TSTP Solution File: SWW245+1 by nanoCoP---2.0

%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW245+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 12:25:49 EDT 2023

% Result   : Theorem 40.29s 39.73s
% Output   : Proof 40.29s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWW245+1 : TPTP v8.1.2. Released v5.2.0.
% 0.03/0.12  % 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 22:48:39 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 40.29/39.73  
% 40.29/39.73  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 40.29/39.73  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 40.29/39.73  %-----------------------------------------------------
% 40.29/39.73  ncf(matrix, plain, [(11881 ^ _199745) ^ [_643470, _643472] : [-(_643470 = c_Groups_Ozero__class_Ozero(t_a)), 11884 ^ _199745 : [(11885 ^ _199745) ^ [_643690] : [11886 ^ _199745 : [(11887 ^ _199745) ^ [] : [-(c_Polynomial_OpCons(t_a, v_c____, v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))], (11889 ^ _199745) ^ [] : [c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_If(tc_Nat_Onat, c_fequal(_643690, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(c_Polynomial_Odegree(t_a, _643690))), _643472)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 11892 ^ _199745 : [(11893 ^ _199745) ^ [] : [c_Polynomial_OpCons(t_a, v_c____, v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))], (11895 ^ _199745) ^ [] : [c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_If(tc_Nat_Onat, c_fequal(_643690, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(c_Polynomial_Odegree(t_a, _643690))), _643472)) = c_Nat_OSuc(c_Polynomial_Odegree(t_a, c_Polynomial_OpCons(t_a, v_c____, v_cs____)))]], hAPP(c_Polynomial_Opoly(t_a, c_Polynomial_OpCons(t_a, v_c____, v_cs____)), 11896 ^ [_643470, _643472, _643690]) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a), hAPP(hAPP(c_Power_Opower__class_Opower(t_a), 11896 ^ [_643470, _643472, _643690]), _643472)), hAPP(c_Polynomial_Opoly(t_a, c_Polynomial_OpCons(t_a, _643470, _643690)), 11896 ^ [_643470, _643472, _643690]))]]], (744 ^ _199745) ^ [_222761, _222763, _222765, _222767] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_222767, _222763) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_222765, _222761)), _222767 = _222765, _222763 = _222761], (754 ^ _199745) ^ [_223148, _223150, _223152, _223154, _223156, _223158] : [-(c_Polynomial_Opcompose(_223158, _223154, _223150) = c_Polynomial_Opcompose(_223156, _223152, _223148)), _223158 = _223156, _223154 = _223152, _223150 = _223148], (768 ^ _199745) ^ [_223608, _223610] : [_223610 = _223608, -(c_Nat_Onat_Onat__size(_223610) = c_Nat_Onat_Onat__size(_223608))], (774 ^ _199745) ^ [_223938, _223940, _223942, _223944, _223946, _223948, _223950, _223952, _223954, _223956] : [-(c_Polynomial_Opoly__rec(_223956, _223952, _223948, _223944, _223940) = c_Polynomial_Opoly__rec(_223954, _223950, _223946, _223942, _223938)), _223956 = _223954, _223952 = _223950, _223948 = _223946, _223944 = _223942, _223940 = _223938], (796 ^ _199745) ^ [_224704, _224706] : [_224706 = _224704, -(c_HOL_Obool_Obool__size(_224706) = c_HOL_Obool_Obool__size(_224704))], (802 ^ _199745) ^ [_224950, _224952, _224954, _224956] : [-(c_Nat_Osize__class_Osize(_224956, _224952) = c_Nat_Osize__class_Osize(_224954, _224950)), _224956 = _224954, _224952 = _224950], (812 ^ _199745) ^ [_225337, _225339, _225341, _225343, _225345, _225347] : [-(c_Power_Opower_Opower(_225347, _225343, _225339) = c_Power_Opower_Opower(_225345, _225341, _225337)), _225347 = _225345, _225343 = _225341, _225339 = _225337], (826 ^ _199745) ^ [_225853, _225855, _225857, _225859, _225861, _225863] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_225863, _225859, _225855) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_225861, _225857, _225853)), _225863 = _225861, _225859 = _225857, _225855 = _225853], (840 ^ _199745) ^ [_226369, _226371, _226373, _226375, _226377, _226379] : [-(c_Polynomial_Oorder(_226379, _226375, _226371) = c_Polynomial_Oorder(_226377, _226373, _226369)), _226379 = _226377, _226375 = _226373, _226371 = _226369], (854 ^ _199745) ^ [_226885, _226887, _226889, _226891, _226893, _226895] : [-(c_Polynomial_Omonom(_226895, _226891, _226887) = c_Polynomial_Omonom(_226893, _226889, _226885)), _226895 = _226893, _226891 = _226889, _226887 = _226885], (868 ^ _199745) ^ [_227401, _227403, _227405, _227407, _227409, _227411] : [-(c_Polynomial_Osynthetic__div(_227411, _227407, _227403) = c_Polynomial_Osynthetic__div(_227409, _227405, _227401)), _227411 = _227409, _227407 = _227405, _227403 = _227401], (882 ^ _199745) ^ [_227917, _227919, _227921, _227923, _227925, _227927] : [-(c_Nat_Onat_Onat__case(_227927, _227923, _227919) = c_Nat_Onat_Onat__case(_227925, _227921, _227917)), _227927 = _227925, _227923 = _227921, _227919 = _227917], (896 ^ _199745) ^ [_228405, _228407, _228409, _228411] : [-(c_Polynomial_OAbs__poly(_228411, _228407) = c_Polynomial_OAbs__poly(_228409, _228405)), _228411 = _228409, _228407 = _228405], (906 ^ _199745) ^ [_228792, _228794, _228796, _228798, _228800, _228802] : [-(c_Polynomial_Opoly__gcd(_228802, _228798, _228794) = c_Polynomial_Opoly__gcd(_228800, _228796, _228792)), _228802 = _228800, _228798 = _228796, _228794 = _228792], (920 ^ _199745) ^ [_229280, _229282, _229284, _229286] : [-(c_Polynomial_Ocoeff(_229286, _229282) = c_Polynomial_Ocoeff(_229284, _229280)), _229286 = _229284, _229282 = _229280], (930 ^ _199745) ^ [_229667, _229669, _229671, _229673, _229675, _229677] : [-(c_Rings_Oinverse__class_Odivide(_229677, _229673, _229669) = c_Rings_Oinverse__class_Odivide(_229675, _229671, _229667)), _229677 = _229675, _229673 = _229671, _229669 = _229667], (944 ^ _199745) ^ [_230183, _230185, _230187, _230189, _230191, _230193] : [-(c_Polynomial_Osmult(_230193, _230189, _230185) = c_Polynomial_Osmult(_230191, _230187, _230183)), _230193 = _230191, _230189 = _230187, _230185 = _230183], (958 ^ _199745) ^ [_230671, _230673, _230675, _230677] : [-(c_Rings_Oinverse__class_Oinverse(_230677, _230673) = c_Rings_Oinverse__class_Oinverse(_230675, _230671)), _230677 = _230675, _230673 = _230671], (968 ^ _199745) ^ [_231030, _231032, _231034, _231036] : [-(c_Groups_Osgn__class_Osgn(_231036, _231032) = c_Groups_Osgn__class_Osgn(_231034, _231030)), _231036 = _231034, _231032 = _231030], (978 ^ _199745) ^ [_231361, _231363] : [_231363 = _231361, -(c_Groups_Oone__class_Oone(_231363) = c_Groups_Oone__class_Oone(_231361))], (984 ^ _199745) ^ [_231635, _231637, _231639, _231641, _231643, _231645] : [-(c_Divides_Odiv__class_Omod(_231645, _231641, _231637) = c_Divides_Odiv__class_Omod(_231643, _231639, _231635)), _231645 = _231643, _231641 = _231639, _231637 = _231635], (998 ^ _199745) ^ [_232151, _232153, _232155, _232157, _232159, _232161] : [-(c_Divides_Odiv__class_Odiv(_232161, _232157, _232153) = c_Divides_Odiv__class_Odiv(_232159, _232155, _232151)), _232161 = _232159, _232157 = _232155, _232153 = _232151], (1012 ^ _199745) ^ [_232667, _232669, _232671, _232673, _232675, _232677] : [-(c_Groups_Ominus__class_Ominus(_232677, _232673, _232669) = c_Groups_Ominus__class_Ominus(_232675, _232671, _232667)), _232677 = _232675, _232673 = _232671, _232669 = _232667], (1026 ^ _199745) ^ [_233155, _233157, _233159, _233161] : [-(c_Groups_Ouminus__class_Ouminus(_233161, _233157) = c_Groups_Ouminus__class_Ouminus(_233159, _233155)), _233161 = _233159, _233157 = _233155], (1036 ^ _199745) ^ [_233514, _233516, _233518, _233520] : [-(c_Groups_Oabs__class_Oabs(_233520, _233516) = c_Groups_Oabs__class_Oabs(_233518, _233514)), _233520 = _233518, _233516 = _233514], (1046 ^ _199745) ^ [_233901, _233903, _233905, _233907, _233909, _233911] : [-(c_Groups_Oplus__class_Oplus(_233911, _233907, _233903) = c_Groups_Oplus__class_Oplus(_233909, _233905, _233901)), _233911 = _233909, _233907 = _233905, _233903 = _233901], (1060 ^ _199745) ^ [_234445, _234447, _234449, _234451, _234453, _234455, _234457, _234459] : [-(c_If(_234459, _234455, _234451, _234447) = c_If(_234457, _234453, _234449, _234445)), _234459 = _234457, _234455 = _234453, _234451 = _234449, _234447 = _234445], (1078 ^ _199745) ^ [_235078, _235080, _235082, _235084] : [-(c_fequal(_235084, _235080) = c_fequal(_235082, _235078)), _235084 = _235082, _235080 = _235078], (1088 ^ _199745) ^ [_235409, _235411] : [_235411 = _235409, -(tc_Polynomial_Opoly(_235411) = tc_Polynomial_Opoly(_235409))], (1094 ^ _199745) ^ [_235627, _235629] : [_235629 = _235627, -(c_Groups_Ozero__class_Ozero(_235629) = c_Groups_Ozero__class_Ozero(_235627))], (1100 ^ _199745) ^ [_235845, _235847] : [_235847 = _235845, -(c_Nat_OSuc(_235847) = c_Nat_OSuc(_235845))], (1106 ^ _199745) ^ [_236091, _236093, _236095, _236097] : [-(c_Polynomial_Odegree(_236097, _236093) = c_Polynomial_Odegree(_236095, _236091)), _236097 = _236095, _236093 = _236091], (1116 ^ _199745) ^ [_236422, _236424] : [_236424 = _236422, -(c_Groups_Otimes__class_Otimes(_236424) = c_Groups_Otimes__class_Otimes(_236422))], (1122 ^ _199745) ^ [_236640, _236642] : [_236642 = _236640, -(c_Power_Opower__class_Opower(_236642) = c_Power_Opower__class_Opower(_236640))], (1128 ^ _199745) ^ [_236886, _236888, _236890, _236892] : [-(hAPP(_236892, _236888) = hAPP(_236890, _236886)), _236892 = _236890, _236888 = _236886], (1138 ^ _199745) ^ [_237245, _237247, _237249, _237251] : [-(c_Polynomial_Opoly(_237251, _237247) = c_Polynomial_Opoly(_237249, _237245)), _237251 = _237249, _237247 = _237245], (1148 ^ _199745) ^ [_237612, _237614, _237616, _237618, _237620, _237622] : [-(c_Polynomial_OpCons(_237622, _237618, _237614) = c_Polynomial_OpCons(_237620, _237616, _237612)), _237622 = _237620, _237618 = _237616, _237614 = _237612], (2 ^ _199745) ^ [_199889] : [-(_199889 = _199889)], (4 ^ _199745) ^ [_199996, _199998] : [_199998 = _199996, -(_199996 = _199998)], (10 ^ _199745) ^ [_200200, _200202, _200204] : [-(_200204 = _200200), _200204 = _200202, _200202 = _200200], (20 ^ _199745) ^ [_200513, _200515] : [-(class_RealVector_Oreal__normed__algebra(_200513)), _200515 = _200513, class_RealVector_Oreal__normed__algebra(_200515)], (30 ^ _199745) ^ [_200808, _200810] : [-(class_Rings_Odivision__ring__inverse__zero(_200808)), _200810 = _200808, class_Rings_Odivision__ring__inverse__zero(_200810)], (40 ^ _199745) ^ [_201103, _201105] : [-(class_Fields_Ofield__inverse__zero(_201103)), _201105 = _201103, class_Fields_Ofield__inverse__zero(_201105)], (50 ^ _199745) ^ [_201398, _201400] : [-(class_RealVector_Oreal__field(_201398)), _201400 = _201398, class_RealVector_Oreal__field(_201400)], (60 ^ _199745) ^ [_201693, _201695] : [-(class_Rings_Odivision__ring(_201693)), _201695 = _201693, class_Rings_Odivision__ring(_201695)], (70 ^ _199745) ^ [_201988, _201990] : [-(class_RealVector_Oreal__normed__field(_201988)), _201990 = _201988, class_RealVector_Oreal__normed__field(_201990)], (80 ^ _199745) ^ [_202311, _202313, _202315, _202317] : [-(c_Polynomial_Opos__poly(_202315, _202311)), c_Polynomial_Opos__poly(_202317, _202313), _202317 = _202315, _202313 = _202311], (94 ^ _199745) ^ [_202727, _202729] : [-(class_Fields_Olinordered__field(_202727)), _202729 = _202727, class_Fields_Olinordered__field(_202729)], (104 ^ _199745) ^ [_203022, _203024] : [-(class_Fields_Olinordered__field__inverse__zero(_203022)), _203024 = _203022, class_Fields_Olinordered__field__inverse__zero(_203024)], (114 ^ _199745) ^ [_203373, _203375, _203377, _203379, _203381, _203383] : [-(c_Rings_Odvd__class_Odvd(_203381, _203377, _203373)), c_Rings_Odvd__class_Odvd(_203383, _203379, _203375), _203383 = _203381, _203379 = _203377, _203375 = _203373], (132 ^ _199745) ^ [_204038, _204040, _204042, _204044, _204046, _204048, _204050, _204052, _204054, _204056] : [-(c_Polynomial_Opdivmod__rel(_204054, _204050, _204046, _204042, _204038)), c_Polynomial_Opdivmod__rel(_204056, _204052, _204048, _204044, _204040), _204056 = _204054, _204052 = _204050, _204048 = _204046, _204044 = _204042, _204040 = _204038], (158 ^ _199745) ^ [_204913, _204915] : [-(class_RealVector_Oreal__normed__div__algebra(_204913)), _204915 = _204913, class_RealVector_Oreal__normed__div__algebra(_204915)], (168 ^ _199745) ^ [_205208, _205210] : [-(class_RealVector_Oreal__normed__algebra__1(_205208)), _205210 = _205208, class_RealVector_Oreal__normed__algebra__1(_205210)], (178 ^ _199745) ^ [_205503, _205505] : [-(class_RealVector_Oreal__normed__vector(_205503)), _205505 = _205503, class_RealVector_Oreal__normed__vector(_205505)], (188 ^ _199745) ^ [_205854, _205856, _205858, _205860, _205862, _205864] : [-(c_Orderings_Oord__class_Oless(_205862, _205858, _205854)), c_Orderings_Oord__class_Oless(_205864, _205860, _205856), _205864 = _205862, _205860 = _205858, _205856 = _205854], (206 ^ _199745) ^ [_206463, _206465, _206467, _206469, _206471, _206473] : [-(c_Orderings_Oord__class_Oless__eq(_206471, _206467, _206463)), c_Orderings_Oord__class_Oless__eq(_206473, _206469, _206465), _206473 = _206471, _206469 = _206467, _206465 = _206463], (224 ^ _199745) ^ [_207016, _207018] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_207016)), _207018 = _207016, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_207018)], (234 ^ _199745) ^ [_207311, _207313] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_207311)), _207313 = _207311, class_Groups_Oordered__cancel__ab__semigroup__add(_207313)], (244 ^ _199745) ^ [_207606, _207608] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_207606)), _207608 = _207606, class_Groups_Oordered__ab__semigroup__add__imp__le(_207608)], (254 ^ _199745) ^ [_207901, _207903] : [-(class_Rings_Olinordered__comm__semiring__strict(_207901)), