomial_Odegree(tc_Complex_Ocomplex, v_s____) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (1286 ^ _227627) ^ [_270086, _270088] : [class_Rings_Ocomm__semiring__1(_270086), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_270086), _270088), _270088)))], (1292 ^ _227627) ^ [_270308, _270310] : [class_Rings_Ocomm__semiring__1(_270308), -(hAPP(hAPP(c_Power_Opower__class_Opower(_270308), _270310), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_270308))], (1298 ^ _227627) ^ [_270536, _270538] : [class_Rings_Ocomm__semiring__1(_270536), -(hAPP(hAPP(c_Power_Opower__class_Opower(_270536), _270538), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _270538)], (1304 ^ _227627) ^ [_270788, _270790, _270792, _270794] : [class_Rings_Ocomm__semiring__1(_270788), -(hAPP(hAPP(c_Power_Opower__class_Opower(_270788), hAPP(hAPP(c_Power_Opower__class_Opower(_270788), _270790), _270792)), _270794) = hAPP(hAPP(c_Power_Opower__class_Opower(_270788), _270790), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _270792), _270794)))], (1310 ^ _227627) ^ [_271096, _271098, _271100, _271102] : [class_Rings_Ocomm__semiring__1(_271096), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_271096), _271098), _271100)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_271096), _271100), _271102)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_271096), _271098), _271102)))], (1324 ^ _227627) ^ [_271552, _271554] : [class_Rings_Ocomm__semiring__1(_271552), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_271552), c_Groups_Ozero__class_Ozero(_271552)), _271554)), -(_271554 = c_Groups_Ozero__class_Ozero(_271552))], (1334 ^ _227627) ^ [_271899, _271901, _271903, _271905] : [class_Rings_Ocomm__semiring__1(_271899), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_271899), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_271899), _271901), _271903)), _271905)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_271899), _271903), _271905)))], (1344 ^ _227627) ^ [_272288, _272290, _272292, _272294] : [class_Rings_Ocomm__semiring__1(_272288), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_272288), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_272288), _272290), _272292)), _272294)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_272288), _272290), _272294)))], (1354 ^ _227627) ^ [_272677, _272679, _272681, _272683] : [class_Rings_Odvd(_272677), _272679 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_272677), _272681), _272683), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_272677), _272681), _272679)))], (1364 ^ _227627) ^ [_273066, _273068, _273070, _273072, _273074] : [class_Rings_Ocomm__semiring__1(_273066), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_273066), _273068), _273070)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_273066), _273072), _273074)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_273066), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_273066), _273068), _273072)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_273066), _273070), _273074))))], (1378 ^ _227627) ^ [_273596, _273598, _273600, _273602] : [class_Rings_Ocomm__semiring__1(_273596), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_273596), _273598), _273600)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_273596), _273598), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_273596), _273602), _273600))))], (1388 ^ _227627) ^ [_273985, _273987, _273989, _273991] : [class_Rings_Ocomm__semiring__1(_273985), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_273985), _273987), _273989)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_273985), _273987), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_273985), _273989), _273991))))], (1398 ^ _227627) ^ [_274360, _274362, _274364] : [class_Rings_Ocomm__semiring__1(_274360), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_274360), _274362), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_274360), _274364), _274362))))], (1404 ^ _227627) ^ [_274618, _274620, _274622] : [class_Rings_Ocomm__semiring__1(_274618), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_274618), _274620), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_274618), _274620), _274622))))], (1410 ^ _227627) ^ [_274862, _274864] : [class_Rings_Ocomm__semiring__1(_274862), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_274862), c_Groups_Oone__class_Oone(_274862)), _274864)))], (1416 ^ _227627) ^ [_275102, _275104, _275106] : [class_Rings_Ocomm__ring__1(_275102), 1419 ^ _227627 : [(1420 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_275102), c_Groups_Ouminus__class_Ouminus(_275102, _275104)), _275106)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_275102), _275104), _275106)))], (1426 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_275102), _275104), _275106)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_275102), c_Groups_Ouminus__class_Ouminus(_275102, _275104)), _275106)))]]], (1432 ^ _227627) ^ [_275641, _275643, _275645] : [class_Rings_Ocomm__ring__1(_275641), 1435 ^ _227627 : [(1436 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_275641), _275643), c_Groups_Ouminus__class_Ouminus(_275641, _275645))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_275641), _275643), _275645)))], (1442 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_275641), _275643), _275645)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_275641), _275643), c_Groups_Ouminus__class_Ouminus(_275641, _275645))))]]], (1448 ^ _227627) ^ [_276194, _276196, _276198, _276200] : [class_Rings_Ocomm__semiring__1(_276194), -(hAPP(hAPP(c_Power_Opower__class_Opower(_276194), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_276194), _276196), _276198)), _276200) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_276194), hAPP(hAPP(c_Power_Opower__class_Opower(_276194), _276196), _276200)), hAPP(hAPP(c_Power_Opower__class_Opower(_276194), _276198), _276200)))], (1454 ^ _227627) ^ [_276480] : [class_Groups_Oab__group__add(_276480), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_276480), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_276480))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_276480)))], (1460 ^ _227627) ^ [_276736, _276738, _276740, _276742] : [class_Rings_Oidom(_276736), 1463 ^ _227627 : [(1474 ^ _227627) ^ [] : [1475 ^ _227627 : [(1476 ^ _227627) ^ [] : [_276738 = c_Groups_Ozero__class_Ozero(_276736)], (1478 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_276736), _276740), _276742))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_276736), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_276736), _276738), _276740)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_276736), _276738), _276742))))], (1464 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_276736), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_276736), _276738), _276740)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_276736), _276738), _276742))), -(_276738 = c_Groups_Ozero__class_Ozero(_276736)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_276736), _276740), _276742)))]]], (1482 ^ _227627) ^ [_277520, _277522, _277524, _277526] : [class_Rings_Oidom(_277520), 1485 ^ _227627 : [(1496 ^ _227627) ^ [] : [1497 ^ _227627 : [(1498 ^ _227627) ^ [] : [_277524 = c_Groups_Ozero__class_Ozero(_277520)], (1500 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_277520), _277522), _277526))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_277520), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_277520), _277522), _277524)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_277520), _277526), _277524))))], (1486 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_277520), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_277520), _277522), _277524)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_277520), _277526), _277524))), -(_277524 = c_Groups_Ozero__class_Ozero(_277520)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_277520), _277522), _277526)))]]], (1504 ^ _227627) ^ [_278290, _278292, _278294] : [class_Rings_Oidom(_278290), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_278290)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_278290)), c_Polynomial_OpCons(_278290, c_Groups_Ouminus__class_Ouminus(_278290, _278292), c_Polynomial_OpCons(_278290, c_Groups_Oone__class_Oone(_278290), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_278290))))), c_Polynomial_Oorder(_278290, _278292, _278294))), _278294)))], (1510 ^ _227627) ^ [_278626, _278628, _278630, _278632, _278634] : [class_Rings_Ocomm__semiring__1(_278626), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_278626), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_278626), _278628), _278630)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_278626), _278632), _278634)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_278626), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_278626), _278628), _278632)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_278626), _278630), _278634)))], (1516 ^ _227627) ^ [_278990, _278992, _278994, _278996, _278998] : [class_Rings_Ocomm__semiring__1(_278990), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_278990), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_278990), _278992), _278994)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_278990), _278996), _278998)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_278990), _278996), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_278990), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_278990), _278992), _278994)), _278998)))], (1522 ^ _227627) ^ [_279354, _279356, _279358, _279360, _279362] : [class_Rings_Ocomm__semiring__1(_279354), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_279354), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_279354), _279356), _279358)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_279354), _279360), _279362)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_279354), _279356), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_279354), _279358), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_279354), _279360), _279362))))], (1528 ^ _227627) ^ [_279704, _279706, _279708, _279710] : [class_Rings_Ocomm__semiring__1(_279704), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_279704), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_279704), _279706), _279708)), _279710) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_279704), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_279704), _279706), _279710)), _279708))], (1534 ^ _227627) ^ [_280016, _280018, _280020, _280022] : [class_Rings_Ocomm__semiring__1(_280016), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_280016), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_280016), _280018), _280020)), _280022) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_280016), _280018), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_280016), _280020), _280022)))], (1540 ^ _227627) ^ [_280328, _280330, _280332, _280334] : [class_Rings_Ocomm__semiring__1(_280328), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_280328), _280330), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_280328), _280332), _280334)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_280328), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_280328), _280330), _280332)), _280334))], (1546 ^ _227627) ^ [_280640, _280642, _280644, _280646] : [class_Rings_Ocomm__semiring__1(_280640), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_280640), _280642), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_280640), _280644), _280646)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_280640), _280644), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_280640), _280642), _280646)))], (1552 ^ _227627) ^ [_280938, _280940, _280942] : [class_Rings_Ocomm__semiring__1(_280938), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_280938), _280940), _280942) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_280938), _280942), _280940))], (1558 ^ _227627) ^ [_281226, _281228, _281230, _281232, _281234] : [class_Groups_Ozero(_281226), 1561 ^ _227627 : [(1562 ^ _227627) ^ [] : [c_Polynomial_OpCons(_281226, _281228, _281230) = c_Polynomial_OpCons(_281226, _281232, _281234), 1565 ^ _227627 : [(1566 ^ _227627) ^ [] : [-(_281228 = _281232)], (1568 ^ _227627) ^ [] : [-(_281230 = _281234)]]], (1570 ^ _227627) ^ [] : [-(c_Polynomial_OpCons(_281226, _281228, _281230) = c_Polynomial_OpCons(_281226, _281232, _281234)), _281228 = _281232, _281230 = _281234]]], (1580 ^ _227627) ^ [_281946, _281948, _281950] : [class_Rings_Ono__zero__divisors(_281946), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_281946), _281948), _281950) = c_Groups_Ozero__class_Ozero(_281946), -(_281948 = c_Groups_Ozero__class_Ozero(_281946)), -(_281950 = c_Groups_Ozero__class_Ozero(_281946))], (1594 ^ _227627) ^ [_282389, _282391, _282393] : [class_Rings_Ono__zero__divisors(_282389), -(_282391 = c_Groups_Ozero__class_Ozero(_282389)), -(_282393 = c_Groups_Ozero__class_Ozero(_282389)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_282389), _282391), _282393) = c_Groups_Ozero__class_Ozero(_282389)], (1608 ^ _227627) ^ [_282838, _282840, _282842] : [class_Rings_Oring__no__zero__divisors(_282838), 1611 ^ _227627 : [(1622 ^ _227627) ^ [] : [1623 ^ _227627 : [(1624 ^ _227627) ^ [] : [_282840 = c_Groups_Ozero__class_Ozero(_282838)], (1626 ^ _227627) ^ [] : [_282842 = c_Groups_Ozero__class_Ozero(_282838)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_282838), _282840), _282842) = c_Groups_Ozero__class_Ozero(_282838))], (1612 ^ _227627) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_282838), _282840), _282842) = c_Groups_Ozero__class_Ozero(_282838), -(_282840 = c_Groups_Ozero__class_Ozero(_282838)), -(_282842 = c_Groups_Ozero__class_Ozero(_282838))]]], (1630 ^ _227627) ^ [_283518, _283520] : [class_Rings_Ocomm__semiring__1(_283518), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_283518), _283520), c_Groups_Ozero__class_Ozero(_283518)) = c_Groups_Ozero__class_Ozero(_283518))], (1636 ^ _227627) ^ [_283750, _283752] : [class_Rings_Omult__zero(_283750), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_283750), _283752), c_Groups_Ozero__class_Ozero(_283750)) = c_Groups_Ozero__class_Ozero(_283750))], (1642 ^ _227627) ^ [_283982, _283984] : [class_Rings_Ocomm__semiring__1(_283982), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_283982), c_Groups_Ozero__class_Ozero(_283982)), _283984) = c_Groups_Ozero__class_Ozero(_283982))], (1648 ^ _227627) ^ [_284214, _284216] : [class_Rings_Omult__zero(_284214), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_284214), c_Groups_Ozero__class_Ozero(_284214)), _284216) = c_Groups_Ozero__class_Ozero(_284214))], (1654 ^ _227627) ^ [_284432] : [class_Rings_Ozero__neq__one(_284432), c_Groups_Ozero__class_Ozero(_284432) = c_Groups_Oone__class_Oone(_284432)], (1660 ^ _227627) ^ [_284629] : [class_Rings_Ozero__neq__one(_284629), c_Groups_Oone__class_Oone(_284629) = c_Groups_Ozero__class_Ozero(_284629)], (1666 ^ _227627) ^ [_284840, _284842] : [class_Rings_Ocomm__semiring__1(_284840), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_284840), _284842), c_Groups_Oone__class_Oone(_284840)) = _284842)], (1672 ^ _227627) ^ [_285068, _285070] : [class_Rings_Ocomm__semiring__1(_285068), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_285068), c_Groups_Oone__class_Oone(_285068)), _285070) = _285070)], (1678 ^ _227627) ^ [_285310, _285312, _285314] : [class_Rings_Oidom(_285310), 1681 ^ _227627 : [(1692 ^ _227627) ^ [] : [1693 ^ _227627 : [(1694 ^ _227627) ^ [] : [_285312 = _285314], (1696 ^ _227627) ^ [] : [_285312 = c_Groups_Ouminus__class_Ouminus(_285310, _285314)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_285310), _285312), _285312) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_285310), _285314), _285314))], (1682 ^ _227627) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_285310), _285312), _285312) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_285310), _285314), _285314), -(_285312 = _285314), -(_285312 = c_Groups_Ouminus__class_Ouminus(_285310, _285314))]]], (1700 ^ _227627) ^ [_286019, _286021, _286023] : [class_Rings_Oring(_286019), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_286019), c_Groups_Ouminus__class_Ouminus(_286019, _286021)), c_Groups_Ouminus__class_Ouminus(_286019, _286023)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_286019), _286021), _286023))], (1706 ^ _227627) ^ [_286291, _286293, _286295] : [class_Rings_Oring(_286291), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_286291), c_Groups_Ouminus__class_Ouminus(_286291, _286293)), _286295) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_286291), _286293), c_Groups_Ouminus__class_Ouminus(_286291, _286295)))], (1712 ^ _227627) ^ [_286563, _286565, _286567] : [class_Rings_Oring(_286563), -(c_Groups_Ouminus__class_Ouminus(_286563, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_286563), _286565), _286567)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_286563), c_Groups_Ouminus__class_Ouminus(_286563, _286565)), _286567))], (1718 ^ _227627) ^ [] : [v_qa____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_pa____), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_qa____), v_na____))))], (1725 ^ _227627) ^ [] : [-(v_pa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____))), 1723 ^ []))], (1727 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), c_Nat_OSuc(c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____)))), v_pa____))], (1729 ^ _227627) ^ [_287101, _287103, _287105] : [class_Rings_Oring__1(_287101), -(hAPP(hAPP(c_Power_Opower__class_Opower(_287101), c_Groups_Ouminus__class_Ouminus(_287101, _287103)), _287105) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_287101), hAPP(hAPP(c_Power_Opower__class_Opower(_287101), c_Groups_Ouminus__class_Ouminus(_287101, c_Groups_Oone__class_Oone(_287101))), _287105)), hAPP(hAPP(c_Power_Opower__class_Opower(_287101), _287103), _287105)))], (1735 ^ _227627) ^ [_287395, _287397] : [class_Power_Opower(_287395), class_Rings_Osemiring__0(_287395), 1742 ^ _227627 : [(1743 ^ _227627) ^ [] : [_287397 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_287395), c_Groups_Ozero__class_Ozero(_287395)), _287397) = c_Groups_Oone__class_Oone(_287395))], (1749 ^ _227627) ^ [] : [-(_287397 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_287395), c_Groups_Ozero__class_Ozero(_287395)), _287397) = c_Groups_Ozero__class_Ozero(_287395))]]], (1755 ^ _227627) ^ [_288010, _288012, _288014] : [class_Rings_Oidom(_288010), -(_288012 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_288010))), 1762 ^ _227627 : [(1763 ^ _227627) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_288010)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_288010)), c_Polynomial_OpCons(_288010, c_Groups_Ouminus__class_Ouminus(_288010, _288014), c_Polynomial_OpCons(_288010, c_Groups_Oone__class_Oone(_288010), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_288010))))), c_Polynomial_Oorder(_288010, _288014, _288012))), _288012)))], (1765 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_288010)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_288010)), c_Polynomial_OpCons(_288010, c_Groups_Ouminus__class_Ouminus(_288010, _288014), c_Polynomial_OpCons(_288010, c_Groups_Oone__class_Oone(_288010), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_288010))))), c_Nat_OSuc(c_Polynomial_Oorder(_288010, _288014, _288012)))), _288012))]]], (1767 ^ _227627) ^ [_288584, _288586, _288588] : [class_Rings_Oidom(_288584), -(_288586 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_288584))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_288584)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_288584)), c_Polynomial_OpCons(_288584, c_Groups_Ouminus__class_Ouminus(_288584, _288588), c_Polynomial_OpCons(_288584, c_Groups_Oone__class_Oone(_288584), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_288584))))), c_Nat_OSuc(c_Polynomial_Oorder(_288584, _288588, _288586)))), _288586))], (1777 ^ _227627) ^ [] : [c_Polynomial_Odegree(tc_Complex_Ocomplex, v_s____) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_pa____), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_qa____), v_na____))))], (1783 ^ _227627) ^ [_289134, _289136, _289138, _289140] : [class_Rings_Ocomm__semiring__1(_289134), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_289134), _289136), _289138)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_289134), hAPP(hAPP(c_Power_Opower__class_Opower(_289134), _289136), _289140)), hAPP(hAPP(c_Power_Opower__class_Opower(_289134), _289138), _289140))))], (1793 ^ _227627) ^ [_289511, _289513] : [class_Power_Opower(_289511), -(hAPP(hAPP(c_Power_Opower__class_Opower(_289511), _289513), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_289511))], (1799 ^ _227627) ^ [_289739, _289741] : [class_Groups_Omonoid__mult(_289739), -(hAPP(hAPP(c_Power_Opower__class_Opower(_289739), c_Groups_Oone__class_Oone(_289739)), _289741) = c_Groups_Oone__class_Oone(_289739))], (1805 ^ _227627) ^ [_289999, _290001, _290003, _290005] : [class_Groups_Ocomm__monoid__mult(_289999), -(hAPP(hAPP(c_Power_Opower__class_Opower(_289999), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_289999), _290001), _290003)), _290005) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_289999), hAPP(hAPP(c_Power_Opower__class_Opower(_289999), _290001), _290005)), hAPP(hAPP(c_Power_Opower__class_Opower(_289999), _290003), _290005)))], (1811 ^ _227627) ^ [] : [v_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (1813 ^ _227627) ^ [] : [-(c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p) = v_n)], (1815 ^ _227627) ^ [_290390] : [hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), _290390) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), -(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q), _290390) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))], (1821 ^ _227627) ^ [] : [-(c_Polynomial_Odegree(tc_Complex_Ocomplex, v_pa____) = v_na____)], (1823 ^ _227627) ^ [_290630] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _290630) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (1825 ^ _227627) ^ [_290754, _290756, _290758] : [class_Int_Oring__char__0(_290754), class_Rings_Oidom(_290754), 1832 ^ _227627 : [(1833 ^ _227627) ^ [] : [c_Polynomial_Opoly(_290754, _290756) = c_Polynomial_Opoly(_290754, _290758), -(_290756 = _290758)], (1839 ^ _227627) ^ [] : [_290756 = _290758, -(c_Polynomial_Opoly(_290754, _290756) = c_Polynomial_Opoly(_290754, _290758))]]], (1855 ^ _227627) ^ [_291632, _291634] : [1856 ^ _227627 : [(1857 ^ _227627) ^ [] : [_291634 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (1859 ^ _227627) ^ [] : [_291632 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _291632), _291634) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (1845 ^ _227627) ^ [_291368, _291370] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _291368), _291370) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_291370 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_291368 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (1863 ^ _227627) ^ [_291944, _291946, _291948] : [class_Groups_Ozero(_291944), -(_291946 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_291944))), -(c_Polynomial_Odegree(_291944, c_Polynomial_OpCons(_291944, _291948, _291946)) = c_Nat_OSuc(c_Polynomial_Odegree(_291944, _291946)))], (1873 ^ _227627) ^ [_292300, _292302, _292304] : [class_Groups_Ozero(_292300), 1876 ^ _227627 : [(1877 ^ _227627) ^ [] : [_292302 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_292300)), -(c_Polynomial_Odegree(_292300, c_Polynomial_OpCons(_292300, _292304, _292302)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1883 ^ _227627) ^ [] : [-(_292302 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_292300))), -(c_Polynomial_Odegree(_292300, c_Polynomial_OpCons(_292300, _292304, _292302)) = c_Nat_OSuc(c_Polynomial_Odegree(_292300, _292302)))]]], (1889 ^ _227627) ^ [_292820] : [class_Groups_Ozero(_292820), -(c_Polynomial_Odegree(_292820, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_292820))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1895 ^ _227627) ^ [_293036, _293038] : [class_Groups_Oab__group__add(_293036), -(c_Polynomial_Odegree(_293036, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_293036), _293038)) = c_Polynomial_Odegree(_293036, _293038))], (1901 ^ _227627) ^ [_293266, _293268] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_293266), c_Groups_Ozero__class_Ozero(_293266)), c_Nat_OSuc(_293268)) = c_Groups_Ozero__class_Ozero(_293266)), class_Power_Opower(_293266), class_Rings_Osemiring__0(_293266)], (1911 ^ _227627) ^ [_293603, _293605, _293607] : [class_Groups_Omonoid__mult(_293603), -(hAPP(hAPP(c_Power_Opower__class_Opower(_293603), _293605), c_Nat_OSuc(_293607)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_293603), hAPP(hAPP(c_Power_Opower__class_Opower(_293603), _293605), _293607)), _293605))], (1917 ^ _227627) ^ [_293883, _293885, _293887] : [class_Power_Opower(_293883), -(hAPP(hAPP(c_Power_Opower__class_Opower(_293883), _293885), c_Nat_OSuc(_293887)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_293883), _293885), hAPP(hAPP(c_Power_Opower__class_Opower(_293883), _293885), _293887)))], (1923 ^ _227627) ^ [_294149, _294151] : [class_Int_Oring__char__0(_294149), class_Rings_Oidom(_294149), 1930 ^ _227627 : [(1931 ^ _227627) ^ [] : [c_Polynomial_Opoly(_294149, _294151) = c_Polynomial_Opoly(_294149, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_294149))), -(_294151 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_294149)))], (1937 ^ _227627) ^ [] : [_294151 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_294149)), -(c_Polynomial_Opoly(_294149, _294151) = c_Polynomial_Opoly(_294149, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_294149))))]]], (1943 ^ _227627) ^ [_294724] : [class_Rings_Ocomm__semiring__1(_294724), -(c_Polynomial_Odegree(_294724, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_294724))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1949 ^ _227627) ^ [_294940, _294942] : [class_Groups_Ozero(_294940), -(c_Polynomial_Odegree(_294940, c_Polynomial_OpCons(_294940, _294942, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_294940)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1955 ^ _227627) ^ [_295184, _295186, _295188] : [class_Rings_Ocomm__semiring__1(_295184), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_295184), hAPP(hAPP(c_Power_Opower__class_Opower(_295184), _295186), _295188)), _295186) = hAPP(hAPP(c_Power_Opower__class_Opower(_295184), _295186), c_Nat_OSuc(_295188)))], (1961 ^ _227627) ^ [_295464, _295466, _295468] : [class_Rings_Ocomm__semiring__1(_295464), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_295464), _295466), hAPP(hAPP(c_Power_Opower__class_Opower(_295464), _295466), _295468)) = hAPP(hAPP(c_Power_Opower__class_Opower(_295464), _295466), c_Nat_OSuc(_295468)))], (1967 ^ _227627) ^ [_295744, _295746, _295748] : [class_Rings_Ocomm__semiring__1(_295744), -(hAPP(hAPP(c_Power_Opower__class_Opower(_295744), _295746), c_Nat_OSuc(_295748)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_295744), _295746), hAPP(hAPP(c_Power_Opower__class_Opower(_295744), _295746), _295748)))], (1973 ^ _227627) ^ [_296010, _296012] : [class_Rings_Ocomm__semiring__0(_296010), -(hAPP(c_Polynomial_Opoly(_296010, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_296010))), _296012) = c_Groups_Ozero__class_Ozero(_296010))], (1979 ^ _227627) ^ [_296270, _296272, _296274, _296276] : [class_Rings_Ocomm__semiring__0(_296270), -(hAPP(c_Polynomial_Opoly(_296270, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_296270)), _296272), _296274)), _296276) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_296270), hAPP(c_Polynomial_Opoly(_296270, _296272), _296276)), hAPP(c_Polynomial_Opoly(_296270, _296274), _296276)))], (1985 ^ _227627) ^ [_296576, _296578, _296580] : [class_Rings_Ocomm__ring(_296576), -(hAPP(c_Polynomial_Opoly(_296576, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_296576), _296578)), _296580) = c_Groups_Ouminus__class_Ouminus(_296576, hAPP(c_Polynomial_Opoly(_296576, _296578), _296580)))], (1991 ^ _227627) ^ [_296858, _296860, _296862, _296864] : [class_Rings_Ocomm__semiring__1(_296858), -(hAPP(c_Polynomial_Opoly(_296858, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_296858)), _296860), _296862)), _296864) = hAPP(hAPP(c_Power_Opower__class_Opower(_296858), hAPP(c_Polynomial_Opoly(_296858, _296860), _296864)), _296862))], (1997 ^ _227627) ^ [_297138, _297140] : [class_Rings_Ocomm__semiring__1(_297138), -(hAPP(c_Polynomial_Opoly(_297138, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_297138))), _297140) = c_Groups_Oone__class_Oone(_297138))], (2003 ^ _227627) ^ [_297398, _297400, _297402, _297404] : [class_Groups_Omonoid__mult(_297398), -(hAPP(hAPP(c_Power_Opower__class_Opower(_297398), _297400), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _297402), _297404)) = hAPP(hAPP(c_Power_Opower__class_Opower(_297398), hAPP(hAPP(c_Power_Opower__class_Opower(_297398), _297400), _297402)), _297404))], (2009 ^ _227627) ^ [_297678, _297680] : [class_Groups_Omonoid__mult(_297678), -(hAPP(hAPP(c_Power_Opower__class_Opower(_297678), _297680), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _297680)], (2015 ^ _227627) ^ [_297916, _297918, _297920] : [class_Rings_Oidom(_297916), 2018 ^ _227627 : [(2029 ^ _227627) ^ [] : [2030 ^ _227627 : [(2031 ^ _227627) ^ [] : [_297918 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_297916))], (2033 ^ _227627) ^ [] : [-(c_Polynomial_Oorder(_297916, _297920, _297918) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], -(hAPP(c_Polynomial_Opoly(_297916, _297918), _297920) = c_Groups_Ozero__class_Ozero(_297916))], (2019 ^ _227627) ^ [] : [hAPP(c_Polynomial_Opoly(_297916, _297918), _297920) = c_Groups_Ozero__class_Ozero(_297916), -(_297918 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_297916))), c_Polynomial_Oorder(_297916, _297920, _297918) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (2037 ^ _227627) ^ [_298618, _298620, _298622] : [class_Rings_Ocomm__semiring__1(_298618), -(c_Polynomial_Odegree(_298618, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_298618)), c_Polynomial_OpCons(_298618, _298620, c_Polynomial_OpCons(_298618, c_Groups_Oone__class_Oone(_298618), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_298618))))), _298622)) = _298622)], (2043 ^ _227627) ^ [_298900, _298902, _298904] : [class_Rings_Oidom(_298900), 2046 ^ _227627 : [(2047 ^ _227627) ^ [] : [hAPP(c_Polynomial_Opoly(_298900, _298902), _298904) = c_Groups_Ozero__class_Ozero(_298900), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_298900)), c_Polynomial_OpCons(_298900, c_Groups_Ouminus__class_Ouminus(_298900, _298904), c_Polynomial_OpCons(_298900, c_Groups_Oone__class_Oone(_298900), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_298900))))), _298902)))], (2053 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_298900)), c_Polynomial_OpCons(_298900, c_Groups_Ouminus__class_Ouminus(_298900, _298904), c_Polynomial_OpCons(_298900, c_Groups_Oone__class_Oone(_298900), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_298900))))), _298902)), -(hAPP(c_Polynomial_Opoly(_298900, _298902), _298904) = c_Groups_Ozero__class_Ozero(_298900))]]], (2059 ^ _227627) ^ [_299490, _299492, _299494] : [class_Rings_Oidom(_299490), 2062 ^ _227627 : [(2063 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_299490)), c_Polynomial_OpCons(_299490, _299492, c_Polynomial_OpCons(_299490, c_Groups_Oone__class_Oone(_299490), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_299490))))), _299494)), -(hAPP(c_Polynomial_Opoly(_299490, _299494), c_Groups_Ouminus__class_Ouminus(_299490, _299492)) = c_Groups_Ozero__class_Ozero(_299490))], (2069 ^ _227627) ^ [] : [hAPP(c_Polynomial_Opoly(_299490, _299494), c_Groups_Ouminus__class_Ouminus(_299490, _299492)) = c_Groups_Ozero__class_Ozero(_299490), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_299490)), c_Polynomial_OpCons(_299490, _299492, c_Polynomial_OpCons(_299490, c_Groups_Oone__class_Oone(_299490), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_299490))))), _299494)))]]], (2075 ^ _227627) ^ [_300080, _300082, _300084] : [class_Power_Opower(_300080), class_Rings_Omult__zero(_300080), class_Rings_Ono__zero__divisors(_300080), class_Rings_Ozero__neq__one(_300080), 2090 ^ _227627 : [(2091 ^ _227627) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_300080), _300082), _300084) = c_Groups_Ozero__class_Ozero(_300080), 2094 ^ _227627 : [(2095 ^ _227627) ^ [] : [-(_300082 = c_Groups_Ozero__class_Ozero(_300080))], (2097 ^ _227627) ^ [] : [_300084 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (2099 ^ _227627) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_300080), _300082), _300084) = c_Groups_Ozero__class_Ozero(_300080)), _300082 = c_Groups_Ozero__class_Ozero(_300080), -(_300084 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (2109 ^ _227627) ^ [_301049, _301051, _301053] : [class_Rings_Oring__1__no__zero__divisors(_301049), -(_301051 = c_Groups_Ozero__class_Ozero(_301049)), hAPP(hAPP(c_Power_Opower__class_Opower(_301049), _301051), _301053) = c_Groups_Ozero__class_Ozero(_301049)], (2119 ^ _227627) ^ [_301398, _301400, _301402] : [class_Groups_Omonoid__mult(_301398), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_301398), hAPP(hAPP(c_Power_Opower__class_Opower(_301398), _301400), _301402)), _301400) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_301398), _301400), hAPP(hAPP(c_Power_Opower__class_Opower(_301398), _301400), _301402)))], (2125 ^ _227627) ^ [_301647] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _301647)))], (2127 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(tc_Complex_Ocomplex, v_s____), v_na____))], (2129 ^ _227627) ^ [_301795] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _301795, v_na____), 2132 ^ _227627 : [(2133 ^ _227627) ^ [_302000, _302002] : [2135 ^ _227627 : [(2136 ^ _227627) ^ [] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, _302002), 2134 ^ [_301795, _302000, _302002]) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))], (2138 ^ _227627) ^ [] : [hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, _302000), 2134 ^ [_301795, _302000, _302002]) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)]], c_Polynomial_Odegree(tc_Complex_Ocomplex, _302002) = _301795, -(_301795 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), _302002), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), _302000), _301795))))]]], (2150 ^ _227627) ^ [_302602] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Oorder(tc_Complex_Ocomplex, _302602, v_pa____), v_na____))], (2152 ^ _227627) ^ [_302728, _302730, _302732] : [class_Rings_Oidom(_302728), 2155 ^ _227627 : [(2166 ^ _227627) ^ [] : [2167 ^ _227627 : [(2168 ^ _227627) ^ [] : [_302730 = _302732], (2170 ^ _227627) ^ [] : [_302730 = c_Groups_Ouminus__class_Ouminus(_302728, _302732)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_302728), _302730), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(_302728), _302732), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (2156 ^ _227627) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_302728), _302730), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(_302728), _302732), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_302730 = _302732), -(_302730 = c_Groups_Ouminus__class_Ouminus(_302728, _302732))]]], (2174 ^ _227627) ^ [_303423, _303425] : [_303423 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _303423), _303425), -(_303425 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_303423 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2184 ^ _227627) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (2186 ^ _227627) ^ [_303817, _303819] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _303817), _303819) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 2189 ^ _227627 : [(2190 ^ _227627) ^ [] : [-(_303817 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (2192 ^ _227627) ^ [] : [-(_303819 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (2194 ^ _227627) ^ [_304066, _304068] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _304066), _304068) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _304066 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _304068 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2204 ^ _227627) ^ [_304379, _304381] : [class_Groups_Ozero(_304379), 2207 ^ _227627 : [(2208 ^ _227627) ^ [] : [_304381 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_304379)), -(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_304379, _304381) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2214 ^ _227627) ^ [] : [-(_304381 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_304379))), -(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_304379, _304381) = c_Nat_OSuc(c_Polynomial_Odegree(_304379, _304381)))]]], (2220 ^ _227627) ^ [_304852] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _304852), _304852)))], (2222 ^ _227627) ^ [_304934] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _304934, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2224 ^ _227627) ^ [_305013] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _305013, c_Nat_OSuc(_305013)))], (2226 ^ _227627) ^ [_305123, _305125] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _305123, _305125), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_305123), c_Nat_OSuc(_305125)))], (2232 ^ _227627) ^ [_305316] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _305316))], (2234 ^ _227627) ^ [_305395] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(_305395)))], (2236 ^ _227627) ^ [_305534, _305536] : [_305534 = _305536, 2239 ^ _227627 : [(2240 ^ _227627) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _305534), _305536)))], (2242 ^ _227627) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _305536), _305534)))]]], (2244 ^ _227627) ^ [_305791, _305793] : [-(_305791 = _305793), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _305791), _305793)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _305793), _305791))], (2254 ^ _227627) ^ [_306141, _306143] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _306141), _306143)), 2259 ^ _227627 : [(2260 ^ _227627) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _306141), _306143)))], (2262 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _306143), _306141))]], -(_306141 = _306143)], (2266 ^ _227627) ^ [_306499, _306501] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _306499), _306501))), 2267 ^ _227627 : [(2274 ^ _227627) ^ [] : [_306499 = _306501], (2268 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _306499), _306501)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _306501), _306499)))]]], (2278 ^ _227627) ^ [_306936, _306938] : [2285 ^ _227627 : [(2286 ^ _227627) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _306936), _306938)))], (2288 ^ _227627) ^ [] : [_306936 = _306938]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _306936), _306938)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _306938), _306936)))], (2290 ^ _227627) ^ [_307296, _307298] : [2297 ^ _227627 : [(2298 ^ _227627) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _307296), _307298)))], (2300 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _307298), _307296))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _307296), _307298)), -(_307296 = _307298)], (2302 ^ _227627) ^ [_307706, _307708] : [-(_307706 = _307708), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _307706), _307708)), 2309 ^ _227627 : [(2310 ^ _227627) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _307706), _307708)))], (2312 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _307708), _307706))]]], (2314 ^ _227627) ^ [_308114, _308116] : [_308114 = _308116, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _308114), _308116)))], (2320 ^ _227627) ^ [_308334, _308336] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _308334), _308336)), 2323 ^ _227627 : [(2324 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _308336), _308334)), -(_308336 = _308334)], (2330 ^ _227627) ^ [] : [_308336 = _308334, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _308336), _308334)))]]], (2336 ^ _227627) ^ [_308819, _308821] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _308819), _308821)), 2341 ^ _227627 : [(2342 ^ _227627) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _308819), _308821)))], (2344 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _308821), _308819))]], -(_308819 = _308821)], (2348 ^ _227627) ^ [_309225, _309227] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _309225), _309227)), -(_309225 = _309227), 2355 ^ _227627 : [(2356 ^ _227627) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _309225), _309227)))], (2358 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _309227), _309225))]]], (2360 ^ _227627) ^ [_309633, _309635] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _309633), _309635)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _309635), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _309633, _309635))], (2370 ^ _227627) ^ [_309960, _309962, _309964] : [_309960 = _309962, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _309962), _309964)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _309960), _309964)))], (2380 ^ _227627) ^ [_310303, _310305, _310307] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _310303), _310305)), _310305 = _310307, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _310303), _310307)))], (2390 ^ _227627) ^ [_310632, _310634] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _310632), _310634)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _310634), _310632)), -(_310632 = _310634)], (2400 ^ _227627) ^ [_310951, _310953] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _310951), _310953)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _310953), _310951)), -(_310951 = _310953)], (2410 ^ _227627) ^ [_311284, _311286, _311288] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _311284), _311286)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _311286), _311288)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _311284), _311288)))], (2420 ^ _227627) ^ [_311637, _311639, _311641] : [_311637 = _311639, 2431 ^ _227627 : [(2432 ^ _227627) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _311637), _311641)))], (2434 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _311641), _311637))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _311639), _311641)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _311641), _311639)))], (2436 ^ _227627) ^ [_312174, _312176, _312178] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _312174), _312176)), 2447 ^ _227627 : [(2448 ^ _227627) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _312174), _312178)))], (2450 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _312178), _312174))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _312176), _312178)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _312178), _312176)))], (2452 ^ _227627) ^ [_312707, _312709] : [_312707 = _312709, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _312707), _312709)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _312709), _312707)))], (2462 ^ _227627) ^ [_313030, _313032] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _313030), _313032)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _313032), _313030))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _313032), _313030)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _313030), _313032)))], (2476 ^ _227627) ^ [_313467, _313469] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _313467), _313469))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _313467), _313469)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _313469), _313467)))], (2486 ^ _227627) ^ [_313799, _313801] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _313799), _313801)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _313801), _313799))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _313801), _313799)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _313799), _313801)))], (2500 ^ _227627) ^ [_314236, _314238] : [_314236 = _314238, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _314236), _314238)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _314238), _314236)))], (2510 ^ _227627) ^ [_314559, _314561] : [_314561 = _314559, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _314559), _314561)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _314561), _314559)))], (2520 ^ _227627) ^ [_314896, _314898, _314900] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _314896), _314898)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _314898), _314896))), _314898 = _314900, 2531 ^ _227627 : [(2532 ^ _227627) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _314896), _314900)))], (2534 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _314900), _314896))]]], (2536 ^ _227627) ^ [_315435, _315437, _315439] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _315435), _315437)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _315437), _315435))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _315437), _315439)), 2547 ^ _227627 : [(2548 ^ _227627) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _315435), _315439)))], (2550 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _315439), _315435))]]], (2552 ^ _227627) ^ [_315970, _315972] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _315970), _315972)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _315972), _315970))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _315972), _315970)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _315970), _315972)))], (2566 ^ _227627) ^ [_316421, _316423, _316425] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _316421), _316423)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _316423), _316421))), 2581 ^ _227627 : [(2582 ^ _227627) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _316421), _316425)))], (2584 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _316425), _316421))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _316423), _316425)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _316425), _316423)))], (2586 ^ _227627) ^ [_317062, _317064] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _317062), _317064)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _317064), _317062))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _317064), _317062)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _317062), _317064)))], (2600 ^ _227627) ^ [_317499, _317501] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_317499), _317501), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _317499, _317501))], (2606 ^ _227627) ^ [_317717, _317719] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _317717, _317719), 2609 ^ _227627 : [(2610 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _317719, c_Nat_OSuc(_317717)), -(_317719 = _317717)], (2616 ^ _227627) ^ [] : [_317719 = _317717, -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _317719, c_Nat_OSuc(_317717)))]]], (2622 ^ _227627) ^ [_318188, _318190] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _318188, _318190), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_318188), _318190))], (2628 ^ _227627) ^ [_318406, _318408] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _318406, _318408), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _318406, c_Nat_OSuc(_318408)))], (2634 ^ _227627) ^ [_318653, _318655] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_318653), _318655), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _318653, _318655))], (2640 ^ _227627) ^ [_318823, _318825] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _318823, _318825), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_318823), _318825))], (2646 ^ _227627) ^ [_319072, _319074] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _319072, c_Nat_OSuc(_319074)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _319072, _319074))], (2652 ^ _227627) ^ [_319242, _319244] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _319242, _319244), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _319242, c_Nat_OSuc(_319244)))], (2658 ^ _227627) ^ [_319491, _319493] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _319491, _319493), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_319491), _319493))], (2664 ^ _227627) ^ [_319661, _319663] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_319661), _319663), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _319661, _319663))], (2670 ^ _227627) ^ [_319851] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _319851, _319851)], (2672 ^ _227627) ^ [_319930] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _319930, _319930))], (2684 ^ _227627) ^ [_320326, _320328] : [2685 ^ _227627 : [(2686 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _320326, _320328)], (2688 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _320328, _320326)]], _320326 = _320328], (2674 ^ _227627) ^ [_320067, _320069] : [-(_320067 = _320069), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _320067, _320069)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _320069, _320067))], (2692 ^ _227627) ^ [_320617, _320619] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _320617, _320619)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _320619, _320617))], (2698 ^ _227627) ^ [_320861, _320863] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _320861, _320863), 2701 ^ _227627 : [(2702 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _320861, _320863))], (2704 ^ _227627) ^ [] : [_320861 = _320863]]], (2706 ^ _227627) ^ [_321103, _321105] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _321103, _321105)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _321103, _321105), -(_321103 = _321105)], (2726 ^ _227627) ^ [_321696, _321698] : [2727 ^ _227627 : [(2728 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _321696, _321698)], (2730 ^ _227627) ^ [] : [_321696 = _321698]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _321696, _321698))], (2716 ^ _227627) ^ [_321440, _321442] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _321440, _321442), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _321440, _321442)), -(_321440 = _321442)], (2734 ^ _227627) ^ [_321986, _321988] : [-(_321986 = _321988), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _321986, _321988)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _321988, _321986))], (2744 ^ _227627) ^ [_322265] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _322265, _322265)], (2746 ^ _227627) ^ [_322373, _322375] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _322373, _322375), _322375 = _322373], (2752 ^ _227627) ^ [_322586, _322588] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _322586, _322588), _322586 = _322588], (2758 ^ _227627) ^ [_322799, _322801] : [_322799 = _322801, -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _322799, _322801))], (2764 ^ _227627) ^ [_323011, _323013] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _323011, _323013), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _323011, _323013))], (2770 ^ _227627) ^ [_323225, _323227] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _323225, _323227), -(_323225 = _323227), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _323225, _323227))], (2780 ^ _227627) ^ [_323545, _323547, _323549] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _323545, _323547), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _323547, _323549), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _323545, _323549))], (2790 ^ _227627) ^ [_323860, _323862] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _323860, _323862), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _323862, _323860), -(_323860 = _323862)], (2800 ^ _227627) ^ [_324163, _324165] : [2801 ^ _227627 : [(2802 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _324163, _324165)], (2804 ^ _227627) ^ [] : [_324163 = _324165]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _324163, _324165))], (2808 ^ _227627) ^ [_324465, _324467, _324469] : [2809 ^ _227627 : [(2810 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _324465, _324467))], (2812 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(_324469, _324467), _324465))]], 2815 ^ _227627 : [(2816 ^ _227627) ^ [] : [-(_324465 = _324467)], (2818 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(_324469, _324467), _324465))]], 2821 ^ _227627 : [(2822 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _324467, _324465))], (2824 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(_324469, _324467), _324465))]], -(hBOOL(hAPP(hAPP(_324469, _324467), _324465)))], (2828 ^ _227627) ^ [_325156, _325158, _325160] : [class_Rings_Olinordered__idom(_325156), -(_325158 = _325160), -(c_Orderings_Oord__class_Oless(_325156, _325158, _325160)), -(c_Orderings_Oord__class_Oless(_325156, _325160, _325158))], (2842 ^ _227627) ^ [_325580, _325582, _325584] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _325580), _325582)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _325580), _325584))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _325580), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _325582, _325584))], (2852 ^ _227627) ^ [_325913] : [-(_325913 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _325913))], (2858 ^ _227627) ^ [_326122, _326124] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _326122, _326124), _326124 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (2864 ^ _227627) ^ [_326335, _326337] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _326335), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _326335, _326337), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _326337), _326335))], (2874 ^ _227627) ^ [_326619] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _326619, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2876 ^ _227627) ^ [_326742] : [-(_326742 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _326742))], (2882 ^ _227627) ^ [_326903] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _326903), _326903 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (2888 ^ _227627) ^ [_327082] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _327082, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2890 ^ _227627) ^ [_327205] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _327205, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_327205 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2896 ^ _227627) ^ [_327363] : [_327363 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _327363, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (2902 ^ _227627) ^ [_327542] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _327542))], (2904 ^ _227627) ^ [_327678, _327680, _327682, _327684] : [class_Rings_Olinordered__semidom(_327678), c_Orderings_Oord__class_Oless(_327678, c_Groups_Oone__class_Oone(_327678), _327680), 2911 ^ _227627 : [(2912 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_327678, hAPP(hAPP(c_Power_Opower__class_Opower(_327678), _327680), _327682), hAPP(hAPP(c_Power_Opower__class_Opower(_327678), _327680), _327684)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _327682, _327684))], (2918 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _327682, _327684), -(c_Orderings_Oord__class_Oless__eq(_327678, hAPP(hAPP(c_Power_Opower__class_Opower(_327678), _327680), _327682), hAPP(hAPP(c_Power_Opower__class_Opower(_327678), _327680), _327684)))]]], (2924 ^ _227627) ^ [_328353, _328355, _328357, _328359] : [class_Rings_Olinordered__semidom(_328353), c_Orderings_Oord__class_Oless(_328353, c_Groups_Oone__class_Oone(_328353), _328355), c_Orderings_Oord__class_Oless__eq(_328353, hAPP(hAPP(c_Power_Opower__class_Opower(_328353), _328355), _328357), hAPP(hAPP(c_Power_Opower__class_Opower(_328353), _328355), _328359)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _328357, _328359))], (2938 ^ _227627) ^ [_328838, _328840] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _328838, _328840)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _328840, c_Nat_OSuc(_328838)))], (2944 ^ _227627) ^ [_329011, _329013] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _329013, c_Nat_OSuc(_329011)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _329011, _329013)], (2960 ^ _227627) ^ [_329521, _329523] : [2961 ^ _227627 : [(2962 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _329521, _329523)], (2964 ^ _227627) ^ [] : [_329521 = _329523]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _329521, c_Nat_OSuc(_329523)))], (2950 ^ _227627) ^ [_329261, _329263] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _329261, c_Nat_OSuc(_329263)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _329261, _329263)), -(_329261 = _329263)], (2968 ^ _227627) ^ [_329844, _329846] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_329844), c_Nat_OSuc(_329846)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _329844, _329846))], (2974 ^ _227627) ^ [_330018, _330020] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _330018, _330020), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_330018), c_Nat_OSuc(_330020)))], (2980 ^ _227627) ^ [_330242, _330244] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _330242, _330244)), 2983 ^ _227627 : [(2984 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _330242, c_Nat_OSuc(_330244)), -(_330242 = _330244)], (2990 ^ _227627) ^ [] : [_330242 = _330244, -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _330242, c_Nat_OSuc(_330244)))]]], (2996 ^ _227627) ^ [_330716, _330718] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _330716, _330718)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _330716, c_Nat_OSuc(_330718)), -(_330718 = _330716)], (3006 ^ _227627) ^ [_331026, _331028] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _331026, _331028), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _331026, c_Nat_OSuc(_331028)))], (3012 ^ _227627) ^ [_331244, _331246] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _331244, _331246), -(c_Nat_OSuc(_331244) = _331246), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_331244), _331246))], (3022 ^ _227627) ^ [_331572, _331574, _331576] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _331572, _331574), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _331574, _331576), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_331572), _331576))], (3032 ^ _227627) ^ [_331891, _331893] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _331891, c_Nat_OSuc(_331893)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _331891, _331893)), -(_331891 = _331893)], (3042 ^ _227627) ^ [_332201, _332203] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_332201), _332203), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _332201, _332203))], (3048 ^ _227627) ^ [_332419, _332421] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_332419), c_Nat_OSuc(_332421)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _332419, _332421))], (3054 ^ _227627) ^ [_332611] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_332611), _332611)], (3056 ^ _227627) ^ [_332750, _332752] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _332750, _332752)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_332752), _332750))], (3062 ^ _227627) ^ [_332923, _332925] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_332925), _332923), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _332923, _332925)], (3078 ^ _227627) ^ [_333437, _333439] : [3079 ^ _227627 : [(3080 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _333437, _333439)], (3082 ^ _227627) ^ [] : [_333437 = c_Nat_OSuc(_333439)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _333437, c_Nat_OSuc(_333439)))], (3068 ^ _227627) ^ [_333173, _333175] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _333173, c_Nat_OSuc(_333175)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _333173, _333175)), -(_333173 = c_Nat_OSuc(_333175))], (3086 ^ _227627) ^ [_333764, _333766] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_333764), c_Nat_OSuc(_333766)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _333764, _333766))], (3092 ^ _227627) ^ [_333938, _333940] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _333938, _333940), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_333938), c_Nat_OSuc(_333940)))], (3098 ^ _227627) ^ [_334162, _334164] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _334162, _334164), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _334162, c_Nat_OSuc(_334164)))], (3104 ^ _227627) ^ [_334380, _334382] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _334380, c_Nat_OSuc(_334382)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _334380, _334382)), -(_334380 = c_Nat_OSuc(_334382))], (3114 ^ _227627) ^ [_334694, _334696] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_334694), _334696), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _334694, _334696))], (3120 ^ _227627) ^ [_334940, _334942, _334944, _334946] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _334940, _334942), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _334944, _334946), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _334940), _334944), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _334942), _334946)))], (3130 ^ _227627) ^ [_335303, _335305, _335307] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _335303, _335305), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _335307), _335303), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _335307), _335305)))], (3136 ^ _227627) ^ [_335561, _335563, _335565] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _335561, _335563), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _335561), _335565), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _335563), _335565)))], (3142 ^ _227627) ^ [_335776] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _335776, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _335776), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _335776), _335776))))], (3144 ^ _227627) ^ [_335867] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _335867, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _335867), _335867)))], (3156 ^ _227627) ^ [_336315, _336317, _336319] : [3157 ^ _227627 : [(3158 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _336317))], (3160 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _336315, _336319)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _336315), _336317), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _336319), _336317)))], (3146 ^ _227627) ^ [_336024, _336026, _336028] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _336024), _336026), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _336028), _336026)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _336026), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _336024, _336028))], (3174 ^ _227627) ^ [_336974, _336976, _336978] : [3175 ^ _227627 : [(3176 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _336974))], (3178 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _336976, _336978)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _336974), _336976), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _336974), _336978)))], (3164 ^ _227627) ^ [_336683, _336685, _336687] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _336683), _336685), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _336683), _336687)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _336683), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _336685, _336687))], (3182 ^ _227627) ^ [_337327, _337329, _337331, _337333] : [class_Rings_Olinordered__semidom(_337327), c_Orderings_Oord__class_Oless(_337327, _337329, _337331), c_Orderings_Oord__class_Oless__eq(_337327, c_Groups_Ozero__class_Ozero(_337327), _337329), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _337333), -(c_Orderings_Oord__class_Oless(_337327, hAPP(hAPP(c_Power_Opower__class_Opower(_337327), _337329), _337333), hAPP(hAPP(c_Power_Opower__class_Opower(_337327), _337331), _337333)))], (3200 ^ _227627) ^ [_337910, _337912, _337914, _337916] : [class_Rings_Olinordered__semiring__strict(_337910), c_Orderings_Oord__class_Oless__eq(_337910, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_337910), _337912), _337914), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_337910), _337912), _337916)), c_Orderings_Oord__class_Oless(_337910, c_Groups_Ozero__class_Ozero(_337910), _337912), -(c_Orderings_Oord__class_Oless__eq(_337910, _337914, _337916))], (3214 ^ _227627) ^ [_338394, _338396, _338398, _338400] : [class_Rings_Olinordered__semiring__strict(_338394), c_Orderings_Oord__class_Oless__eq(_338394, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_338394), _338396), _338398), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_338394), _338400), _338398)), c_Orderings_Oord__class_Oless(_338394, c_Groups_Ozero__class_Ozero(_338394), _338398), -(c_Orderings_Oord__class_Oless__eq(_338394, _338396, _338400))], (3228 ^ _227627) ^ [_338878, _338880, _338882, _338884] : [class_Rings_Olinordered__semiring__strict(_338878), c_Orderings_Oord__class_Oless(_338878, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_338878), _338880), _338882), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_338878), _338880), _338884)), c_Orderings_Oord__class_Oless__eq(_338878, c_Groups_Ozero__class_Ozero(_338878), _338880), -(c_Orderings_Oord__class_Oless(_338878, _338882, _338884))], (3242 ^ _227627) ^ [_339362, _339364, _339366, _339368] : [class_Rings_Olinordered__semiring(_339362), c_Orderings_Oord__class_Oless(_339362, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339362), _339364), _339366), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339362), _339364), _339368)), c_Orderings_Oord__class_Oless__eq(_339362, c_Groups_Ozero__class_Ozero(_339362), _339364), -(c_Orderings_Oord__class_Oless(_339362, _339366, _339368))], (3256 ^ _227627) ^ [_339846, _339848, _339850, _339852] : [class_Rings_Olinordered__semiring__strict(_339846), c_Orderings_Oord__class_Oless(_339846, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339846), _339848), _339850), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339846), _339852), _339850)), c_Orderings_Oord__class_Oless__eq(_339846, c_Groups_Ozero__class_Ozero(_339846), _339850), -(c_Orderings_Oord__class_Oless(_339846, _339848, _339852))], (3270 ^ _227627) ^ [_340330, _340332, _340334, _340336] : [class_Rings_Olinordered__semiring(_340330), c_Orderings_Oord__class_Oless(_340330, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_340330), _340332), _340334), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_340330), _340336), _340334)), c_Orderings_Oord__class_Oless__eq(_340330, c_Groups_Ozero__class_Ozero(_340330), _340334), -(c_Orderings_Oord__class_Oless(_340330, _340332, _340336))], (3284 ^ _227627) ^ [_340828, _340830, _340832, _340834, _340836] : [class_Rings_Olinordered__semiring__strict(_340828), c_Orderings_Oord__class_Oless__eq(_340828, _340830, _340832), c_Orderings_Oord__class_Oless(_340828, _340834, _340836), c_Orderings_Oord__class_Oless(_340828, c_Groups_Ozero__class_Ozero(_340828), _340830), c_Orderings_Oord__class_Oless__eq(_340828, c_Groups_Ozero__class_Ozero(_340828), _340834), -(c_Orderings_Oord__class_Oless(_340828, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_340828), _340830), _340834), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_340828), _340832), _340836)))], (3306 ^ _227627) ^ [_341550, _341552, _341554, _341556, _341558] : [class_Rings_Olinordered__semiring__strict(_341550), c_Orderings_Oord__class_Oless(_341550, _341552, _341554), c_Orderings_Oord__class_Oless__eq(_341550, _341556, _341558), c_Orderings_Oord__class_Oless__eq(_341550, c_Groups_Ozero__class_Ozero(_341550), _341552), c_Orderings_Oord__class_Oless(_341550, c_Groups_Ozero__class_Ozero(_341550), _341556), -(c_Orderings_Oord__class_Oless(_341550, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_341550), _341552), _341556), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_341550), _341554), _341558)))], (3328 ^ _227627) ^ [_342272, _342274, _342276, _342278, _342280] : [class_Rings_Olinordered__semiring__strict(_342272), c_Orderings_Oord__class_Oless(_342272, _342274, _342276), c_Orderings_Oord__class_Oless(_342272, _342278, _342280), c_Orderings_Oord__class_Oless__eq(_342272, c_Groups_Ozero__class_Ozero(_342272), _342274), c_Orderings_Oord__class_Oless__eq(_342272, c_Groups_Ozero__class_Ozero(_342272), _342278), -(c_Orderings_Oord__class_Oless(_342272, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_342272), _342274), _342278), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_342272), _342276), _342280)))], (3350 ^ _227627) ^ [_342994, _342996, _342998, _343000, _343002] : [class_Rings_Olinordered__semiring__strict(_342994), c_Orderings_Oord__class_Oless(_342994, _342996, _342998), c_Orderings_Oord__class_Oless(_342994, _343000, _343002), c_Orderings_Oord__class_Oless(_342994, c_Groups_Ozero__class_Ozero(_342994), _342998), c_Orderings_Oord__class_Oless__eq(_342994, c_Groups_Ozero__class_Ozero(_342994), _343000), -(c_Orderings_Oord__class_Oless(_342994, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_342994), _342996), _343000), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_342994), _342998), _343002)))], (3372 ^ _227627) ^ [_343702, _343704, _343706, _343708] : [class_Rings_Olinordered__ring__strict(_343702), c_Orderings_Oord__class_Oless(_343702, _343704, c_Groups_Ozero__class_Ozero(_343702)), 3379 ^ _227627 : [(3380 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_343702, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_343702), _343704), _343706), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_343702), _343704), _343708)), -(c_Orderings_Oord__class_Oless__eq(_343702, _343708, _343706))], (3386 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_343702, _343708, _343706), -(c_Orderings_Oord__class_Oless__eq(_343702, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_343702), _343704), _343706), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_343702), _343704), _343708)))]]], (3392 ^ _227627) ^ [_344377, _344379, _344381, _344383] : [class_Rings_Olinordered__ring__strict(_344377), c_Orderings_Oord__class_Oless(_344377, c_Groups_Ozero__class_Ozero(_344377), _344379), 3399 ^ _227627 : [(3400 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_344377, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_344377), _344379), _344381), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_344377), _344379), _344383)), -(c_Orderings_Oord__class_Oless__eq(_344377, _344381, _344383))], (3406 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_344377, _344381, _344383), -(c_Orderings_Oord__class_Oless__eq(_344377, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_344377), _344379), _344381), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_344377), _344379), _344383)))]]], (3412 ^ _227627) ^ [_345052, _345054, _345056, _345058] : [class_Rings_Olinordered__semidom(_345052), c_Orderings_Oord__class_Oless(_345052, hAPP(hAPP(c_Power_Opower__class_Opower(_345052), _345054), _345056), hAPP(hAPP(c_Power_Opower__class_Opower(_345052), _345058), _345056)), c_Orderings_Oord__class_Oless__eq(_345052, c_Groups_Ozero__class_Ozero(_345052), _345058), -(c_Orderings_Oord__class_Oless(_345052, _345054, _345058))], (3426 ^ _227627) ^ [_345536, _345538, _345540, _345542] : [class_Rings_Olinordered__semidom(_345536), c_Orderings_Oord__class_Oless(_345536, c_Groups_Oone__class_Oone(_345536), _345538), 3433 ^ _227627 : [(3434 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_345536, hAPP(hAPP(c_Power_Opower__class_Opower(_345536), _345538), _345540), hAPP(hAPP(c_Power_Opower__class_Opower(_345536), _345538), _345542)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _345540, _345542))], (3440 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _345540, _345542), -(c_Orderings_Oord__class_Oless(_345536, hAPP(hAPP(c_Power_Opower__class_Opower(_345536), _345538), _345540), hAPP(hAPP(c_Power_Opower__class_Opower(_345536), _345538), _345542)))]]], (3446 ^ _227627) ^ [_346211, _346213, _346215, _346217] : [class_Rings_Olinordered__semidom(_346211), c_Orderings_Oord__class_Oless(_346211, c_Groups_Oone__class_Oone(_346211), _346213), c_Orderings_Oord__class_Oless(_346211, hAPP(hAPP(c_Power_Opower__class_Opower(_346211), _346213), _346215), hAPP(hAPP(c_Power_Opower__class_Opower(_346211), _346213), _346217)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _346215, _346217))], (3460 ^ _227627) ^ [_346695, _346697, _346699, _346701] : [class_Rings_Olinordered__semidom(_346695), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _346697, _346699), c_Orderings_Oord__class_Oless(_346695, c_Groups_Oone__class_Oone(_346695), _346701), -(c_Orderings_Oord__class_Oless(_346695, hAPP(hAPP(c_Power_Opower__class_Opower(_346695), _346701), _346697), hAPP(hAPP(c_Power_Opower__class_Opower(_346695), _346701), _346699)))], (3474 ^ _227627) ^ [_347179, _347181, _347183, _347185] : [class_Rings_Olinordered__semidom(_347179), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _347181, _347183), c_Orderings_Oord__class_Oless__eq(_347179, c_Groups_Oone__class_Oone(_347179), _347185), -(c_Orderings_Oord__class_Oless__eq(_347179, hAPP(hAPP(c_Power_Opower__class_Opower(_347179), _347185), _347181), hAPP(hAPP(c_Power_Opower__class_Opower(_347179), _347185), _347183)))], (3488 ^ _227627) ^ [_347649, _347651, _347653] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _347649), c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _347649), _347651), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _347649), _347653)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _347651, _347653))], (3508 ^ _227627) ^ [_348285, _348287] : [3509 ^ _227627 : [(3510 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _348285)], (3512 ^ _227627) ^ [] : [_348287 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _348285), _348287)))], (3498 ^ _227627) ^ [_348017, _348019] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _348017), _348019)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _348017)), -(_348019 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3516 ^ _227627) ^ [_348616, _348618] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _348616, c_Nat_OSuc(_348618)), -(_348616 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 3524 ^ _227627 : [(3525 ^ _227627) ^ [] : [-(_348616 = c_Nat_OSuc(3523 ^ [_348616, _348618]))], (3527 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 3523 ^ [_348616, _348618], _348618))]]], (3529 ^ _227627) ^ [_349028, _349030] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _349028, c_Nat_OSuc(_349030))), 3530 ^ _227627 : [(3531 ^ _227627) ^ [] : [_349028 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3533 ^ _227627) ^ [_349197] : [_349028 = c_Nat_OSuc(_349197), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _349197, _349030)]]], (3541 ^ _227627) ^ [_349495] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _349495, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_349495 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3547 ^ _227627) ^ [_349653] : [_349653 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _349653, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (3553 ^ _227627) ^ [_349876] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _349876), -(_349876 = c_Nat_OSuc(3556 ^ [_349876]))], (3560 ^ _227627) ^ [_350091] : [3561 ^ _227627 : [(3562 ^ _227627) ^ [_350162] : [_350091 = c_Nat_OSuc(_350162)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _350091))], (3566 ^ _227627) ^ [_350339, _350341, _350343] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _350339), _350341)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _350339), _350343))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _350339), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _350341), _350343)))], (3576 ^ _227627) ^ [_350708, _350710, _350712] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _350708, _350710), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _350712), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _350712), _350708), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _350712), _350710)))], (3586 ^ _227627) ^ [_351061, _351063, _351065] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _351061, _351063), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _351065), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _351061), _351065), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _351063), _351065)))], (3596 ^ _227627) ^ [_351443, _351445, _351447] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _351443), _351445), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _351447), _351445)), 3599 ^ _227627 : [(3600 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _351445))], (3602 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _351443, _351447))]]], (3604 ^ _227627) ^ [_351718, _351720, _351722] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _351718), _351720), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _351722), _351720))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _351720), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _351718, _351722)], (3614 ^ _227627) ^ [_352102, _352104, _352106] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _352102), _352104), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _352102), _352106)), 3617 ^ _227627 : [(3618 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _352102))], (3620 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _352104, _352106))]]], (3622 ^ _227627) ^ [_352377, _352379, _352381] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _352377), _352379), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _352377), _352381))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _352377), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _352379, _352381)], (3632 ^ _227627) ^ [_352747, _352749] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _352747), _352749)), 3635 ^ _227627 : [(3636 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _352747))], (3638 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _352749))]]], (3640 ^ _227627) ^ [_353002, _353004] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _353002), _353004))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _353002), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _353004)], (3650 ^ _227627) ^ [_353364, _353366, _353368] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_353364)), _353366), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_353364)), _353368)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _353366, _353368))], (3656 ^ _227627) ^ [_353568, _353570, _353572] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _353570, _353572), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_353568)), _353570), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_353568)), _353572)))], (3662 ^ _227627) ^ [_353865, _353867, _353869] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_353865)), _353867), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_353865)), _353869)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _353867, _353869))], (3668 ^ _227627) ^ [_354069, _354071, _354073] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _354071, _354073), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_354069)), _354071), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_354069)), _354073)))], (3674 ^ _227627) ^ [_354351, _354353, _354355, _354357] : [class_Rings_Olinordered__semidom(_354351), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _354353, _354355), c_Orderings_Oord__class_Oless(_354351, c_Groups_Ozero__class_Ozero(_354351), _354357), c_Orderings_Oord__class_Oless(_354351, _354357, c_Groups_Oone__class_Oone(_354351)), -(c_Orderings_Oord__class_Oless(_354351, hAPP(hAPP(c_Power_Opower__class_Opower(_354351), _354357), _354355), hAPP(hAPP(c_Power_Opower__class_Opower(_354351), _354357), _354353)))], (3692 ^ _227627) ^ [_354938, _354940, _354942, _354944] : [class_Rings_Olinordered__semidom(_354938), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _354940, _354942), c_Orderings_Oord__class_Oless__eq(_354938, c_Groups_Ozero__class_Ozero(_354938), _354944), c_Orderings_Oord__class_Oless__eq(_354938, _354944, c_Groups_Oone__class_Oone(_354938)), -(c_Orderings_Oord__class_Oless__eq(_354938, hAPP(hAPP(c_Power_Opower__class_Opower(_354938), _354944), _354942), hAPP(hAPP(c_Power_Opower__class_Opower(_354938), _354944), _354940)))], (3710 ^ _227627) ^ [_355525, _355527, _355529, _355531] : [class_Rings_Olinordered__semidom(_355525), hAPP(hAPP(c_Power_Opower__class_Opower(_355525), _355527), _355529) = hAPP(hAPP(c_Power_Opower__class_Opower(_355525), _355531), _355529), c_Orderings_Oord__class_Oless__eq(_355525, c_Groups_Ozero__class_Ozero(_355525), _355527), c_Orderings_Oord__class_Oless__eq(_355525, c_Groups_Ozero__class_Ozero(_355525), _355531), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _355529), -(_355527 = _355531)], (3732 ^ _227627) ^ [_356193, _356195, _356197] : [class_Rings_Olinordered__semidom(_356193), c_Orderings_Oord__class_Oless(_356193, c_Groups_Oone__class_Oone(_356193), _356195), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _356197), -(c_Orderings_Oord__class_Oless(_356193, c_Groups_Oone__class_Oone(_356193), hAPP(hAPP(c_Power_Opower__class_Opower(_356193), _356195), _356197)))], (3746 ^ _227627) ^ [_356651, _356653, _356655, _356657] : [class_Rings_Olinordered__ring__strict(_356651), c_Orderings_Oord__class_Oless(_356651, _356653, _356655), c_Orderings_Oord__class_Oless(_356651, _356657, c_Groups_Ozero__class_Ozero(_356651)), -(c_Orderings_Oord__class_Oless(_356651, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_356651), _356657), _356655), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_356651), _356657), _356653)))], (3760 ^ _227627) ^ [_357135, _357137, _357139, _357141] : [class_Rings_Olinordered__ring__strict(_357135), c_Orderings_Oord__class_Oless(_357135, _357137, _357139), c_Orderings_Oord__class_Oless(_357135, _357141, c_Groups_Ozero__class_Ozero(_357135)), -(c_Orderings_Oord__class_Oless(_357135, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_357135), _357139), _357141), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_357135), _357137), _357141)))], (3774 ^ _227627) ^ [_357619, _357621, _357623, _357625] : [class_Rings_Olinordered__comm__semiring__strict(_357619), c_Orderings_Oord__class_Oless(_357619, _357621, _357623), c_Orderings_Oord__class_Oless(_357619, c_Groups_Ozero__class_Ozero(_357619), _357625), -(c_Orderings_Oord__class_Oless(_357619, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_357619), _357625), _357621), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_357619), _357625), _357623)))], (3788 ^ _227627) ^ [_358103, _358105, _358107, _358109] : [class_Rings_Olinordered__semiring__strict(_358103), c_Orderings_Oord__class_Oless(_358103, _358105, _358107), c_Orderings_Oord__class_Oless(_358103, c_Groups_Ozero__class_Ozero(_358103), _358109), -(c_Orderings_Oord__class_Oless(_358103, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_358103), _358109), _358105), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_358103), _358109), _358107)))], (3802 ^ _227627) ^ [_358587, _358589, _358591, _358593] : [class_Rings_Olinordered__semiring__strict(_358587), c_Orderings_Oord__class_Oless(_358587, _358589, _358591), c_Orderings_Oord__class_Oless(_358587, c_Groups_Ozero__class_Ozero(_358587), _358593), -(c_Orderings_Oord__class_Oless(_358587, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_358587), _358589), _358593), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_358587), _358591), _358593)))], (3816 ^ _227627) ^ [_359057, _359059, _359061] : [class_Rings_Olinordered__ring__strict(_359057), c_Orderings_Oord__class_Oless(_359057, _359059, c_Groups_Ozero__class_Ozero(_359057)), c_Orderings_Oord__class_Oless(_359057, _359061, c_Groups_Ozero__class_Ozero(_359057)), -(c_Orderings_Oord__class_Oless(_359057, c_Groups_Ozero__class_Ozero(_359057), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_359057), _359059), _359061)))], (3830 ^ _227627) ^ [_359505, _359507, _359509] : [class_Rings_Olinordered__semiring__strict(_359505), c_Orderings_Oord__class_Oless(_359505, _359507, c_Groups_Ozero__class_Ozero(_359505)), c_Orderings_Oord__class_Oless(_359505, c_Groups_Ozero__class_Ozero(_359505), _359509), -(c_Orderings_Oord__class_Oless(_359505, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_359505), _359507), _359509), c_Groups_Ozero__class_Ozero(_359505)))], (3844 ^ _227627) ^ [_359967, _359969, _359971, _359973] : [class_Rings_Olinordered__ring__strict(_359967), c_Orderings_Oord__class_Oless(_359967, _359969, c_Groups_Ozero__class_Ozero(_359967)), 3851 ^ _227627 : [(3852 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_359967, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_359967), _359969), _359971), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_359967), _359969), _359973)), -(c_Orderings_Oord__class_Oless(_359967, _359973, _359971))], (3858 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_359967, _359973, _359971), -(c_Orderings_Oord__class_Oless(_359967, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_359967), _359969), _359971), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_359967), _359969), _359973)))]]], (3864 ^ _227627) ^ [_360628, _360630, _360632] : [class_Rings_Olinordered__semiring__strict(_360628), c_Orderings_Oord__class_Oless(_360628, c_Groups_Ozero__class_Ozero(_360628), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_360628), _360630), _360632)), c_Orderings_Oord__class_Oless(_360628, c_Groups_Ozero__class_Ozero(_360628), _360632), -(c_Orderings_Oord__class_Oless(_360628, c_Groups_Ozero__class_Ozero(_360628), _360630))], (3878 ^ _227627) ^ [_361076, _361078, _361080] : [class_Rings_Olinordered__semiring__strict(_361076), c_Orderings_Oord__class_Oless(_361076, c_Groups_Ozero__class_Ozero(_361076), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_361076), _361078), _361080)), c_Orderings_Oord__class_Oless(_361076, c_Groups_Ozero__class_Ozero(_361076), _361078), -(c_Orderings_Oord__class_Oless(_361076, c_Groups_Ozero__class_Ozero(_361076), _361080))], (3892 ^ _227627) ^ [_361524, _361526, _361528] : [class_Rings_Olinordered__semiring__strict(_361524), c_Orderings_Oord__class_Oless(_361524, c_Groups_Ozero__class_Ozero(_361524), _361526), c_Orderings_Oord__class_Oless(_361524, _361528, c_Groups_Ozero__class_Ozero(_361524)), -(c_Orderings_Oord__class_Oless(_361524, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_361524), _361528), _361526), c_Groups_Ozero__class_Ozero(_361524)))], (3906 ^ _227627) ^ [_361972, _361974, _361976] : [class_Rings_Olinordered__semiring__strict(_361972), c_Orderings_Oord__class_Oless(_361972, c_Groups_Ozero__class_Ozero(_361972), _361974), c_Orderings_Oord__class_Oless(_361972, _361976, c_Groups_Ozero__class_Ozero(_361972)), -(c_Orderings_Oord__class_Oless(_361972, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_361972), _361974), _361976), c_Groups_Ozero__class_Ozero(_361972)))], (3920 ^ _227627) ^ [_362420, _362422, _362424] : [class_Rings_Olinordered__semiring__strict(_362420), c_Orderings_Oord__class_Oless(_362420, c_Groups_Ozero__class_Ozero(_362420), _362422), c_Orderings_Oord__class_Oless(_362420, c_Groups_Ozero__class_Ozero(_362420), _362424), -(c_Orderings_Oord__class_Oless(_362420, c_Groups_Ozero__class_Ozero(_362420), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_362420), _362422), _362424)))], (3934 ^ _227627) ^ [_362882, _362884, _362886, _362888] : [class_Rings_Olinordered__ring__strict(_362882), c_Orderings_Oord__class_Oless(_362882, c_Groups_Ozero__class_Ozero(_362882), _362884), 3941 ^ _227627 : [(3942 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_362882, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_362882), _362884), _362886), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_362882), _362884), _362888)), -(c_Orderings_Oord__class_Oless(_362882, _362886, _362888))], (3948 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_362882, _362886, _362888), -(c_Orderings_Oord__class_Oless(_362882, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_362882), _362884), _362886), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_362882), _362884), _362888)))]]], (3954 ^ _227627) ^ [_363557, _363559, _363561, _363563] : [class_Rings_Olinordered__ring__strict(_363557), 3957 ^ _227627 : [(3958 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_363557, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_363557), _363559), _363561), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_363557), _363559), _363563)), 3963 ^ _227627 : [(3964 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(_363557, c_Groups_Ozero__class_Ozero(_363557), _363559))], (3966 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(_363557, _363561, _363563))]], 3967 ^ _227627 : [(3968 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(_363557, _363559, c_Groups_Ozero__class_Ozero(_363557)))], (3970 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(_363557, _363563, _363561))]]], (3972 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(_363557, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_363557), _363559), _363561), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_363557), _363559), _363563))), 3973 ^ _227627 : [(3974 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_363557, c_Groups_Ozero__class_Ozero(_363557), _363559), c_Orderings_Oord__class_Oless(_363557, _363561, _363563)], (3980 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_363557, _363559, c_Groups_Ozero__class_Ozero(_363557)), c_Orderings_Oord__class_Oless(_363557, _363563, _363561)]]]]], (3988 ^ _227627) ^ [_364660, _364662, _364664, _364666] : [class_Rings_Olinordered__ring__strict(_364660), 3991 ^ _227627 : [(3992 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_364660, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_364660), _364662), _364664), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_364660), _364666), _364664)), 3997 ^ _227627 : [(3998 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(_364660, c_Groups_Ozero__class_Ozero(_364660), _364664))], (4000 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(_364660, _364662, _364666))]], 4001 ^ _227627 : [(4002 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(_364660, _364664, c_Groups_Ozero__class_Ozero(_364660)))], (4004 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(_364660, _364666, _364662))]]], (4006 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(_364660, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_364660), _364662), _364664), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_364660), _364666), _364664))), 4007 ^ _227627 : [(4008 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_364660, c_Groups_Ozero__class_Ozero(_364660), _364664), c_Orderings_Oord__class_Oless(_364660, _364662, _364666)], (4014 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_364660, _364664, c_Groups_Ozero__class_Ozero(_364660)), c_Orderings_Oord__class_Oless(_364660, _364666, _364662)]]]]], (4022 ^ _227627) ^ [_365735, _365737] : [class_Rings_Olinordered__ring(_365735), c_Orderings_Oord__class_Oless(_365735, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_365735), _365737), _365737), c_Groups_Ozero__class_Ozero(_365735))], (4028 ^ _227627) ^ [_365952] : [class_Rings_Olinordered__semidom(_365952), -(c_Orderings_Oord__class_Oless(_365952, c_Groups_Ozero__class_Ozero(_365952), c_Groups_Oone__class_Oone(_365952)))], (4034 ^ _227627) ^ [_366150] : [class_Rings_Olinordered__semidom(_366150), c_Orderings_Oord__class_Oless(_366150, c_Groups_Oone__class_Oone(_366150), c_Groups_Ozero__class_Ozero(_366150))], (4040 ^ _227627) ^ [_366377, _366379, _366381] : [class_Rings_Oordered__cancel__semiring(_366377), -(c_Orderings_Oord__class_Oless__eq(_366377, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_366377), _366379), _366381), c_Groups_Ozero__class_Ozero(_366377))), 4045 ^ _227627 : [(4046 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_366377, c_Groups_Ozero__class_Ozero(_366377), _366379), c_Orderings_Oord__class_Oless__eq(_366377, _366381, c_Groups_Ozero__class_Ozero(_366377))], (4052 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_366377, _366379, c_Groups_Ozero__class_Ozero(_366377)), c_Orderings_Oord__class_Oless__eq(_366377, c_Groups_Ozero__class_Ozero(_366377), _366381)]]], (4060 ^ _227627) ^ [_367006, _367008, _367010] : [class_Rings_Oordered__ring(_367006), -(c_Orderings_Oord__class_Oless__eq(_367006, c_Groups_Ozero__class_Ozero(_367006), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_367006), _367008), _367010))), 4065 ^ _227627 : [(4066 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_367006, c_Groups_Ozero__class_Ozero(_367006), _367008), c_Orderings_Oord__class_Oless__eq(_367006, c_Groups_Ozero__class_Ozero(_367006), _367010)], (4072 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_367006, _367008, c_Groups_Ozero__class_Ozero(_367006)), c_Orderings_Oord__class_Oless__eq(_367006, _367010, c_Groups_Ozero__class_Ozero(_367006))]]], (4080 ^ _227627) ^ [_367663, _367665, _367667, _367669, _367671] : [class_Rings_Oordered__semiring(_367663), c_Orderings_Oord__class_Oless__eq(_367663, _367665, _367667), c_Orderings_Oord__class_Oless__eq(_367663, _367669, _367671), c_Orderings_Oord__class_Oless__eq(_367663, c_Groups_Ozero__class_Ozero(_367663), _367667), c_Orderings_Oord__class_Oless__eq(_367663, c_Groups_Ozero__class_Ozero(_367663), _367669), -(c_Orderings_Oord__class_Oless__eq(_367663, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_367663), _367665), _367669), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_367663), _367667), _367671)))], (4102 ^ _227627) ^ [_368385, _368387, _368389, _368391, _368393] : [class_Rings_Oordered__semiring(_368385), c_Orderings_Oord__class_Oless__eq(_368385, _368387, _368389), c_Orderings_Oord__class_Oless__eq(_368385, _368391, _368393), c_Orderings_Oord__class_Oless__eq(_368385, c_Groups_Ozero__class_Ozero(_368385), _368387), c_Orderings_Oord__class_Oless__eq(_368385, c_Groups_Ozero__class_Ozero(_368385), _368391), -(c_Orderings_Oord__class_Oless__eq(_368385, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_368385), _368387), _368391), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_368385), _368389), _368393)))], (4124 ^ _227627) ^ [_369093, _369095, _369097, _369099] : [class_Rings_Oordered__ring(_369093), c_Orderings_Oord__class_Oless__eq(_369093, _369095, _369097), c_Orderings_Oord__class_Oless__eq(_369093, _369099, c_Groups_Ozero__class_Ozero(_369093)), -(c_Orderings_Oord__class_Oless__eq(_369093, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_369093), _369099), _369097), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_369093), _369099), _369095)))], (4138 ^ _227627) ^ [_369577, _369579, _369581, _369583] : [class_Rings_Oordered__ring(_369577), c_Orderings_Oord__class_Oless__eq(_369577, _369579, _369581), c_Orderings_Oord__class_Oless__eq(_369577, _369583, c_Groups_Ozero__class_Ozero(_369577)), -(c_Orderings_Oord__class_Oless__eq(_369577, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_369577), _369581), _369583), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_369577), _369579), _369583)))], (4152 ^ _227627) ^ [_370061, _370063, _370065, _370067] : [class_Rings_Oordered__comm__semiring(_370061), c_Orderings_Oord__class_Oless__eq(_370061, _370063, _370065), c_Orderings_Oord__class_Oless__eq(_370061, c_Groups_Ozero__class_Ozero(_370061), _370067), -(c_Orderings_Oord__class_Oless__eq(_370061, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_370061), _370067), _370063), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_370061), _370067), _370065)))], (4166 ^ _227627) ^ [_370545, _370547, _370549, _370551] : [class_Rings_Oordered__semiring(_370545), c_Orderings_Oord__class_Oless__eq(_370545, _370547, _370549), c_Orderings_Oord__class_Oless__eq(_370545, c_Groups_Ozero__class_Ozero(_370545), _370551), -(c_Orderings_Oord__class_Oless__eq(_370545, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_370545), _370551), _370547), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_370545), _370551), _370549)))], (4180 ^ _227627) ^ [_371029, _371031, _371033, _371035] : [class_Rings_Oordered__semiring(_371029), c_Orderings_Oord__class_Oless__eq(_371029, _371031, _371033), c_Orderings_Oord__class_Oless__eq(_371029, c_Groups_Ozero__class_Ozero(_371029), _371035), -(c_Orderings_Oord__class_Oless__eq(_371029, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_371029), _371031), _371035), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_371029), _371033), _371035)))], (4194 ^ _227627) ^ [_371499, _371501, _371503] : [class_Rings_Oordered__ring(_371499), c_Orderings_Oord__class_Oless__eq(_371499, _371501, c_Groups_Ozero__class_Ozero(_371499)), c_Orderings_Oord__class_Oless__eq(_371499, _371503, c_Groups_Ozero__class_Ozero(_371499)), -(c_Orderings_Oord__class_Oless__eq(_371499, c_Groups_Ozero__class_Ozero(_371499), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_371499), _371501), _371503)))], (4208 ^ _227627) ^ [_371947, _371949, _371951] : [class_Rings_Oordered__cancel__semiring(_371947), c_Orderings_Oord__class_Oless__eq(_371947, _371949, c_Groups_Ozero__class_Ozero(_371947)), c_Orderings_Oord__class_Oless__eq(_371947, c_Groups_Ozero__class_Ozero(_371947), _371951), -(c_Orderings_Oord__class_Oless__eq(_371947, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_371947), _371949), _371951), c_Groups_Ozero__class_Ozero(_371947)))], (4222 ^ _227627) ^ [_372395, _372397, _372399] : [class_Rings_Oordered__cancel__semiring(_372395), c_Orderings_Oord__class_Oless__eq(_372395, c_Groups_Ozero__class_Ozero(_372395), _372397), c_Orderings_Oord__class_Oless__eq(_372395, _372399, c_Groups_Ozero__class_Ozero(_372395)), -(c_Orderings_Oord__class_Oless__eq(_372395, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_372395), _372399), _372397), c_Groups_Ozero__class_Ozero(_372395)))], (4236 ^ _227627) ^ [_372843, _372845, _372847] : [class_Rings_Oordered__cancel__semiring(_372843), c_Orderings_Oord__class_Oless__eq(_372843, c_Groups_Ozero__class_Ozero(_372843), _372845), c_Orderings_Oord__class_Oless__eq(_372843, _372847, c_Groups_Ozero__class_Ozero(_372843)), -(c_Orderings_Oord__class_Oless__eq(_372843, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_372843), _372845), _372847), c_Groups_Ozero__class_Ozero(_372843)))], (4250 ^ _227627) ^ [_373291, _373293, _373295] : [class_Rings_Oordered__cancel__semiring(_373291), c_Orderings_Oord__class_Oless__eq(_373291, c_Groups_Ozero__class_Ozero(_373291), _373293), c_Orderings_Oord__class_Oless__eq(_373291, c_Groups_Ozero__class_Ozero(_373291), _373295), -(c_Orderings_Oord__class_Oless__eq(_373291, c_Groups_Ozero__class_Ozero(_373291), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_373291), _373293), _373295)))], (4264 ^ _227627) ^ [_373739, _373741, _373743] : [class_Rings_Olinordered__ring__strict(_373739), 4267 ^ _227627 : [(4268 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_373739, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_373739), _373741), _373743), c_Groups_Ozero__class_Ozero(_373739)), 4273 ^ _227627 : [(4274 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_373739, c_Groups_Ozero__class_Ozero(_373739), _373741))], (4276 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_373739, _373743, c_Groups_Ozero__class_Ozero(_373739)))]], 4277 ^ _227627 : [(4278 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_373739, _373741, c_Groups_Ozero__class_Ozero(_373739)))], (4280 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_373739, c_Groups_Ozero__class_Ozero(_373739), _373743))]]], (4282 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_373739, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_373739), _373741), _373743), c_Groups_Ozero__class_Ozero(_373739))), 4283 ^ _227627 : [(4284 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_373739, c_Groups_Ozero__class_Ozero(_373739), _373741), c_Orderings_Oord__class_Oless__eq(_373739, _373743, c_Groups_Ozero__class_Ozero(_373739))], (4290 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_373739, _373741, c_Groups_Ozero__class_Ozero(_373739)), c_Orderings_Oord__class_Oless__eq(_373739, c_Groups_Ozero__class_Ozero(_373739), _373743)]]]]], (4298 ^ _227627) ^ [_374788, _374790, _374792] : [class_Rings_Olinordered__ring__strict(_374788), 4301 ^ _227627 : [(4302 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_374788, c_Groups_Ozero__class_Ozero(_374788), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_374788), _374790), _374792)), 4307 ^ _227627 : [(4308 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_374788, c_Groups_Ozero__class_Ozero(_374788), _374790))], (4310 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_374788, c_Groups_Ozero__class_Ozero(_374788), _374792))]], 4311 ^ _227627 : [(4312 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_374788, _374790, c_Groups_Ozero__class_Ozero(_374788)))], (4314 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_374788, _374792, c_Groups_Ozero__class_Ozero(_374788)))]]], (4316 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_374788, c_Groups_Ozero__class_Ozero(_374788), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_374788), _374790), _374792))), 4317 ^ _227627 : [(4318 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_374788, c_Groups_Ozero__class_Ozero(_374788), _374790), c_Orderings_Oord__class_Oless__eq(_374788, c_Groups_Ozero__class_Ozero(_374788), _374792)], (4324 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_374788, _374790, c_Groups_Ozero__class_Ozero(_374788)), c_Orderings_Oord__class_Oless__eq(_374788, _374792, c_Groups_Ozero__class_Ozero(_374788))]]]]], (4332 ^ _227627) ^ [_375823, _375825] : [class_Rings_Olinordered__ring(_375823), -(c_Orderings_Oord__class_Oless__eq(_375823, c_Groups_Ozero__class_Ozero(_375823), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_375823), _375825), _375825)))], (4338 ^ _227627) ^ [_376053, _376055] : [class_Rings_Olinordered__idom(_376053), 4341 ^ _227627 : [(4342 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_376053, _376055, c_Groups_Ouminus__class_Ouminus(_376053, _376055)), -(c_Orderings_Oord__class_Oless(_376053, _376055, c_Groups_Ozero__class_Ozero(_376053)))], (4348 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_376053, _376055, c_Groups_Ozero__class_Ozero(_376053)), -(c_Orderings_Oord__class_Oless(_376053, _376055, c_Groups_Ouminus__class_Ouminus(_376053, _376055)))]]], (4354 ^ _227627) ^ [_376546, _376548, _376550] : [class_Rings_Olinordered__semidom(_376546), c_Orderings_Oord__class_Oless(_376546, c_Groups_Oone__class_Oone(_376546), _376548), c_Orderings_Oord__class_Oless(_376546, c_Groups_Oone__class_Oone(_376546), _376550), -(c_Orderings_Oord__class_Oless(_376546, c_Groups_Oone__class_Oone(_376546), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_376546), _376548), _376550)))], (4368 ^ _227627) ^ [_376994, _376996, _376998] : [class_Rings_Olinordered__semidom(_376994), c_Orderings_Oord__class_Oless(_376994, c_Groups_Ozero__class_Ozero(_376994), _376996), -(c_Orderings_Oord__class_Oless(_376994, c_Groups_Ozero__class_Ozero(_376994), hAPP(hAPP(c_Power_Opower__class_Opower(_376994), _376996), _376998)))], (4378 ^ _227627) ^ [_377315] : [class_Rings_Olinordered__semidom(_377315), -(c_Orderings_Oord__class_Oless__eq(_377315, c_Groups_Ozero__class_Ozero(_377315), c_Groups_Oone__class_Oone(_377315)))], (4384 ^ _227627) ^ [_377513] : [class_Rings_Olinordered__semidom(_377513), c_Orderings_Oord__class_Oless__eq(_377513, c_Groups_Oone__class_Oone(_377513), c_Groups_Ozero__class_Ozero(_377513))], (4390 ^ _227627) ^ [_377740, _377742, _377744] : [class_Rings_Olinordered__semidom(_377740), c_Orderings_Oord__class_Oless__eq(_377740, c_Groups_Ozero__class_Ozero(_377740), _377742), -(c_Orderings_Oord__class_Oless__eq(_377740, c_Groups_Ozero__class_Ozero(_377740), hAPP(hAPP(c_Power_Opower__class_Opower(_377740), _377742), _377744)))], (4400 ^ _227627) ^ [_378103, _378105, _378107, _378109] : [class_Rings_Olinordered__semidom(_378103), c_Orderings_Oord__class_Oless__eq(_378103, _378105, _378107), c_Orderings_Oord__class_Oless__eq(_378103, c_Groups_Ozero__class_Ozero(_378103), _378105), -(c_Orderings_Oord__class_Oless__eq(_378103, hAPP(hAPP(c_Power_Opower__class_Opower(_378103), _378105), _378109), hAPP(hAPP(c_Power_Opower__class_Opower(_378103), _378107), _378109)))], (4414 ^ _227627) ^ [_378587, _378589, _378591, _378593] : [class_Rings_Olinordered__semidom(_378587), c_Orderings_Oord__class_Oless(_378587, c_Groups_Oone__class_Oone(_378587), _378589), 4421 ^ _227627 : [(4422 ^ _227627) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_378587), _378589), _378591) = hAPP(hAPP(c_Power_Opower__class_Opower(_378587), _378589), _378593), -(_378591 = _378593)], (4428 ^ _227627) ^ [] : [_378591 = _378593, -(hAPP(hAPP(c_Power_Opower__class_Opower(_378587), _378589), _378591) = hAPP(hAPP(c_Power_Opower__class_Opower(_378587), _378589), _378593))]]], (4434 ^ _227627) ^ [_379242, _379244, _379246] : [class_Rings_Olinordered__semidom(_379242), c_Orderings_Oord__class_Oless__eq(_379242, c_Groups_Oone__class_Oone(_379242), _379244), -(c_Orderings_Oord__class_Oless__eq(_379242, c_Groups_Oone__class_Oone(_379242), hAPP(hAPP(c_Power_Opower__class_Opower(_379242), _379244), _379246)))], (4444 ^ _227627) ^ [_379577, _379579] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _379577), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _379579), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _379579), _379577)))], (4454 ^ _227627) ^ [_379894, _379896] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _379894), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _379896), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _379894, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _379894), _379896)))], (4464 ^ _227627) ^ [_380211, _380213] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _380211), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _380213), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _380211, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _380213), _380211)))], (4474 ^ _227627) ^ [_380557, _380559] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _380557), _380559)), 4477 ^ _227627 : [(4478 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _380557))], (4480 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _380559))]]], (4482 ^ _227627) ^ [_380812, _380814] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _380812), _380814))), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _380812), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _380814)], (4492 ^ _227627) ^ [_381131, _381133] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _381131), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _381131), _381133)))], (4498 ^ _227627) ^ [_381385, _381387, _381389, _381391] : [class_Rings_Ocomm__semiring__1(_381385), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _381387, _381389), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_381385), hAPP(hAPP(c_Power_Opower__class_Opower(_381385), _381391), _381387)), hAPP(hAPP(c_Power_Opower__class_Opower(_381385), _381391), _381389))))], (4508 ^ _227627) ^ [_381792, _381794, _381796, _381798, _381800] : [class_Rings_Ocomm__semiring__1(_381792), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_381792), _381794), _381796)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _381798, _381800), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_381792), hAPP(hAPP(c_Power_Opower__class_Opower(_381792), _381794), _381798)), hAPP(hAPP(c_Power_Opower__class_Opower(_381792), _381796), _381800))))], (4522 ^ _227627) ^ [_382324, _382326, _382328, _382330, _382332] : [class_Rings_Ocomm__semiring__1(_382324), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_382324), hAPP(hAPP(c_Power_Opower__class_Opower(_382324), _382326), _382328)), _382330)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _382332, _382328), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_382324), hAPP(hAPP(c_Power_Opower__class_Opower(_382324), _382326), _382332)), _382330)))], (4536 ^ _227627) ^ [_382814, _382816] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _382814), 4539 ^ _227627 : [(4540 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _382816), _382814)), _382814)), -(_382816 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (4546 ^ _227627) ^ [] : [_382816 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _382816), _382814)), _382814)))]]], (4552 ^ _227627) ^ [_383309, _383311] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _383309), 4555 ^ _227627 : [(4556 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _383309), _383311)), _383309)), -(_383311 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (4562 ^ _227627) ^ [] : [_383311 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _383309), _383311)), _383309)))]]], (4568 ^ _227627) ^ [_383818, _383820, _383822] : [class_Rings_Olinordered__semidom(_383818), c_Orderings_Oord__class_Oless__eq(_383818, c_Groups_Ozero__class_Ozero(_383818), _383820), c_Orderings_Oord__class_Oless__eq(_383818, _383820, c_Groups_Oone__class_Oone(_383818)), -(c_Orderings_Oord__class_Oless__eq(_383818, hAPP(hAPP(c_Power_Opower__class_Opower(_383818), _383820), c_Nat_OSuc(_383822)), _383820))], (4582 ^ _227627) ^ [_384266, _384268, _384270] : [class_Rings_Olinordered__idom(_384266), c_Orderings_Oord__class_Oless__eq(_384266, c_Groups_Ozero__class_Ozero(_384266), _384268), c_Orderings_Oord__class_Oless__eq(_384266, c_Groups_Ozero__class_Ozero(_384266), _384270), c_Orderings_Oord__class_Oless__eq(_384266, _384270, c_Groups_Oone__class_Oone(_384266)), -(c_Orderings_Oord__class_Oless__eq(_384266, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_384266), _384270), _384268), _384268))], (4600 ^ _227627) ^ [_384809, _384811, _384813] : [class_Rings_Olinordered__idom(_384809), c_Orderings_Oord__class_Oless__eq(_384809, c_Groups_Ozero__class_Ozero(_384809), _384811), c_Orderings_Oord__class_Oless__eq(_384809, c_Groups_Ozero__class_Ozero(_384809), _384813), c_Orderings_Oord__class_Oless__eq(_384809, _384813, c_Groups_Oone__class_Oone(_384809)), -(c_Orderings_Oord__class_Oless__eq(_384809, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_384809), _384811), _384813), _384811))], (4618 ^ _227627) ^ [_385352, _385354, _385356] : [class_Rings_Olinordered__semidom(_385352), c_Orderings_Oord__class_Oless(_385352, c_Groups_Oone__class_Oone(_385352), _385354), -(c_Orderings_Oord__class_Oless(_385352, hAPP(hAPP(c_Power_Opower__class_Opower(_385352), _385354), _385356), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_385352), _385354), hAPP(hAPP(c_Power_Opower__class_Opower(_385352), _385354), _385356))))], (4628 ^ _227627) ^ [_385729, _385731, _385733] : [class_Rings_Olinordered__semidom(_385729), c_Orderings_Oord__class_Oless(_385729, c_Groups_Oone__class_Oone(_385729), _385731), -(c_Orderings_Oord__class_Oless(_385729, c_Groups_Oone__class_Oone(_385729), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_385729), _385731), hAPP(hAPP(c_Power_Opower__class_Opower(_385729), _385731), _385733))))], (4638 ^ _227627) ^ [_386108, _386110, _386112, _386114] : [class_Rings_Olinordered__semidom(_386108), c_Orderings_Oord__class_Oless__eq(_386108, hAPP(hAPP(c_Power_Opower__class_Opower(_386108), _386110), c_Nat_OSuc(_386112)), hAPP(hAPP(c_Power_Opower__class_Opower(_386108), _386114), c_Nat_OSuc(_386112))), c_Orderings_Oord__class_Oless__eq(_386108, c_Groups_Ozero__class_Ozero(_386108), _386114), -(c_Orderings_Oord__class_Oless__eq(_386108, _386110, _386114))], (4652 ^ _227627) ^ [_386600, _386602, _386604, _386606] : [class_Rings_Olinordered__semidom(_386600), hAPP(hAPP(c_Power_Opower__class_Opower(_386600), _386602), c_Nat_OSuc(_386604)) = hAPP(hAPP(c_Power_Opower__class_Opower(_386600), _386606), c_Nat_OSuc(_386604)), c_Orderings_Oord__class_Oless__eq(_386600, c_Groups_Ozero__class_Ozero(_386600), _386602), c_Orderings_Oord__class_Oless__eq(_386600, c_Groups_Ozero__class_Ozero(_386600), _386606), -(_386602 = _386606)], (4670 ^ _227627) ^ [_387177, _387179, _387181] : [class_Rings_Olinordered__semidom(_387177), c_Orderings_Oord__class_Oless(_387177, c_Groups_Oone__class_Oone(_387177), _387179), -(c_Orderings_Oord__class_Oless(_387177, c_Groups_Oone__class_Oone(_387177), hAPP(hAPP(c_Power_Opower__class_Opower(_387177), _387179), c_Nat_OSuc(_387181))))], (4680 ^ _227627) ^ [_387530, _387532, _387534] : [class_Groups_Ozero(_387530), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_387530, c_Polynomial_OpCons(_387530, _387532, _387534)), c_Nat_OSuc(c_Polynomial_Odegree(_387530, _387534))))], (4686 ^ _227627) ^ [_387740] : [_387740 = c_Nat_OSuc(_387740)], (4688 ^ _227627) ^ [_387819] : [c_Nat_OSuc(_387819) = _387819], (4690 ^ _227627) ^ [_387957, _387959] : [c_Nat_OSuc(_387957) = c_Nat_OSuc(_387959), -(_387957 = _387959)], (4696 ^ _227627) ^ [_388127, _388129] : [_388127 = _388129, -(c_Nat_OSuc(_388127) = c_Nat_OSuc(_388129))], (4702 ^ _227627) ^ [_388347, _388349] : [c_Nat_OSuc(_388347) = c_Nat_OSuc(_388349), -(_388347 = _388349)], (4708 ^ _227627) ^ [_388564, _388566, _388568] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _388564), _388566)), _388568) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _388564), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _388566), _388568)))], (4710 ^ _227627) ^ [_388684, _388686] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _388684), _388686) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _388686), _388684))], (4712 ^ _227627) ^ [_388819, _388821, _388823] : [class_Rings_Oidom(_388819), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_388819)), _388821), _388823)), -(_388823 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_388819))), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_388819, _388821), c_Polynomial_Odegree(_388819, _388823)))], (4726 ^ _227627) ^ [_389277] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _389277), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(_389277 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (4732 ^ _227627) ^ [_389443] : [_389443 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _389443), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (4738 ^ _227627) ^ [_389673, _389675, _389677] : [class_Rings_Ocomm__semiring__1(_389673), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_389673, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_389673)), _389675), _389677)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Polynomial_Odegree(_389673, _389675)), _389677)))], (4744 ^ _227627) ^ [_389947, _389949, _389951] : [class_Rings_Oidom(_389947), -(_389949 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_389947))), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Oorder(_389947, _389951, _389949), c_Polynomial_Odegree(_389947, _389949)))], (4754 ^ _227627) ^ [_390295, _390297, _390299] : [class_Rings_Olinordered__semidom(_390295), c_Orderings_Oord__class_Oless(_390295, c_Groups_Ozero__class_Ozero(_390295), _390297), c_Orderings_Oord__class_Oless(_390295, _390297, c_Groups_Oone__class_Oone(_390295)), -(c_Orderings_Oord__class_Oless(_390295, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_390295), _390297), hAPP(hAPP(c_Power_Opower__class_Opower(_390295), _390297), _390299)), hAPP(hAPP(c_Power_Opower__class_Opower(_390295), _390297), _390299)))], (4768 ^ _227627) ^ [_390771, _390773, _390775] : [class_Rings_Olinordered__semidom(_390771), c_Orderings_Oord__class_Oless(_390771, c_Groups_Ozero__class_Ozero(_390771), _390773), c_Orderings_Oord__class_Oless(_390771, _390773, c_Groups_Oone__class_Oone(_390771)), -(c_Orderings_Oord__class_Oless(_390771, hAPP(hAPP(c_Power_Opower__class_Opower(_390771), _390773), c_Nat_OSuc(_390775)), c_Groups_Oone__class_Oone(_390771)))], (4782 ^ _227627) ^ [_391223, _391225, _391227] : [class_Rings_Ocomm__semiring__1(_391223), 4787 ^ _227627 : [(4788 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _391225)], (4790 ^ _227627) ^ [] : [_391227 = c_Groups_Oone__class_Oone(_391223)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_391223), _391227), hAPP(hAPP(c_Power_Opower__class_Opower(_391223), _391227), _391225))))], (4794 ^ _227627) ^ [_391642, _391644] : [class_Groups_Ozero(_391642), 4797 ^ _227627 : [(4798 ^ _227627) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_391642, _391644) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_391644 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_391642)))], (4804 ^ _227627) ^ [] : [_391644 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_391642)), -(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_391642, _391644) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (4810 ^ _227627) ^ [_392091] : [c_Nat_OSuc(_392091) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (4812 ^ _227627) ^ [_392170] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_392170)], (4814 ^ _227627) ^ [_392294] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _392294), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_392294 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (4820 ^ _227627) ^ [_392460] : [_392460 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _392460), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (4826 ^ _227627) ^ [_392646] : [c_Nat_OSuc(_392646) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (4828 ^ _227627) ^ [_392725] : [c_Nat_OSuc(_392725) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (4830 ^ _227627) ^ [_392804] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_392804)], (4832 ^ _227627) ^ [_392883] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_392883)], (4844 ^ _227627) ^ [_393321, _393323, _393325] : [4845 ^ _227627 : [(4846 ^ _227627) ^ [] : [_393321 = _393325], (4848 ^ _227627) ^ [] : [_393323 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _393321), _393323) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _393325), _393323))], (4834 ^ _227627) ^ [_393035, _393037, _393039] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _393035), _393037) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _393039), _393037), -(_393035 = _393039), -(_393037 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4862 ^ _227627) ^ [_393968, _393970, _393972] : [4863 ^ _227627 : [(4864 ^ _227627) ^ [] : [_393970 = _393972], (4866 ^ _227627) ^ [] : [_393968 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _393968), _393970) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _393968), _393972))], (4852 ^ _227627) ^ [_393682, _393684, _393686] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _393682), _393684) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _393682), _393686), -(_393684 = _393686), -(_393682 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4880 ^ _227627) ^ [_394579, _394581] : [4881 ^ _227627 : [(4882 ^ _227627) ^ [] : [_394579 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (4884 ^ _227627) ^ [] : [_394581 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _394579), _394581) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4870 ^ _227627) ^ [_394315, _394317] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _394315), _394317) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_394315 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_394317 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4888 ^ _227627) ^ [_394848] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _394848), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4890 ^ _227627) ^ [_394932] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _394932) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4892 ^ _227627) ^ [_395085, _395087, _395089] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_395085)), _395087) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_395085)), _395089), -(_395087 = _395089)], (4898 ^ _227627) ^ [_395285, _395287, _395289] : [_395287 = _395289, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_395285)), _395287) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_395285)), _395289))], (4904 ^ _227627) ^ [_395564, _395566] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _395564), _395566) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 4907 ^ _227627 : [(4908 ^ _227627) ^ [] : [-(_395564 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (4910 ^ _227627) ^ [] : [-(_395566 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (4912 ^ _227627) ^ [_395813, _395815] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _395813), _395815) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _395813 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _395815 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (4922 ^ _227627) ^ [_396097] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _396097), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _396097)], (4924 ^ _227627) ^ [_396239, _396241] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _396239), _396241), 4927 ^ _227627 : [(4928 ^ _227627) ^ [] : [-(_396239 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (4930 ^ _227627) ^ [] : [-(_396241 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (4932 ^ _227627) ^ [_396488, _396490] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _396488), _396490)), _396488 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _396490 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (4942 ^ _227627) ^ [_396772] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _396772) = _396772)], (4944 ^ _227627) ^ [_396896, _396898, _396900] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _396896), 4947 ^ _227627 : [(4948 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _396896), _396898), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _396896), _396900)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _396898, _396900))], (4954 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _396898, _396900), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _396896), _396898), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _396896), _396900)))]]], (4960 ^ _227627) ^ [_397430, _397432, _397434] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _397430), 4963 ^ _227627 : [(4964 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _397430), _397432)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _397430), _397434))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _397432), _397434)))], (4970 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _397432), _397434)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _397430), _397432)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _397430), _397434))))]]], (4976 ^ _227627) ^ [_397988, _397990, _397992] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _397988), _397990)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _397992), _397990))), -(_397990 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _397988), _397992)))], (4986 ^ _227627) ^ [_398358, _398360, _398362] : [-(_398358 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 4989 ^ _227627 : [(4990 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _398360), _398358)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _398362), _398358))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _398360), _398362)))], (4996 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _398360), _398362)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _398360), _398358)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _398362), _398358))))]]], (5012 ^ _227627) ^ [_399200, _399202] : [5013 ^ _227627 : [(5014 ^ _227627) ^ [] : [_399202 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5016 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _399200)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _399200), _399202)))], (5002 ^ _227627) ^ [_398932, _398934] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _398932), _398934)), -(_398934 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _398932))], (5030 ^ _227627) ^ [_399851, _399853, _399855] : [5031 ^ _227627 : [(5032 ^ _227627) ^ [] : [_399851 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5034 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _399853), _399855))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _399851), _399853)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _399851), _399855))))], (5020 ^ _227627) ^ [_399545, _399547, _399549] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _399545), _399547)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _399545), _399549))), -(_399545 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _399547), _399549)))], (5038 ^ _227627) ^ [_400203, _400205, _400207] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _400203), 5041 ^ _227627 : [(5042 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _400203), _400205), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _400203), _400207)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _400205, _400207))], (5048 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _400205, _400207), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _400203), _400205), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _400203), _400207)))]]], (5054 ^ _227627) ^ [_400737, _400739, _400741] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _400737), 5057 ^ _227627 : [(5058 ^ _227627) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _400737), _400739) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _400737), _400741), -(_400739 = _400741)], (5064 ^ _227627) ^ [] : [_400739 = _400741, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _400737), _400739) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _400737), _400741))]]], (5070 ^ _227627) ^ [_401251, _401253] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _401251), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _401253), _401251)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _401253))], (5080 ^ _227627) ^ [_401578, _401580, _401582] : [-(_401578 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 5083 ^ _227627 : [(5084 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _401580), _401578)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _401582), _401578))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _401580), _401582)))], (5090 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _401580), _401582)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _401580), _401578)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _401582), _401578))))]]], (5096 ^ _227627) ^ [_402137, _402139, _402141] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _402137), _402139)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _402141), _402139))), -(_402139 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _402137), _402141)))], (5106 ^ _227627) ^ [_402464] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _402464), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (5118 ^ _227627) ^ [_402905, _402907, _402909] : [5119 ^ _227627 : [(5120 ^ _227627) ^ [] : [_402905 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5122 ^ _227627) ^ [] : [_402907 = _402909]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _402905), _402907) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _402905), _402909))], (5108 ^ _227627) ^ [_402619, _402621, _402623] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _402619), _402621) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _402619), _402623), -(_402619 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_402621 = _402623)], (5126 ^ _227627) ^ [_403194] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _403194)))], (5128 ^ _227627) ^ [_403289] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _403289, c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_403289 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_403289 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (5138 ^ _227627) ^ [_403581, _403583] : [class_Groups_Oordered__ab__group__add(_403581), 5141 ^ _227627 : [(5142 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_403581, c_Groups_Ozero__class_Ozero(_403581), c_Groups_Ouminus__class_Ouminus(_403581, _403583)), -(c_Orderings_Oord__class_Oless(_403581, _403583, c_Groups_Ozero__class_Ozero(_403581)))], (5148 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_403581, _403583, c_Groups_Ozero__class_Ozero(_403581)), -(c_Orderings_Oord__class_Oless(_403581, c_Groups_Ozero__class_Ozero(_403581), c_Groups_Ouminus__class_Ouminus(_403581, _403583)))]]], (5154 ^ _227627) ^ [_404066, _404068] : [class_Groups_Oordered__ab__group__add(_404066), 5157 ^ _227627 : [(5158 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_404066, c_Groups_Ouminus__class_Ouminus(_404066, _404068), c_Groups_Ozero__class_Ozero(_404066)), -(c_Orderings_Oord__class_Oless(_404066, c_Groups_Ozero__class_Ozero(_404066), _404068))], (5164 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_404066, c_Groups_Ozero__class_Ozero(_404066), _404068), -(c_Orderings_Oord__class_Oless(_404066, c_Groups_Ouminus__class_Ouminus(_404066, _404068), c_Groups_Ozero__class_Ozero(_404066)))]]], (5170 ^ _227627) ^ [_404551, _404553] : [class_Groups_Olinordered__ab__group__add(_404551), 5173 ^ _227627 : [(5174 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_404551, c_Groups_Ouminus__class_Ouminus(_404551, _404553), _404553), -(c_Orderings_Oord__class_Oless(_404551, c_Groups_Ozero__class_Ozero(_404551), _404553))], (5180 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_404551, c_Groups_Ozero__class_Ozero(_404551), _404553), -(c_Orderings_Oord__class_Oless(_404551, c_Groups_Ouminus__class_Ouminus(_404551, _404553), _404553))]]], (5186 ^ _227627) ^ [_405030, _405032] : [class_Groups_Oordered__ab__group__add(_405030), 5189 ^ _227627 : [(5190 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_405030, c_Groups_Ozero__class_Ozero(_405030), c_Groups_Ouminus__class_Ouminus(_405030, _405032)), -(c_Orderings_Oord__class_Oless__eq(_405030, _405032, c_Groups_Ozero__class_Ozero(_405030)))], (5196 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_405030, _405032, c_Groups_Ozero__class_Ozero(_405030)), -(c_Orderings_Oord__class_Oless__eq(_405030, c_Groups_Ozero__class_Ozero(_405030), c_Groups_Ouminus__class_Ouminus(_405030, _405032)))]]], (5202 ^ _227627) ^ [_405515, _405517] : [class_Groups_Olinordered__ab__group__add(_405515), 5205 ^ _227627 : [(5206 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_405515, _405517, c_Groups_Ouminus__class_Ouminus(_405515, _405517)), -(c_Orderings_Oord__class_Oless__eq(_405515, _405517, c_Groups_Ozero__class_Ozero(_405515)))], (5212 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_405515, _405517, c_Groups_Ozero__class_Ozero(_405515)), -(c_Orderings_Oord__class_Oless__eq(_405515, _405517, c_Groups_Ouminus__class_Ouminus(_405515, _405517)))]]], (5218 ^ _227627) ^ [_405994, _405996] : [class_Groups_Ozero(_405994), 5221 ^ _227627 : [(5222 ^ _227627) ^ [] : [c_Groups_Ozero__class_Ozero(_405994) = _405996, -(_405996 = c_Groups_Ozero__class_Ozero(_405994))], (5228 ^ _227627) ^ [] : [_405996 = c_Groups_Ozero__class_Ozero(_405994), -(c_Groups_Ozero__class_Ozero(_405994) = _405996)]]], (5234 ^ _227627) ^ [_406492, _406494, _406496, _406498] : [class_Groups_Oab__semigroup__mult(_406492), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_406492), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_406492), _406494), _406496)), _406498) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_406492), _406494), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_406492), _406496), _406498)))], (5240 ^ _227627) ^ [_406776, _406778] : [class_Groups_Oone(_406776), 5243 ^ _227627 : [(5244 ^ _227627) ^ [] : [c_Groups_Oone__class_Oone(_406776) = _406778, -(_406778 = c_Groups_Oone__class_Oone(_406776))], (5250 ^ _227627) ^ [] : [_406778 = c_Groups_Oone__class_Oone(_406776), -(c_Groups_Oone__class_Oone(_406776) = _406778)]]], (5256 ^ _227627) ^ [_407260, _407262, _407264] : [class_Groups_Ogroup__add(_407260), 5259 ^ _227627 : [(5260 ^ _227627) ^ [] : [c_Groups_Ouminus__class_Ouminus(_407260, _407262) = c_Groups_Ouminus__class_Ouminus(_407260, _407264), -(_407262 = _407264)], (5266 ^ _227627) ^ [] : [_407262 = _407264, -(c_Groups_Ouminus__class_Ouminus(_407260, _407262) = c_Groups_Ouminus__class_Ouminus(_407260, _407264))]]], (5272 ^ _227627) ^ [_407766, _407768, _407770] : [class_Groups_Ogroup__add(_407766), 5275 ^ _227627 : [(5276 ^ _227627) ^ [] : [c_Groups_Ouminus__class_Ouminus(_407766, _407768) = _407770, -(c_Groups_Ouminus__class_Ouminus(_407766, _407770) = _407768)], (5282 ^ _227627) ^ [] : [c_Groups_Ouminus__class_Ouminus(_407766, _407770) = _407768, -(c_Groups_Ouminus__class_Ouminus(_407766, _407768) = _407770)]]], (5288 ^ _227627) ^ [_408272, _408274, _408276] : [class_Groups_Ogroup__add(_408272), 5291 ^ _227627 : [(5292 ^ _227627) ^ [] : [_408274 = c_Groups_Ouminus__class_Ouminus(_408272, _408276), -(_408276 = c_Groups_Ouminus__class_Ouminus(_408272, _408274))], (5298 ^ _227627) ^ [] : [_408276 = c_Groups_Ouminus__class_Ouminus(_408272, _408274), -(_408274 = c_Groups_Ouminus__class_Ouminus(_408272, _408276))]]], (5304 ^ _227627) ^ [_408764, _408766] : [class_Groups_Ogroup__add(_408764), -(c_Groups_Ouminus__class_Ouminus(_408764, c_Groups_Ouminus__class_Ouminus(_408764, _408766)) = _408766)], (5310 ^ _227627) ^ [_408984, _408986] : [class_Groups_Olinordered__ab__group__add(_408984), 5313 ^ _227627 : [(5314 ^ _227627) ^ [] : [c_Groups_Ouminus__class_Ouminus(_408984, _408986) = _408986, -(_408986 = c_Groups_Ozero__class_Ozero(_408984))], (5320 ^ _227627) ^ [] : [_408986 = c_Groups_Ozero__class_Ozero(_408984), -(c_Groups_Ouminus__class_Ouminus(_408984, _408986) = _408986)]]], (5326 ^ _227627) ^ [_409457, _409459] : [class_Groups_Ogroup__add(_409457), 5329 ^ _227627 : [(5330 ^ _227627) ^ [] : [c_Groups_Ouminus__class_Ouminus(_409457, _409459) = c_Groups_Ozero__class_Ozero(_409457), -(_409459 = c_Groups_Ozero__class_Ozero(_409457))], (5336 ^ _227627) ^ [] : [_409459 = c_Groups_Ozero__class_Ozero(_409457), -(c_Groups_Ouminus__class_Ouminus(_409457, _409459) = c_Groups_Ozero__class_Ozero(_409457))]]], (5342 ^ _227627) ^ [_409936, _409938] : [class_Groups_Olinordered__ab__group__add(_409936), 5345 ^ _227627 : [(5346 ^ _227627) ^ [] : [_409938 = c_Groups_Ouminus__class_Ouminus(_409936, _409938), -(_409938 = c_Groups_Ozero__class_Ozero(_409936))], (5352 ^ _227627) ^ [] : [_409938 = c_Groups_Ozero__class_Ozero(_409936), -(_409938 = c_Groups_Ouminus__class_Ouminus(_409936, _409938))]]], (5358 ^ _227627) ^ [_410409, _410411] : [class_Groups_Ogroup__add(_410409), 5361 ^ _227627 : [(5362 ^ _227627) ^ [] : [c_Groups_Ozero__class_Ozero(_410409) = c_Groups_Ouminus__class_Ouminus(_410409, _410411), -(c_Groups_Ozero__class_Ozero(_410409) = _410411)], (5368 ^ _227627) ^ [] : [c_Groups_Ozero__class_Ozero(_410409) = _410411, -(c_Groups_Ozero__class_Ozero(_410409) = c_Groups_Ouminus__class_Ouminus(_410409, _410411))]]], (5374 ^ _227627) ^ [_410874] : [class_Groups_Ogroup__add(_410874), -(c_Groups_Ouminus__class_Ouminus(_410874, c_Groups_Ozero__class_Ozero(_410874)) = c_Groups_Ozero__class_Ozero(_410874))], (5380 ^ _227627) ^ [_411090, _411092] : [class_Groups_Ocomm__monoid__mult(_411090), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_411090), _411092), c_Groups_Oone__class_Oone(_411090)) = _411092)], (5386 ^ _227627) ^ [_411318, _411320] : [class_Groups_Omonoid__mult(_411318), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_411318), _411320), c_Groups_Oone__class_Oone(_411318)) = _411320)], (5392 ^ _227627) ^ [_411546, _411548] : [class_Groups_Ocomm__monoid__mult(_411546), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_411546), c_Groups_Oone__class_Oone(_411546)), _411548) = _411548)], (5398 ^ _227627) ^ [_411774, _411776] : [class_Groups_Omonoid__mult(_411774), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_411774), c_Groups_Oone__class_Oone(_411774)), _411776) = _411776)], (5404 ^ _227627) ^ [_412016, _412018, _412020] : [class_Groups_Oordered__ab__group__add(_412016), c_Orderings_Oord__class_Oless__eq(_412016, _412018, _412020), -(c_Orderings_Oord__class_Oless__eq(_412016, c_Groups_Ouminus__class_Ouminus(_412016, _412020), c_Groups_Ouminus__class_Ouminus(_412016, _412018)))], (5414 ^ _227627) ^ [_412353, _412355, _412357] : [class_Groups_Oordered__ab__group__add(_412353), 5417 ^ _227627 : [(5418 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_412353, c_Groups_Ouminus__class_Ouminus(_412353, _412355), c_Groups_Ouminus__class_Ouminus(_412353, _412357)), -(c_Orderings_Oord__class_Oless__eq(_412353, _412357, _412355))], (5424 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_412353, _412357, _412355), -(c_Orderings_Oord__class_Oless__eq(_412353, c_Groups_Ouminus__class_Ouminus(_412353, _412355), c_Groups_Ouminus__class_Ouminus(_412353, _412357)))]]], (5430 ^ _227627) ^ [_412865, _412867, _412869] : [class_Groups_Oordered__ab__group__add(_412865), 5433 ^ _227627 : [(5434 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_412865, c_Groups_Ouminus__class_Ouminus(_412865, _412867), _412869), -(c_Orderings_Oord__class_Oless__eq(_412865, c_Groups_Ouminus__class_Ouminus(_412865, _412869), _412867))], (5440 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_412865, c_Groups_Ouminus__class_Ouminus(_412865, _412869), _412867), -(c_Orderings_Oord__class_Oless__eq(_412865, c_Groups_Ouminus__class_Ouminus(_412865, _412867), _412869))]]], (5446 ^ _227627) ^ [_413377, _413379, _413381] : [class_Groups_Oordered__ab__group__add(_413377), 5449 ^ _227627 : [(5450 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_413377, _413379, c_Groups_Ouminus__class_Ouminus(_413377, _413381)), -(c_Orderings_Oord__class_Oless__eq(_413377, _413381, c_Groups_Ouminus__class_Ouminus(_413377, _413379)))], (5456 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_413377, _413381, c_Groups_Ouminus__class_Ouminus(_413377, _413379)), -(c_Orderings_Oord__class_Oless__eq(_413377, _413379, c_Groups_Ouminus__class_Ouminus(_413377, _413381)))]]], (5462 ^ _227627) ^ [_413889, _413891, _413893] : [class_Groups_Oordered__ab__group__add(_413889), 5465 ^ _227627 : [(5466 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_413889, c_Groups_Ouminus__class_Ouminus(_413889, _413891), c_Groups_Ouminus__class_Ouminus(_413889, _413893)), -(c_Orderings_Oord__class_Oless(_413889, _413893, _413891))], (5472 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_413889, _413893, _413891), -(c_Orderings_Oord__class_Oless(_413889, c_Groups_Ouminus__class_Ouminus(_413889, _413891), c_Groups_Ouminus__class_Ouminus(_413889, _413893)))]]], (5478 ^ _227627) ^ [_414401, _414403, _414405] : [class_Groups_Oordered__ab__group__add(_414401), 5481 ^ _227627 : [(5482 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_414401, c_Groups_Ouminus__class_Ouminus(_414401, _414403), _414405), -(c_Orderings_Oord__class_Oless(_414401, c_Groups_Ouminus__class_Ouminus(_414401, _414405), _414403))], (5488 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_414401, c_Groups_Ouminus__class_Ouminus(_414401, _414405), _414403), -(c_Orderings_Oord__class_Oless(_414401, c_Groups_Ouminus__class_Ouminus(_414401, _414403), _414405))]]], (5494 ^ _227627) ^ [_414913, _414915, _414917] : [class_Groups_Oordered__ab__group__add(_414913), 5497 ^ _227627 : [(5498 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_414913, _414915, c_Groups_Ouminus__class_Ouminus(_414913, _414917)), -(c_Orderings_Oord__class_Oless(_414913, _414917, c_Groups_Ouminus__class_Ouminus(_414913, _414915)))], (5504 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_414913, _414917, c_Groups_Ouminus__class_Ouminus(_414913, _414915)), -(c_Orderings_Oord__class_Oless(_414913, _414915, c_Groups_Ouminus__class_Ouminus(_414913, _414917)))]]], (5510 ^ _227627) ^ [_415411, _415413] : [class_Groups_Olinordered__ab__group__add(_415411), 5513 ^ _227627 : [(5514 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_415411, c_Groups_Ouminus__class_Ouminus(_415411, _415413), _415413), -(c_Orderings_Oord__class_Oless__eq(_415411, c_Groups_Ozero__class_Ozero(_415411), _415413))], (5520 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_415411, c_Groups_Ozero__class_Ozero(_415411), _415413), -(c_Orderings_Oord__class_Oless__eq(_415411, c_Groups_Ouminus__class_Ouminus(_415411, _415413), _415413))]]], (5526 ^ _227627) ^ [_415890, _415892] : [class_Groups_Oordered__ab__group__add(_415890), 5529 ^ _227627 : [(5530 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_415890, c_Groups_Ouminus__class_Ouminus(_415890, _415892), c_Groups_Ozero__class_Ozero(_415890)), -(c_Orderings_Oord__class_Oless__eq(_415890, c_Groups_Ozero__class_Ozero(_415890), _415892))], (5536 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_415890, c_Groups_Ozero__class_Ozero(_415890), _415892), -(c_Orderings_Oord__class_Oless__eq(_415890, c_Groups_Ouminus__class_Ouminus(_415890, _415892), c_Groups_Ozero__class_Ozero(_415890)))]]], (5542 ^ _227627) ^ [_416375, _416377] : [class_Orderings_Opreorder(_416375), -(c_Orderings_Oord__class_Oless__eq(_416375, _416377, _416377))], (5548 ^ _227627) ^ [_416571] : [class_Power_Opower(_416571), -(c_Power_Opower__class_Opower(_416571) = c_Power_Opower_Opower(_416571, c_Groups_Oone__class_Oone(_416571), c_Groups_Otimes__class_Otimes(_416571)))], (5554 ^ _227627) ^ [_416792, _416794, _416796] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _416792), _416794)), _416796) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _416792), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _416794), _416796)))], (5556 ^ _227627) ^ [_416941, _416943, _416945] : [class_Rings_Ocomm__semiring__0(_416941), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_416941, c_Polynomial_Opcompose(_416941, _416943, _416945)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Polynomial_Odegree(_416941, _416943)), c_Polynomial_Odegree(_416941, _416945))))], (5562 ^ _227627) ^ [_417195, _417197] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _417195, _417197), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _417195, _417197))], (5568 ^ _227627) ^ [_417409, _417411] : [class_Rings_Ocomm__semiring__0(_417409), -(c_Polynomial_Opcompose(_417409, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_417409)), _417411) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_417409)))], (5574 ^ _227627) ^ [_417669, _417671, _417673, _417675] : [class_Rings_Ocomm__semiring__0(_417669), -(hAPP(c_Polynomial_Opoly(_417669, c_Polynomial_Opcompose(_417669, _417671, _417673)), _417675) = hAPP(c_Polynomial_Opoly(_417669, _417671), hAPP(c_Polynomial_Opoly(_417669, _417673), _417675)))], (5580 ^ _227627) ^ [_417946, _417948, _417950, _417952] : [-(hAPP(hAPP(c_Power_Opower_Opower(_417946, _417948, _417950), _417952), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _417948)], (5582 ^ _227627) ^ [_418096, _418098, _418100, _418102, _418104] : [-(hAPP(hAPP(c_Power_Opower_Opower(_418096, _418098, _418100), _418102), c_Nat_OSuc(_418104)) = hAPP(hAPP(_418100, _418102), hAPP(hAPP(c_Power_Opower_Opower(_418096, _418098, _418100), _418102), _418104)))], (5584 ^ _227627) ^ [_418253, _418255, _418257] : [class_Orderings_Olinorder(_418253), -(c_Orderings_Oord__class_Oless__eq(_418253, _418255, _418257)), -(c_Orderings_Oord__class_Oless__eq(_418253, _418257, _418255))], (5594 ^ _227627) ^ [_418609, _418611, _418613, _418615, _418617] : [class_Orderings_Oord(_418609), c_Orderings_Oord__class_Oless__eq(tc_fun(_418611, _418609), _418613, _418615), -(c_Orderings_Oord__class_Oless__eq(_418609, hAPP(_418613, _418617), hAPP(_418615, _418617)))], (5604 ^ _227627) ^ [_418986, _418988, _418990, _418992] : [class_Orderings_Oorder(_418986), c_Orderings_Oord__class_Oless__eq(_418986, _418988, _418990), c_Orderings_Oord__class_Oless__eq(_418986, _418992, _418988), -(c_Orderings_Oord__class_Oless__eq(_418986, _418992, _418990))], (5618 ^ _227627) ^ [_419420, _419422, _419424] : [class_Orderings_Oorder(_419420), c_Orderings_Oord__class_Oless__eq(_419420, _419422, _419424), c_Orderings_Oord__class_Oless__eq(_419420, _419424, _419422), -(_419424 = _419422)], (5632 ^ _227627) ^ [_419852, _419854, _419856, _419858] : [class_Orderings_Opreorder(_419852), c_Orderings_Oord__class_Oless__eq(_419852, _419854, _419856), c_Orderings_Oord__class_Oless__eq(_419852, _419856, _419858), -(c_Orderings_Oord__class_Oless__eq(_419852, _419854, _419858))], (5646 ^ _227627) ^ [_420286, _420288, _420290] : [class_Orderings_Oorder(_420286), c_Orderings_Oord__class_Oless__eq(_420286, _420288, _420290), c_Orderings_Oord__class_Oless__eq(_420286, _420290, _420288), -(_420288 = _420290)], (5660 ^ _227627) ^ [_420718, _420720, _420722, _420724] : [class_Orderings_Oorder(_420718), c_Orderings_Oord__class_Oless__eq(_420718, _420720, _420722), _420720 = _420724, -(c_Orderings_Oord__class_Oless__eq(_420718, _420724, _420722))], (5674 ^ _227627) ^ [_421164, _421166, _421168, _421170] : [class_Orderings_Oord(_421164), c_Orderings_Oord__class_Oless__eq(_421164, _421166, _421168), _421168 = _421170, -(c_Orderings_Oord__class_Oless__eq(_421164, _421166, _421170))], (5688 ^ _227627) ^ [_421610, _421612, _421614, _421616] : [class_Orderings_Oorder(_421610), _421612 = _421614, c_Orderings_Oord__class_Oless__eq(_421610, _421616, _421614), -(c_Orderings_Oord__class_Oless__eq(_421610, _421616, _421612))], (5702 ^ _227627) ^ [_422056, _422058, _422060, _422062] : [class_Orderings_Oord(_422056), _422058 = _422060, c_Orderings_Oord__class_Oless__eq(_422056, _422060, _422062), -(c_Orderings_Oord__class_Oless__eq(_422056, _422058, _422062))], (5716 ^ _227627) ^ [_422488, _422490, _422492] : [class_Orderings_Oorder(_422488), c_Orderings_Oord__class_Oless__eq(_422488, _422490, _422492), 5723 ^ _227627 : [(5724 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_422488, _422492, _422490), -(_422492 = _422490)], (5730 ^ _227627) ^ [] : [_422492 = _422490, -(c_Orderings_Oord__class_Oless__eq(_422488, _422492, _422490))]]], (5736 ^ _227627) ^ [_423102, _423104, _423106, _423108, _423110] : [class_Orderings_Oord(_423102), c_Orderings_Oord__class_Oless__eq(tc_fun(_423104, _423102), _423106, _423108), -(c_Orderings_Oord__class_Oless__eq(_423102, hAPP(_423106, _423110), hAPP(_423108, _423110)))], (5746 ^ _227627) ^ [_423465, _423467, _423469] : [class_Orderings_Opreorder(_423465), _423467 = _423469, -(c_Orderings_Oord__class_Oless__eq(_423465, _423467, _423469))], (5756 ^ _227627) ^ [_423788, _423790, _423792] : [class_Orderings_Oorder(_423788), 5759 ^ _227627 : [(5760 ^ _227627) ^ [] : [_423790 = _423792, 5763 ^ _227627 : [(5764 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_423788, _423790, _423792))], (5766 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_423788, _423792, _423790))]]], (5768 ^ _227627) ^ [] : [-(_423790 = _423792), c_Orderings_Oord__class_Oless__eq(_423788, _423790, _423792), c_Orderings_Oord__class_Oless__eq(_423788, _423792, _423790)]]], (5778 ^ _227627) ^ [_424446, _424448, _424450] : [class_Orderings_Olinorder(_424446), -(c_Orderings_Oord__class_Oless__eq(_424446, _424448, _424450)), -(c_Orderings_Oord__class_Oless__eq(_424446, _424450, _424448))], (5788 ^ _227627) ^ [_424786, _424788, _424790, _424792] : [class_Orderings_Oord(_424786), 5791 ^ _227627 : [(5792 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_424788, _424786), _424790, _424792), 5795 ^ _227627 : [(5796 ^ _227627) ^ [_425045] : [-(c_Orderings_Oord__class_Oless__eq(_424786, hAPP(_424790, _425045), hAPP(_424792, _425045)))]]], (5798 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_424786, hAPP(_424790, 5799 ^ [_424786, _424788, _424790, _424792]), hAPP(_424792, 5799 ^ [_424786, _424788, _424790, _424792])), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_424788, _424786), _424790, _424792))]]], (5805 ^ _227627) ^ [_425427, _425429, _425431] : [class_Orderings_Olinorder(_425427), -(c_Orderings_Oord__class_Oless(_425427, _425429, _425431)), -(_425429 = _425431), -(c_Orderings_Oord__class_Oless(_425427, _425431, _425429))], (5819 ^ _227627) ^ [_425851, _425853, _425855] : [class_Orderings_Opreorder(_425851), c_Orderings_Oord__class_Oless(_425851, _425853, _425855), c_Orderings_Oord__class_Oless(_425851, _425855, _425853)], (5829 ^ _227627) ^ [_426191, _426193, _426195, _426197] : [class_Orderings_Oorder(_426191), c_Orderings_Oord__class_Oless(_426191, _426193, _426195), c_Orderings_Oord__class_Oless(_426191, _426197, _426193), -(c_Orderings_Oord__class_Oless(_426191, _426197, _426195))], (5843 ^ _227627) ^ [_426639, _426641, _426643, _426645] : [class_Orderings_Opreorder(_426639), c_Orderings_Oord__class_Oless(_426639, _426641, _426643), c_Orderings_Oord__class_Oless(_426639, _426643, _426645), -(c_Orderings_Oord__class_Oless(_426639, _426641, _426645))], (5857 ^ _227627) ^ [_427087, _427089, _427091, _427093] : [class_Orderings_Oorder(_427087), c_Orderings_Oord__class_Oless(_427087, _427089, _427091), _427089 = _427093, -(c_Orderings_Oord__class_Oless(_427087, _427093, _427091))], (5871 ^ _227627) ^ [_427533, _427535, _427537, _427539] : [class_Orderings_Oord(_427533), c_Orderings_Oord__class_Oless(_427533, _427535, _427537), _427537 = _427539, -(c_Orderings_Oord__class_Oless(_427533, _427535, _427539))], (5885 ^ _227627) ^ [_427979, _427981, _427983, _427985] : [class_Orderings_Oorder(_427979), _427981 = _427983, c_Orderings_Oord__class_Oless(_427979, _427985, _427983), -(c_Orderings_Oord__class_Oless(_427979, _427985, _427981))], (5899 ^ _227627) ^ [_428425, _428427, _428429, _428431] : [class_Orderings_Oord(_428425), _428427 = _428429, c_Orderings_Oord__class_Oless(_428425, _428429, _428431), -(c_Orderings_Oord__class_Oless(_428425, _428427, _428431))], (5913 ^ _227627) ^ [_428857, _428859, _428861] : [class_Orderings_Oorder(_428857), c_Orderings_Oord__class_Oless(_428857, _428859, _428861), c_Orderings_Oord__class_Oless(_428857, _428861, _428859)], (5923 ^ _227627) ^ [_429183, _429185, _429187] : [class_Orderings_Opreorder(_429183), c_Orderings_Oord__class_Oless(_429183, _429185, _429187), c_Orderings_Oord__class_Oless(_429183, _429187, _429185)], (5933 ^ _227627) ^ [_429509, _429511, _429513] : [class_Orderings_Oorder(_429509), c_Orderings_Oord__class_Oless(_429509, _429511, _429513), _429513 = _429511], (5943 ^ _227627) ^ [_429833, _429835, _429837] : [class_Orderings_Oorder(_429833), c_Orderings_Oord__class_Oless(_429833, _429835, _429837), _429835 = _429837], (5953 ^ _227627) ^ [_430157, _430159, _430161] : [class_Orderings_Opreorder(_430157), c_Orderings_Oord__class_Oless(_430157, _430159, _430161), c_Orderings_Oord__class_Oless(_430157, _430161, _430159)], (5963 ^ _227627) ^ [_430483, _430485, _430487] : [class_Orderings_Opreorder(_430483), c_Orderings_Oord__class_Oless(_430483, _430485, _430487), c_Orderings_Oord__class_Oless(_430483, _430487, _430485)], (5973 ^ _227627) ^ [_430809, _430811, _430813] : [class_Orderings_Oorder(_430809), c_Orderings_Oord__class_Oless(_430809, _430811, _430813), _430811 = _430813], (5983 ^ _227627) ^ [_431133, _431135, _431137] : [class_Orderings_Olinorder(_431133), -(_431135 = _431137), -(c_Orderings_Oord__class_Oless(_431133, _431135, _431137)), -(c_Orderings_Oord__class_Oless(_431133, _431137, _431135))], (5997 ^ _227627) ^ [_431557, _431559, _431561] : [class_Orderings_Olinorder(_431557), -(c_Orderings_Oord__class_Oless(_431557, _431559, _431561)), 6004 ^ _227627 : [(6005 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(_431557, _431561, _431559)), -(_431561 = _431559)], (6011 ^ _227627) ^ [] : [_431561 = _431559, c_Orderings_Oord__class_Oless(_431557, _431561, _431559)]]], (6017 ^ _227627) ^ [_432148, _432150, _432152] : [class_Orderings_Olinorder(_432148), -(c_Orderings_Oord__class_Oless(_432148, _432150, _432152)), -(_432150 = _432152), -(c_Orderings_Oord__class_Oless(_432148, _432152, _432150))], (6031 ^ _227627) ^ [_432568, _432570, _432572] : [class_Orderings_Olinorder(_432568), 6034 ^ _227627 : [(6045 ^ _227627) ^ [] : [6046 ^ _227627 : [(6047 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_432568, _432572, _432570)], (6049 ^ _227627) ^ [] : [_432570 = _432572]], c_Orderings_Oord__class_Oless(_432568, _432570, _432572)], (6035 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(_432568, _432570, _432572)), -(c_Orderings_Oord__class_Oless(_432568, _432572, _432570)), -(_432570 = _432572)]]], (6053 ^ _227627) ^ [_433228, _433230, _433232] : [class_Orderings_Olinorder(_433228), 6056 ^ _227627 : [(6067 ^ _227627) ^ [] : [6068 ^ _227627 : [(6069 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_433228, _433230, _433232)], (6071 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_433228, _433232, _433230)]], _433230 = _433232], (6057 ^ _227627) ^ [] : [-(_433230 = _433232), -(c_Orderings_Oord__class_Oless(_433228, _433230, _433232)), -(c_Orderings_Oord__class_Oless(_433228, _433232, _433230))]]], (6075 ^ _227627) ^ [_433874, _433876] : [class_Orderings_Opreorder(_433874), c_Orderings_Oord__class_Oless(_433874, _433876, _433876)], (6081 ^ _227627) ^ [_434099, _434101, _434103] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _434099), _434101)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _434099), _434103))), -(_434099 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _434101), _434103)))], (6091 ^ _227627) ^ [_434455, _434457] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _434455), _434457)), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _434457), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _434455, _434457))], (6101 ^ _227627) ^ [_434768, _434770] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _434768), c_Orderings_Oord__class_Oless(tc_Int_Oint, _434768, _434770), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _434770), _434768))], (6111 ^ _227627) ^ [_435082, _435084] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _435082), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _435084), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _435082), _435084)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _435084), _435082)), -(_435082 = _435084)], (6129 ^ _227627) ^ [_435611, _435613, _435615, _435617] : [class_Orderings_Oorder(_435611), c_Orderings_Oord__class_Oless__eq(_435611, _435613, _435615), c_Orderings_Oord__class_Oless(_435611, _435617, _435613), -(c_Orderings_Oord__class_Oless(_435611, _435617, _435615))], (6143 ^ _227627) ^ [_436059, _436061, _436063, _436065] : [class_Orderings_Opreorder(_436059), c_Orderings_Oord__class_Oless__eq(_436059, _436061, _436063), c_Orderings_Oord__class_Oless(_436059, _436063, _436065), -(c_Orderings_Oord__class_Oless(_436059, _436061, _436065))], (6157 ^ _227627) ^ [_436507, _436509, _436511, _436513] : [class_Orderings_Oorder(_436507), c_Orderings_Oord__class_Oless(_436507, _436509, _436511), c_Orderings_Oord__class_Oless__eq(_436507, _436513, _436509), -(c_Orderings_Oord__class_Oless(_436507, _436513, _436511))], (6171 ^ _227627) ^ [_436955, _436957, _436959, _436961] : [class_Orderings_Opreorder(_436955), c_Orderings_Oord__class_Oless(_436955, _436957, _436959), c_Orderings_Oord__class_Oless__eq(_436955, _436959, _436961), -(c_Orderings_Oord__class_Oless(_436955, _436957, _436961))], (6185 ^ _227627) ^ [_437389, _437391, _437393] : [class_Orderings_Oorder(_437389), c_Orderings_Oord__class_Oless__eq(_437389, _437391, _437393), -(_437393 = _437391), -(c_Orderings_Oord__class_Oless(_437389, _437391, _437393))], (6199 ^ _227627) ^ [_437810, _437812, _437814] : [class_Orderings_Oorder(_437810), c_Orderings_Oord__class_Oless__eq(_437810, _437812, _437814), -(_437812 = _437814), -(c_Orderings_Oord__class_Oless(_437810, _437812, _437814))], (6213 ^ _227627) ^ [_438231, _438233, _438235] : [class_Orderings_Oorder(_438231), c_Orderings_Oord__class_Oless__eq(_438231, _438233, _438235), -(c_Orderings_Oord__class_Oless(_438231, _438233, _438235)), -(_438233 = _438235)], (6227 ^ _227627) ^ [_438650, _438652, _438654] : [class_Orderings_Olinorder(_438650), c_Orderings_Oord__class_Oless__eq(_438650, _438652, _438654), 6234 ^ _227627 : [(6235 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(_438650, _438652, _438654)), -(_438652 = _438654)], (6241 ^ _227627) ^ [] : [_438652 = _438654, c_Orderings_Oord__class_Oless(_438650, _438652, _438654)]]], (6247 ^ _227627) ^ [_439238, _439240, _439242] : [class_Orderings_Opreorder(_439238), c_Orderings_Oord__class_Oless(_439238, _439240, _439242), -(c_Orderings_Oord__class_Oless__eq(_439238, _439240, _439242))], (6257 ^ _227627) ^ [_439563, _439565, _439567] : [class_Orderings_Olinorder(_439563), c_Orderings_Oord__class_Oless__eq(_439563, _439565, _439567), c_Orderings_Oord__class_Oless(_439563, _439567, _439565)], (6267 ^ _227627) ^ [_439889, _439891, _439893] : [class_Orderings_Oorder(_439889), -(_439891 = _439893), c_Orderings_Oord__class_Oless__eq(_439889, _439893, _439891), -(c_Orderings_Oord__class_Oless(_439889, _439893, _439891))], (6281 ^ _227627) ^ [_440310, _440312, _440314] : [class_Orderings_Oorder(_440310), -(_440312 = _440314), c_Orderings_Oord__class_Oless__eq(_440310, _440312, _440314), -(c_Orderings_Oord__class_Oless(_440310, _440312, _440314))], (6295 ^ _227627) ^ [_440731, _440733, _440735] : [class_Orderings_Olinorder(_440731), -(c_Orderings_Oord__class_Oless(_440731, _440733, _440735)), 6302 ^ _227627 : [(6303 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_440731, _440733, _440735), -(_440733 = _440735)], (6309 ^ _227627) ^ [] : [_440733 = _440735, -(c_Orderings_Oord__class_Oless__eq(_440731, _440733, _440735))]]], (6315 ^ _227627) ^ [_441320, _441322, _441324] : [class_Orderings_Olinorder(_441320), -(c_Orderings_Oord__class_Oless__eq(_441320, _441322, _441324)), -(c_Orderings_Oord__class_Oless(_441320, _441324, _441322))], (6325 ^ _227627) ^ [_441648, _441650, _441652] : [class_Orderings_Olinorder(_441648), -(c_Orderings_Oord__class_Oless(_441648, _441650, _441652)), -(c_Orderings_Oord__class_Oless__eq(_441648, _441652, _441650))], (6335 ^ _227627) ^ [_441976, _441978, _441980] : [class_Orderings_Oorder(_441976), 6338 ^ _227627 : [(6349 ^ _227627) ^ [] : [6350 ^ _227627 : [(6351 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_441976, _441978, _441980)], (6353 ^ _227627) ^ [] : [_441978 = _441980]], -(c_Orderings_Oord__class_Oless__eq(_441976, _441978, _441980))], (6339 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_441976, _441978, _441980), -(c_Orderings_Oord__class_Oless(_441976, _441978, _441980)), -(_441978 = _441980)]]], (6357 ^ _227627) ^ [_442634, _442636, _442638] : [class_Orderings_Opreorder(_442634), 6360 ^ _227627 : [(6361 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_442634, _442636, _442638), 6364 ^ _227627 : [(6365 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_442634, _442636, _442638))], (6367 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_442634, _442638, _442636)]]], (6369 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(_442634, _442636, _442638)), c_Orderings_Oord__class_Oless__eq(_442634, _442636, _442638), -(c_Orderings_Oord__class_Oless__eq(_442634, _442638, _442636))]]], (6379 ^ _227627) ^ [_443297, _443299, _443301] : [class_Orderings_Oorder(_443297), 6382 ^ _227627 : [(6383 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_443297, _443299, _443301), 6386 ^ _227627 : [(6387 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_443297, _443299, _443301))], (6389 ^ _227627) ^ [] : [_443299 = _443301]]], (6391 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(_443297, _443299, _443301)), c_Orderings_Oord__class_Oless__eq(_443297, _443299, _443301), -(_443299 = _443301)]]], (6401 ^ _227627) ^ [_443957, _443959, _443961] : [class_Orderings_Olinorder(_443957), -(c_Orderings_Oord__class_Oless__eq(_443957, _443959, _443961)), -(c_Orderings_Oord__class_Oless(_443957, _443961, _443959))], (6411 ^ _227627) ^ [_444283, _444285, _444287] : [class_Orderings_Olinorder(_444283), 6414 ^ _227627 : [(6415 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_444283, _444285, _444287)), -(c_Orderings_Oord__class_Oless(_444283, _444287, _444285))], (6421 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_444283, _444287, _444285), c_Orderings_Oord__class_Oless__eq(_444283, _444285, _444287)]]], (6427 ^ _227627) ^ [_444779, _444781, _444783] : [class_Orderings_Olinorder(_444779), 6430 ^ _227627 : [(6431 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(_444779, _444781, _444783)), -(c_Orderings_Oord__class_Oless__eq(_444779, _444783, _444781))], (6437 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_444779, _444783, _444781), c_Orderings_Oord__class_Oless(_444779, _444781, _444783)]]], (6443 ^ _227627) ^ [_445275, _445277, _445279] : [class_Rings_Olinordered__idom(_445275), 6446 ^ _227627 : [(6447 ^ _227627) ^ [] : [c_Polynomial_Opos__poly(_445275, c_Polynomial_OpCons(_445275, _445277, _445279)), -(c_Polynomial_Opos__poly(_445275, _445279)), 6454 ^ _227627 : [(6455 ^ _227627) ^ [] : [-(_445279 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_445275)))], (6457 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(_445275, c_Groups_Ozero__class_Ozero(_445275), _445277))]]], (6459 ^ _227627) ^ [] : [-(c_Polynomial_Opos__poly(_445275, c_Polynomial_OpCons(_445275, _445277, _445279))), 6460 ^ _227627 : [(6461 ^ _227627) ^ [] : [c_Polynomial_Opos__poly(_445275, _445279)], (6463 ^ _227627) ^ [] : [_445279 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_445275)), c_Orderings_Oord__class_Oless(_445275, c_Groups_Ozero__class_Ozero(_445275), _445277)]]]]], (6471 ^ _227627) ^ [_446124, _446126, _446128] : [class_RealVector_Oreal__normed__algebra(_446124), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_446124), _446126), c_Groups_Ouminus__class_Ouminus(_446124, _446128)) = c_Groups_Ouminus__class_Ouminus(_446124, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_446124), _446126), _446128)))], (6477 ^ _227627) ^ [_446396, _446398, _446400] : [class_RealVector_Oreal__normed__algebra(_446396), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_446396), _446398), c_Groups_Ouminus__class_Ouminus(_446396, _446400)) = c_Groups_Ouminus__class_Ouminus(_446396, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_446396), _446398), _446400)))], (6483 ^ _227627) ^ [_446668, _446670, _446672] : [class_RealVector_Oreal__normed__algebra(_446668), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_446668), c_Groups_Ouminus__class_Ouminus(_446668, _446670)), _446672) = c_Groups_Ouminus__class_Ouminus(_446668, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_446668), _446670), _446672)))], (6489 ^ _227627) ^ [_446940, _446942, _446944] : [class_RealVector_Oreal__normed__algebra(_446940), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_446940), c_Groups_Ouminus__class_Ouminus(_446940, _446942)), _446944) = c_Groups_Ouminus__class_Ouminus(_446940, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_446940), _446942), _446944)))], (6495 ^ _227627) ^ [_447197, _447199, _447201] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _447197), _447199)), _447201) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _447197), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _447199), _447201)))], (6497 ^ _227627) ^ [_447317, _447319] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _447317)), _447319) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _447317), _447319)))], (6499 ^ _227627) ^ [_447429, _447431] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _447429), _447431) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _447431), _447429))], (6501 ^ _227627) ^ [_447521] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _447521), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _447521)], (6503 ^ _227627) ^ [_447605] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _447605) = _447605)], (6505 ^ _227627) ^ [] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (6507 ^ _227627) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (6509 ^ _227627) ^ [_447820, _447822] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _447820, _447822), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _447822, _447820), -(_447820 = _447822)], (6519 ^ _227627) ^ [_448137, _448139, _448141] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _448137, _448139), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _448139, _448141), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _448137, _448141))], (6529 ^ _227627) ^ [_448452, _448454] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _448452, _448454)), -(_448452 = _448454), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _448454, _448452))], (6539 ^ _227627) ^ [_448786, _448788] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _448786, _448788), 6542 ^ _227627 : [(6543 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _448786, _448788))], (6545 ^ _227627) ^ [] : [_448786 = _448788]]], (6547 ^ _227627) ^ [_449028, _449030] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _449028, _449030)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _449028, _449030), -(_449028 = _449030)], (6557 ^ _227627) ^ [_449364, _449366, _449368, _449370] : [class_Orderings_Oord(_449364), 6560 ^ _227627 : [(6561 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_fun(_449366, _449364), _449368, _449370), 6564 ^ _227627 : [(6565 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_fun(_449366, _449364), _449368, _449370))], (6567 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_449366, _449364), _449370, _449368)]]], (6569 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_fun(_449366, _449364), _449368, _449370)), c_Orderings_Oord__class_Oless__eq(tc_fun(_449366, _449364), _449368, _449370), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_449366, _449364), _449370, _449368))]]], (6579 ^ _227627) ^ [_450062, _450064] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _450062, _450064)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _450064, _450062))], (6585 ^ _227627) ^ [_450248] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _450248, _450248))], (6587 ^ _227627) ^ [_450370, _450372, _450374] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _450370, _450372), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _450374), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _450374), _450370), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _450374), _450372)))], (6597 ^ _227627) ^ [_450709, _450711] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _450709), 6600 ^ _227627 : [(6601 ^ _227627) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _450709), _450711) = c_Groups_Oone__class_Oone(tc_Int_Oint), 6604 ^ _227627 : [(6605 ^ _227627) ^ [] : [-(_450709 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (6607 ^ _227627) ^ [] : [-(_450711 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (6609 ^ _227627) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _450709), _450711) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _450709 = c_Groups_Oone__class_Oone(tc_Int_Oint), _450711 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (6619 ^ _227627) ^ [_451362] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _451362), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _451362))], (6625 ^ _227627) ^ [_451522] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _451522), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _451522))], (6631 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (6633 ^ _227627) ^ [_451771] : [class_Rings_Olinordered__idom(_451771), c_Polynomial_Opos__poly(_451771, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_451771)))], (6639 ^ _227627) ^ [_451996, _451998, _452000] : [class_Rings_Olinordered__idom(_451996), c_Polynomial_Opos__poly(_451996, _451998), c_Polynomial_Opos__poly(_451996, _452000), -(c_Polynomial_Opos__poly(_451996, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_451996)), _451998), _452000)))], (6653 ^ _227627) ^ [_452416, _452418] : [class_Rings_Olinordered__idom(_452416), -(_452418 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_452416))), -(c_Polynomial_Opos__poly(_452416, _452418)), -(c_Polynomial_Opos__poly(_452416, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_452416), _452418)))], (6667 ^ _227627) ^ [_452822, _452824] : [class_RealVector_Oreal__normed__algebra(_452822), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_452822), _452824), c_Groups_Ozero__class_Ozero(_452822)) = c_Groups_Ozero__class_Ozero(_452822))], (6673 ^ _227627) ^ [_453054, _453056] : [class_RealVector_Oreal__normed__algebra(_453054), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_453054), _453056), c_Groups_Ozero__class_Ozero(_453054)) = c_Groups_Ozero__class_Ozero(_453054))], (6679 ^ _227627) ^ [_453286, _453288] : [class_RealVector_Oreal__normed__algebra(_453286), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_453286), c_Groups_Ozero__class_Ozero(_453286)), _453288) = c_Groups_Ozero__class_Ozero(_453286))], (6685 ^ _227627) ^ [_453518, _453520] : [class_RealVector_Oreal__normed__algebra(_453518), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_453518), c_Groups_Ozero__class_Ozero(_453518)), _453520) = c_Groups_Ozero__class_Ozero(_453518))], (6691 ^ _227627) ^ [_453750, _453752] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _453750), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _453750), _453752)))], (6697 ^ _227627) ^ [_453990, _453992, _453994] : [-(_453990 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 6700 ^ _227627 : [(6701 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _453992), _453994)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _453990), _453992)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _453990), _453994))))], (6707 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _453990), _453992)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _453990), _453994))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _453992), _453994)))]]], (6713 ^ _227627) ^ [_454535, _454537] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _454535), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _454537), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _454535), _454537)))], (6723 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (6725 ^ _227627) ^ [_454876] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _454876)) = _454876)], (6727 ^ _227627) ^ [_455018, _455020] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _455018), _455020)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _455018), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _455020))))], (6733 ^ _227627) ^ [_455206, _455208] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _455206), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _455208))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _455206), _455208)))], (6739 ^ _227627) ^ [_455473, _455475] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _455473), _455475)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _455473)), _455475)))], (6745 ^ _227627) ^ [_455661, _455663] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _455661)), _455663)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _455661), _455663)))], (6751 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (6753 ^ _227627) ^ [_455966, _455968, _455970] : [class_Lattices_Oboolean__algebra(_455966), 6756 ^ _227627 : [(6757 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_455966, c_Groups_Ouminus__class_Ouminus(_455966, _455968), c_Groups_Ouminus__class_Ouminus(_455966, _455970)), -(c_Orderings_Oord__class_Oless__eq(_455966, _455970, _455968))], (6763 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_455966, _455970, _455968), -(c_Orderings_Oord__class_Oless__eq(_455966, c_Groups_Ouminus__class_Ouminus(_455966, _455968), c_Groups_Ouminus__class_Ouminus(_455966, _455970)))]]], (6769 ^ _227627) ^ [_456478, _456480, _456482] : [class_Lattices_Oboolean__algebra(_456478), c_Orderings_Oord__class_Oless__eq(_456478, _456480, _456482), -(c_Orderings_Oord__class_Oless__eq(_456478, c_Groups_Ouminus__class_Ouminus(_456478, _456482), c_Groups_Ouminus__class_Ouminus(_456478, _456480)))], (6779 ^ _227627) ^ [_456829, _456831, _456833, _456835] : [class_Rings_Ocomm__ring__1(_456829), -(hAPP(c_Polynomial_Opoly(_456829, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_456829)), c_Polynomial_Omonom(_456829, c_Groups_Oone__class_Oone(_456829), _456831)), _456833)), _456835) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_456829), hAPP(hAPP(c_Power_Opower__class_Opower(_456829), _456835), _456831)), hAPP(c_Polynomial_Opoly(_456829, _456833), _456835)))], (6785 ^ _227627) ^ [_457193, _457195, _457197, _457199, _457201, _457203] : [class_Groups_Ozero(_457193), hAPP(hAPP(hAPP(_457195, c_Groups_Ozero__class_Ozero(_457193)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_457193))), _457197) = _457197, -(c_Polynomial_Opoly__rec(_457199, _457193, _457197, _457195, c_Polynomial_OpCons(_457193, _457201, _457203)) = hAPP(hAPP(hAPP(_457195, _457201), _457203), c_Polynomial_Opoly__rec(_457199, _457193, _457197, _457195, _457203)))], (6795 ^ _227627) ^ [_457638, _457640, _457642, _457644] : [class_Groups_Ozero(_457638), 6798 ^ _227627 : [(6799 ^ _227627) ^ [] : [c_Polynomial_Omonom(_457638, _457640, _457642) = c_Polynomial_Omonom(_457638, _457644, _457642), -(_457640 = _457644)], (6805 ^ _227627) ^ [] : [_457640 = _457644, -(c_Polynomial_Omonom(_457638, _457640, _457642) = c_Polynomial_Omonom(_457638, _457644, _457642))]]], (6811 ^ _227627) ^ [_458166, _458168, _458170] : [class_Groups_Ozero(_458166), 6814 ^ _227627 : [(6815 ^ _227627) ^ [] : [c_Polynomial_Omonom(_458166, _458168, _458170) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_458166)), -(_458168 = c_Groups_Ozero__class_Ozero(_458166))], (6821 ^ _227627) ^ [] : [_458168 = c_Groups_Ozero__class_Ozero(_458166), -(c_Polynomial_Omonom(_458166, _458168, _458170) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_458166)))]]], (6827 ^ _227627) ^ [_458670, _458672] : [class_Groups_Ozero(_458670), -(c_Polynomial_Omonom(_458670, c_Groups_Ozero__class_Ozero(_458670), _458672) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_458670)))], (6833 ^ _227627) ^ [_458912, _458914, _458916] : [class_Groups_Ozero(_458912), -(_458914 = c_Groups_Ozero__class_Ozero(_458912)), -(c_Polynomial_Odegree(_458912, c_Polynomial_Omonom(_458912, _458914, _458916)) = _458916)], (6843 ^ _227627) ^ [_459254, _459256, _459258] : [class_Groups_Ozero(_459254), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_459254, c_Polynomial_Omonom(_459254, _459256, _459258)), _459258))], (6849 ^ _227627) ^ [_459498, _459500, _459502] : [class_Groups_Oab__group__add(_459498), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_459498), c_Polynomial_Omonom(_459498, _459500, _459502)) = c_Polynomial_Omonom(_459498, c_Groups_Ouminus__class_Ouminus(_459498, _459500), _459502))], (6855 ^ _227627) ^ [_459758, _459760, _459762] : [class_Lattices_Oab__semigroup__idem__mult(_459758), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_459758), _459760), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_459758), _459760), _459762)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_459758), _459760), _459762))], (6861 ^ _227627) ^ [_460020, _460022] : [class_Lattices_Oab__semigroup__idem__mult(_460020), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_460020), _460022), _460022) = _460022)], (6867 ^ _227627) ^ [_460244, _460246] : [class_Lattices_Oab__semigroup__idem__mult(_460244), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_460244), _460246), _460246) = _460246)], (6873 ^ _227627) ^ [_460482, _460484, _460486] : [class_Lattices_Oboolean__algebra(_460482), 6876 ^ _227627 : [(6877 ^ _227627) ^ [] : [c_Groups_Ouminus__class_Ouminus(_460482, _460484) = c_Groups_Ouminus__class_Ouminus(_460482, _460486), -(_460484 = _460486)], (6883 ^ _227627) ^ [] : [_460484 = _460486, -(c_Groups_Ouminus__class_Ouminus(_460482, _460484) = c_Groups_Ouminus__class_Ouminus(_460482, _460486))]]], (6889 ^ _227627) ^ [_461002, _461004, _461006, _461008] : [class_Groups_Ouminus(_461002), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_461004, _461002), _461006), _461008) = c_Groups_Ouminus__class_Ouminus(_461002, hAPP(_461006, _461008)))], (6895 ^ _227627) ^ [_461252, _461254] : [class_Lattices_Oboolean__algebra(_461252), -(c_Groups_Ouminus__class_Ouminus(_461252, c_Groups_Ouminus__class_Ouminus(_461252, _461254)) = _461254)], (6901 ^ _227627) ^ [_461486, _461488, _461490] : [class_Groups_Ozero(_461486), -(c_Polynomial_Omonom(_461486, _461488, c_Nat_OSuc(_461490)) = c_Polynomial_OpCons(_461486, c_Groups_Ozero__class_Ozero(_461486), c_Polynomial_Omonom(_461486, _461488, _461490)))], (6907 ^ _227627) ^ [_461760, _461762, _461764, _461766] : [class_Rings_Ocomm__semiring__1(_461760), -(hAPP(c_Polynomial_Opoly(_461760, c_Polynomial_Omonom(_461760, _461762, _461764)), _461766) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_461760), _461762), hAPP(hAPP(c_Power_Opower__class_Opower(_461760), _461766), _461764)))], (6913 ^ _227627) ^ [_462032, _462034] : [class_Groups_Ozero(_462032), -(c_Polynomial_Omonom(_462032, _462034, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(_462032, _462034, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_462032))))], (6919 ^ _227627) ^ [_462292, _462294, _462296, _462298] : [class_Groups_Ozero(_462292), hAPP(hAPP(hAPP(_462294, c_Groups_Ozero__class_Ozero(_462292)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_462292))), _462296) = _462296, -(c_Polynomial_Opoly__rec(_462298, _462292, _462296, _462294, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_462292))) = _462296)], (6929 ^ _227627) ^ [_462715, _462717, _462719, _462721, _462723, _462725] : [class_Groups_Ozero(_462715), -(c_Polynomial_Opoly__rec(_462717, _462715, _462719, _462721, c_Polynomial_OpCons(_462715, _462723, _462725)) = hAPP(hAPP(hAPP(_462721, _462723), _462725), c_If(_462717, c_fequal(_462725, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_462715))), _462719, c_Polynomial_Opoly__rec(_462717, _462715, _462719, _462721, _462725))))], (6935 ^ _227627) ^ [_463035, _463037, _463039] : [class_Rings_Ocomm__semiring__0(_463035), 6938 ^ _227627 : [(6939 ^ _227627) ^ [] : [c_Polynomial_Osynthetic__div(_463035, _463037, _463039) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_463035)), -(c_Polynomial_Odegree(_463035, _463037) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6945 ^ _227627) ^ [] : [c_Polynomial_Odegree(_463035, _463037) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Polynomial_Osynthetic__div(_463035, _463037, _463039) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_463035)))]]], (6951 ^ _227627) ^ [_463556, _463558, _463560] : [class_Groups_Ozero(_463556), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_463556, _463558), _463560), hAPP(c_Polynomial_Ocoeff(_463556, _463558), _463560) = c_Groups_Ozero__class_Ozero(_463556), -(_463558 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_463556))), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_463556, _463558), _463560))], (6969 ^ _227627) ^ [_464104, _464106, _464108] : [class_Groups_Omonoid__mult(_464104), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _464106), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_464104), hAPP(hAPP(c_Power_Opower__class_Opower(_464104), _464108), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _464106, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _464108) = hAPP(hAPP(c_Power_Opower__class_Opower(_464104), _464108), _464106))], (6979 ^ _227627) ^ [_464497, _464499, _464501, _464503] : [class_Orderings_Oorder(_464497), c_Orderings_Oorder_Omono(tc_Nat_Onat, _464497, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _464499), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _464501), _464503)), -(c_Orderings_Oord__class_Oless__eq(_464497, hAPP(_464499, _464501), hAPP(_464499, _464503)))], (6993 ^ _227627) ^ [_464981, _464983, _464985, _464987, _464989] : [class_Groups_Ominus(_464981), -(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_464983, _464981), _464985, _464987), _464989) = c_Groups_Ominus__class_Ominus(_464981, hAPP(_464985, _464989), hAPP(_464987, _464989)))], (6999 ^ _227627) ^ [_465275, _465277, _465279, _465281] : [class_Groups_Oab__group__add(_465275), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_465275), c_Polynomial_Omonom(_465275, _465277, _465279), c_Polynomial_Omonom(_465275, _465281, _465279)) = c_Polynomial_Omonom(_465275, c_Groups_Ominus__class_Ominus(_465275, _465277, _465281), _465279))], (7005 ^ _227627) ^ [_465553, _465555, _465557] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _465553, _465555), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _465553, _465557), 7012 ^ _227627 : [(7013 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _465555, _465553), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _465557, _465553)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _465555, _465557))], (7019 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _465555, _465557), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _465555, _465553), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _465557, _465553)))]]], (7025 ^ _227627) ^ [_466170, _466172, _466174] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _466170, _466172), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _466170, _466174), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _466172, _466170), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _466174, _466170)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _466172, _466174))], (7035 ^ _227627) ^ [_466529, _466531, _466533] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _466529, _466531), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _466529, _466533), 7042 ^ _227627 : [(7043 ^ _227627) ^ [] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _466531, _466529) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _466533, _466529), -(_466531 = _466533)], (7049 ^ _227627) ^ [] : [_466531 = _466533, -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _466531, _466529) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _466533, _466529))]]], (7055 ^ _227627) ^ [_467126, _467128] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _467126, _467128), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _467128, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _467128, _467126)) = _467126)], (7061 ^ _227627) ^ [_467368, _467370, _467372] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _467368, _467370), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _467368, _467372), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _467370, _467372)))], (7067 ^ _227627) ^ [_467618, _467620, _467622] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _467618, _467620), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _467622, _467620), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _467622, _467618)))], (7073 ^ _227627) ^ [_467839, _467841] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _467839, _467841), _467839))], (7075 ^ _227627) ^ [_467952, _467954, _467956] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _467952), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _467954, _467956)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _467952), _467954), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _467952), _467956)))], (7077 ^ _227627) ^ [_468088, _468090, _468092] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _468088, _468090)), _468092) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _468088), _468092), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _468090), _468092)))], (7079 ^ _227627) ^ [_468253, _468255, _468257, _468259] : [class_RealVector_Oreal__normed__algebra(_468253), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_468253), _468255), c_Groups_Ominus__class_Ominus(_468253, _468257, _468259)) = c_Groups_Ominus__class_Ominus(_468253, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_468253), _468255), _468257), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_468253), _468255), _468259)))], (7085 ^ _227627) ^ [_468565, _468567, _468569, _468571] : [class_RealVector_Oreal__normed__algebra(_468565), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_468565), _468567), c_Groups_Ominus__class_Ominus(_468565, _468569, _468571)) = c_Groups_Ominus__class_Ominus(_468565, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_468565), _468567), _468569), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_468565), _468567), _468571)))], (7091 ^ _227627) ^ [_468877, _468879, _468881, _468883] : [class_RealVector_Oreal__normed__algebra(_468877), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_468877), c_Groups_Ominus__class_Ominus(_468877, _468879, _468881)), _468883) = c_Groups_Ominus__class_Ominus(_468877, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_468877), _468879), _468883), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_468877), _468881), _468883)))], (7097 ^ _227627) ^ [_469189, _469191, _469193, _469195] : [class_RealVector_Oreal__normed__algebra(_469189), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_469189), c_Groups_Ominus__class_Ominus(_469189, _469191, _469193)), _469195) = c_Groups_Ominus__class_Ominus(_469189, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_469189), _469191), _469195), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_469189), _469193), _469195)))], (7103 ^ _227627) ^ [_469444] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _469444) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7105 ^ _227627) ^ [_469526] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _469526, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _469526)], (7107 ^ _227627) ^ [_469608] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _469608, _469608) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7109 ^ _227627) ^ [_469719, _469721] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _469719, _469721) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _469721, _469719) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_469719 = _469721)], (7119 ^ _227627) ^ [_470048, _470050, _470052] : [class_Groups_Ogroup__add(_470048), 7122 ^ _227627 : [(7123 ^ _227627) ^ [] : [c_Groups_Ominus__class_Ominus(_470048, _470050, _470052) = c_Groups_Ozero__class_Ozero(_470048), -(_470050 = _470052)], (7129 ^ _227627) ^ [] : [_470050 = _470052, -(c_Groups_Ominus__class_Ominus(_470048, _470050, _470052) = c_Groups_Ozero__class_Ozero(_470048))]]], (7135 ^ _227627) ^ [_470554, _470556, _470558] : [class_Groups_Oab__group__add(_470554), 7138 ^ _227627 : [(7139 ^ _227627) ^ [] : [_470556 = _470558, -(c_Groups_Ominus__class_Ominus(_470554, _470556, _470558) = c_Groups_Ozero__class_Ozero(_470554))], (7145 ^ _227627) ^ [] : [c_Groups_Ominus__class_Ominus(_470554, _470556, _470558) = c_Groups_Ozero__class_Ozero(_470554), -(_470556 = _470558)]]], (7151 ^ _227627) ^ [_471046, _471048] : [class_Groups_Ogroup__add(_471046), -(c_Groups_Ominus__class_Ominus(_471046, _471048, _471048) = c_Groups_Ozero__class_Ozero(_471046))], (7157 ^ _227627) ^ [_471266, _471268] : [class_Groups_Ogroup__add(_471266), -(c_Groups_Ominus__class_Ominus(_471266, _471268, c_Groups_Ozero__class_Ozero(_471266)) = _471268)], (7163 ^ _227627) ^ [_471528, _471530, _471532, _471534, _471536] : [class_Groups_Oordered__ab__group__add(_471528), c_Groups_Ominus__class_Ominus(_471528, _471530, _471532) = c_Groups_Ominus__class_Ominus(_471528, _471534, _471536), 7170 ^ _227627 : [(7171 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_471528, _471530, _471532), -(c_Orderings_Oord__class_Oless__eq(_471528, _471534, _471536))], (7177 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_471528, _471534, _471536), -(c_Orderings_Oord__class_Oless__eq(_471528, _471530, _471532))]]], (7183 ^ _227627) ^ [_472185, _472187, _472189, _472191] : [class_Rings_Ocomm__ring__1(_472185), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_472185), _472187), _472189)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_472185), _472187), _472191)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_472185), _472187), c_Groups_Ominus__class_Ominus(_472185, _472189, _472191))))], (7197 ^ _227627) ^ [_472691, _472693, _472695, _472697, _472699] : [class_Groups_Oab__group__add(_472691), c_Groups_Ominus__class_Ominus(_472691, _472693, _472695) = c_Groups_Ominus__class_Ominus(_472691, _472697, _472699), 7204 ^ _227627 : [(7205 ^ _227627) ^ [] : [_472693 = _472695, -(_472697 = _472699)], (7211 ^ _227627) ^ [] : [_472697 = _472699, -(_472693 = _472695)]]], (7217 ^ _227627) ^ [_473313, _473315, _473317] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _473313, _473315), _473317) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _473313, _473317), _473315))], (7219 ^ _227627) ^ [_473468, _473470, _473472, _473474] : [class_Rings_Ocomm__ring(_473468), -(hAPP(c_Polynomial_Opoly(_473468, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_473468), _473470, _473472)), _473474) = c_Groups_Ominus__class_Ominus(_473468, hAPP(c_Polynomial_Opoly(_473468, _473470), _473474), hAPP(c_Polynomial_Opoly(_473468, _473472), _473474)))], (7225 ^ _227627) ^ [_473758, _473760, _473762] : [class_Groups_Ozero(_473758), 7228 ^ _227627 : [(7229 ^ _227627) ^ [] : [_473760 = _473762, 7232 ^ _227627 : [(7233 ^ _227627) ^ [_474006] : [-(hAPP(c_Polynomial_Ocoeff(_473758, _473760), _474006) = hAPP(c_Polynomial_Ocoeff(_473758, _473762), _474006))]]], (7235 ^ _227627) ^ [] : [hAPP(c_Polynomial_Ocoeff(_473758, _473760), 7236 ^ [_473758, _473760, _473762]) = hAPP(c_Polynomial_Ocoeff(_473758, _473762), 7236 ^ [_473758, _473760, _473762]), -(_473760 = _473762)]]], (7242 ^ _227627) ^ [_474383, _474385, _474387] : [class_Groups_Ozero(_474383), 7245 ^ _227627 : [(7246 ^ _227627) ^ [] : [c_Polynomial_Ocoeff(_474383, _474385) = c_Polynomial_Ocoeff(_474383, _474387), -(_474385 = _474387)], (7252 ^ _227627) ^ [] : [_474385 = _474387, -(c_Polynomial_Ocoeff(_474383, _474385) = c_Polynomial_Ocoeff(_474383, _474387))]]], (7258 ^ _227627) ^ [_474903, _474905, _474907, _474909] : [class_Groups_Oab__group__add(_474903), -(hAPP(c_Polynomial_Ocoeff(_474903, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_474903), _474905, _474907)), _474909) = c_Groups_Ominus__class_Ominus(_474903, hAPP(c_Polynomial_Ocoeff(_474903, _474905), _474909), hAPP(c_Polynomial_Ocoeff(_474903, _474907), _474909)))], (7264 ^ _227627) ^ [_475221, _475223, _475225, _475227, _475229] : [class_Groups_Oab__group__add(_475221), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_475221), c_Polynomial_OpCons(_475221, _475223, _475225), c_Polynomial_OpCons(_475221, _475227, _475229)) = c_Polynomial_OpCons(_475221, c_Groups_Ominus__class_Ominus(_475221, _475223, _475227), c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_475221), _475225, _475229)))], (7270 ^ _227627) ^ [_475517, _475519, _475521] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _475517), _475519)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _475517), _475521)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _475517), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _475519, _475521))))], (7280 ^ _227627) ^ [_475849, _475851] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_475849), c_Nat_OSuc(_475851)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _475849, _475851))], (7282 ^ _227627) ^ [_475969, _475971, _475973] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_475969), _475971), c_Nat_OSuc(_475973)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _475969, _475971), _475973))], (7284 ^ _227627) ^ [_476114, _476116, _476118] : [class_Groups_Oab__group__add(_476114), -(c_Groups_Ouminus__class_Ouminus(_476114, c_Groups_Ominus__class_Ominus(_476114, _476116, _476118)) = c_Groups_Ominus__class_Ominus(_476114, _476118, _476116))], (7290 ^ _227627) ^ [_476364, _476366, _476368] : [class_Rings_Ocomm__semiring__0(_476364), -(c_Polynomial_Odegree(_476364, c_Polynomial_Osynthetic__div(_476364, _476366, _476368)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Polynomial_Odegree(_476364, _476366), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (7296 ^ _227627) ^ [_476648, _476650, _476652, _476654, _476656] : [class_Groups_Oordered__ab__group__add(_476648), c_Groups_Ominus__class_Ominus(_476648, _476650, _476652) = c_Groups_Ominus__class_Ominus(_476648, _476654, _476656), 7303 ^ _227627 : [(7304 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_476648, _476650, _476652), -(c_Orderings_Oord__class_Oless(_476648, _476654, _476656))], (7310 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_476648, _476654, _476656), -(c_Orderings_Oord__class_Oless(_476648, _476650, _476652))]]], (7316 ^ _227627) ^ [_477291, _477293, _477295] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _477291, _477293), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _477291, _477295), _477293))], (7322 ^ _227627) ^ [_477533, _477535, _477537] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _477533, _477535), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _477533, _477537), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _477537, _477535), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _477537, _477533)))], (7332 ^ _227627) ^ [_477878, _477880, _477882] : [class_Groups_Oordered__ab__group__add(_477878), 7335 ^ _227627 : [(7336 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_477878, _477880, _477882), -(c_Orderings_Oord__class_Oless__eq(_477878, c_Groups_Ominus__class_Ominus(_477878, _477880, _477882), c_Groups_Ozero__class_Ozero(_477878)))], (7342 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_477878, c_Groups_Ominus__class_Ominus(_477878, _477880, _477882), c_Groups_Ozero__class_Ozero(_477878)), -(c_Orderings_Oord__class_Oless__eq(_477878, _477880, _477882))]]], (7348 ^ _227627) ^ [_478390, _478392, _478394] : [class_Groups_Oordered__ab__group__add(_478390), 7351 ^ _227627 : [(7352 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_478390, _478392, _478394), -(c_Orderings_Oord__class_Oless(_478390, c_Groups_Ominus__class_Ominus(_478390, _478392, _478394), c_Groups_Ozero__class_Ozero(_478390)))], (7358 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_478390, c_Groups_Ominus__class_Ominus(_478390, _478392, _478394), c_Groups_Ozero__class_Ozero(_478390)), -(c_Orderings_Oord__class_Oless(_478390, _478392, _478394))]]], (7364 ^ _227627) ^ [_478888, _478890] : [class_Groups_Ogroup__add(_478888), -(c_Groups_Ominus__class_Ominus(_478888, c_Groups_Ozero__class_Ozero(_478888), _478890) = c_Groups_Ouminus__class_Ouminus(_478888, _478890))], (7370 ^ _227627) ^ [_479114, _479116] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _479114), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _479116), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _479116, _479114), _479116))], (7380 ^ _227627) ^ [_479456, _479458] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _479456, _479458)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _479458, _479456))], (7386 ^ _227627) ^ [_479630, _479632] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _479632, _479630), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _479630, _479632)))], (7392 ^ _227627) ^ [_479839, _479841] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _479839, _479841), c_Nat_OSuc(_479839)))], (7394 ^ _227627) ^ [_479955, _479957] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _479955, _479957), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _479955, _479957) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7400 ^ _227627) ^ [_480204, _480206] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _480204, _480206) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _480204, _480206))], (7406 ^ _227627) ^ [_480376, _480378] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _480376, _480378), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _480376, _480378) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7412 ^ _227627) ^ [_480598, _480600] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _480598, _480600), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_480600), _480598) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _480600, _480598)))], (7418 ^ _227627) ^ [_480834, _480836] : [class_Groups_Ozero(_480834), -(hAPP(c_Polynomial_Ocoeff(_480834, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_480834))), _480836) = c_Groups_Ozero__class_Ozero(_480834))], (7424 ^ _227627) ^ [_481080, _481082, _481084] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _481080, _481082), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _481080, _481084), 7431 ^ _227627 : [(7432 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _481082, _481080), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _481084, _481080)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _481082, _481084))], (7438 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _481082, _481084), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _481082, _481080), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _481084, _481080)))]]], (7444 ^ _227627) ^ [_481697, _481699, _481701] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _481697, _481699), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _481701, _481697), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _481697, _481701), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _481699, _481701)))], (7454 ^ _227627) ^ [_482042, _482044, _482046] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _482042), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _482044, _482046))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _482042), _482046)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _482046, _482044), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _482042), _482044)))], (7468 ^ _227627) ^ [_482498, _482500, _482502] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _482498), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _482500, _482502))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _482498), _482500)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _482502, _482500), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _482498), _482502)))], (7482 ^ _227627) ^ [_482925, _482927] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _482925, c_Nat_OSuc(_482927)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _482925, c_Groups_Oone__class_Oone(tc_Nat_Onat)), _482927))], (7484 ^ _227627) ^ [_483019] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_483019), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _483019)], (7486 ^ _227627) ^ [_483146, _483148, _483150] : [class_Groups_Ozero(_483146), -(hAPP(c_Polynomial_Ocoeff(_483146, c_Polynomial_OpCons(_483146, _483148, _483150)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _483148)], (7492 ^ _227627) ^ [_483408, _483410, _483412, _483414] : [class_Groups_Ozero(_483408), -(hAPP(c_Polynomial_Ocoeff(_483408, c_Polynomial_OpCons(_483408, _483410, _483412)), c_Nat_OSuc(_483414)) = hAPP(c_Polynomial_Ocoeff(_483408, _483412), _483414))], (7498 ^ _227627) ^ [_483692, _483694, _483696, _483698] : [class_Groups_Ozero(_483692), 7501 ^ _227627 : [(7502 ^ _227627) ^ [] : [_483694 = _483696, -(hAPP(c_Polynomial_Ocoeff(_483692, c_Polynomial_Omonom(_483692, _483698, _483694)), _483696) = _483698)], (7508 ^ _227627) ^ [] : [-(_483694 = _483696), -(hAPP(c_Polynomial_Ocoeff(_483692, c_Polynomial_Omonom(_483692, _483698, _483694)), _483696) = c_Groups_Ozero__class_Ozero(_483692))]]], (7514 ^ _227627) ^ [_484232, _484234] : [class_Rings_Ocomm__semiring__0(_484232), -(c_Polynomial_Osynthetic__div(_484232, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_484232)), _484234) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_484232)))], (7520 ^ _227627) ^ [_484478, _484480, _484482] : [class_Groups_Oab__group__add(_484478), -(hAPP(c_Polynomial_Ocoeff(_484478, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_484478), _484480)), _484482) = c_Groups_Ouminus__class_Ouminus(_484478, hAPP(c_Polynomial_Ocoeff(_484478, _484480), _484482)))], (7526 ^ _227627) ^ [_484746, _484748, _484750] : [class_Rings_Oidom(_484746), hAPP(c_Polynomial_Ocoeff(_484746, _484748), c_Polynomial_Odegree(_484746, _484748)) = hAPP(c_Polynomial_Ocoeff(_484746, _484750), c_Polynomial_Odegree(_484746, _484750)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_484746)), _484748), _484750)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_484746)), _484750), _484748)), -(_484748 = _484750)], (7544 ^ _227627) ^ [_485297] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _485297), -(c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _485297, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _485297)], (7550 ^ _227627) ^ [_485515, _485517] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _485515), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _485515, c_Nat_OSuc(_485517)), _485515))], (7556 ^ _227627) ^ [_485755, _485757, _485759] : [class_Groups_Ozero(_485755), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_485755, _485757), _485759), -(hAPP(c_Polynomial_Ocoeff(_485755, _485757), _485759) = c_Groups_Ozero__class_Ozero(_485755))], (7566 ^ _227627) ^ [_486100, _486102, _486104] : [class_Groups_Ozero(_486100), -(hAPP(c_Polynomial_Ocoeff(_486100, _486102), _486104) = c_Groups_Ozero__class_Ozero(_486100)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _486104, c_Polynomial_Odegree(_486100, _486102)))], (7576 ^ _227627) ^ [_486434, _486436] : [class_Groups_Ozero(_486434), 7579 ^ _227627 : [(7580 ^ _227627) ^ [] : [hAPP(c_Polynomial_Ocoeff(_486434, _486436), c_Polynomial_Odegree(_486434, _486436)) = c_Groups_Ozero__class_Ozero(_486434), -(_486436 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_486434)))], (7586 ^ _227627) ^ [] : [_486436 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_486434)), -(hAPP(c_Polynomial_Ocoeff(_486434, _486436), c_Polynomial_Odegree(_486434, _486436)) = c_Groups_Ozero__class_Ozero(_486434))]]], (7592 ^ _227627) ^ [_486937, _486939] : [class_Groups_Ozero(_486937), -(_486939 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_486937))), hAPP(c_Polynomial_Ocoeff(_486937, _486939), c_Polynomial_Odegree(_486937, _486939)) = c_Groups_Ozero__class_Ozero(_486937)], (7602 ^ _227627) ^ [_487254] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _487254), -(_487254 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _487254, c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (7608 ^ _227627) ^ [_487458] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _487458), -(c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _487458, c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _487458)], (7614 ^ _227627) ^ [_487704, _487706, _487708, _487710] : [class_Rings_Ocomm__semiring__0(_487704), -(c_Polynomial_Osynthetic__div(_487704, c_Polynomial_OpCons(_487704, _487706, _487708), _487710) = c_Polynomial_OpCons(_487704, hAPP(c_Polynomial_Opoly(_487704, _487708), _487710), c_Polynomial_Osynthetic__div(_487704, _487708, _487710)))], (7620 ^ _227627) ^ [_487988, _487990] : [_487988 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _487990), _487988) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (7626 ^ _227627) ^ [_488162, _488164] : [-(_488162 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _488164), _488162) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _488164), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _488164), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _488162, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (7632 ^ _227627) ^ [_488421, _488423] : [class_Rings_Ocomm__semiring__1(_488421), 7635 ^ _227627 : [(7636 ^ _227627) ^ [] : [_488423 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Polynomial_Ocoeff(_488421, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_488421))), _488423) = c_Groups_Oone__class_Oone(_488421))], (7642 ^ _227627) ^ [] : [-(_488423 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_Polynomial_Ocoeff(_488421, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_488421))), _488423) = c_Groups_Ozero__class_Ozero(_488421))]]], (7648 ^ _227627) ^ [_488933, _488935] : [class_Rings_Olinordered__idom(_488933), 7651 ^ _227627 : [(7652 ^ _227627) ^ [] : [c_Polynomial_Opos__poly(_488933, _488935), -(c_Orderings_Oord__class_Oless(_488933, c_Groups_Ozero__class_Ozero(_488933), hAPP(c_Polynomial_Ocoeff(_488933, _488935), c_Polynomial_Odegree(_488933, _488935))))], (7658 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_488933, c_Groups_Ozero__class_Ozero(_488933), hAPP(c_Polynomial_Ocoeff(_488933, _488935), c_Polynomial_Odegree(_488933, _488935))), -(c_Polynomial_Opos__poly(_488933, _488935))]]], (7664 ^ _227627) ^ [_489441, _489443, _489445] : [class_Rings_Ocomm__semiring__1(_489441), -(hAPP(c_Polynomial_Ocoeff(_489441, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_489441)), c_Polynomial_OpCons(_489441, _489443, c_Polynomial_OpCons(_489441, c_Groups_Oone__class_Oone(_489441), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_489441))))), _489445)), _489445) = c_Groups_Oone__class_Oone(_489441))], (7670 ^ _227627) ^ [_489733, _489735, _489737] : [class_Power_Opower(_489733), 7673 ^ _227627 : [(7674 ^ _227627) ^ [] : [_489735 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_489733), _489737), _489735) = c_Groups_Oone__class_Oone(_489733))], (7680 ^ _227627) ^ [] : [-(_489735 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_489733), _489737), _489735) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_489733), _489737), hAPP(hAPP(c_Power_Opower__class_Opower(_489733), _489737), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _489735, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (7686 ^ _227627) ^ [_490317, _490319, _490321, _490323] : [class_Groups_Omonoid__mult(_490317), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _490319, _490321), -(hAPP(hAPP(c_Power_Opower__class_Opower(_490317), _490323), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_490321), _490319)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_490317), hAPP(hAPP(c_Power_Opower__class_Opower(_490317), _490323), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _490321, _490319))), _490323))], (7696 ^ _227627) ^ [_490718, _490720, _490722] : [class_Rings_Ocomm__ring__1(_490718), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_490718), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_490718)), c_Polynomial_OpCons(_490718, c_Groups_Ouminus__class_Ouminus(_490718, _490720), c_Polynomial_OpCons(_490718, c_Groups_Oone__class_Oone(_490718), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_490718))))), c_Polynomial_Osynthetic__div(_490718, _490722, _490720)), c_Polynomial_OpCons(_490718, hAPP(c_Polynomial_Opoly(_490718, _490722), _490720), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_490718)))) = _490722)], (7702 ^ _227627) ^ [_491048, _491050, _491052] : [class_Groups_Oab__group__add(_491048), -(c_Groups_Ominus__class_Ominus(_491048, c_Groups_Ouminus__class_Ouminus(_491048, _491050), c_Groups_Ouminus__class_Ouminus(_491048, _491052)) = c_Groups_Ouminus__class_Ouminus(_491048, c_Groups_Ominus__class_Ominus(_491048, _491050, _491052)))], (7708 ^ _227627) ^ [_491295, _491297, _491299] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _491295, _491297)), _491299) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _491295), _491299), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _491297), _491299)))], (7710 ^ _227627) ^ [_491431, _491433, _491435] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _491431), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _491433, _491435)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _491431), _491433), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _491431), _491435)))], (7712 ^ _227627) ^ [_491568, _491570] : [class_Groups_Oab__group__add(_491568), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_491568), _491570, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_491568))) = _491570)], (7718 ^ _227627) ^ [_491810, _491812, _491814] : [class_Rings_Olinordered__idom(_491810), 7721 ^ _227627 : [(7732 ^ _227627) ^ [] : [7733 ^ _227627 : [(7734 ^ _227627) ^ [] : [_491812 = _491814], (7736 ^ _227627) ^ [] : [c_Polynomial_Opos__poly(_491810, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_491810), _491814, _491812))]], -(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(_491810), _491812, _491814))], (7722 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(_491810), _491812, _491814), -(_491812 = _491814), -(c_Polynomial_Opos__poly(_491810, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_491810), _491814, _491812)))]]], (7740 ^ _227627) ^ [_492489, _492491, _492493] : [class_Groups_Ogroup__add(_492489), -(c_Groups_Oplus__class_Oplus(_492489, c_Groups_Ominus__class_Ominus(_492489, _492491, _492493), _492493) = _492491)], (7746 ^ _227627) ^ [_492733, _492735, _492737] : [class_Groups_Ogroup__add(_492733), -(c_Groups_Ominus__class_Ominus(_492733, c_Groups_Oplus__class_Oplus(_492733, _492735, _492737), _492737) = _492735)], (7752 ^ _227627) ^ [_492991, _492993, _492995, _492997] : [class_Groups_Ocomm__monoid__add(_492991), -(hAPP(c_Polynomial_Ocoeff(_492991, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_492991), _492993, _492995)), _492997) = c_Groups_Oplus__class_Oplus(_492991, hAPP(c_Polynomial_Ocoeff(_492991, _492993), _492997), hAPP(c_Polynomial_Ocoeff(_492991, _492995), _492997)))], (7758 ^ _227627) ^ [_493281, _493283, _493285] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _493281), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _493283, _493285))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _493281), _493285)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _493281), _493283)))], (7768 ^ _227627) ^ [_493642, _493644, _493646] : [class_Groups_Ogroup__add(_493642), -(c_Groups_Oplus__class_Oplus(_493642, c_Groups_Ouminus__class_Ouminus(_493642, _493644), c_Groups_Oplus__class_Oplus(_493642, _493644, _493646)) = _493646)], (7774 ^ _227627) ^ [_493892, _493894, _493896] : [class_Groups_Ogroup__add(_493892), -(c_Groups_Oplus__class_Oplus(_493892, _493894, c_Groups_Oplus__class_Oplus(_493892, c_Groups_Ouminus__class_Ouminus(_493892, _493894), _493896)) = _493896)], (7780 ^ _227627) ^ [_494142, _494144, _494146] : [class_Groups_Ogroup__add(_494142), -(c_Groups_Ouminus__class_Ouminus(_494142, c_Groups_Oplus__class_Oplus(_494142, _494144, _494146)) = c_Groups_Oplus__class_Oplus(_494142, c_Groups_Ouminus__class_Ouminus(_494142, _494146), c_Groups_Ouminus__class_Ouminus(_494142, _494144)))], (7786 ^ _227627) ^ [_494404, _494406, _494408] : [class_Groups_Oab__group__add(_494404), -(c_Groups_Ouminus__class_Ouminus(_494404, c_Groups_Oplus__class_Oplus(_494404, _494406, _494408)) = c_Groups_Oplus__class_Oplus(_494404, c_Groups_Ouminus__class_Ouminus(_494404, _494406), c_Groups_Ouminus__class_Ouminus(_494404, _494408)))], (7792 ^ _227627) ^ [_494666, _494668, _494670] : [class_Rings_Olinordered__idom(_494666), 7795 ^ _227627 : [(7796 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_494666), _494668, _494670), -(c_Polynomial_Opos__poly(_494666, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_494666), _494670, _494668)))], (7802 ^ _227627) ^ [] : [c_Polynomial_Opos__poly(_494666, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_494666), _494670, _494668)), -(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_494666), _494668, _494670))]]], (7808 ^ _227627) ^ [_495195, _495197, _495199, _495201] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_495195), c_Orderings_Oord__class_Oless(_495195, c_Groups_Oplus__class_Oplus(_495195, _495197, _495199), c_Groups_Oplus__class_Oplus(_495195, _495197, _495201)), -(c_Orderings_Oord__class_Oless(_495195, _495199, _495201))], (7818 ^ _227627) ^ [_495560, _495562, _495564, _495566] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_495560), c_Orderings_Oord__class_Oless(_495560, c_Groups_Oplus__class_Oplus(_495560, _495562, _495564), c_Groups_Oplus__class_Oplus(_495560, _495566, _495564)), -(c_Orderings_Oord__class_Oless(_495560, _495562, _495566))], (7828 ^ _227627) ^ [_495939, _495941, _495943, _495945, _495947] : [class_Groups_Oordered__cancel__ab__semigroup__add(_495939), c_Orderings_Oord__class_Oless(_495939, _495941, _495943), c_Orderings_Oord__class_Oless(_495939, _495945, _495947), -(c_Orderings_Oord__class_Oless(_495939, c_Groups_Oplus__class_Oplus(_495939, _495941, _495945), c_Groups_Oplus__class_Oplus(_495939, _495943, _495947)))], (7842 ^ _227627) ^ [_496417, _496419, _496421, _496423] : [class_Groups_Oordered__cancel__ab__semigroup__add(_496417), c_Orderings_Oord__class_Oless(_496417, _496419, _496421), -(c_Orderings_Oord__class_Oless(_496417, c_Groups_Oplus__class_Oplus(_496417, _496423, _496419), c_Groups_Oplus__class_Oplus(_496417, _496423, _496421)))], (7852 ^ _227627) ^ [_496782, _496784, _496786, _496788] : [class_Groups_Oordered__cancel__ab__semigroup__add(_496782), c_Orderings_Oord__class_Oless(_496782, _496784, _496786), -(c_Orderings_Oord__class_Oless(_496782, c_Groups_Oplus__class_Oplus(_496782, _496784, _496788), c_Groups_Oplus__class_Oplus(_496782, _496786, _496788)))], (7862 ^ _227627) ^ [_497147, _497149, _497151, _497153] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_497147), 7865 ^ _227627 : [(7866 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_497147, c_Groups_Oplus__class_Oplus(_497147, _497149, _497151), c_Groups_Oplus__class_Oplus(_497147, _497149, _497153)), -(c_Orderings_Oord__class_Oless(_497147, _497151, _497153))], (7872 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_497147, _497151, _497153), -(c_Orderings_Oord__class_Oless(_497147, c_Groups_Oplus__class_Oplus(_497147, _497149, _497151), c_Groups_Oplus__class_Oplus(_497147, _497149, _497153)))]]], (7878 ^ _227627) ^ [_497695, _497697, _497699, _497701] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_497695), 7881 ^ _227627 : [(7882 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_497695, c_Groups_Oplus__class_Oplus(_497695, _497697, _497699), c_Groups_Oplus__class_Oplus(_497695, _497701, _497699)), -(c_Orderings_Oord__class_Oless(_497695, _497697, _497701))], (7888 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_497695, _497697, _497701), -(c_Orderings_Oord__class_Oless(_497695, c_Groups_Oplus__class_Oplus(_497695, _497697, _497699), c_Groups_Oplus__class_Oplus(_497695, _497701, _497699)))]]], (7894 ^ _227627) ^ [_498229, _498231, _498233] : [class_Rings_Olinordered__idom(_498229), c_Polynomial_Opos__poly(_498229, _498231), c_Polynomial_Opos__poly(_498229, _498233), -(c_Polynomial_Opos__poly(_498229, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_498229), _498231, _498233)))], (7908 ^ _227627) ^ [_498683, _498685, _498687, _498689, _498691] : [class_Rings_Ocomm__semiring__1(_498683), -(c_Groups_Oplus__class_Oplus(_498683, c_Groups_Oplus__class_Oplus(_498683, _498685, _498687), c_Groups_Oplus__class_Oplus(_498683, _498689, _498691)) = c_Groups_Oplus__class_Oplus(_498683, c_Groups_Oplus__class_Oplus(_498683, _498685, _498689), c_Groups_Oplus__class_Oplus(_498683, _498687, _498691)))], (7914 ^ _227627) ^ [_498985, _498987, _498989, _498991] : [class_Rings_Ocomm__semiring__1(_498985), -(c_Groups_Oplus__class_Oplus(_498985, c_Groups_Oplus__class_Oplus(_498985, _498987, _498989), _498991) = c_Groups_Oplus__class_Oplus(_498985, c_Groups_Oplus__class_Oplus(_498985, _498987, _498991), _498989))], (7920 ^ _227627) ^ [_499265, _499267, _499269, _499271] : [class_Rings_Ocomm__semiring__1(_499265), -(c_Groups_Oplus__class_Oplus(_499265, c_Groups_Oplus__class_Oplus(_499265, _499267, _499269), _499271) = c_Groups_Oplus__class_Oplus(_499265, _499267, c_Groups_Oplus__class_Oplus(_499265, _499269, _499271)))], (7926 ^ _227627) ^ [_499545, _499547, _499549, _499551] : [class_Rings_Ocomm__semiring__1(_499545), -(c_Groups_Oplus__class_Oplus(_499545, _499547, c_Groups_Oplus__class_Oplus(_499545, _499549, _499551)) = c_Groups_Oplus__class_Oplus(_499545, c_Groups_Oplus__class_Oplus(_499545, _499547, _499549), _499551))], (7932 ^ _227627) ^ [_499825, _499827, _499829, _499831] : [class_Rings_Ocomm__semiring__1(_499825), -(c_Groups_Oplus__class_Oplus(_499825, _499827, c_Groups_Oplus__class_Oplus(_499825, _499829, _499831)) = c_Groups_Oplus__class_Oplus(_499825, _499829, c_Groups_Oplus__class_Oplus(_499825, _499827, _499831)))], (7938 ^ _227627) ^ [_500091, _500093, _500095] : [class_Rings_Ocomm__semiring__1(_500091), -(c_Groups_Oplus__class_Oplus(_500091, _500093, _500095) = c_Groups_Oplus__class_Oplus(_500091, _500095, _500093))], (7944 ^ _227627) ^ [_500349, _500351, _500353, _500355] : [class_Rings_Ocomm__semiring__0(_500349), -(hAPP(c_Polynomial_Opoly(_500349, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_500349), _500351, _500353)), _500355) = c_Groups_Oplus__class_Oplus(_500349, hAPP(c_Polynomial_Opoly(_500349, _500351), _500355), hAPP(c_Polynomial_Opoly(_500349, _500353), _500355)))], (7950 ^ _227627) ^ [_500667, _500669, _500671, _500673, _500675] : [class_Groups_Ocomm__monoid__add(_500667), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_500667), c_Polynomial_OpCons(_500667, _500669, _500671), c_Polynomial_OpCons(_500667, _500673, _500675)) = c_Polynomial_OpCons(_500667, c_Groups_Oplus__class_Oplus(_500667, _500669, _500673), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_500667), _500671, _500675)))], (7956 ^ _227627) ^ [_500977, _500979, _500981, _500983] : [class_Rings_Ocomm__semiring__1(_500977), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_500977), _500979), _500981)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_500977), _500979), _500983)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_500977), _500979), c_Groups_Oplus__class_Oplus(_500977, _500981, _500983))))], (7970 ^ _227627) ^ [_501469, _501471, _501473, _501475] : [class_Groups_Ocancel__semigroup__add(_501469), c_Groups_Oplus__class_Oplus(_501469, _501471, _501473) = c_Groups_Oplus__class_Oplus(_501469, _501475, _501473), -(_501471 = _501475)], (7980 ^ _227627) ^ [_501830, _501832, _501834, _501836] : [class_Groups_Ocancel__ab__semigroup__add(_501830), c_Groups_Oplus__class_Oplus(_501830, _501832, _501834) = c_Groups_Oplus__class_Oplus(_501830, _501832, _501836), -(_501834 = _501836)], (7990 ^ _227627) ^ [_502191, _502193, _502195, _502197] : [class_Groups_Ocancel__semigroup__add(_502191), c_Groups_Oplus__class_Oplus(_502191, _502193, _502195) = c_Groups_Oplus__class_Oplus(_502191, _502193, _502197), -(_502195 = _502197)], (8000 ^ _227627) ^ [_502552, _502554, _502556, _502558] : [class_Groups_Ocancel__semigroup__add(_502552), 8003 ^ _227627 : [(8004 ^ _227627) ^ [] : [c_Groups_Oplus__class_Oplus(_502552, _502554, _502556) = c_Groups_Oplus__class_Oplus(_502552, _502558, _502556), -(_502554 = _502558)], (8010 ^ _227627) ^ [] : [_502554 = _502558, -(c_Groups_Oplus__class_Oplus(_502552, _502554, _502556) = c_Groups_Oplus__class_Oplus(_502552, _502558, _502556))]]], (8016 ^ _227627) ^ [_503094, _503096, _503098, _503100] : [class_Groups_Ocancel__semigroup__add(_503094), 8019 ^ _227627 : [(8020 ^ _227627) ^ [] : [c_Groups_Oplus__class_Oplus(_503094, _503096, _503098) = c_Groups_Oplus__class_Oplus(_503094, _503096, _503100), -(_503098 = _503100)], (8026 ^ _227627) ^ [] : [_503098 = _503100, -(c_Groups_Oplus__class_Oplus(_503094, _503096, _503098) = c_Groups_Oplus__class_Oplus(_503094, _503096, _503100))]]], (8032 ^ _227627) ^ [_503636, _503638, _503640, _503642] : [class_Groups_Oab__semigroup__add(_503636), -(c_Groups_Oplus__class_Oplus(_503636, c_Groups_Oplus__class_Oplus(_503636, _503638, _503640), _503642) = c_Groups_Oplus__class_Oplus(_503636, _503638, c_Groups_Oplus__class_Oplus(_503636, _503640, _503642)))], (8038 ^ _227627) ^ [_503916, _503918, _503920, _503922] : [class_Rings_Ocomm__semiring__0(_503916), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_503916)), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_503916), _503918, _503920)), _503922) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_503916), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_503916)), _503918), _503922), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_503916)), _503920), _503922)))], (8044 ^ _227627) ^ [_504248, _504250, _504252, _504254] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_504248), 8047 ^ _227627 : [(8048 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_504248, c_Groups_Oplus__class_Oplus(_504248, _504250, _504252), c_Groups_Oplus__class_Oplus(_504248, _504254, _504252)), -(c_Orderings_Oord__class_Oless__eq(_504248, _504250, _504254))], (8054 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_504248, _504250, _504254), -(c_Orderings_Oord__class_Oless__eq(_504248, c_Groups_Oplus__class_Oplus(_504248, _504250, _504252), c_Groups_Oplus__class_Oplus(_504248, _504254, _504252)))]]], (8060 ^ _227627) ^ [_504796, _504798, _504800, _504802] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_504796), 8063 ^ _227627 : [(8064 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_504796, c_Groups_Oplus__class_Oplus(_504796, _504798, _504800), c_Groups_Oplus__class_Oplus(_504796, _504798, _504802)), -(c_Orderings_Oord__class_Oless__eq(_504796, _504800, _504802))], (8070 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_504796, _504800, _504802), -(c_Orderings_Oord__class_Oless__eq(_504796, c_Groups_Oplus__class_Oplus(_504796, _504798, _504800), c_Groups_Oplus__class_Oplus(_504796, _504798, _504802)))]]], (8076 ^ _227627) ^ [_505344, _505346, _505348, _505350] : [class_Groups_Oordered__ab__semigroup__add(_505344), c_Orderings_Oord__class_Oless__eq(_505344, _505346, _505348), -(c_Orderings_Oord__class_Oless__eq(_505344, c_Groups_Oplus__class_Oplus(_505344, _505346, _505350), c_Groups_Oplus__class_Oplus(_505344, _505348, _505350)))], (8086 ^ _227627) ^ [_505709, _505711, _505713, _505715] : [class_Groups_Oordered__ab__semigroup__add(_505709), c_Orderings_Oord__class_Oless__eq(_505709, _505711, _505713), -(c_Orderings_Oord__class_Oless__eq(_505709, c_Groups_Oplus__class_Oplus(_505709, _505715, _505711), c_Groups_Oplus__class_Oplus(_505709, _505715, _505713)))], (8096 ^ _227627) ^ [_506088, _506090, _506092, _506094, _506096] : [class_Groups_Oordered__ab__semigroup__add(_506088), c_Orderings_Oord__class_Oless__eq(_506088, _506090, _506092), c_Orderings_Oord__class_Oless__eq(_506088, _506094, _506096), -(c_Orderings_Oord__class_Oless__eq(_506088, c_Groups_Oplus__class_Oplus(_506088, _506090, _506094), c_Groups_Oplus__class_Oplus(_506088, _506092, _506096)))], (8110 ^ _227627) ^ [_506566, _506568, _506570, _506572] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_506566), c_Orderings_Oord__class_Oless__eq(_506566, c_Groups_Oplus__class_Oplus(_506566, _506568, _506570), c_Groups_Oplus__class_Oplus(_506566, _506572, _506570)), -(c_Orderings_Oord__class_Oless__eq(_506566, _506568, _506572))], (8120 ^ _227627) ^ [_506931, _506933, _506935, _506937] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_506931), c_Orderings_Oord__class_Oless__eq(_506931, c_Groups_Oplus__class_Oplus(_506931, _506933, _506935), c_Groups_Oplus__class_Oplus(_506931, _506933, _506937)), -(c_Orderings_Oord__class_Oless__eq(_506931, _506935, _506937))], (8130 ^ _227627) ^ [_507268, _507270] : [class_Groups_Omonoid__add(_507268), -(c_Groups_Oplus__class_Oplus(_507268, c_Groups_Ozero__class_Ozero(_507268), _507270) = _507270)], (8136 ^ _227627) ^ [_507488, _507490] : [class_Groups_Ocomm__monoid__add(_507488), -(c_Groups_Oplus__class_Oplus(_507488, c_Groups_Ozero__class_Ozero(_507488), _507490) = _507490)], (8142 ^ _227627) ^ [_507708, _507710] : [class_Groups_Olinordered__ab__group__add(_507708), 8145 ^ _227627 : [(8146 ^ _227627) ^ [] : [c_Groups_Ozero__class_Ozero(_507708) = c_Groups_Oplus__class_Oplus(_507708, _507710, _507710), -(_507710 = c_Groups_Ozero__class_Ozero(_507708))], (8152 ^ _227627) ^ [] : [_507710 = c_Groups_Ozero__class_Ozero(_507708), -(c_Groups_Ozero__class_Ozero(_507708) = c_Groups_Oplus__class_Oplus(_507708, _507710, _507710))]]], (8158 ^ _227627) ^ [_508190, _508192] : [class_Groups_Omonoid__add(_508190), -(c_Groups_Oplus__class_Oplus(_508190, _508192, c_Groups_Ozero__class_Ozero(_508190)) = _508192)], (8164 ^ _227627) ^ [_508410, _508412] : [class_Groups_Ocomm__monoid__add(_508410), -(c_Groups_Oplus__class_Oplus(_508410, _508412, c_Groups_Ozero__class_Ozero(_508410)) = _508412)], (8170 ^ _227627) ^ [_508658, _508660, _508662, _508664] : [class_RealVector_Oreal__normed__algebra(_508658), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_508658), c_Groups_Oplus__class_Oplus(_508658, _508660, _508662)), _508664) = c_Groups_Oplus__class_Oplus(_508658, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_508658), _508660), _508664), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_508658), _508662), _508664)))], (8176 ^ _227627) ^ [_508970, _508972, _508974, _508976] : [class_RealVector_Oreal__normed__algebra(_508970), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_508970), c_Groups_Oplus__class_Oplus(_508970, _508972, _508974)), _508976) = c_Groups_Oplus__class_Oplus(_508970, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_508970), _508972), _508976), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_508970), _508974), _508976)))], (8182 ^ _227627) ^ [_509282, _509284, _509286, _509288] : [class_RealVector_Oreal__normed__algebra(_509282), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_509282), _509284), c_Groups_Oplus__class_Oplus(_509282, _509286, _509288)) = c_Groups_Oplus__class_Oplus(_509282, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_509282), _509284), _509286), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_509282), _509284), _509288)))], (8188 ^ _227627) ^ [_509594, _509596, _509598, _509600] : [class_RealVector_Oreal__normed__algebra(_509594), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_509594), _509596), c_Groups_Oplus__class_Oplus(_509594, _509598, _509600)) = c_Groups_Oplus__class_Oplus(_509594, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_509594), _509596), _509598), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_509594), _509596), _509600)))], (8194 ^ _227627) ^ [_509920, _509922, _509924, _509926, _509928] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_509920), 8197 ^ _227627 : [(8208 ^ _227627) ^ [] : [8209 ^ _227627 : [(8210 ^ _227627) ^ [] : [_509922 = _509926], (8212 ^ _227627) ^ [] : [_509924 = _509928]], -(c_Groups_Oplus__class_Oplus(_509920, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_509920), _509922), _509924), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_509920), _509926), _509928)) = c_Groups_Oplus__class_Oplus(_509920, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_509920), _509922), _509928), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_509920), _509926), _509924)))], (8198 ^ _227627) ^ [] : [c_Groups_Oplus__class_Oplus(_509920, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_509920), _509922), _509924), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_509920), _509926), _509928)) = c_Groups_Oplus__class_Oplus(_509920, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_509920), _509922), _509928), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_509920), _509926), _509924)), -(_509922 = _509926), -(_509924 = _509928)]]], (8216 ^ _227627) ^ [_510764, _510766, _510768, _510770, _510772] : [class_Rings_Osemiring(_510764), -(c_Groups_Oplus__class_Oplus(_510764, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_510764), _510766), _510768), c_Groups_Oplus__class_Oplus(_510764, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_510764), _510770), _510768), _510772)) = c_Groups_Oplus__class_Oplus(_510764, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_510764), c_Groups_Oplus__class_Oplus(_510764, _510766, _510770)), _510768), _510772))], (8222 ^ _227627) ^ [_511098, _511100, _511102, _511104] : [class_Rings_Ocomm__semiring__1(_511098), -(c_Groups_Oplus__class_Oplus(_511098, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_511098), _511100), _511102), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_511098), _511104), _511102)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_511098), c_Groups_Oplus__class_Oplus(_511098, _511100, _511104)), _511102))], (8228 ^ _227627) ^ [_511410, _511412, _511414, _511416] : [class_Rings_Ocomm__semiring__1(_511410), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_511410), c_Groups_Oplus__class_Oplus(_511410, _511412, _511414)), _511416) = c_Groups_Oplus__class_Oplus(_511410, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_511410), _511412), _511416), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_511410), _511414), _511416)))], (8234 ^ _227627) ^ [_511722, _511724, _511726, _511728] : [class_Rings_Ocomm__semiring(_511722), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_511722), c_Groups_Oplus__class_Oplus(_511722, _511724, _511726)), _511728) = c_Groups_Oplus__class_Oplus(_511722, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_511722), _511724), _511728), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_511722), _511726), _511728)))], (8240 ^ _227627) ^ [_512048, _512050, _512052, _512054, _512056] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_512048), 8243 ^ _227627 : [(8254 ^ _227627) ^ [] : [-(c_Groups_Oplus__class_Oplus(_512048, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_512048), _512050), _512054), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_512048), _512052), _512056)) = c_Groups_Oplus__class_Oplus(_512048, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_512048), _512050), _512056), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_512048), _512052), _512054))), 8257 ^ _227627 : [(8258 ^ _227627) ^ [] : [_512050 = _512052], (8260 ^ _227627) ^ [] : [_512054 = _512056]]], (8244 ^ _227627) ^ [] : [c_Groups_Oplus__class_Oplus(_512048, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_512048), _512050), _512054), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_512048), _512052), _512056)) = c_Groups_Oplus__class_Oplus(_512048, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_512048), _512050), _512056), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_512048), _512052), _512054)), -(_512050 = _512052), -(_512054 = _512056)]]], (8262 ^ _227627) ^ [_512884, _512886, _512888, _512890] : [class_Rings_Ocomm__semiring__1(_512884), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_512884), _512886), c_Groups_Oplus__class_Oplus(_512884, _512888, _512890)) = c_Groups_Oplus__class_Oplus(_512884, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_512884), _512886), _512888), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_512884), _512886), _512890)))], (8268 ^ _227627) ^ [_513182, _513184, _513186] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_513182), 8271 ^ _227627 : [(8272 ^ _227627) ^ [] : [_513184 = c_Groups_Oplus__class_Oplus(_513182, _513184, _513186), -(_513186 = c_Groups_Ozero__class_Ozero(_513182))], (8278 ^ _227627) ^ [] : [_513186 = c_Groups_Ozero__class_Ozero(_513182), -(_513184 = c_Groups_Oplus__class_Oplus(_513182, _513184, _513186))]]], (8284 ^ _227627) ^ [_513674, _513676] : [class_Rings_Ocomm__semiring__1(_513674), -(c_Groups_Oplus__class_Oplus(_513674, _513676, c_Groups_Ozero__class_Ozero(_513674)) = _513676)], (8290 ^ _227627) ^ [_513894, _513896] : [class_Rings_Ocomm__semiring__1(_513894), -(c_Groups_Oplus__class_Oplus(_513894, c_Groups_Ozero__class_Ozero(_513894), _513896) = _513896)], (8296 ^ _227627) ^ [_514114, _514116] : [class_Groups_Ocomm__monoid__add(_514114), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_514114), _514116, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_514114))) = _514116)], (8302 ^ _227627) ^ [_514342, _514344] : [class_Groups_Ocomm__monoid__add(_514342), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_514342), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_514342)), _514344) = _514344)], (8308 ^ _227627) ^ [_514570, _514572] : [class_Groups_Olinordered__ab__group__add(_514570), 8311 ^ _227627 : [(8312 ^ _227627) ^ [] : [c_Groups_Oplus__class_Oplus(_514570, _514572, _514572) = c_Groups_Ozero__class_Ozero(_514570), -(_514572 = c_Groups_Ozero__class_Ozero(_514570))], (8318 ^ _227627) ^ [] : [_514572 = c_Groups_Ozero__class_Ozero(_514570), -(c_Groups_Oplus__class_Oplus(_514570, _514572, _514572) = c_Groups_Ozero__class_Ozero(_514570))]]], (8324 ^ _227627) ^ [_515080, _515082, _515084, _515086] : [class_Groups_Ocomm__monoid__add(_515080), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_515080), c_Polynomial_Omonom(_515080, _515082, _515084), c_Polynomial_Omonom(_515080, _515086, _515084)) = c_Polynomial_Omonom(_515080, c_Groups_Oplus__class_Oplus(_515080, _515082, _515086), _515084))], (8330 ^ _227627) ^ [_515344, _515346] : [class_Groups_Olinordered__ab__group__add(_515344), 8333 ^ _227627 : [(8334 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_515344, c_Groups_Ozero__class_Ozero(_515344), c_Groups_Oplus__class_Oplus(_515344, _515346, _515346)), -(c_Orderings_Oord__class_Oless__eq(_515344, c_Groups_Ozero__class_Ozero(_515344), _515346))], (8340 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_515344, c_Groups_Ozero__class_Ozero(_515344), _515346), -(c_Orderings_Oord__class_Oless__eq(_515344, c_Groups_Ozero__class_Ozero(_515344), c_Groups_Oplus__class_Oplus(_515344, _515346, _515346)))]]], (8346 ^ _227627) ^ [_515832, _515834] : [class_Groups_Olinordered__ab__group__add(_515832), 8349 ^ _227627 : [(8350 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_515832, c_Groups_Oplus__class_Oplus(_515832, _515834, _515834), c_Groups_Ozero__class_Ozero(_515832)), -(c_Orderings_Oord__class_Oless__eq(_515832, _515834, c_Groups_Ozero__class_Ozero(_515832)))], (8356 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_515832, _515834, c_Groups_Ozero__class_Ozero(_515832)), -(c_Orderings_Oord__class_Oless__eq(_515832, c_Groups_Oplus__class_Oplus(_515832, _515834, _515834), c_Groups_Ozero__class_Ozero(_515832)))]]], (8362 ^ _227627) ^ [_516334, _516336, _516338] : [class_Groups_Oordered__comm__monoid__add(_516334), c_Orderings_Oord__class_Oless__eq(_516334, c_Groups_Ozero__class_Ozero(_516334), _516336), c_Orderings_Oord__class_Oless__eq(_516334, c_Groups_Ozero__class_Ozero(_516334), _516338), -(c_Orderings_Oord__class_Oless__eq(_516334, c_Groups_Ozero__class_Ozero(_516334), c_Groups_Oplus__class_Oplus(_516334, _516336, _516338)))], (8376 ^ _227627) ^ [_516774, _516776, _516778] : [class_Groups_Oordered__comm__monoid__add(_516774), c_Orderings_Oord__class_Oless__eq(_516774, c_Groups_Ozero__class_Ozero(_516774), _516776), c_Orderings_Oord__class_Oless__eq(_516774, c_Groups_Ozero__class_Ozero(_516774), _516778), 8387 ^ _227627 : [(8388 ^ _227627) ^ [] : [c_Groups_Oplus__class_Oplus(_516774, _516776, _516778) = c_Groups_Ozero__class_Ozero(_516774), 8391 ^ _227627 : [(8392 ^ _227627) ^ [] : [-(_516776 = c_Groups_Ozero__class_Ozero(_516774))], (8394 ^ _227627) ^ [] : [-(_516778 = c_Groups_Ozero__class_Ozero(_516774))]]], (8396 ^ _227627) ^ [] : [-(c_Groups_Oplus__class_Oplus(_516774, _516776, _516778) = c_Groups_Ozero__class_Ozero(_516774)), _516776 = c_Groups_Ozero__class_Ozero(_516774), _516778 = c_Groups_Ozero__class_Ozero(_516774)]]], (8406 ^ _227627) ^ [_517668, _517670, _517672, _517674] : [class_Groups_Oordered__comm__monoid__add(_517668), c_Orderings_Oord__class_Oless__eq(_517668, c_Groups_Ozero__class_Ozero(_517668), _517670), c_Orderings_Oord__class_Oless__eq(_517668, _517672, _517674), -(c_Orderings_Oord__class_Oless__eq(_517668, _517672, c_Groups_Oplus__class_Oplus(_517668, _517670, _517674)))], (8420 ^ _227627) ^ [_518128, _518130, _518132, _518134] : [class_Groups_Oordered__comm__monoid__add(_518128), c_Orderings_Oord__class_Oless__eq(_518128, c_Groups_Ozero__class_Ozero(_518128), _518130), c_Orderings_Oord__class_Oless__eq(_518128, _518132, _518134), -(c_Orderings_Oord__class_Oless__eq(_518128, _518132, c_Groups_Oplus__class_Oplus(_518128, _518134, _518130)))], (8434 ^ _227627) ^ [_518574, _518576, _518578] : [class_Groups_Oordered__comm__monoid__add(_518574), c_Orderings_Oord__class_Oless__eq(_518574, _518576, c_Groups_Ozero__class_Ozero(_518574)), c_Orderings_Oord__class_Oless__eq(_518574, _518578, c_Groups_Ozero__class_Ozero(_518574)), -(c_Orderings_Oord__class_Oless__eq(_518574, c_Groups_Oplus__class_Oplus(_518574, _518576, _518578), c_Groups_Ozero__class_Ozero(_518574)))], (8448 ^ _227627) ^ [_519000, _519002] : [class_Groups_Olinordered__ab__group__add(_519000), 8451 ^ _227627 : [(8452 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_519000, c_Groups_Ozero__class_Ozero(_519000), c_Groups_Oplus__class_Oplus(_519000, _519002, _519002)), -(c_Orderings_Oord__class_Oless(_519000, c_Groups_Ozero__class_Ozero(_519000), _519002))], (8458 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_519000, c_Groups_Ozero__class_Ozero(_519000), _519002), -(c_Orderings_Oord__class_Oless(_519000, c_Groups_Ozero__class_Ozero(_519000), c_Groups_Oplus__class_Oplus(_519000, _519002, _519002)))]]], (8464 ^ _227627) ^ [_519488, _519490] : [class_Groups_Olinordered__ab__group__add(_519488), 8467 ^ _227627 : [(8468 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_519488, c_Groups_Oplus__class_Oplus(_519488, _519490, _519490), c_Groups_Ozero__class_Ozero(_519488)), -(c_Orderings_Oord__class_Oless(_519488, _519490, c_Groups_Ozero__class_Ozero(_519488)))], (8474 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_519488, _519490, c_Groups_Ozero__class_Ozero(_519488)), -(c_Orderings_Oord__class_Oless(_519488, c_Groups_Oplus__class_Oplus(_519488, _519490, _519490), c_Groups_Ozero__class_Ozero(_519488)))]]], (8480 ^ _227627) ^ [_519990, _519992, _519994] : [class_Groups_Oordered__comm__monoid__add(_519990), c_Orderings_Oord__class_Oless(_519990, c_Groups_Ozero__class_Ozero(_519990), _519992), c_Orderings_Oord__class_Oless(_519990, c_Groups_Ozero__class_Ozero(_519990), _519994), -(c_Orderings_Oord__class_Oless(_519990, c_Groups_Ozero__class_Ozero(_519990), c_Groups_Oplus__class_Oplus(_519990, _519992, _519994)))], (8494 ^ _227627) ^ [_520430, _520432, _520434] : [class_Groups_Oordered__comm__monoid__add(_520430), c_Orderings_Oord__class_Oless(_520430, _520432, c_Groups_Ozero__class_Ozero(_520430)), c_Orderings_Oord__class_Oless(_520430, _520434, c_Groups_Ozero__class_Ozero(_520430)), -(c_Orderings_Oord__class_Oless(_520430, c_Groups_Oplus__class_Oplus(_520430, _520432, _520434), c_Groups_Ozero__class_Ozero(_520430)))], (8508 ^ _227627) ^ [_520884, _520886, _520888, _520890] : [class_Rings_Olinordered__semidom(_520884), c_Orderings_Oord__class_Oless(_520884, c_Groups_Ozero__class_Ozero(_520884), _520886), c_Orderings_Oord__class_Oless(_520884, _520888, _520890), -(c_Orderings_Oord__class_Oless(_520884, _520888, c_Groups_Oplus__class_Oplus(_520884, _520886, _520890)))], (8522 ^ _227627) ^ [_521316, _521318] : [class_Rings_Olinordered__idom(_521316), 8525 ^ _227627 : [(8526 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_521316, c_Groups_Oplus__class_Oplus(_521316, _521318, _521318), c_Groups_Ozero__class_Ozero(_521316)), -(c_Orderings_Oord__class_Oless(_521316, _521318, c_Groups_Ozero__class_Ozero(_521316)))], (8532 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_521316, _521318, c_Groups_Ozero__class_Ozero(_521316)), -(c_Orderings_Oord__class_Oless(_521316, c_Groups_Oplus__class_Oplus(_521316, _521318, _521318), c_Groups_Ozero__class_Ozero(_521316)))]]], (8538 ^ _227627) ^ [_521846, _521848, _521850, _521852, _521854] : [class_Groups_Oordered__cancel__ab__semigroup__add(_521846), c_Orderings_Oord__class_Oless(_521846, _521848, _521850), c_Orderings_Oord__class_Oless__eq(_521846, _521852, _521854), -(c_Orderings_Oord__class_Oless(_521846, c_Groups_Oplus__class_Oplus(_521846, _521848, _521852), c_Groups_Oplus__class_Oplus(_521846, _521850, _521854)))], (8552 ^ _227627) ^ [_522338, _522340, _522342, _522344, _522346] : [class_Groups_Oordered__cancel__ab__semigroup__add(_522338), c_Orderings_Oord__class_Oless__eq(_522338, _522340, _522342), c_Orderings_Oord__class_Oless(_522338, _522344, _522346), -(c_Orderings_Oord__class_Oless(_522338, c_Groups_Oplus__class_Oplus(_522338, _522340, _522344), c_Groups_Oplus__class_Oplus(_522338, _522342, _522346)))], (8566 ^ _227627) ^ [_522802, _522804, _522806] : [class_Rings_Olinordered__ring__strict(_522802), 8569 ^ _227627 : [(8570 ^ _227627) ^ [] : [c_Groups_Oplus__class_Oplus(_522802, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_522802), _522804), _522804), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_522802), _522806), _522806)) = c_Groups_Ozero__class_Ozero(_522802), 8573 ^ _227627 : [(8574 ^ _227627) ^ [] : [-(_522804 = c_Groups_Ozero__class_Ozero(_522802))], (8576 ^ _227627) ^ [] : [-(_522806 = c_Groups_Ozero__class_Ozero(_522802))]]], (8578 ^ _227627) ^ [] : [-(c_Groups_Oplus__class_Oplus(_522802, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_522802), _522804), _522804), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_522802), _522806), _522806)) = c_Groups_Ozero__class_Ozero(_522802)), _522804 = c_Groups_Ozero__class_Ozero(_522802), _522806 = c_Groups_Ozero__class_Ozero(_522802)]]], (8588 ^ _227627) ^ [_523574, _523576, _523578, _523580, _523582, _523584] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_523574), -(_523576 = c_Groups_Ozero__class_Ozero(_523574)), c_Groups_Oplus__class_Oplus(_523574, _523578, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_523574), _523576), _523582)) = c_Groups_Oplus__class_Oplus(_523574, _523580, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_523574), _523576), _523584)), _523578 = _523580, -(_523582 = _523584)], (8606 ^ _227627) ^ [_524180, _524182] : [class_Rings_Olinordered__semidom(_524180), -(c_Orderings_Oord__class_Oless(_524180, _524182, c_Groups_Oplus__class_Oplus(_524180, _524182, c_Groups_Oone__class_Oone(_524180))))], (8612 ^ _227627) ^ [_524416, _524418, _524420] : [class_Groups_Ogroup__add(_524416), c_Groups_Oplus__class_Oplus(_524416, _524418, _524420) = c_Groups_Ozero__class_Ozero(_524416), -(c_Groups_Ouminus__class_Ouminus(_524416, _524418) = _524420)], (8622 ^ _227627) ^ [_524741, _524743] : [class_Groups_Oab__group__add(_524741), -(c_Groups_Oplus__class_Oplus(_524741, c_Groups_Ouminus__class_Ouminus(_524741, _524743), _524743) = c_Groups_Ozero__class_Ozero(_524741))], (8628 ^ _227627) ^ [_524967, _524969] : [class_Groups_Ogroup__add(_524967), -(c_Groups_Oplus__class_Oplus(_524967, c_Groups_Ouminus__class_Ouminus(_524967, _524969), _524969) = c_Groups_Ozero__class_Ozero(_524967))], (8634 ^ _227627) ^ [_525207, _525209, _525211] : [class_Groups_Ogroup__add(_525207), 8637 ^ _227627 : [(8638 ^ _227627) ^ [] : [_525209 = c_Groups_Ouminus__class_Ouminus(_525207, _525211), -(c_Groups_Oplus__class_Oplus(_525207, _525209, _525211) = c_Groups_Ozero__class_Ozero(_525207))], (8644 ^ _227627) ^ [] : [c_Groups_Oplus__class_Oplus(_525207, _525209, _525211) = c_Groups_Ozero__class_Ozero(_525207), -(_525209 = c_Groups_Ouminus__class_Ouminus(_525207, _525211))]]], (8650 ^ _227627) ^ [_525708, _525710] : [class_Groups_Ogroup__add(_525708), -(c_Groups_Oplus__class_Oplus(_525708, _525710, c_Groups_Ouminus__class_Ouminus(_525708, _525710)) = c_Groups_Ozero__class_Ozero(_525708))], (8656 ^ _227627) ^ [_525948, _525950, _525952] : [class_Groups_Ogroup__add(_525948), 8659 ^ _227627 : [(8660 ^ _227627) ^ [] : [c_Groups_Oplus__class_Oplus(_525948, _525950, _525952) = c_Groups_Ozero__class_Ozero(_525948), -(_525952 = c_Groups_Ouminus__class_Ouminus(_525948, _525950))], (8666 ^ _227627) ^ [] : [_525952 = c_Groups_Ouminus__class_Ouminus(_525948, _525950), -(c_Groups_Oplus__class_Oplus(_525948, _525950, _525952) = c_Groups_Ozero__class_Ozero(_525948))]]], (8672 ^ _227627) ^ [_526463, _526465, _526467] : [class_Rings_Ocomm__semiring__1(_526463), -(c_Groups_Oplus__class_Oplus(_526463, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_526463), _526465), _526467), _526467) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_526463), c_Groups_Oplus__class_Oplus(_526463, _526465, c_Groups_Oone__class_Oone(_526463))), _526467))], (8678 ^ _227627) ^ [_526743, _526745, _526747] : [class_Rings_Ocomm__semiring__1(_526743), -(c_Groups_Oplus__class_Oplus(_526743, _526745, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_526743), _526747), _526745)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_526743), c_Groups_Oplus__class_Oplus(_526743, _526747, c_Groups_Oone__class_Oone(_526743))), _526745))], (8684 ^ _227627) ^ [_527009, _527011] : [class_Rings_Ocomm__semiring__1(_527009), -(c_Groups_Oplus__class_Oplus(_527009, _527011, _527011) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_527009), c_Groups_Oplus__class_Oplus(_527009, c_Groups_Oone__class_Oone(_527009), c_Groups_Oone__class_Oone(_527009))), _527011))], (8690 ^ _227627) ^ [_527299, _527301, _527303, _527305, _527307] : [class_Rings_Oring(_527299), -(c_Groups_Ominus__class_Ominus(_527299, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_527299), _527301), _527303), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_527299), _527305), _527307)) = c_Groups_Oplus__class_Oplus(_527299, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_527299), _527301), c_Groups_Ominus__class_Ominus(_527299, _527303, _527307)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_527299), c_Groups_Ominus__class_Ominus(_527299, _527301, _527305)), _527307)))], (8696 ^ _227627) ^ [_527677, _527679, _527681, _527683, _527685, _527687] : [class_Rings_Oring(_527677), 8699 ^ _227627 : [(8700 ^ _227627) ^ [] : [c_Groups_Oplus__class_Oplus(_527677, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_527677), _527679), _527681), _527683) = c_Groups_Oplus__class_Oplus(_527677, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_527677), _527685), _527681), _527687), -(_527683 = c_Groups_Oplus__class_Oplus(_527677, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_527677), c_Groups_Ominus__class_Ominus(_527677, _527685, _527679)), _527681), _527687))], (8706 ^ _227627) ^ [] : [_527683 = c_Groups_Oplus__class_Oplus(_527677, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_527677), c_Groups_Ominus__class_Ominus(_527677, _527685, _527679)), _527681), _527687), -(c_Groups_Oplus__class_Oplus(_527677, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_527677), _527679), _527681), _527683) = c_Groups_Oplus__class_Oplus(_527677, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_527677), _527685), _527681), _527687))]]], (8712 ^ _227627) ^ [_528375, _528377, _528379, _528381, _528383, _528385] : [class_Rings_Oring(_528375), 8715 ^ _227627 : [(8716 ^ _227627) ^ [] : [c_Groups_Oplus__class_Oplus(_528375, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_528375), _528377), _528379), _528381) = c_Groups_Oplus__class_Oplus(_528375, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_528375), _528383), _528379), _528385), -(c_Groups_Oplus__class_Oplus(_528375, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_528375), c_Groups_Ominus__class_Ominus(_528375, _528377, _528383)), _528379), _528381) = _528385)], (8722 ^ _227627) ^ [] : [c_Groups_Oplus__class_Oplus(_528375, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_528375), c_Groups_Ominus__class_Ominus(_528375, _528377, _528383)), _528379), _528381) = _528385, -(c_Groups_Oplus__class_Oplus(_528375, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_528375), _528377), _528379), _528381) = c_Groups_Oplus__class_Oplus(_528375, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_528375), _528383), _528379), _528385))]]], (8728 ^ _227627) ^ [_529059, _529061, _529063, _529065, _529067] : [class_RealVector_Oreal__normed__algebra(_529059), -(c_Groups_Ominus__class_Ominus(_529059, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_529059), _529061), _529063), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_529059), _529065), _529067)) = c_Groups_Oplus__class_Oplus(_529059, c_Groups_Oplus__class_Oplus(_529059, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_529059), c_Groups_Ominus__class_Ominus(_529059, _529061, _529065)), c_Groups_Ominus__class_Ominus(_529059, _529063, _529067)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_529059), c_Groups_Ominus__class_Ominus(_529059, _529061, _529065)), _529067)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_529059), _529065), c_Groups_Ominus__class_Ominus(_529059, _529063, _529067))))], (8734 ^ _227627) ^ [_529435, _529437, _529439] : [class_Groups_Ogroup__add(_529435), -(c_Groups_Ominus__class_Ominus(_529435, _529437, c_Groups_Ouminus__class_Ouminus(_529435, _529439)) = c_Groups_Oplus__class_Oplus(_529435, _529437, _529439))], (8740 ^ _227627) ^ [_529685, _529687, _529689] : [class_Groups_Oab__group__add(_529685), -(c_Groups_Ominus__class_Ominus(_529685, _529687, _529689) = c_Groups_Oplus__class_Oplus(_529685, _529687, c_Groups_Ouminus__class_Ouminus(_529685, _529689)))], (8746 ^ _227627) ^ [_529935, _529937, _529939] : [class_Groups_Ogroup__add(_529935), -(c_Groups_Ominus__class_Ominus(_529935, _529937, _529939) = c_Groups_Oplus__class_Oplus(_529935, _529937, c_Groups_Ouminus__class_Ouminus(_529935, _529939)))], (8752 ^ _227627) ^ [_530185, _530187, _530189] : [class_Rings_Ocomm__ring__1(_530185), -(c_Groups_Ominus__class_Ominus(_530185, _530187, _530189) = c_Groups_Oplus__class_Oplus(_530185, _530187, c_Groups_Ouminus__class_Ouminus(_530185, _530189)))], (8758 ^ _227627) ^ [_530450, _530452] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _530450, _530452), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _530450, _530452), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (8764 ^ _227627) ^ [_530624, _530626] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _530624, _530626), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _530624, _530626))], (8770 ^ _227627) ^ [_530876, _530878, _530880, _530882] : [class_Groups_Oab__group__add(_530876), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_530876, _530878), _530880), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_530876, _530882), _530880), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_530876, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_530876), _530878, _530882)), _530880))], (8784 ^ _227627) ^ [_531354, _531356, _531358, _531360] : [class_Groups_Oab__group__add(_531354), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_531354, _531356), _531358), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_531354, _531360), _531358), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_531354, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_531354), _531356, _531360)), _531358))], (8798 ^ _227627) ^ [_531818, _531820, _531822] : [class_Groups_Ocomm__monoid__add(_531818), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_531818, _531820), c_Polynomial_Odegree(_531818, _531822)), -(c_Polynomial_Odegree(_531818, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_531818), _531822, _531820)) = c_Polynomial_Odegree(_531818, _531822))], (8808 ^ _227627) ^ [_532177, _532179, _532181] : [class_Groups_Ocomm__monoid__add(_532177), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_532177, _532179), c_Polynomial_Odegree(_532177, _532181)), -(c_Polynomial_Odegree(_532177, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_532177), _532179, _532181)) = c_Polynomial_Odegree(_532177, _532181))], (8818 ^ _227627) ^ [_532550, _532552, _532554, _532556] : [class_Groups_Ocomm__monoid__add(_532550), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_532550, _532552), _532554), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_532550, _532556), _532554), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_532550, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_532550), _532552, _532556)), _532554))], (8832 ^ _227627) ^ [_533028, _533030, _533032, _533034] : [class_Groups_Ocomm__monoid__add(_533028), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_533028, _533030), _533032), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_533028, _533034), _533032), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_533028, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_533028), _533030, _533034)), _533032))], (8846 ^ _227627) ^ [_533478, _533480] : [class_Groups_Oab__group__add(_533478), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_533478), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_533478)), _533480) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_533478), _533480))], (8852 ^ _227627) ^ [_533730, _533732, _533734] : [class_Groups_Oordered__comm__monoid__add(_533730), c_Orderings_Oord__class_Oless(_533730, c_Groups_Ozero__class_Ozero(_533730), _533732), c_Orderings_Oord__class_Oless__eq(_533730, c_Groups_Ozero__class_Ozero(_533730), _533734), -(c_Orderings_Oord__class_Oless(_533730, c_Groups_Ozero__class_Ozero(_533730), c_Groups_Oplus__class_Oplus(_533730, _533732, _533734)))], (8866 ^ _227627) ^ [_534170, _534172, _534174] : [class_Groups_Oordered__comm__monoid__add(_534170), c_Orderings_Oord__class_Oless__eq(_534170, c_Groups_Ozero__class_Ozero(_534170), _534172), c_Orderings_Oord__class_Oless(_534170, c_Groups_Ozero__class_Ozero(_534170), _534174), -(c_Orderings_Oord__class_Oless(_534170, c_Groups_Ozero__class_Ozero(_534170), c_Groups_Oplus__class_Oplus(_534170, _534172, _534174)))], (8880 ^ _227627) ^ [_534624, _534626, _534628, _534630] : [class_Groups_Oordered__comm__monoid__add(_534624), c_Orderings_Oord__class_Oless(_534624, c_Groups_Ozero__class_Ozero(_534624), _534626), c_Orderings_Oord__class_Oless__eq(_534624, _534628, _534630), -(c_Orderings_Oord__class_Oless(_534624, _534628, c_Groups_Oplus__class_Oplus(_534624, _534626, _534630)))], (8894 ^ _227627) ^ [_535084, _535086, _535088, _535090] : [class_Groups_Oordered__comm__monoid__add(_535084), c_Orderings_Oord__class_Oless__eq(_535084, c_Groups_Ozero__class_Ozero(_535084), _535086), c_Orderings_Oord__class_Oless(_535084, _535088, _535090), -(c_Orderings_Oord__class_Oless(_535084, _535088, c_Groups_Oplus__class_Oplus(_535084, _535086, _535090)))], (8908 ^ _227627) ^ [_535530, _535532, _535534] : [class_Groups_Oordered__comm__monoid__add(_535530), c_Orderings_Oord__class_Oless(_535530, _535532, c_Groups_Ozero__class_Ozero(_535530)), c_Orderings_Oord__class_Oless__eq(_535530, _535534, c_Groups_Ozero__class_Ozero(_535530)), -(c_Orderings_Oord__class_Oless(_535530, c_Groups_Oplus__class_Oplus(_535530, _535532, _535534), c_Groups_Ozero__class_Ozero(_535530)))], (8922 ^ _227627) ^ [_535970, _535972, _535974] : [class_Groups_Oordered__comm__monoid__add(_535970), c_Orderings_Oord__class_Oless__eq(_535970, _535972, c_Groups_Ozero__class_Ozero(_535970)), c_Orderings_Oord__class_Oless(_535970, _535974, c_Groups_Ozero__class_Ozero(_535970)), -(c_Orderings_Oord__class_Oless(_535970, c_Groups_Oplus__class_Oplus(_535970, _535972, _535974), c_Groups_Ozero__class_Ozero(_535970)))], (8936 ^ _227627) ^ [_536410, _536412, _536414] : [class_Rings_Olinordered__ring__strict(_536410), 8939 ^ _227627 : [(8940 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_536410, c_Groups_Oplus__class_Oplus(_536410, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_536410), _536412), _536412), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_536410), _536414), _536414)), c_Groups_Ozero__class_Ozero(_536410)), 8943 ^ _227627 : [(8944 ^ _227627) ^ [] : [-(_536412 = c_Groups_Ozero__class_Ozero(_536410))], (8946 ^ _227627) ^ [] : [-(_536414 = c_Groups_Ozero__class_Ozero(_536410))]]], (8948 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_536410, c_Groups_Oplus__class_Oplus(_536410, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_536410), _536412), _536412), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_536410), _536414), _536414)), c_Groups_Ozero__class_Ozero(_536410))), _536412 = c_Groups_Ozero__class_Ozero(_536410), _536414 = c_Groups_Ozero__class_Ozero(_536410)]]], (8958 ^ _227627) ^ [_537143, _537145, _537147] : [class_Rings_Olinordered__ring(_537143), -(c_Orderings_Oord__class_Oless__eq(_537143, c_Groups_Ozero__class_Ozero(_537143), c_Groups_Oplus__class_Oplus(_537143, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_537143), _537145), _537145), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_537143), _537147), _537147))))], (8964 ^ _227627) ^ [_537417, _537419, _537421] : [class_Rings_Olinordered__ring__strict(_537417), 8967 ^ _227627 : [(8978 ^ _227627) ^ [] : [8979 ^ _227627 : [(8980 ^ _227627) ^ [] : [-(_537419 = c_Groups_Ozero__class_Ozero(_537417))], (8982 ^ _227627) ^ [] : [-(_537421 = c_Groups_Ozero__class_Ozero(_537417))]], -(c_Orderings_Oord__class_Oless(_537417, c_Groups_Ozero__class_Ozero(_537417), c_Groups_Oplus__class_Oplus(_537417, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_537417), _537419), _537419), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_537417), _537421), _537421))))], (8968 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_537417, c_Groups_Ozero__class_Ozero(_537417), c_Groups_Oplus__class_Oplus(_537417, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_537417), _537419), _537419), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_537417), _537421), _537421))), _537419 = c_Groups_Ozero__class_Ozero(_537417), _537421 = c_Groups_Ozero__class_Ozero(_537417)]]], (8986 ^ _227627) ^ [_538154, _538156, _538158] : [class_Rings_Olinordered__ring(_538154), c_Orderings_Oord__class_Oless(_538154, c_Groups_Oplus__class_Oplus(_538154, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_538154), _538156), _538156), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_538154), _538158), _538158)), c_Groups_Ozero__class_Ozero(_538154))], (8992 ^ _227627) ^ [_538401] : [class_Rings_Olinordered__semidom(_538401), -(c_Orderings_Oord__class_Oless(_538401, c_Groups_Ozero__class_Ozero(_538401), c_Groups_Oplus__class_Oplus(_538401, c_Groups_Oone__class_Oone(_538401), c_Groups_Oone__class_Oone(_538401))))], (8998 ^ _227627) ^ [_538681, _538683, _538685, _538687, _538689, _538691] : [class_Rings_Oordered__ring(_538681), 9001 ^ _227627 : [(9002 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_538681, c_Groups_Oplus__class_Oplus(_538681, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_538681), _538683), _538685), _538687), c_Groups_Oplus__class_Oplus(_538681, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_538681), _538689), _538685), _538691)), -(c_Orderings_Oord__class_Oless__eq(_538681, _538687, c_Groups_Oplus__class_Oplus(_538681, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_538681), c_Groups_Ominus__class_Ominus(_538681, _538689, _538683)), _538685), _538691)))], (9008 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_538681, _538687, c_Groups_Oplus__class_Oplus(_538681, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_538681), c_Groups_Ominus__class_Ominus(_538681, _538689, _538683)), _538685), _538691)), -(c_Orderings_Oord__class_Oless__eq(_538681, c_Groups_Oplus__class_Oplus(_538681, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_538681), _538683), _538685), _538687), c_Groups_Oplus__class_Oplus(_538681, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_538681), _538689), _538685), _538691)))]]], (9014 ^ _227627) ^ [_539385, _539387, _539389, _539391, _539393, _539395] : [class_Rings_Oordered__ring(_539385), 9017 ^ _227627 : [(9018 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_539385, c_Groups_Oplus__class_Oplus(_539385, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_539385), _539387), _539389), _539391), c_Groups_Oplus__class_Oplus(_539385, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_539385), _539393), _539389), _539395)), -(c_Orderings_Oord__class_Oless__eq(_539385, c_Groups_Oplus__class_Oplus(_539385, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_539385), c_Groups_Ominus__class_Ominus(_539385, _539387, _539393)), _539389), _539391), _539395))], (9024 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(_539385, c_Groups_Oplus__class_Oplus(_539385, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_539385), c_Groups_Ominus__class_Ominus(_539385, _539387, _539393)), _539389), _539391), _539395), -(c_Orderings_Oord__class_Oless__eq(_539385, c_Groups_Oplus__class_Oplus(_539385, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_539385), _539387), _539389), _539391), c_Groups_Oplus__class_Oplus(_539385, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_539385), _539393), _539389), _539395)))]]], (9030 ^ _227627) ^ [_540089, _540091, _540093, _540095, _540097, _540099] : [class_Rings_Oordered__ring(_540089), 9033 ^ _227627 : [(9034 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_540089, c_Groups_Oplus__class_Oplus(_540089, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540089), _540091), _540093), _540095), c_Groups_Oplus__class_Oplus(_540089, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540089), _540097), _540093), _540099)), -(c_Orderings_Oord__class_Oless(_540089, c_Groups_Oplus__class_Oplus(_540089, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540089), c_Groups_Ominus__class_Ominus(_540089, _540091, _540097)), _540093), _540095), _540099))], (9040 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_540089, c_Groups_Oplus__class_Oplus(_540089, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540089), c_Groups_Ominus__class_Ominus(_540089, _540091, _540097)), _540093), _540095), _540099), -(c_Orderings_Oord__class_Oless(_540089, c_Groups_Oplus__class_Oplus(_540089, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540089), _540091), _540093), _540095), c_Groups_Oplus__class_Oplus(_540089, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540089), _540097), _540093), _540099)))]]], (9046 ^ _227627) ^ [_540793, _540795, _540797, _540799, _540801, _540803] : [class_Rings_Oordered__ring(_540793), 9049 ^ _227627 : [(9050 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_540793, c_Groups_Oplus__class_Oplus(_540793, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540793), _540795), _540797), _540799), c_Groups_Oplus__class_Oplus(_540793, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540793), _540801), _540797), _540803)), -(c_Orderings_Oord__class_Oless(_540793, _540799, c_Groups_Oplus__class_Oplus(_540793, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540793), c_Groups_Ominus__class_Ominus(_540793, _540801, _540795)), _540797), _540803)))], (9056 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_540793, _540799, c_Groups_Oplus__class_Oplus(_540793, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540793), c_Groups_Ominus__class_Ominus(_540793, _540801, _540795)), _540797), _540803)), -(c_Orderings_Oord__class_Oless(_540793, c_Groups_Oplus__class_Oplus(_540793, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540793), _540795), _540797), _540799), c_Groups_Oplus__class_Oplus(_540793, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540793), _540801), _540797), _540803)))]]], (9062 ^ _227627) ^ [_541455, _541457, _541459] : [class_Rings_Odvd(_541455), class_Rings_Osemiring__0(_541455), 9069 ^ _227627 : [(9070 ^ _227627) ^ [] : [9071 ^ _227627 : [(9072 ^ _227627) ^ [_541770] : [hBOOL(hAPP(_541457, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_541455), _541459), _541770)))]], 9074 ^ _227627 : [(9075 ^ _227627) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_541455), _541459), c_Groups_Oplus__class_Oplus(_541455, 9073 ^ [_541455, _541457, _541459], c_Groups_Ozero__class_Ozero(_541455)))))], (9077 ^ _227627) ^ [] : [-(hBOOL(hAPP(_541457, 9073 ^ [_541455, _541457, _541459])))]]], (9079 ^ _227627) ^ [] : [-(hBOOL(hAPP(_541457, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_541455), _541459), 9086 ^ [_541455, _541457, _541459])))), 9080 ^ _227627 : [(9081 ^ _227627) ^ [_542122] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_541455), _541459), c_Groups_Oplus__class_Oplus(_541455, _542122, c_Groups_Ozero__class_Ozero(_541455)))), hBOOL(hAPP(_541457, _542122))]]]]], (9090 ^ _227627) ^ [_542519, _542521] : [class_Rings_Oring__1(_542519), -(c_Groups_Ominus__class_Ominus(_542519, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_542519), _542521), _542521), c_Groups_Oone__class_Oone(_542519)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_542519), c_Groups_Oplus__class_Oplus(_542519, _542521, c_Groups_Oone__class_Oone(_542519))), c_Groups_Ominus__class_Ominus(_542519, _542521, c_Groups_Oone__class_Oone(_542519))))], (9096 ^ _227627) ^ [_542823, _542825, _542827, _542829] : [class_Rings_Ocomm__ring(_542823), class_Rings_Odvd(_542823), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_542823), _542825), _542827)), 9107 ^ _227627 : [(9108 ^ _227627) ^ [_543250, _543252] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_542823), _542825), c_Groups_Oplus__class_Oplus(_542823, _543252, _542829))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_542823), _542825), c_Groups_Oplus__class_Oplus(_542823, c_Groups_Ominus__class_Ominus(_542823, _543252, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_542823), _543250), _542827)), _542829))))], (9114 ^ _227627) ^ [_543512, _543514] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_542823), _542825), c_Groups_Oplus__class_Oplus(_542823, c_Groups_Ominus__class_Ominus(_542823, _543514, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_542823), _543512), _542827)), _542829))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_542823), _542825), c_Groups_Oplus__class_Oplus(_542823, _543514, _542829))))]]], (9120 ^ _227627) ^ [_543863, _543865, _543867, _543869] : [class_Rings_Ocomm__ring(_543863), class_Rings_Odvd(_543863), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_543863), _543865), _543867)), 9131 ^ _227627 : [(9132 ^ _227627) ^ [_544290, _544292] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_543863), _543865), c_Groups_Oplus__class_Oplus(_543863, _544292, _543869))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_543863), _543865), c_Groups_Oplus__class_Oplus(_543863, c_Groups_Ominus__class_Ominus(_543863, _544292, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_543863), _544290), _543867)), _543869))))], (9138 ^ _227627) ^ [_544552, _544554] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_543863), _543865), c_Groups_Oplus__class_Oplus(_543863, c_Groups_Ominus__class_Ominus(_543863, _544554, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_543863), _544552), _543867)), _543869))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_543863), _543865), c_Groups_Oplus__class_Oplus(_543863, _544554, _543869))))]]], (9144 ^ _227627) ^ [_544904, _544906] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _544904, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _544906, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _544904, _544906))], (9150 ^ _227627) ^ [_545078, _545080] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _545078, _545080), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _545078, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _545080, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (9156 ^ _227627) ^ [_545330, _545332, _545334, _545336] : [class_Rings_Ocomm__semiring__0(_545330), -(hAPP(c_Polynomial_Opoly(_545330, c_Polynomial_OpCons(_545330, _545332, _545334)), _545336) = c_Groups_Oplus__class_Oplus(_545330, _545332, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_545330), _545336), hAPP(c_Polynomial_Opoly(_545330, _545334), _545336))))], (9162 ^ _227627) ^ [_545662, _545664, _545666, _545668, _545670, _545672] : [class_Rings_Olinordered__semiring__1(_545662), c_Orderings_Oord__class_Oless__eq(_545662, _545664, _545666), c_Orderings_Oord__class_Oless__eq(_545662, _545668, _545666), c_Orderings_Oord__class_Oless__eq(_545662, c_Groups_Ozero__class_Ozero(_545662), _545670), c_Orderings_Oord__class_Oless__eq(_545662, c_Groups_Ozero__class_Ozero(_545662), _545672), c_Groups_Oplus__class_Oplus(_545662, _545670, _545672) = c_Groups_Oone__class_Oone(_545662), -(c_Orderings_Oord__class_Oless__eq(_545662, c_Groups_Oplus__class_Oplus(_545662, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_545662), _545670), _545664), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_545662), _545672), _545668)), _545666))], (9188 ^ _227627) ^ [_546545, _546547, _546549, _546551, _546553, _546555] : [class_Rings_Olinordered__semiring__1__strict(_546545), c_Orderings_Oord__class_Oless(_546545, _546547, _546549), c_Orderings_Oord__class_Oless(_546545, _546551, _546549), c_Orderings_Oord__class_Oless__eq(_546545, c_Groups_Ozero__class_Ozero(_546545), _546553), c_Orderings_Oord__class_Oless__eq(_546545, c_Groups_Ozero__class_Ozero(_546545), _546555), c_Groups_Oplus__class_Oplus(_546545, _546553, _546555) = c_Groups_Oone__class_Oone(_546545), -(c_Orderings_Oord__class_Oless(_546545, c_Groups_Oplus__class_Oplus(_546545, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_546545), _546553), _546547), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_546545), _546555), _546551)), _546549))], (9214 ^ _227627) ^ [_547400, _547402, _547404, _547406] : [class_Rings_Ocomm__semiring__0(_547400), -(c_Polynomial_Opcompose(_547400, c_Polynomial_OpCons(_547400, _547402, _547404), _547406) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_547400), c_Polynomial_OpCons(_547400, _547402, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_547400))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_547400)), _547406), c_Polynomial_Opcompose(_547400, _547404, _547406))))], (9220 ^ _227627) ^ [_547706, _547708, _547710] : [class_Rings_Ocomm__ring__1(_547706), -(c_Groups_Ominus__class_Ominus(_547706, hAPP(hAPP(c_Power_Opower__class_Opower(_547706), _547708), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(hAPP(c_Power_Opower__class_Opower(_547706), _547710), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_547706), c_Groups_Ominus__class_Ominus(_547706, _547708, _547710)), c_Groups_Oplus__class_Oplus(_547706, _547708, _547710)))], (9226 ^ _227627) ^ [_548034, _548036, _548038, _548040, _548042] : [class_Fields_Ofield(_548034), 9229 ^ _227627 : [(9252 ^ _227627) ^ [] : [-(c_Polynomial_Opdivmod__rel(_548034, _548036, _548038, _548040, _548042)), _548036 = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_548034), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_548034)), _548040), _548038), _548042), 9259 ^ _227627 : [(9260 ^ _227627) ^ [] : [-(_548038 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_548034)))], (9262 ^ _227627) ^ [] : [_548040 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_548034))]], 9263 ^ _227627 : [(9264 ^ _227627) ^ [] : [_548038 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_548034))], (9266 ^ _227627) ^ [] : [_548042 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_548034))], (9268 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_548034, _548042), c_Polynomial_Odegree(_548034, _548038))]]], (9230 ^ _227627) ^ [] : [c_Polynomial_Opdivmod__rel(_548034, _548036, _548038, _548040, _548042), 9233 ^ _227627 : [(9234 ^ _227627) ^ [] : [-(_548036 = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_548034), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_548034)), _548040), _548038), _548042))], (9236 ^ _227627) ^ [] : [_548038 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_548034)), -(_548040 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_548034)))], (9242 ^ _227627) ^ [] : [-(_548038 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_548034))), -(_548042 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_548034))), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_548034, _548042), c_Polynomial_Odegree(_548034, _548038)))]]]]], (9272 ^ _227627) ^ [_549588, _549590, _549592, _549594, _549596] : [class_Groups_Oab__group__add(_549588), -(c_Groups_Ominus__class_Ominus(_549588, c_Groups_Oplus__class_Oplus(_549588, _549590, _549592), c_Groups_Oplus__class_Oplus(_549588, _549594, _549596)) = c_Groups_Oplus__class_Oplus(_549588, c_Groups_Ominus__class_Ominus(_549588, _549590, _549594), c_Groups_Ominus__class_Ominus(_549588, _549592, _549596)))], (9278 ^ _227627) ^ [_549876, _549878, _549880] : [class_Groups_Ozero(_549876), 9284 ^ _227627 : [(9285 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _549878, 9283 ^ [_549876, _549878, _549880]))], (9287 ^ _227627) ^ [] : [hAPP(c_Polynomial_Ocoeff(_549876, _549880), 9283 ^ [_549876, _549878, _549880]) = c_Groups_Ozero__class_Ozero(_549876)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_549876, _549880), _549878))], (9291 ^ _227627) ^ [_550358, _550360] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _550358, _550360), _550360) = _550358)], (9293 ^ _227627) ^ [_550460, _550462] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _550460, _550462), _550460) = _550462)], (9295 ^ _227627) ^ [_550576, _550578, _550580] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _550576, _550578), _550580) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _550576, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _550578, _550580)))], (9297 ^ _227627) ^ [_550702, _550704, _550706] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _550702, _550704), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _550702, _550706)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _550704, _550706))], (9299 ^ _227627) ^ [_550828, _550830, _550832] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _550828, _550830), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _550832, _550830)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _550828, _550832))], (9301 ^ _227627) ^ [_550940, _550942] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _550940, _550942)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _550940), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _550942)))], (9303 ^ _227627) ^ [_551051, _551053] : [-(c_Groups_Ominus__class_Ominus(tc_Int_Oint, _551051, _551053) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _551051, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _551053)))], (9305 ^ _227627) ^ [_551156, _551158] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _551156, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _551158)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _551156, _551158))], (9307 ^ _227627) ^ [_551290, _551292, _551294] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _551290, _551292), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _551290, _551294), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _551292, _551294)))], (9313 ^ _227627) ^ [_551540, _551542, _551544] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _551540, _551542), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _551540, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _551544, _551542)))], (9319 ^ _227627) ^ [_551782, _551784, _551786] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _551782, _551784), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _551782, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _551784, _551786)))], (9325 ^ _227627) ^ [_552024, _552026, _552028] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _552024, _552026), _552028), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _552024, _552028))], (9331 ^ _227627) ^ [_552280, _552282, _552284, _552286] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _552280, _552282), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _552284, _552282) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _552280, _552286), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _552284, _552286))], (9341 ^ _227627) ^ [_552647, _552649, _552651, _552653] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _552647, _552649), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _552651, _552653), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _552647, _552651), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _552649, _552653)))], (9351 ^ _227627) ^ [_553002, _553004, _553006] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _553002, _553004), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _553002, _553006), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _553004, _553006)))], (9357 ^ _227627) ^ [_553252, _553254, _553256] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _553252, _553254), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _553252, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _553256, _553254)))], (9363 ^ _227627) ^ [_553494, _553496, _553498] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _553494, _553496), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _553494, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _553496, _553498)))], (9369 ^ _227627) ^ [_553765, _553767, _553769] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _553765, _553767), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _553765, _553769)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _553767, _553769))], (9375 ^ _227627) ^ [_553953, _553955, _553957] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _553955, _553957), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _553953, _553955), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _553953, _553957)))], (9381 ^ _227627) ^ [_554175, _554177] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _554175, _554177), _554177)], (9383 ^ _227627) ^ [_554273, _554275] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _554273, _554275), _554273)], (9385 ^ _227627) ^ [_554372, _554374] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Nat_OSuc(_554372), _554374) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _554372, c_Nat_OSuc(_554374)))], (9387 ^ _227627) ^ [_554478, _554480] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Nat_OSuc(_554478), _554480) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _554478, _554480)))], (9389 ^ _227627) ^ [_554584, _554586] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _554584, c_Nat_OSuc(_554586)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _554584, _554586)))], (9391 ^ _227627) ^ [_554734, _554736] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _554734), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _554736, _554734))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _554734), _554736)))], (9397 ^ _227627) ^ [_554924, _554926] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _554924), _554926)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _554924), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _554926, _554924))))], (9403 ^ _227627) ^ [_555163, _555165, _555167] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _555163, _555165)), _555167) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _555163), _555167), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _555165), _555167)))], (9405 ^ _227627) ^ [_555299, _555301, _555303] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _555299), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _555301, _555303)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _555299), _555301), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _555299), _555303)))], (9407 ^ _227627) ^ [_555449, _555451, _555453, _555455] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _555449), _555451), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _555453), _555451), _555455)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _555449, _555453)), _555451), _555455))], (9409 ^ _227627) ^ [_555581, _555583] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _555581, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _555583, _555581)))], (9411 ^ _227627) ^ [_555680, _555682] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _555680, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _555680, _555682)))], (9413 ^ _227627) ^ [_555823, _555825] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _555823, _555825), -(_555825 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _555823, 9416 ^ [_555823, _555825]))], (9420 ^ _227627) ^ [_556056, _556058] : [9421 ^ _227627 : [(9422 ^ _227627) ^ [_556131] : [_556058 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _556056, _556131)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _556056, _556058))], (9426 ^ _227627) ^ [_556343, _556345, _556347] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _556343, _556345), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _556343, _556347)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _556345, _556347))], (9432 ^ _227627) ^ [_556531, _556533, _556535] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _556533, _556535), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _556531, _556533), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _556531, _556535)))], (9438 ^ _227627) ^ [_556783, _556785, _556787] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _556783, _556785), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _556783, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _556785, _556787)))], (9444 ^ _227627) ^ [_557025, _557027, _557029] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _557025, _557027), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _557025, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _557029, _557027)))], (9450 ^ _227627) ^ [_557267, _557269, _557271] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _557267, _557269), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _557267, _557271), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _557269, _557271)))], (9456 ^ _227627) ^ [_557531, _557533, _557535, _557537] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _557531, _557533), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _557535, _557537), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _557531, _557535), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _557533, _557537)))], (9466 ^ _227627) ^ [_557886, _557888, _557890] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _557886, _557888), _557890), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _557888, _557890))], (9472 ^ _227627) ^ [_558128, _558130, _558132] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _558128, _558130), _558132), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _558128, _558132))], (9478 ^ _227627) ^ [_558370, _558372, _558374] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _558370, _558372), _558374), 9481 ^ _227627 : [(9482 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _558370, _558374))], (9484 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _558372, _558374))]]], (9486 ^ _227627) ^ [_558681, _558683] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _558681, _558683) = _558681, -(_558683 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9492 ^ _227627) ^ [_558928, _558930] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _558928, _558930) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 9495 ^ _227627 : [(9496 ^ _227627) ^ [] : [-(_558928 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9498 ^ _227627) ^ [] : [-(_558930 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (9500 ^ _227627) ^ [_559173, _559175] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _559173, _559175) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _559173 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _559175 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (9510 ^ _227627) ^ [_559453] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _559453, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _559453)], (9512 ^ _227627) ^ [_559535] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _559535) = _559535)], (9514 ^ _227627) ^ [_559660, _559662, _559664] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _559660, _559662), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _559664, _559660), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _559664, _559662)))], (9520 ^ _227627) ^ [_559910, _559912, _559914] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _559910, _559912), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _559910, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _559914, _559912)))], (9526 ^ _227627) ^ [_560152, _560154, _560156] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _560152, _560154), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _560152, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _560154, _560156)))], (9532 ^ _227627) ^ [_560351] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _560351) = _560351)], (9534 ^ _227627) ^ [_560433] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _560433, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _560433)], (9536 ^ _227627) ^ [_560543, _560545, _560547] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _560543), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _560545, _560547)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _560543), _560545), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _560543), _560547)))], (9538 ^ _227627) ^ [_560679, _560681, _560683] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _560679, _560681)), _560683) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _560679), _560683), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _560681), _560683)))], (9540 ^ _227627) ^ [_560816, _560818] : [class_Fields_Ofield(_560816), -(c_Polynomial_Opdivmod__rel(_560816, _560818, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_560816)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_560816)), _560818))], (9546 ^ _227627) ^ [_561046, _561048] : [class_Fields_Ofield(_561046), -(c_Polynomial_Opdivmod__rel(_561046, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_561046)), _561048, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_561046)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_561046))))], (9552 ^ _227627) ^ [_561312, _561314, _561316, _561318] : [class_Fields_Ofield(_561312), 9555 ^ _227627 : [(9556 ^ _227627) ^ [] : [c_Polynomial_Opdivmod__rel(_561312, _561314, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_561312)), _561316, _561318), 9559 ^ _227627 : [(9560 ^ _227627) ^ [] : [-(_561316 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_561312)))], (9562 ^ _227627) ^ [] : [-(_561318 = _561314)]]], (9564 ^ _227627) ^ [] : [-(c_Polynomial_Opdivmod__rel(_561312, _561314, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_561312)), _561316, _561318)), _561316 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_561312)), _561318 = _561314]]], (9574 ^ _227627) ^ [_562033, _562035, _562037, _562039] : [class_Fields_Ofield(_562033), 9577 ^ _227627 : [(9578 ^ _227627) ^ [] : [c_Polynomial_Opdivmod__rel(_562033, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_562033)), _562035, _562037, _562039), 9581 ^ _227627 : [(9582 ^ _227627) ^ [] : [-(_562037 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_562033)))], (9584 ^ _227627) ^ [] : [-(_562039 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_562033)))]]], (9586 ^ _227627) ^ [] : [-(c_Polynomial_Opdivmod__rel(_562033, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_562033)), _562035, _562037, _562039)), _562037 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_562033)), _562039 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_562033))]]], (9596 ^ _227627) ^ [_562808, _562810, _562812, _562814, _562816, _562818, _562820] : [class_Fields_Ofield(_562808), c_Polynomial_Opdivmod__rel(_562808, _562810, _562812, _562814, _562816), c_Polynomial_Opdivmod__rel(_562808, _562810, _562812, _562818, _562820), -(_562814 = _562818)], (9610 ^ _227627) ^ [_563346, _563348, _563350, _563352, _563354, _563356, _563358] : [class_Fields_Ofield(_563346), c_Polynomial_Opdivmod__rel(_563346, _563348, _563350, _563352, _563354), c_Polynomial_Opdivmod__rel(_563346, _563348, _563350, _563356, _563358), -(_563354 = _563358)], (9624 ^ _227627) ^ [_563884, _563886, _563888, _563890, _563892, _563894, _563896] : [class_Fields_Ofield(_563884), c_Polynomial_Opdivmod__rel(_563884, _563886, _563888, _563890, _563892), c_Polynomial_Opdivmod__rel(_563884, _563886, _563888, _563894, _563896), 9635 ^ _227627 : [(9636 ^ _227627) ^ [] : [-(_563890 = _563894)], (9638 ^ _227627) ^ [] : [-(_563892 = _563896)]]], (9640 ^ _227627) ^ [_564465, _564467, _564469, _564471] : [class_Groups_Omonoid__mult(_564465), -(hAPP(hAPP(c_Power_Opower__class_Opower(_564465), _564467), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _564469, _564471)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_564465), hAPP(hAPP(c_Power_Opower__class_Opower(_564465), _564467), _564469)), hAPP(hAPP(c_Power_Opower__class_Opower(_564465), _564467), _564471)))], (9646 ^ _227627) ^ [_564785, _564787, _564789, _564791] : [class_Rings_Ocomm__semiring__1(_564785), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_564785), hAPP(hAPP(c_Power_Opower__class_Opower(_564785), _564787), _564789)), hAPP(hAPP(c_Power_Opower__class_Opower(_564785), _564787), _564791)) = hAPP(hAPP(c_Power_Opower__class_Opower(_564785), _564787), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _564789, _564791)))], (9652 ^ _227627) ^ [_565106, _565108] : [c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _565106, _565108), 9657 ^ _227627 : [(9658 ^ _227627) ^ [] : [-(_565106 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (9660 ^ _227627) ^ [] : [-(_565108 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 9661 ^ _227627 : [(9662 ^ _227627) ^ [] : [-(_565106 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9664 ^ _227627) ^ [] : [-(_565108 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (9666 ^ _227627) ^ [_565516, _565518] : [-(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _565516, _565518)), 9667 ^ _227627 : [(9668 ^ _227627) ^ [] : [_565516 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _565518 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (9674 ^ _227627) ^ [] : [_565516 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _565518 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (9682 ^ _227627) ^ [_566017, _566019] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _566017, _566019) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 9687 ^ _227627 : [(9688 ^ _227627) ^ [] : [-(_566017 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (9690 ^ _227627) ^ [] : [-(_566019 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 9691 ^ _227627 : [(9692 ^ _227627) ^ [] : [-(_566017 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9694 ^ _227627) ^ [] : [-(_566019 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (9696 ^ _227627) ^ [_566427, _566429] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _566427, _566429) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 9697 ^ _227627 : [(9698 ^ _227627) ^ [] : [_566427 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _566429 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (9704 ^ _227627) ^ [] : [_566427 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _566429 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (9722 ^ _227627) ^ [_567194, _567196] : [9723 ^ _227627 : [(9724 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _567194)], (9726 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _567196)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _567194, _567196)))], (9712 ^ _227627) ^ [_566928, _566930] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _566928, _566930)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _566928)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _566930))], (9730 ^ _227627) ^ [_567494, _567496] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _567494), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _567496), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _567494, _567496)))], (9740 ^ _227627) ^ [_567792, _567794] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _567792, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _567792, _567794))))], (9742 ^ _227627) ^ [_567893, _567895] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _567893, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _567895, _567893))))], (9744 ^ _227627) ^ [_568038, _568040] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _568038, _568040), -(_568040 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _568038, 9747 ^ [_568038, _568040])))], (9751 ^ _227627) ^ [_568277, _568279] : [9752 ^ _227627 : [(9753 ^ _227627) ^ [_568354] : [_568279 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _568277, _568354))]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _568277, _568279))], (9757 ^ _227627) ^ [_568495] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _568495), _568495) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (9759 ^ _227627) ^ [_568638, _568640, _568642, _568644] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _568638, _568640), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _568642, _568644), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _568638, _568642), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _568640, _568644)))], (9769 ^ _227627) ^ [_568964, _568966] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _568964, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _568964, _568966)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9771 ^ _227627) ^ [_569066, _569068] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _569066), c_Nat_OSuc(_569068)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _569066, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _569066), _569068)))], (9773 ^ _227627) ^ [_569178, _569180] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_569178)), _569180) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _569180, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _569178), _569180)))], (9785 ^ _227627) ^ [_569598, _569600] : [9786 ^ _227627 : [(9787 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _569598, _569600)], (9789 ^ _227627) ^ [] : [_569598 = _569600]], -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _569598, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _569600, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (9775 ^ _227627) ^ [_569334, _569336] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _569334, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _569336, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _569334, _569336)), -(_569334 = _569336)], (9793 ^ _227627) ^ [_569896, _569898] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _569896, _569898)), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _569898, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _569896, _569898)) = _569896)], (9799 ^ _227627) ^ [_570170, _570172, _570174] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _570170, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _570172, _570174)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _570170, _570174), _570172))], (9805 ^ _227627) ^ [_570358, _570360, _570362] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _570358, _570362), _570360), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _570358, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _570360, _570362)))], (9811 ^ _227627) ^ [_570567] : [-(c_Nat_OSuc(_570567) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _570567))], (9813 ^ _227627) ^ [_570651] : [-(c_Nat_OSuc(_570651) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _570651, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (9815 ^ _227627) ^ [_570735] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _570735), _570735) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (9817 ^ _227627) ^ [_570863, _570865, _570867] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _570863, _570865), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _570867, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _570865, _570863)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _570867, _570863), _570865))], (9823 ^ _227627) ^ [_571156, _571158, _571160] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _571156, _571158), _571160), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _571156, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _571160, _571158)))], (9829 ^ _227627) ^ [_571344, _571346, _571348] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _571344, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _571348, _571346)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _571344, _571346), _571348))], (9835 ^ _227627) ^ [_571596, _571598, _571600] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _571596, _571598), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _571600, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _571598, _571600), _571596)))], (9841 ^ _227627) ^ [_571832, _571834] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _571832, _571834), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _571832, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _571834, _571832)) = _571834)], (9847 ^ _227627) ^ [_572074, _572076, _572078] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _572074, _572076), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _572078, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _572076, _572074)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _572078, _572076), _572074))], (9853 ^ _227627) ^ [_572338, _572340, _572342] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _572338, _572340), 9856 ^ _227627 : [(9857 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _572342, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _572340, _572338)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _572342, _572338), _572340))], (9863 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _572342, _572338), _572340), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _572342, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _572340, _572338)))]]], (9869 ^ _227627) ^ [_572846, _572848] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _572846, _572848), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _572848, _572846), _572846) = _572848)], (9875 ^ _227627) ^ [_573088, _573090, _573092] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _573088, _573090), 9878 ^ _227627 : [(9879 ^ _227627) ^ [] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _573090, _573088) = _573092, -(_573090 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _573092, _573088))], (9885 ^ _227627) ^ [] : [_573090 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _573092, _573088), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _573090, _573088) = _573092)]]], (9891 ^ _227627) ^ [_573604, _573606, _573608] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _573604, _573606), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _573608, _573606), _573604) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _573608, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _573606, _573604)))], (9897 ^ _227627) ^ [_573868, _573870, _573872] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _573868, _573870), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _573870, _573868), _573872) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _573870, _573872), _573868))], (9903 ^ _227627) ^ [_574132, _574134, _574136] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _574132, _574134), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _574134, _574136), _574132) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _574134, _574132), _574136))], (9909 ^ _227627) ^ [_574424, _574426, _574428, _574430, _574432] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _574424), _574426)), 9912 ^ _227627 : [(9913 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _574424), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _574428, _574430))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _574424), c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _574428, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _574432), _574426)), _574430))))], (9919 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _574424), c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _574428, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _574432), _574426)), _574430))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _574424), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _574428, _574430))))]]], (9925 ^ _227627) ^ [_575069, _575071, _575073] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _575069), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _575071, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _575069), _575073)))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _575069), _575071)))], (9931 ^ _227627) ^ [_575277, _575279, _575281] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _575277), _575279)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _575277), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _575279, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _575277), _575281)))))], (9937 ^ _227627) ^ [_575534, _575536, _575538] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _575534), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _575536, _575538)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _575534), _575536)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _575534), _575538)))], (9955 ^ _227627) ^ [_576255, _576257, _576259] : [-(hBOOL(hAPP(_576255, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _576257, _576259)))), 9958 ^ _227627 : [(9959 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _576257, _576259))], (9961 ^ _227627) ^ [] : [hBOOL(hAPP(_576255, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 9963 ^ _227627 : [(9964 ^ _227627) ^ [] : [-(_576257 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _576259, 9962 ^ [_576255, _576257, _576259]))], (9966 ^ _227627) ^ [] : [hBOOL(hAPP(_576255, 9962 ^ [_576255, _576257, _576259]))]]], (9939 ^ _227627) ^ [_575716, _575718, _575720] : [hBOOL(hAPP(_575716, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _575718, _575720))), 9942 ^ _227627 : [(9943 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _575718, _575720), -(hBOOL(hAPP(_575716, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (9949 ^ _227627) ^ [_576054] : [_575718 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _575720, _576054), -(hBOOL(hAPP(_575716, _576054)))]]], (9986 ^ _227627) ^ [_577416, _577418, _577420] : [-(hBOOL(hAPP(_577416, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _577418, _577420)))), 9989 ^ _227627 : [(9990 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _577418, _577420))], (9992 ^ _227627) ^ [] : [hBOOL(hAPP(_577416, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 9994 ^ _227627 : [(9995 ^ _227627) ^ [] : [-(_577418 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _577420, 9993 ^ [_577416, _577418, _577420]))], (9997 ^ _227627) ^ [] : [hBOOL(hAPP(_577416, 9993 ^ [_577416, _577418, _577420]))]]], (9970 ^ _227627) ^ [_576885, _576887, _576889] : [hBOOL(hAPP(_576885, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _576887, _576889))), 9973 ^ _227627 : [(9974 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _576887, _576889), -(hBOOL(hAPP(_576885, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (9980 ^ _227627) ^ [_577217] : [_576887 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _576889, _577217), -(hBOOL(hAPP(_576885, _577217)))]]], (10001 ^ _227627) ^ [_578010] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _578010), _578010), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _578010, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (10007 ^ _227627) ^ [_578186] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _578186, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _578186), _578186), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (10013 ^ _227627) ^ [_578441, _578443] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _578441, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _578443, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _578441, _578443))], (10019 ^ _227627) ^ [_578615, _578617] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _578615, _578617), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _578615, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _578617, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (10025 ^ _227627) ^ [_578868, _578870] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _578868, c_Groups_Oone__class_Oone(tc_Int_Oint)), _578870), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _578868, _578870))], (10031 ^ _227627) ^ [_579042, _579044] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _579042, _579044), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _579042, c_Groups_Oone__class_Oone(tc_Int_Oint)), _579044))], (10037 ^ _227627) ^ [_579266, _579268] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _579266, _579268), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _579266, c_Groups_Oone__class_Oone(tc_Int_Oint)), _579268))], (10043 ^ _227627) ^ [_579502, _579504, _579506] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _579502, _579504), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _579506, c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _579504, _579502))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _579506, _579502), c_Nat_OSuc(_579504)))], (10049 ^ _227627) ^ [_579774, _579776, _579778] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _579774, _579776), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _579776, _579774)), _579778) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_579776), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _579774, _579778)))], (10055 ^ _227627) ^ [_580074, _580076, _580078, _580080, _580082] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _580074, _580076), 10058 ^ _227627 : [(10059 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _580076), _580078), _580080), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _580074), _580078), _580082)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _580076, _580074)), _580078), _580080), _580082))], (10065 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _580076, _580074)), _580078), _580080), _580082), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _580076), _580078), _580080), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _580074), _580078), _580082)))]]], (10071 ^ _227627) ^ [_580734, _580736, _580738, _580740, _580742] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _580734, _580736), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _580736), _580738), _580740), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _580734), _580738), _580742)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _580736, _580734)), _580738), _580740), _580742))], (10077 ^ _227627) ^ [_581090, _581092, _581094, _581096, _581098] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _581090, _581092), 10080 ^ _227627 : [(10081 ^ _227627) ^ [] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _581092), _581094), _581096) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _581090), _581094), _581098), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _581092, _581090)), _581094), _581096) = _581098)], (10087 ^ _227627) ^ [] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _581092, _581090)), _581094), _581096) = _581098, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _581092), _581094), _581096) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _581090), _581094), _581098))]]], (10093 ^ _227627) ^ [_581744, _581746, _581748, _581750, _581752] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _581744, _581746), 10096 ^ _227627 : [(10097 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _581744), _581748), _581750), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _581746), _581748), _581752)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _581750, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _581746, _581744)), _581748), _581752)))], (10103 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _581750, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _581746, _581744)), _581748), _581752)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _581744), _581748), _581750), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _581746), _581748), _581752)))]]], (10109 ^ _227627) ^ [_582404, _582406, _582408, _582410, _582412] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _582404, _582406), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _582404), _582408), _582410), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _582406), _582408), _582412)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _582410, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _582406, _582404)), _582408), _582412)))], (10115 ^ _227627) ^ [_582760, _582762, _582764, _582766, _582768] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _582760, _582762), 10118 ^ _227627 : [(10119 ^ _227627) ^ [] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _582760), _582764), _582766) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _582762), _582764), _582768), -(_582766 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _582762, _582760)), _582764), _582768))], (10125 ^ _227627) ^ [] : [_582766 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _582762, _582760)), _582764), _582768), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _582760), _582764), _582766) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _582762), _582764), _582768))]]], (10131 ^ _227627) ^ [_583456, _583458, _583460, _583462, _583464, _583466, _583468, _583470] : [class_Fields_Ofield(_583456), c_Polynomial_Opdivmod__rel(_583456, _583458, _583460, _583462, _583464), c_Polynomial_Opdivmod__rel(_583456, _583462, _583466, _583468, _583470), -(c_Polynomial_Opdivmod__rel(_583456, _583458, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_583456)), _583460), _583466), _583468, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_583456), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_583456)), _583460), _583470), _583464)))], (10145 ^ _227627) ^ [_584010, _584012, _584014] : [class_Rings_Ocomm__semiring__0(_584010), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_584010, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_584010)), _584012), _584014)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Polynomial_Odegree(_584010, _584012), c_Polynomial_Odegree(_584010, _584014))))], (10151 ^ _227627) ^ [_584286, _584288, _584290] : [class_Rings_Oidom(_584286), -(_584288 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_584286))), -(_584290 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_584286))), -(c_Polynomial_Odegree(_584286, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_584286)), _584288), _584290)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Polynomial_Odegree(_584286, _584288), c_Polynomial_Odegree(_584286, _584290)))], (10165 ^ _227627) ^ [_584796, _584798, _584800, _584802, _584804] : [class_Rings_Ocomm__semiring__0(_584796), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_584796)), c_Polynomial_Omonom(_584796, _584798, _584800)), c_Polynomial_Omonom(_584796, _584802, _584804)) = c_Polynomial_Omonom(_584796, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_584796), _584798), _584802), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _584800, _584804)))], (10171 ^ _227627) ^ [_585076] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _585076), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _585076)))], (10177 ^ _227627) ^ [_585312, _585314] : [_585312 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _585312, _585314) = _585314)], (10183 ^ _227627) ^ [_585482, _585484] : [-(_585482 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _585482, _585484) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _585482, c_Groups_Oone__class_Oone(tc_Nat_Onat)), _585484)))], (10189 ^ _227627) ^ [_585767, _585769, _585771, _585773, _585775] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _585767, _585769), 10192 ^ _227627 : [(10193 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _585767), _585771), _585773), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _585769), _585771), _585775)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _585773, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _585769, _585767)), _585771), _585775)))], (10199 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _585773, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _585769, _585767)), _585771), _585775)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _585767), _585771), _585773), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _585769), _585771), _585775)))]]], (10205 ^ _227627) ^ [_586427, _586429, _586431, _586433, _586435] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _586427, _586429), 10208 ^ _227627 : [(10209 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _586429), _586431), _586433), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _586427), _586431), _586435)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _586429, _586427)), _586431), _586433), _586435))], (10215 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _586429, _586427)), _586431), _586433), _586435), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _586429), _586431), _586433), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _586427), _586431), _586435)))]]], (10221 ^ _227627) ^ [_587065, _587067] : [_587065 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _587065), _587067) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10227 ^ _227627) ^ [_587239, _587241] : [-(_587239 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _587239), _587241) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _587241, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _587239, c_Groups_Oone__class_Oone(tc_Nat_Onat))), _587241)))], (10233 ^ _227627) ^ [_587508, _587510, _587512] : [class_Rings_Ocomm__semiring__0(_587508), -(hAPP(c_Polynomial_Ocoeff(_587508, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_587508)), _587510), _587512)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Polynomial_Odegree(_587508, _587510), c_Polynomial_Odegree(_587508, _587512))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_587508), hAPP(c_Polynomial_Ocoeff(_587508, _587510), c_Polynomial_Odegree(_587508, _587510))), hAPP(c_Polynomial_Ocoeff(_587508, _587512), c_Polynomial_Odegree(_587508, _587512))))], (10239 ^ _227627) ^ [_587840, _587842, _587844] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _587840), _587840 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _587842, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _587840), _587844)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _587842, _587840), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _587844))], (10253 ^ _227627) ^ [_588282, _588284, _588286] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _588282), _588282 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _588284, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _588282), _588286)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _588284), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _588286, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (10267 ^ _227627) ^ [_588709, _588711, _588713] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _588709, _588711), _588713) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _588709, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _588711, _588713)))], (10269 ^ _227627) ^ [_588835, _588837, _588839] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _588835, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _588837, _588839)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _588837, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _588835, _588839)))], (10271 ^ _227627) ^ [_588947, _588949] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _588947, _588949) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _588949, _588947))], (10273 ^ _227627) ^ [_589107, _589109, _589111] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _589107, _589109) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _589111, _589109), -(_589107 = _589111)], (10279 ^ _227627) ^ [_589291, _589293, _589295] : [_589291 = _589295, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _589291, _589293) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _589295, _589293))], (10285 ^ _227627) ^ [_589568, _589570, _589572] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _589568, _589570) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _589568, _589572), -(_589570 = _589572)], (10291 ^ _227627) ^ [_589752, _589754, _589756] : [_589754 = _589756, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _589752, _589754) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _589752, _589756))], (10297 ^ _227627) ^ [_589985, _589987, _589989] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _589985, _589987), _589989) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _589985, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _589987, _589989)))], (10299 ^ _227627) ^ [_590111, _590113, _590115] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _590111, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _590113, _590115)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _590113, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _590111, _590115)))], (10301 ^ _227627) ^ [_590223, _590225] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _590223, _590225) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _590225, _590223))], (10303 ^ _227627) ^ [_590354, _590356, _590358] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _590354), _590356), _590358)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _590358, _590354), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _590354), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _590356))], (10317 ^ _227627) ^ [_590798, _590800, _590802] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _590798), _590800), _590802), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _590802), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _590798), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _590800, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (10331 ^ _227627) ^ [_591270, _591272, _591274, _591276, _591278] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _591270), _591272), _591274), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _591270), _591276), _591278)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _591274), c_Orderings_Oord__class_Oless(tc_Int_Oint, _591274, _591270), c_Orderings_Oord__class_Oless(tc_Int_Oint, _591278, _591270), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _591272, _591276))], (10349 ^ _227627) ^ [_591907, _591909, _591911, _591913, _591915, _591917] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _591907), _591909), _591911) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _591913), _591915), _591917), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _591913), _591915), _591917)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _591917, _591913), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _591911), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _591913), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _591913, _591907), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _591909, _591915))], (10375 ^ _227627) ^ [_592780, _592782, _592784, _592786, _592788] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _592780), _592782), _592784), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _592780), _592786), _592788)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _592788, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _592780, _592788), c_Orderings_Oord__class_Oless(tc_Int_Oint, _592780, _592784), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _592786, _592782))], (10393 ^ _227627) ^ [_593417, _593419, _593421, _593423, _593425, _593427] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _593417), _593419), _593421) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _593423), _593425), _593427), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _593423), _593425), _593427), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _593421, _593417), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _593427), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _593423), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _593423, _593417), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _593425, _593419))], (10419 ^ _227627) ^ [_594268, _594270] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _594268, _594270), -(c_Nat__Transfer_Otsub(_594270, _594268) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _594270, _594268))], (10425 ^ _227627) ^ [_594446, _594448] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _594446, _594448)), -(c_Nat__Transfer_Otsub(_594448, _594446) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (10431 ^ _227627) ^ [_594698, _594700] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _594698, _594700), -(_594700 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _594698, 10434 ^ [_594698, _594700]))], (10438 ^ _227627) ^ [_594931, _594933] : [10439 ^ _227627 : [(10440 ^ _227627) ^ [_595006] : [_594933 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _594931, _595006)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _594931, _594933))], (10444 ^ _227627) ^ [_595175, _595177] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _595175), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _595177), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Nat__Transfer_Otsub(_595175, _595177)))], (10454 ^ _227627) ^ [_595486, _595488] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _595486, _595488), -(c_Nat__Transfer_Otsub(_595488, _595486) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _595488, _595486))], (10460 ^ _227627) ^ [_595712, _595714] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _595712), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _595714), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _595714), _595712), _595714) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _595714), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _595712, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (10470 ^ _227627) ^ [_596055, _596057] : [class_Rings_Olinordered__idom(_596055), 10473 ^ _227627 : [(10474 ^ _227627) ^ [] : [_596057 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_596055)), -(c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(_596055), _596057) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_596055)))], (10480 ^ _227627) ^ [] : [-(_596057 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_596055))), 10483 ^ _227627 : [(10484 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_596055), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_596055)), _596057), -(c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(_596055), _596057) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_596055)))], (10490 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_596055), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_596055)), _596057)), -(c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(_596055), _596057) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_596055), c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_596055))))]]]]], (10496 ^ _227627) ^ [_596912, _596914] : [c_Divides_Odiv__class_Odiv(tc_Int_Oint, _596912, _596914) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_596914 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 10505 ^ _227627 : [(10506 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _596912))], (10508 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _596912, _596914))]], 10509 ^ _227627 : [(10510 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _596912, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (10512 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _596914, _596912))]]], (10514 ^ _227627) ^ [_597420, _597422] : [-(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _597420, _597422) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 10515 ^ _227627 : [(10516 ^ _227627) ^ [] : [_597422 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (10518 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _597420), c_Orderings_Oord__class_Oless(tc_Int_Oint, _597420, _597422)], (10524 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _597420, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _597422, _597420)]]], (10532 ^ _227627) ^ [_597973, _597975] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _597973), 10535 ^ _227627 : [(10536 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _597975, _597973)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _597975))], (10542 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _597975), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _597975, _597973)))]]], (10548 ^ _227627) ^ [_598453, _598455] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _598453), 10551 ^ _227627 : [(10552 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _598455, _598453)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _598453, _598455))], (10558 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _598453, _598455), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _598455, _598453)))]]], (10564 ^ _227627) ^ [_598933, _598935] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _598933), 10567 ^ _227627 : [(10568 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _598933, _598935)), 10571 ^ _227627 : [(10572 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _598935, _598933))], (10574 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _598935))]]], (10576 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _598933, _598935))), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _598935, _598933), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _598935)]]], (10586 ^ _227627) ^ [_599588, _599590, _599592] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _599588), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _599590), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _599590, _599592), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _599588, _599592), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _599588, _599590)))], (10600 ^ _227627) ^ [_600014, _600016] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _600014), c_Orderings_Oord__class_Oless(tc_Int_Oint, _600016, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _600014, _600016), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (10610 ^ _227627) ^ [_600327, _600329] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _600327), c_Orderings_Oord__class_Oless(tc_Int_Oint, _600327, _600329), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _600327, _600329) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (10620 ^ _227627) ^ [_600638, _600640] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _600638, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 10623 ^ _227627 : [(10624 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _600640, _600638)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _600640, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (10630 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _600640, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _600640, _600638)))]]], (10636 ^ _227627) ^ [_601118, _601120] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _601118, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _601120), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _601118, _601120), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (10646 ^ _227627) ^ [_601445, _601447, _601449] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _601445, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _601447), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _601447, _601449), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _601445, _601447), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _601445, _601449)))], (10660 ^ _227627) ^ [_601871, _601873] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _601871, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _601873, _601871), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _601871, _601873) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (10670 ^ _227627) ^ [_602196, _602198, _602200] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _602196, _602198), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _602200), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _602196, _602200), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _602198, _602200)))], (10680 ^ _227627) ^ [_602541, _602543, _602545] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _602541, _602543), c_Orderings_Oord__class_Oless(tc_Int_Oint, _602545, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _602543, _602545), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _602541, _602545)))], (10690 ^ _227627) ^ [_602872, _602874] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _602872), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _602874), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _602872, _602874), _602872))], (10700 ^ _227627) ^ [_603199, _603201, _603203] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _603199), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _603201, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _603203), _603199)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _603201, _603203), _603199))], (10706 ^ _227627) ^ [_603453, _603455] : [class_RealVector_Oreal__normed__vector(_603453), -(c_Groups_Osgn__class_Osgn(_603453, c_Groups_Ouminus__class_Ouminus(_603453, _603455)) = c_Groups_Ouminus__class_Ouminus(_603453, c_Groups_Osgn__class_Osgn(_603453, _603455)))], (10712 ^ _227627) ^ [_603671] : [class_RealVector_Oreal__normed__algebra__1(_603671), -(c_Groups_Osgn__class_Osgn(_603671, c_Groups_Oone__class_Oone(_603671)) = c_Groups_Oone__class_Oone(_603671))], (10718 ^ _227627) ^ [_603887, _603889] : [class_Rings_Olinordered__idom(_603887), -(c_Groups_Osgn__class_Osgn(_603887, c_Groups_Osgn__class_Osgn(_603887, _603889)) = c_Groups_Osgn__class_Osgn(_603887, _603889))], (10724 ^ _227627) ^ [_604127, _604129, _604131] : [class_Rings_Olinordered__idom(_604127), -(c_Groups_Osgn__class_Osgn(_604127, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_604127), _604129), _604131)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_604127), c_Groups_Osgn__class_Osgn(_604127, _604129)), c_Groups_Osgn__class_Osgn(_604127, _604131)))], (10730 ^ _227627) ^ [_604391, _604393] : [class_Rings_Olinordered__idom(_604391), 10733 ^ _227627 : [(10734 ^ _227627) ^ [] : [c_Groups_Osgn__class_Osgn(_604391, _604393) = c_Groups_Ozero__class_Ozero(_604391), -(_604393 = c_Groups_Ozero__class_Ozero(_604391))], (10740 ^ _227627) ^ [] : [_604393 = c_Groups_Ozero__class_Ozero(_604391), -(c_Groups_Osgn__class_Osgn(_604391, _604393) = c_Groups_Ozero__class_Ozero(_604391))]]], (10746 ^ _227627) ^ [_604856] : [class_Groups_Osgn__if(_604856), -(c_Groups_Osgn__class_Osgn(_604856, c_Groups_Ozero__class_Ozero(_604856)) = c_Groups_Ozero__class_Ozero(_604856))], (10752 ^ _227627) ^ [_605086, _605088, _605090] : [class_RealVector_Oreal__normed__div__algebra(_605086), -(c_Groups_Osgn__class_Osgn(_605086, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_605086), _605088), _605090)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_605086), c_Groups_Osgn__class_Osgn(_605086, _605088)), c_Groups_Osgn__class_Osgn(_605086, _605090)))], (10758 ^ _227627) ^ [_605350, _605352] : [class_RealVector_Oreal__normed__vector(_605350), 10761 ^ _227627 : [(10762 ^ _227627) ^ [] : [c_Groups_Osgn__class_Osgn(_605350, _605352) = c_Groups_Ozero__class_Ozero(_605350), -(_605352 = c_Groups_Ozero__class_Ozero(_605350))], (10768 ^ _227627) ^ [] : [_605352 = c_Groups_Ozero__class_Ozero(_605350), -(c_Groups_Osgn__class_Osgn(_605350, _605352) = c_Groups_Ozero__class_Ozero(_605350))]]], (10774 ^ _227627) ^ [_605815] : [class_RealVector_Oreal__normed__vector(_605815), -(c_Groups_Osgn__class_Osgn(_605815, c_Groups_Ozero__class_Ozero(_605815)) = c_Groups_Ozero__class_Ozero(_605815))], (10780 ^ _227627) ^ [_606031, _606033] : [class_Rings_Olinordered__idom(_606031), 10783 ^ _227627 : [(10784 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_606031, c_Groups_Osgn__class_Osgn(_606031, _606033), c_Groups_Ozero__class_Ozero(_606031)), -(c_Orderings_Oord__class_Oless(_606031, _606033, c_Groups_Ozero__class_Ozero(_606031)))], (10790 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_606031, _606033, c_Groups_Ozero__class_Ozero(_606031)), -(c_Orderings_Oord__class_Oless(_606031, c_Groups_Osgn__class_Osgn(_606031, _606033), c_Groups_Ozero__class_Ozero(_606031)))]]], (10796 ^ _227627) ^ [_606516, _606518] : [class_Rings_Olinordered__idom(_606516), 10799 ^ _227627 : [(10800 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_606516, c_Groups_Ozero__class_Ozero(_606516), c_Groups_Osgn__class_Osgn(_606516, _606518)), -(c_Orderings_Oord__class_Oless(_606516, c_Groups_Ozero__class_Ozero(_606516), _606518))], (10806 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_606516, c_Groups_Ozero__class_Ozero(_606516), _606518), -(c_Orderings_Oord__class_Oless(_606516, c_Groups_Ozero__class_Ozero(_606516), c_Groups_Osgn__class_Osgn(_606516, _606518)))]]], (10812 ^ _227627) ^ [_606972] : [-(c_Divides_Odiv__class_Odiv(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _606972) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (10814 ^ _227627) ^ [_607083, _607085] : [class_Divides_Osemiring__div(_607083), -(c_Divides_Odiv__class_Odiv(_607083, c_Groups_Ozero__class_Ozero(_607083), _607085) = c_Groups_Ozero__class_Ozero(_607083))], (10820 ^ _227627) ^ [_607307, _607309] : [class_Divides_Osemiring__div(_607307), -(c_Divides_Odiv__class_Odiv(_607307, _607309, c_Groups_Ozero__class_Ozero(_607307)) = c_Groups_Ozero__class_Ozero(_607307))], (10826 ^ _227627) ^ [_607531, _607533] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _607531), _607533)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _607531), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _607533, _607531)) = _607533)], (10832 ^ _227627) ^ [_607799, _607801, _607803, _607805] : [class_Divides_Osemiring__div(_607799), -(_607801 = c_Groups_Ozero__class_Ozero(_607799)), -(c_Divides_Odiv__class_Odiv(_607799, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_607799), _607801), _607803), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_607799), _607801), _607805)) = c_Divides_Odiv__class_Odiv(_607799, _607803, _607805))], (10842 ^ _227627) ^ [_608199, _608201, _608203, _608205] : [class_Divides_Osemiring__div(_608199), -(_608201 = c_Groups_Ozero__class_Ozero(_608199)), -(c_Divides_Odiv__class_Odiv(_608199, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_608199), _608203), _608201), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_608199), _608205), _608201)) = c_Divides_Odiv__class_Odiv(_608199, _608203, _608205))], (10852 ^ _227627) ^ [_608585, _608587, _608589] : [class_Divides_Osemiring__div(_608585), -(_608587 = c_Groups_Ozero__class_Ozero(_608585)), -(c_Divides_Odiv__class_Odiv(_608585, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_608585), _608587), _608589), _608587) = _608589)], (10862 ^ _227627) ^ [_608937, _608939, _608941] : [class_Divides_Osemiring__div(_608937), -(_608939 = c_Groups_Ozero__class_Ozero(_608937)), -(c_Divides_Odiv__class_Odiv(_608937, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_608937), _608941), _608939), _608939) = _608941)], (10872 ^ _227627) ^ [_609303, _609305, _609307, _609309] : [class_Divides_Osemiring__div(_609303), 10875 ^ _227627 : [(10876 ^ _227627) ^ [] : [_609305 = c_Groups_Ozero__class_Ozero(_609303), -(c_Divides_Odiv__class_Odiv(_609303, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_609303), _609305), _609307), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_609303), _609305), _609309)) = c_Groups_Ozero__class_Ozero(_609303))], (10882 ^ _227627) ^ [] : [-(_609305 = c_Groups_Ozero__class_Ozero(_609303)), -(c_Divides_Odiv__class_Odiv(_609303, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_609303), _609305), _609307), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_609303), _609305), _609309)) = c_Divides_Odiv__class_Odiv(_609303, _609307, _609309))]]], (10888 ^ _227627) ^ [_609913, _609915, _609917] : [class_Divides_Osemiring__div(_609913), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_609913), _609915), _609917)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_609913), _609915), c_Divides_Odiv__class_Odiv(_609913, _609917, _609915)) = _609917)], (10898 ^ _227627) ^ [_610286, _610288, _610290, _610292] : [class_Divides_Osemiring__div(_610286), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_610286), _610288), _610290)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_610286), _610292), c_Divides_Odiv__class_Odiv(_610286, _610290, _610288)) = c_Divides_Odiv__class_Odiv(_610286, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_610286), _610292), _610290), _610288))], (10908 ^ _227627) ^ [_610679, _610681, _610683] : [class_Divides_Osemiring__div(_610679), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_610679), _610681), _610683)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_610679), c_Divides_Odiv__class_Odiv(_610679, _610683, _610681)), _610681) = _610683)], (10918 ^ _227627) ^ [_611052, _611054, _611056, _611058] : [class_Divides_Osemiring__div(_611052), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_611052), _611054), _611056)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_611052), c_Divides_Odiv__class_Odiv(_611052, _611056, _611054)), _611058) = c_Divides_Odiv__class_Odiv(_611052, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_611052), _611056), _611058), _611054))], (10928 ^ _227627) ^ [_611473, _611475, _611477, _611479, _611481] : [class_Divides_Osemiring__div(_611473), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_611473), _611475), _611477)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_611473), _611479), _611481)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_611473), c_Divides_Odiv__class_Odiv(_611473, _611477, _611475)), c_Divides_Odiv__class_Odiv(_611473, _611481, _611479)) = c_Divides_Odiv__class_Odiv(_611473, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_611473), _611477), _611481), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_611473), _611475), _611479)))], (10942 ^ _227627) ^ [_612029, _612031, _612033, _612035] : [class_Divides_Osemiring__div(_612029), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_612029), _612031), _612033)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_612029), c_Divides_Odiv__class_Odiv(_612029, _612033, _612031)), _612035) = c_Divides_Odiv__class_Odiv(_612029, hAPP(hAPP(c_Power_Opower__class_Opower(_612029), _612033), _612035), hAPP(hAPP(c_Power_Opower__class_Opower(_612029), _612031), _612035)))], (10952 ^ _227627) ^ [_612452, _612454, _612456, _612458] : [class_Divides_Osemiring__div(_612452), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_612452), _612454), _612456)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_612452), _612454), _612458)), 10963 ^ _227627 : [(10964 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_612452), c_Divides_Odiv__class_Odiv(_612452, _612456, _612454)), c_Divides_Odiv__class_Odiv(_612452, _612458, _612454))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_612452), _612456), _612458)))], (10970 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_612452), _612456), _612458)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_612452), c_Divides_Odiv__class_Odiv(_612452, _612456, _612454)), c_Divides_Odiv__class_Odiv(_612452, _612458, _612454))))]]], (10976 ^ _227627) ^ [_613230, _613232] : [class_Divides_Osemiring__div(_613230), -(c_Divides_Odiv__class_Odiv(_613230, _613232, c_Groups_Oone__class_Oone(_613230)) = _613232)], (10982 ^ _227627) ^ [_613450, _613452] : [class_Divides_Osemiring__div(_613450), -(_613452 = c_Groups_Ozero__class_Ozero(_613450)), -(c_Divides_Odiv__class_Odiv(_613450, _613452, _613452) = c_Groups_Oone__class_Oone(_613450))], (10992 ^ _227627) ^ [_613752] : [-(_613752 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _613752, _613752) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (10998 ^ _227627) ^ [_613981, _613983, _613985] : [class_Divides_Oring__div(_613981), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_613981), _613983), _613985)), -(c_Divides_Odiv__class_Odiv(_613981, _613985, c_Groups_Ouminus__class_Ouminus(_613981, _613983)) = c_Groups_Ouminus__class_Ouminus(_613981, c_Divides_Odiv__class_Odiv(_613981, _613985, _613983)))], (11008 ^ _227627) ^ [_614344, _614346, _614348] : [class_Divides_Oring__div(_614344), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_614344), _614346), _614348)), -(c_Divides_Odiv__class_Odiv(_614344, c_Groups_Ouminus__class_Ouminus(_614344, _614348), _614346) = c_Groups_Ouminus__class_Ouminus(_614344, c_Divides_Odiv__class_Odiv(_614344, _614348, _614346)))], (11018 ^ _227627) ^ [_614678, _614680] : [-(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _614678, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _614680)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _614678), _614680))], (11020 ^ _227627) ^ [_614786, _614788] : [-(c_Divides_Odiv__class_Odiv(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _614786), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _614788)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint, _614786, _614788))], (11022 ^ _227627) ^ [_614909, _614911] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _614909), 11025 ^ _227627 : [(11026 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _614911, _614909), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _614911, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (11032 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _614911, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _614911, _614909), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (11038 ^ _227627) ^ [_615389, _615391] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _615389, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 11041 ^ _227627 : [(11042 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _615391, _615389), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _615391))], (11048 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _615391), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _615391, _615389), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (11054 ^ _227627) ^ [_615869, _615871] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _615869, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _615871), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _615869, _615871), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (11064 ^ _227627) ^ [_616182, _616184] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _616182), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _616184), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _616182, _616184)))], (11074 ^ _227627) ^ [_616523, _616525, _616527, _616529] : [class_Divides_Osemiring__div(_616523), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_616523), _616525), _616527)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_616523), _616525), _616529)), -(c_Divides_Odiv__class_Odiv(_616523, c_Groups_Oplus__class_Oplus(_616523, _616527, _616529), _616525) = c_Groups_Oplus__class_Oplus(_616523, c_Divides_Odiv__class_Odiv(_616523, _616527, _616525), c_Divides_Odiv__class_Odiv(_616523, _616529, _616525)))], (11088 ^ _227627) ^ [_617033, _617035, _617037, _617039] : [class_Divides_Osemiring__div(_617033), -(_617035 = c_Groups_Ozero__class_Ozero(_617033)), -(c_Divides_Odiv__class_Odiv(_617033, c_Groups_Oplus__class_Oplus(_617033, _617037, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_617033), _617035), _617039)), _617035) = c_Groups_Oplus__class_Oplus(_617033, _617039, c_Divides_Odiv__class_Odiv(_617033, _617037, _617035)))], (11098 ^ _227627) ^ [_617433, _617435, _617437, _617439] : [class_Divides_Osemiring__div(_617433), -(_617435 = c_Groups_Ozero__class_Ozero(_617433)), -(c_Divides_Odiv__class_Odiv(_617433, c_Groups_Oplus__class_Oplus(_617433, _617437, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_617433), _617439), _617435)), _617435) = c_Groups_Oplus__class_Oplus(_617433, _617439, c_Divides_Odiv__class_Odiv(_617433, _617437, _617435)))], (11108 ^ _227627) ^ [_617819, _617821, _617823] : [class_Divides_Osemiring__div(_617819), -(_617821 = c_Groups_Ozero__class_Ozero(_617819)), -(c_Divides_Odiv__class_Odiv(_617819, c_Groups_Oplus__class_Oplus(_617819, _617821, _617823), _617821) = c_Groups_Oplus__class_Oplus(_617819, c_Divides_Odiv__class_Odiv(_617819, _617823, _617821), c_Groups_Oone__class_Oone(_617819)))], (11118 ^ _227627) ^ [_618183, _618185, _618187] : [class_Divides_Osemiring__div(_618183), -(_618185 = c_Groups_Ozero__class_Ozero(_618183)), -(c_Divides_Odiv__class_Odiv(_618183, c_Groups_Oplus__class_Oplus(_618183, _618187, _618185), _618185) = c_Groups_Oplus__class_Oplus(_618183, c_Divides_Odiv__class_Odiv(_618183, _618187, _618185), c_Groups_Oone__class_Oone(_618183)))], (11128 ^ _227627) ^ [_618575, _618577, _618579, _618581, _618583] : [class_Divides_Osemiring__div(_618575), -(_618577 = c_Groups_Ozero__class_Ozero(_618575)), -(_618579 = c_Groups_Ozero__class_Ozero(_618575)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_618575), _618577), _618581)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_618575), _618579), _618583)), 11147 ^ _227627 : [(11148 ^ _227627) ^ [] : [c_Divides_Odiv__class_Odiv(_618575, _618581, _618577) = c_Divides_Odiv__class_Odiv(_618575, _618583, _618579), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_618575), _618581), _618579) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_618575), _618577), _618583))], (11154 ^ _227627) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_618575), _618581), _618579) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_618575), _618577), _618583), -(c_Divides_Odiv__class_Odiv(_618575, _618581, _618577) = c_Divides_Odiv__class_Odiv(_618575, _618583, _618579))]]], (11160 ^ _227627) ^ [_619627, _619629, _619631, _619633] : [class_Divides_Osemiring__div(_619627), -(_619629 = c_Groups_Ozero__class_Ozero(_619627)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_619627), _619629), _619631)), 11171 ^ _227627 : [(11172 ^ _227627) ^ [] : [c_Divides_Odiv__class_Odiv(_619627, _619631, _619629) = _619633, -(_619631 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_619627), _619633), _619629))], (11178 ^ _227627) ^ [] : [_619631 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_619627), _619633), _619629), -(c_Divides_Odiv__class_Odiv(_619627, _619631, _619629) = _619633)]]], (11184 ^ _227627) ^ [_620368, _620370] : [class_Rings_Olinordered__idom(_620368), c_Orderings_Oord__class_Oless(_620368, c_Groups_Ozero__class_Ozero(_620368), _620370), -(c_Groups_Osgn__class_Osgn(_620368, _620370) = c_Groups_Oone__class_Oone(_620368))], (11194 ^ _227627) ^ [_620681, _620683] : [class_Rings_Olinordered__idom(_620681), 11197 ^ _227627 : [(11198 ^ _227627) ^ [] : [c_Groups_Osgn__class_Osgn(_620681, _620683) = c_Groups_Oone__class_Oone(_620681), -(c_Orderings_Oord__class_Oless(_620681, c_Groups_Ozero__class_Ozero(_620681), _620683))], (11204 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_620681, c_Groups_Ozero__class_Ozero(_620681), _620683), -(c_Groups_Osgn__class_Osgn(_620681, _620683) = c_Groups_Oone__class_Oone(_620681))]]], (11210 ^ _227627) ^ [_621163, _621165] : [class_Groups_Osgn__if(_621163), 11213 ^ _227627 : [(11214 ^ _227627) ^ [] : [_621165 = c_Groups_Ozero__class_Ozero(_621163), -(c_Groups_Osgn__class_Osgn(_621163, _621165) = c_Groups_Ozero__class_Ozero(_621163))], (11220 ^ _227627) ^ [] : [-(_621165 = c_Groups_Ozero__class_Ozero(_621163)), 11223 ^ _227627 : [(11224 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_621163, c_Groups_Ozero__class_Ozero(_621163), _621165), -(c_Groups_Osgn__class_Osgn(_621163, _621165) = c_Groups_Oone__class_Oone(_621163))], (11230 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(_621163, c_Groups_Ozero__class_Ozero(_621163), _621165)), -(c_Groups_Osgn__class_Osgn(_621163, _621165) = c_Groups_Ouminus__class_Ouminus(_621163, c_Groups_Oone__class_Oone(_621163)))]]]]], (11236 ^ _227627) ^ [_621939, _621941] : [class_Rings_Olinordered__idom(_621939), c_Orderings_Oord__class_Oless(_621939, _621941, c_Groups_Ozero__class_Ozero(_621939)), -(c_Groups_Osgn__class_Osgn(_621939, _621941) = c_Groups_Ouminus__class_Ouminus(_621939, c_Groups_Oone__class_Oone(_621939)))], (11246 ^ _227627) ^ [_622258, _622260] : [class_Rings_Olinordered__idom(_622258), 11249 ^ _227627 : [(11250 ^ _227627) ^ [] : [c_Groups_Osgn__class_Osgn(_622258, _622260) = c_Groups_Ouminus__class_Ouminus(_622258, c_Groups_Oone__class_Oone(_622258)), -(c_Orderings_Oord__class_Oless(_622258, _622260, c_Groups_Ozero__class_Ozero(_622258)))], (11256 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(_622258, _622260, c_Groups_Ozero__class_Ozero(_622258)), -(c_Groups_Osgn__class_Osgn(_622258, _622260) = c_Groups_Ouminus__class_Ouminus(_622258, c_Groups_Oone__class_Oone(_622258)))]]], (11308 ^ _227627) ^ [_624412, _624414, _624416] : [-(hBOOL(hAPP(_624412, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _624414, _624416)))), 11311 ^ _227627 : [(11312 ^ _227627) ^ [] : [-(_624416 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (11314 ^ _227627) ^ [] : [hBOOL(hAPP(_624412, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], 11317 ^ _227627 : [(11318 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _624416))], (11322 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), 11320 ^ [_624412, _624414, _624416]))], (11324 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, 11320 ^ [_624412, _624414, _624416], _624416))], (11326 ^ _227627) ^ [] : [-(_624414 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _624416), 11319 ^ [_624412, _624414, _624416]), 11320 ^ [_624412, _624414, _624416]))], (11328 ^ _227627) ^ [] : [hBOOL(hAPP(_624412, 11319 ^ [_624412, _624414, _624416]))]], 11329 ^ _227627 : [(11330 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _624416, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (11334 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _624416, 11332 ^ [_624412, _624414, _624416]))], (11336 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, 11332 ^ [_624412, _624414, _624416], c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (11338 ^ _227627) ^ [] : [-(_624414 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _624416), 11331 ^ [_624412, _624414, _624416]), 11332 ^ [_624412, _624414, _624416]))], (11340 ^ _227627) ^ [] : [hBOOL(hAPP(_624412, 11331 ^ [_624412, _624414, _624416]))]]], (11262 ^ _227627) ^ [_622792, _622794, _622796] : [hBOOL(hAPP(_622792, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _622794, _622796))), 11265 ^ _227627 : [(11266 ^ _227627) ^ [] : [_622796 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_622792, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (11272 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _622796), 11275 ^ _227627 : [(11276 ^ _227627) ^ [_623313] : [-(hBOOL(hAPP(_622792, _623313))), 11277 ^ _227627 : [(11278 ^ _227627) ^ [_623435] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _623435), c_Orderings_Oord__class_Oless(tc_Int_Oint, _623435, _622796), _622794 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _622796), _623313), _623435)]]]]], (11290 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _622796, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 11293 ^ _227627 : [(11294 ^ _227627) ^ [_623907] : [-(hBOOL(hAPP(_622792, _623907))), 11295 ^ _227627 : [(11296 ^ _227627) ^ [_624029] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _622796, _624029), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _624029, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _622794 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _622796), _623907), _624029)]]]]]]], (11344 ^ _227627) ^ [_626061, _626063, _626065, _626067] : [_626061 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _626063), _626065), _626067), -(_626063 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _626061, _626063) = _626065), 11351 ^ _227627 : [(11352 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _626063))], (11354 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _626067), c_Orderings_Oord__class_Oless(tc_Int_Oint, _626067, _626063)]], 11359 ^ _227627 : [(11360 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _626063)], (11362 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _626063, _626067), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _626067, c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (11374 ^ _227627) ^ [_626992, _626994] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _626992), -(c_SMT_Oz3div(_626994, _626992) = c_Divides_Odiv__class_Odiv(tc_Int_Oint, _626994, _626992))], (11380 ^ _227627) ^ [_627170, _627172] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _627170)), -(c_SMT_Oz3div(_627172, _627170) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _627172, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _627170))))], (11386 ^ _227627) ^ [_627427, _627429, _627431] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _627427), 11392 ^ _227627 : [(11393 ^ _227627) ^ [] : [-(hBOOL(hAPP(_627429, 11391 ^ [_627427, _627429, _627431])))], (11395 ^ _227627) ^ [] : [hBOOL(hAPP(_627429, c_Groups_Ominus__class_Ominus(tc_Int_Oint, 11391 ^ [_627427, _627429, _627431], _627427)))]], c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _627431), 11400 ^ _227627 : [(11401 ^ _227627) ^ [_627942] : [hBOOL(hAPP(_627429, _627942)), -(hBOOL(hAPP(_627429, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _627942, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _627431), _627427)))))]]], (11407 ^ _227627) ^ [_628254, _628256, _628258, _628260, _628262] : [class_Fields_Ofield(_628254), c_Polynomial_Opdivmod__rel(_628254, _628256, _628258, _628260, _628262), -(c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_628254), _628256, _628258) = _628260)], (11417 ^ _227627) ^ [_628633, _628635, _628637] : [_628633 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _628633), _628635), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _628633), _628637)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11423 ^ _227627) ^ [_628833, _628835, _628837] : [-(_628833 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _628833), _628835), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _628833), _628837)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _628835, _628837))], (11429 ^ _227627) ^ [_629108, _629110, _629112] : [class_Fields_Ofield(_629108), -(c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_629108), c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_629108), _629110), _629112) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_629108), c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_629108), _629110, _629112)))], (11435 ^ _227627) ^ [_629380, _629382, _629384] : [class_Fields_Ofield(_629380), -(c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_629380), _629382, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_629380), _629384)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_629380), c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_629380), _629382, _629384)))], (11441 ^ _227627) ^ [_629666, _629668, _629670, _629672] : [class_Fields_Ofield(_629666), -(c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_629666), _629668, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_629666)), _629670), _629672)) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_629666), c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_629666), _629668, _629670), _629672))], (11447 ^ _227627) ^ [_629956, _629958, _629960] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _629956), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _629956), _629958), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _629956), _629960)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _629958, _629960))], (11453 ^ _227627) ^ [_630213, _630215, _630217] : [-(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _630213, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _630215), _630217)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _630213, _630215), _630217))], (11455 ^ _227627) ^ [_630313] : [-(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _630313, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _630313)], (11457 ^ _227627) ^ [_630424, _630426] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _630424), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _630426), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _630426, _630424), _630426))], (11467 ^ _227627) ^ [_630737, _630739] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _630737), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _630737), _630739), _630737) = _630739)], (11473 ^ _227627) ^ [_630969, _630971] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _630969), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _630971), _630969), _630969) = _630971)], (11479 ^ _227627) ^ [_631215, _631217, _631219] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _631215), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _631215, _631217), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _631219, _631217), c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _631219, _631215)))], (11489 ^ _227627) ^ [_631546, _631548] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _631546, _631548), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _631546, _631548) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11495 ^ _227627) ^ [_631780, _631782, _631784] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _631780, _631782), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _631780, _631784), c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _631782, _631784)))], (11501 ^ _227627) ^ [_632001, _632003] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _632001, _632003), _632001))], (11503 ^ _227627) ^ [_632129, _632131, _632133] : [class_Fields_Ofield(_632129), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_632129, _632131), c_Polynomial_Odegree(_632129, _632133)), -(c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_632129), _632131, _632133) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_632129)))], (11513 ^ _227627) ^ [_632470, _632472] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _632470), 11516 ^ _227627 : [(11517 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _632472, _632470), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _632472, _632470) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11523 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _632472, _632470)), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _632472, _632470) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _632472, _632470), _632470)))]]], (11529 ^ _227627) ^ [_632978, _632980] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _632978), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _632980, _632978)), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _632980, _632978) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _632980, _632978), _632978)))], (11563 ^ _227627) ^ [_634134, _634136, _634138] : [-(hBOOL(hAPP(_634134, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _634136, _634138)))), 11566 ^ _227627 : [(11567 ^ _227627) ^ [] : [-(_634138 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11569 ^ _227627) ^ [] : [hBOOL(hAPP(_634134, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 11570 ^ _227627 : [(11571 ^ _227627) ^ [] : [_634138 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11575 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 11573 ^ [_634134, _634136, _634138], _634138))], (11577 ^ _227627) ^ [] : [-(_634136 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _634138), 11572 ^ [_634134, _634136, _634138]), 11573 ^ [_634134, _634136, _634138]))], (11579 ^ _227627) ^ [] : [hBOOL(hAPP(_634134, 11572 ^ [_634134, _634136, _634138]))]]], (11539 ^ _227627) ^ [_633355, _633357, _633359] : [hBOOL(hAPP(_633355, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _633357, _633359))), 11542 ^ _227627 : [(11543 ^ _227627) ^ [] : [_633359 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_633355, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (11549 ^ _227627) ^ [] : [-(_633359 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 11552 ^ _227627 : [(11553 ^ _227627) ^ [_633809, _633811] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _633809, _633359), _633357 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _633359), _633811), _633809), -(hBOOL(hAPP(_633355, _633811)))]]]]], (11583 ^ _227627) ^ [_635017] : [_635017 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _635017) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (11589 ^ _227627) ^ [_635179] : [-(_635179 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 11592 ^ _227627 : [(11593 ^ _227627) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _635179), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _635179) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (11599 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _635179)), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _635179) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (11605 ^ _227627) ^ [_635693, _635695, _635697] : [hBOOL(hAPP(_635693, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _635695, _635697))), 11610 ^ _227627 : [(11611 ^ _227627) ^ [] : [-(_635697 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11613 ^ _227627) ^ [] : [-(hBOOL(hAPP(_635693, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]], 11615 ^ _227627 : [(11616 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _635697), 11614 ^ [_635693, _635695, _635697]), _635695))], (11618 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _635695, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _635697), c_Nat_OSuc(11614 ^ [_635693, _635695, _635697]))))], (11620 ^ _227627) ^ [] : [-(hBOOL(hAPP(_635693, 11614 ^ [_635693, _635695, _635697])))]]], (11622 ^ _227627) ^ [_636348, _636350, _636352] : [-(hBOOL(hAPP(_636348, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _636350, _636352)))), 11623 ^ _227627 : [(11624 ^ _227627) ^ [] : [_636352 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_636348, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (11630 ^ _227627) ^ [_636642] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _636352), _636642), _636350), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _636350, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _636352), c_Nat_OSuc(_636642))), hBOOL(hAPP(_636348, _636642))]]], (11642 ^ _227627) ^ [_637079, _637081, _637083] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _637079), 11645 ^ _227627 : [(11656 ^ _227627) ^ [] : [_637081 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _637083, _637079), 11659 ^ _227627 : [(11660 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _637079), _637081), _637083))], (11662 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _637083, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _637079), c_Nat_OSuc(_637081))))]]], (11646 ^ _227627) ^ [] : [-(_637081 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _637083, _637079)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _637079), _637081), _637083), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _637083, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _637079), c_Nat_OSuc(_637081)))]]], (11664 ^ _227627) ^ [_637781, _637783] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _637781), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _637781, _637783), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _637783, _637781) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _637783, _637781), _637781)))], (11674 ^ _227627) ^ [_638126, _638128, _638130] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _638126), 11680 ^ _227627 : [(11681 ^ _227627) ^ [] : [-(hBOOL(hAPP(_638128, 11679 ^ [_638126, _638128, _638130])))], (11683 ^ _227627) ^ [] : [hBOOL(hAPP(_638128, c_Groups_Oplus__class_Oplus(tc_Int_Oint, 11679 ^ [_638126, _638128, _638130], _638126)))]], c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _638130), 11688 ^ _227627 : [(11689 ^ _227627) ^ [_638641] : [hBOOL(hAPP(_638128, _638641)), -(hBOOL(hAPP(_638128, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _638641, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _638130), _638126)))))]]], (11695 ^ _227627) ^ [_638925, _638927, _638929] : [class_Fields_Ofield(_638925), 11698 ^ _227627 : [(11709 ^ _227627) ^ [] : [11710 ^ _227627 : [(11711 ^ _227627) ^ [] : [-(_638927 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_638925)))], (11713 ^ _227627) ^ [] : [-(_638929 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_638925)))]], -(hAPP(c_Polynomial_Ocoeff(_638925, c_Polynomial_Opoly__gcd(_638925, _638927, _638929)), c_Polynomial_Odegree(_638925, c_Polynomial_Opoly__gcd(_638925, _638927, _638929))) = c_Groups_Oone__class_Oone(_638925))], (11699 ^ _227627) ^ [] : [-(hAPP(c_Polynomial_Ocoeff(_638925, c_Polynomial_Opoly__gcd(_638925, _638927, _638929)), c_Polynomial_Odegree(_638925, c_Polynomial_Opoly__gcd(_638925, _638927, _638929))) = c_Groups_Ozero__class_Ozero(_638925)), _638927 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_638925)), _638929 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_638925))]]], (11717 ^ _227627) ^ [_639697, _639699, _639701] : [class_Fields_Ofield(_639697), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_639697)), c_Polynomial_Opoly__gcd(_639697, _639699, _639701)), _639701)))], (11723 ^ _227627) ^ [_639951, _639953, _639955] : [class_Fields_Ofield(_639951), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_639951)), c_Polynomial_Opoly__gcd(_639951, _639953, _639955)), _639953)))], (11729 ^ _227627) ^ [_640191, _640193] : [class_Fields_Ofield(_640191), -(c_Polynomial_Opoly__gcd(_640191, _640193, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_640191))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_640191)))], (11735 ^ _227627) ^ [_640423, _640425] : [class_Fields_Ofield(_640423), -(c_Polynomial_Opoly__gcd(_640423, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_640423)), _640425) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_640423)))], (11741 ^ _227627) ^ [_640641] : [class_Fields_Ofield(_640641), -(c_Polynomial_Opoly__gcd(_640641, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_640641)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_640641))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_640641)))], (11747 ^ _227627) ^ [_640889, _640891, _640893] : [class_Fields_Ofield(_640889), 11750 ^ _227627 : [(11751 ^ _227627) ^ [] : [c_Polynomial_Opoly__gcd(_640889, _640891, _640893) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_640889)), 11754 ^ _227627 : [(11755 ^ _227627) ^ [] : [-(_640891 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_640889)))], (11757 ^ _227627) ^ [] : [-(_640893 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_640889)))]]], (11759 ^ _227627) ^ [] : [-(c_Polynomial_Opoly__gcd(_640889, _640891, _640893) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_640889))), _640891 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_640889)), _640893 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_640889))]]], (11769 ^ _227627) ^ [_641603, _641605, _641607, _641609] : [class_Fields_Ofield(_641603), -(c_Polynomial_Opoly__gcd(_641603, c_Polynomial_Opoly__gcd(_641603, _641605, _641607), _641609) = c_Polynomial_Opoly__gcd(_641603, _641605, c_Polynomial_Opoly__gcd(_641603, _641607, _641609)))], (11775 ^ _227627) ^ [_641883, _641885, _641887, _641889] : [class_Fields_Ofield(_641883), -(c_Polynomial_Opoly__gcd(_641883, _641885, c_Polynomial_Opoly__gcd(_641883, _641887, _641889)) = c_Polynomial_Opoly__gcd(_641883, _641887, c_Polynomial_Opoly__gcd(_641883, _641885, _641889)))], (11781 ^ _227627) ^ [_642149, _642151, _642153] : [class_Fields_Ofield(_642149), -(c_Polynomial_Opoly__gcd(_642149, _642151, _642153) = c_Polynomial_Opoly__gcd(_642149, _642153, _642151))], (11787 ^ _227627) ^ [_642393, _642395, _642397] : [class_Fields_Ofield(_642393), -(c_Polynomial_Opoly__gcd(_642393, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_642393), _642395), _642397) = c_Polynomial_Opoly__gcd(_642393, _642395, _642397))], (11793 ^ _227627) ^ [_642647, _642649, _642651] : [class_Fields_Ofield(_642647), -(c_Polynomial_Opoly__gcd(_642647, _642649, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_642647), _642651)) = c_Polynomial_Opoly__gcd(_642647, _642649, _642651))], (11799 ^ _227627) ^ [_642915, _642917, _642919, _642921] : [class_Fields_Ofield(_642915), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_642915)), _642917), _642919)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_642915)), _642917), _642921)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_642915)), _642917), c_Polynomial_Opoly__gcd(_642915, _642919, _642921))))], (11813 ^ _227627) ^ [_643419, _643421, _643423, _643425] : [class_Fields_Ofield(_643419), 11816 ^ _227627 : [(11817 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_643419)), _643421), c_Polynomial_Opoly__gcd(_643419, _643423, _643425))), 11820 ^ _227627 : [(11821 ^ _227627) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_643419)), _643421), _643423)))], (11823 ^ _227627) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_643419)), _643421), _643425)))]]], (11825 ^ _227627) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_643419)), _643421), c_Polynomial_Opoly__gcd(_643419, _643423, _643425)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_643419)), _643421), _643423)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_643419)), _643421), _643425))]]], (11835 ^ _227627) ^ [_644200, _644202, _644204, _644206] : [class_Fields_Ofield(_644200), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_644200)), _644202), _644204)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_644200)), _644202), _644206)), 11849 ^ _227627 : [(11850 ^ _227627) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_644200)), 11848 ^ [_644200, _644202, _644204, _644206]), _644204)))], (11852 ^ _227627) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_644200)), 11848 ^ [_644200, _644202, _644204, _644206]), _644206)))], (11854 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_644200)), 11848 ^ [_644200, _644202, _644204, _644206]), _644202))]], -(c_Polynomial_Opoly__gcd(_644200, _644204, _644206) = _644202), 11859 ^ _227627 : [(11860 ^ _227627) ^ [] : [-(_644204 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_644200)))], (11862 ^ _227627) ^ [] : [-(_644206 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_644200)))], (11864 ^ _227627) ^ [] : [hAPP(c_Polynomial_Ocoeff(_644200, _644202), c_Polynomial_Odegree(_644200, _644202)) = c_Groups_Ozero__class_Ozero(_644200)]], 11865 ^ _227627 : [(11872 ^ _227627) ^ [] : [hAPP(c_Polynomial_Ocoeff(_644200, _644202), c_Polynomial_Odegree(_644200, _644202)) = c_Groups_Oone__class_Oone(_644200)], (11866 ^ _227627) ^ [] : [_644204 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_644200)), _644206 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_644200))]]], (11876 ^ _227627) ^ [_645702, _645704] : [-(hBOOL(hAPP(_645702, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_645702, _645704)), 11884 ^ _227627 : [(11885 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 11883 ^ [_645702, _645704], _645704))], (11893 ^ _227627) ^ [] : [-(hBOOL(hAPP(_645702, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, 11883 ^ [_645702, _645704], c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (11887 ^ _227627) ^ [_646138] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _646138, 11883 ^ [_645702, _645704]), hBOOL(hAPP(_645702, _646138))]]], (11895 ^ _227627) ^ [_646465, _646467, _646469] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _646465), 11898 ^ _227627 : [(11917 ^ _227627) ^ [] : [11920 ^ _227627 : [(11921 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), 11919 ^ [_646465, _646467, _646469]))], (11923 ^ _227627) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, 11919 ^ [_646465, _646467, _646469], _646465))], (11925 ^ _227627) ^ [] : [-(_646469 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _646465), 11918 ^ [_646465, _646467, _646469]), 11919 ^ [_646465, _646467, _646469]))], (11927 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(_646467, 11918 ^ [_646465, _646467, _646469]), 11919 ^ [_646465, _646467, _646469]))]], -(hBOOL(hAPP(hAPP(_646467, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _646469, _646465)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _646469, _646465))))], (11899 ^ _227627) ^ [] : [hBOOL(hAPP(hAPP(_646467, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _646469, _646465)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _646469, _646465))), 11902 ^ _227627 : [(11903 ^ _227627) ^ [_646800, _646802] : [-(hBOOL(hAPP(hAPP(_646467, _646802), _646800))), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _646800), c_Orderings_Oord__class_Oless(tc_Int_Oint, _646800, _646465), _646469 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _646465), _646802), _646800)]]]]], (11931 ^ _227627) ^ [_647893] : [class_Groups_Ocancel__comm__monoid__add(_647893), -(class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(_647893)))], (11937 ^ _227627) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex))], (11939 ^ _227627) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat))], (11941 ^ _227627) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint))], (11943 ^ _227627) ^ [_648256, _648258] : [class_Lattices_Oboolean__algebra(_648256), -(class_Lattices_Oboolean__algebra(tc_fun(_648258, _648256)))], (11949 ^ _227627) ^ [_648468, _648470] : [class_Orderings_Opreorder(_648468), -(class_Orderings_Opreorder(tc_fun(_648470, _648468)))], (11955 ^ _227627) ^ [_648680, _648682] : [class_Orderings_Oorder(_648680), -(class_Orderings_Oorder(tc_fun(_648682, _648680)))], (11961 ^ _227627) ^ [_648892, _648894] : [class_Orderings_Oord(_648892), -(class_Orderings_Oord(tc_fun(_648894, _648892)))], (11967 ^ _227627) ^ [_649104, _649106] : [class_Groups_Ouminus(_649104), -(class_Groups_Ouminus(tc_fun(_649106, _649104)))], (11973 ^ _227627) ^ [_649316, _649318] : [class_Groups_Ominus(_649316), -(class_Groups_Ominus(tc_fun(_649318, _649316)))], (11979 ^ _227627) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (11981 ^ _227627) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (11983 ^ _227627) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (11985 ^ _227627) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (11987 ^ _227627) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (11989 ^ _227627) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (11991 ^ _227627) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (11993 ^ _227627) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (11995 ^ _227627) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (11997 ^ _227627) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (11999 ^ _227627) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (12001 ^ _227627) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (12003 ^ _227627) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (12005 ^ _227627) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (12007 ^ _227627) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (12009 ^ _227627) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (12011 ^ _227627) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (12013 ^ _227627) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (12015 ^ _227627) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (12017 ^ _227627) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (12019 ^ _227627) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (12021 ^ _227627) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (12023 ^ _227627) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (12025 ^ _227627) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (12027 ^ _227627) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (12029 ^ _227627) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (12031 ^ _227627) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (12033 ^ _227627) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (12035 ^ _227627) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (12037 ^ _227627) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Int_Oint))], (12039 ^ _227627) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (12041 ^ _227627) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (12043 ^ _227627) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (12045 ^ _227627) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (12047 ^ _227627) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (12049 ^ _227627) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (12051 ^ _227627) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (12053 ^ _227627) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (12055 ^ _227627) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (12057 ^ _227627) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (12059 ^ _227627) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (12061 ^ _227627) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (12063 ^ _227627) ^ [] : [-(class_Divides_Oring__div(tc_Int_Oint))], (12065 ^ _227627) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (12067 ^ _227627) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (12069 ^ _227627) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (12071 ^ _227627) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (12073 ^ _227627) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (12075 ^ _227627) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (12077 ^ _227627) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (12079 ^ _227627) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (12081 ^ _227627) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (12083 ^ _227627) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (12085 ^ _227627) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (12087 ^ _227627) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (12089 ^ _227627) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (12091 ^ _227627) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (12093 ^ _227627) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (12095 ^ _227627) ^ [] : [-(class_Rings_Odvd(tc_Int_Oint))], (12097 ^ _227627) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (12099 ^ _227627) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (12101 ^ _227627) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (12103 ^ _227627) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (12105 ^ _227627) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (12107 ^ _227627) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (12109 ^ _227627) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (12111 ^ _227627) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (12113 ^ _227627) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (12115 ^ _227627) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (12117 ^ _227627) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (12119 ^ _227627) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (12121 ^ _227627) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (12123 ^ _227627) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (12125 ^ _227627) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (12127 ^ _227627) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (12129 ^ _227627) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (12131 ^ _227627) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (12133 ^ _227627) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (12135 ^ _227627) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (12137 ^ _227627) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Nat_Onat))], (12139 ^ _227627) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (12141 ^ _227627) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (12143 ^ _227627) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (12145 ^ _227627) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (12147 ^ _227627) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (12149 ^ _227627) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (12151 ^ _227627) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (12153 ^ _227627) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (12155 ^ _227627) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (12157 ^ _227627) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (12159 ^ _227627) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (12161 ^ _227627) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (12163 ^ _227627) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (12165 ^ _227627) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (12167 ^ _227627) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (12169 ^ _227627) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (12171 ^ _227627) ^ [] : [-(class_Rings_Odvd(tc_Nat_Onat))], (12173 ^ _227627) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (12175 ^ _227627) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (12177 ^ _227627) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (12179 ^ _227627) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (12181 ^ _227627) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (12183 ^ _227627) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (12185 ^ _227627) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex))], (12187 ^ _227627) ^ [] : [-(class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex))], (12189 ^ _227627) ^ [] : [-(class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex))], (12191 ^ _227627) ^ [] : [-(class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex))], (12193 ^ _227627) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex))], (12195 ^ _227627) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex))], (12197 ^ _227627) ^ [] : [-(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex))], (12199 ^ _227627) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex))], (12201 ^ _227627) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex))], (12203 ^ _227627) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex))], (12205 ^ _227627) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex))], (12207 ^ _227627) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex))], (12209 ^ _227627) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex))], (12211 ^ _227627) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex))], (12213 ^ _227627) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex))], (12215 ^ _227627) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex))], (12217 ^ _227627) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Complex_Ocomplex))], (12219 ^ _227627) ^ [] : [-(class_Groups_Oab__group__add(tc_Complex_Ocomplex))], (12221 ^ _227627) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Complex_Ocomplex))], (12223 ^ _227627) ^ [] : [-(class_Groups_Omonoid__mult(tc_Complex_Ocomplex))], (12225 ^ _227627) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex))], (12227 ^ _227627) ^ [] : [-(class_Groups_Omonoid__add(tc_Complex_Ocomplex))], (12229 ^ _227627) ^ [] : [-(class_Rings_Osemiring__0(tc_Complex_Ocomplex))], (12231 ^ _227627) ^ [] : [-(class_Groups_Ogroup__add(tc_Complex_Ocomplex))], (12233 ^ _227627) ^ [] : [-(class_Rings_Omult__zero(tc_Complex_Ocomplex))], (12235 ^ _227627) ^ [] : [-(class_Rings_Ocomm__ring(tc_Complex_Ocomplex))], (12237 ^ _227627) ^ [] : [-(class_Int_Oring__char__0(tc_Complex_Ocomplex))], (12239 ^ _227627) ^ [] : [-(class_Rings_Osemiring(tc_Complex_Ocomplex))], (12241 ^ _227627) ^ [] : [-(class_Groups_Ouminus(tc_Complex_Ocomplex))], (12243 ^ _227627) ^ [] : [-(class_Rings_Oring__1(tc_Complex_Ocomplex))], (12245 ^ _227627) ^ [] : [-(class_Groups_Ominus(tc_Complex_Ocomplex))], (12247 ^ _227627) ^ [] : [-(class_Fields_Ofield(tc_Complex_Ocomplex))], (12249 ^ _227627) ^ [] : [-(class_Power_Opower(tc_Complex_Ocomplex))], (12251 ^ _227627) ^ [] : [-(class_Groups_Ozero(tc_Complex_Ocomplex))], (12253 ^ _227627) ^ [] : [-(class_Rings_Oring(tc_Complex_Ocomplex))], (12255 ^ _227627) ^ [] : [-(class_Rings_Oidom(tc_Complex_Ocomplex))], (12257 ^ _227627) ^ [] : [-(class_Groups_Oone(tc_Complex_Ocomplex))], (12259 ^ _227627) ^ [] : [-(class_Rings_Odvd(tc_Complex_Ocomplex))], (12261 ^ _227627) ^ [_656987] : [class_Rings_Oidom(_656987), -(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(_656987)))], (12267 ^ _227627) ^ [_657177] : [class_Rings_Olinordered__idom(_657177), -(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(_657177)))], (12273 ^ _227627) ^ [_657367] : [class_Rings_Olinordered__idom(_657367), -(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(_657367)))], (12279 ^ _227627) ^ [_657557] : [class_Rings_Olinordered__idom(_657557), -(class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(_657557)))], (12285 ^ _227627) ^ [_657747] : [class_Rings_Olinordered__idom(_657747), -(class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(_657747)))], (12291 ^ _227627) ^ [_657937] : [class_Rings_Olinordered__idom(_657937), -(class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(_657937)))], (12297 ^ _227627) ^ [_658127] : [class_Rings_Olinordered__idom(_658127), -(class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(_658127)))], (12303 ^ _227627) ^ [_658317] : [class_Rings_Olinordered__idom(_658317), -(class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(_658317)))], (12309 ^ _227627) ^ [_658507] : [class_Rings_Olinordered__idom(_658507), -(class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(_658507)))], (12315 ^ _227627) ^ [_658697] : [class_Groups_Ocancel__comm__monoid__add(_658697), -(class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(_658697)))], (12321 ^ _227627) ^ [_658887] : [class_Rings_Oidom(_658887), -(class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(_658887)))], (12327 ^ _227627) ^ [_659077] : [class_Rings_Olinordered__idom(_659077), -(class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(_659077)))], (12333 ^ _227627) ^ [_659267] : [class_Rings_Olinordered__idom(_659267), -(class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(_659267)))], (12339 ^ _227627) ^ [_659457] : [class_Rings_Oidom(_659457), -(class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(_659457)))], (12345 ^ _227627) ^ [_659647] : [class_Rings_Olinordered__idom(_659647), -(class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(_659647)))], (12351 ^ _227627) ^ [_659837] : [class_Rings_Olinordered__idom(_659837), -(class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(_659837)))], (12357 ^ _227627) ^ [_660027] : [class_Rings_Olinordered__idom(_660027), -(class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(_660027)))], (12363 ^ _227627) ^ [_660217] : [class_Groups_Ocancel__comm__monoid__add(_660217), -(class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(_660217)))], (12369 ^ _227627) ^ [_660407] : [class_Rings_Olinordered__idom(_660407), -(class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(_660407)))], (12375 ^ _227627) ^ [_660597] : [class_Rings_Olinordered__idom(_660597), -(class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(_660597)))], (12381 ^ _227627) ^ [_660787] : [class_Rings_Ocomm__semiring__0(_660787), -(class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(_660787)))], (12387 ^ _227627) ^ [_660977] : [class_Rings_Ocomm__semiring__1(_660977), -(class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(_660977)))], (12393 ^ _227627) ^ [_661167] : [class_Groups_Ocomm__monoid__add(_661167), -(class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(_661167)))], (12399 ^ _227627) ^ [_661357] : [class_Rings_Olinordered__idom(_661357), -(class_Rings_Oordered__semiring(tc_Polynomial_Opoly(_661357)))], (12405 ^ _227627) ^ [_661547] : [class_Rings_Oidom(_661547), -(class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(_661547)))], (12411 ^ _227627) ^ [_661737] : [class_Groups_Ocomm__monoid__add(_661737), -(class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(_661737)))], (12417 ^ _227627) ^ [_661927] : [class_Rings_Olinordered__idom(_661927), -(class_Rings_Olinordered__ring(tc_Polynomial_Opoly(_661927)))], (12423 ^ _227627) ^ [_662117] : [class_Rings_Olinordered__idom(_662117), -(class_Rings_Olinordered__idom(tc_Polynomial_Opoly(_662117)))], (12429 ^ _227627) ^ [_662307] : [class_Rings_Ocomm__semiring__1(_662307), -(class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(_662307)))], (12435 ^ _227627) ^ [_662497] : [class_Rings_Ocomm__semiring__0(_662497), -(class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(_662497)))], (12441 ^ _227627) ^ [_662687] : [class_Fields_Ofield(_662687), -(class_Divides_Osemiring__div(tc_Polynomial_Opoly(_662687)))], (12447 ^ _227627) ^ [_662877] : [class_Rings_Ocomm__semiring__0(_662877), -(class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(_662877)))], (12453 ^ _227627) ^ [_663067] : [class_Groups_Oab__group__add(_663067), -(class_Groups_Oab__group__add(tc_Polynomial_Opoly(_663067)))], (12459 ^ _227627) ^ [_663257] : [class_Rings_Ocomm__semiring__1(_663257), -(class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(_663257)))], (12465 ^ _227627) ^ [_663447] : [class_Rings_Olinordered__idom(_663447), -(class_Rings_Oordered__ring(tc_Polynomial_Opoly(_663447)))], (12471 ^ _227627) ^ [_663637] : [class_Rings_Olinordered__idom(_663637), -(class_Orderings_Opreorder(tc_Polynomial_Opoly(_663637)))], (12477 ^ _227627) ^ [_663827] : [class_Rings_Olinordered__idom(_663827), -(class_Orderings_Olinorder(tc_Polynomial_Opoly(_663827)))], (12483 ^ _227627) ^ [_664017] : [class_Rings_Ocomm__semiring__1(_664017), -(class_Groups_Omonoid__mult(tc_Polynomial_Opoly(_664017)))], (12489 ^ _227627) ^ [_664207] : [class_Rings_Ocomm__ring__1(_664207), -(class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(_664207)))], (12495 ^ _227627) ^ [_664397] : [class_Groups_Ocomm__monoid__add(_664397), -(class_Groups_Omonoid__add(tc_Polynomial_Opoly(_664397)))], (12501 ^ _227627) ^ [_664587] : [class_Rings_Ocomm__semiring__0(_664587), -(class_Rings_Osemiring__0(tc_Polynomial_Opoly(_664587)))], (12507 ^ _227627) ^ [_664777] : [class_Groups_Oab__group__add(_664777), -(class_Groups_Ogroup__add(tc_Polynomial_Opoly(_664777)))], (12513 ^ _227627) ^ [_664967] : [class_Fields_Ofield(_664967), -(class_Divides_Oring__div(tc_Polynomial_Opoly(_664967)))], (12519 ^ _227627) ^ [_665157] : [class_Rings_Ocomm__semiring__0(_665157), -(class_Rings_Omult__zero(tc_Polynomial_Opoly(_665157)))], (12525 ^ _227627) ^ [_665347] : [class_Rings_Ocomm__ring(_665347), -(class_Rings_Ocomm__ring(tc_Polynomial_Opoly(_665347)))], (12531 ^ _227627) ^ [_665537] : [class_Rings_Olinordered__idom(_665537), -(class_Orderings_Oorder(tc_Polynomial_Opoly(_665537)))], (12537 ^ _227627) ^ [_665727] : [class_Rings_Olinordered__idom(_665727), -(class_Int_Oring__char__0(tc_Polynomial_Opoly(_665727)))], (12543 ^ _227627) ^ [_665917] : [class_Rings_Ocomm__semiring__0(_665917), -(class_Rings_Osemiring(tc_Polynomial_Opoly(_665917)))], (12549 ^ _227627) ^ [_666107] : [class_Rings_Olinordered__idom(_666107), -(class_Orderings_Oord(tc_Polynomial_Opoly(_666107)))], (12555 ^ _227627) ^ [_666297] : [class_Groups_Oab__group__add(_666297), -(class_Groups_Ouminus(tc_Polynomial_Opoly(_666297)))], (12561 ^ _227627) ^ [_666487] : [class_Rings_Olinordered__idom(_666487), -(class_Groups_Osgn__if(tc_Polynomial_Opoly(_666487)))], (12567 ^ _227627) ^ [_666677] : [class_Rings_Ocomm__ring__1(_666677), -(class_Rings_Oring__1(tc_Polynomial_Opoly(_666677)))], (12573 ^ _227627) ^ [_666867] : [class_Groups_Oab__group__add(_666867), -(class_Groups_Ominus(tc_Polynomial_Opoly(_666867)))], (12579 ^ _227627) ^ [_667057] : [class_Rings_Ocomm__semiring__1(_667057), -(class_Power_Opower(tc_Polynomial_Opoly(_667057)))], (12585 ^ _227627) ^ [_667247] : [class_Groups_Ozero(_667247), -(class_Groups_Ozero(tc_Polynomial_Opoly(_667247)))], (12591 ^ _227627) ^ [_667437] : [class_Rings_Ocomm__ring(_667437), -(class_Rings_Oring(tc_Polynomial_Opoly(_667437)))], (12597 ^ _227627) ^ [_667627] : [class_Rings_Oidom(_667627), -(class_Rings_Oidom(tc_Polynomial_Opoly(_667627)))], (12603 ^ _227627) ^ [_667817] : [class_Rings_Ocomm__semiring__1(_667817), -(class_Groups_Oone(tc_Polynomial_Opoly(_667817)))], (12609 ^ _227627) ^ [_668007] : [class_Rings_Ocomm__semiring__1(_668007), -(class_Rings_Odvd(tc_Polynomial_Opoly(_668007)))], (12615 ^ _227627) ^ [_668211, _668213] : [hBOOL(c_fequal(_668211, _668213)), -(_668211 = _668213)], (12621 ^ _227627) ^ [_668427, _668429] : [_668427 = _668429, -(hBOOL(c_fequal(_668427, _668429)))], (12627 ^ _227627) ^ [] : [12628 ^ _227627 : [(12629 ^ _227627) ^ [_668623] : [v_s____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), _668623)]], -(v_thesis____)]], input).
% 144.57/140.24  ncf('1',plain,[v_thesis____],start(12633 ^ 0)).
% 144.57/140.24  ncf('1.1',plain,[-(v_thesis____), 12629 : v_s____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex), v_s____, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))))],extension(12627 ^ 1,bind([[_668623], [c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex), v_s____, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))]]))).
% 144.57/140.24  ncf('1.1.1',plain,[-(v_s____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex), v_s____, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex), v_s____, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))) = v_s____],extension(4 ^ 4,bind([[_227878, _227880], [v_s____, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex), v_s____, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))))]]))).
% 144.57/140.24  ncf('1.1.1.1',plain,[-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex), v_s____, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))) = v_s____), class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), v_s____))],extension(10888 ^ 5,bind([[_609913, _609915, _609917], [tc_Polynomial_Opoly(tc_Complex_Ocomplex), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), v_s____]]))).
% 144.57/140.24  ncf('1.1.1.1.1',plain,[-(class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), class_Fields_Ofield(tc_Complex_Ocomplex)],extension(12441 ^ 6,bind([[_662687], [tc_Complex_Ocomplex]]))).
% 144.57/140.24  ncf('1.1.1.1.1.1',plain,[-(class_Fields_Ofield(tc_Complex_Ocomplex))],extension(12247 ^ 7)).
% 144.57/140.24  ncf('1.1.1.1.2',plain,[-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), v_s____)))],extension(1157 ^ 6)).
% 144.57/140.24  %-----------------------------------------------------
% 144.57/140.24  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
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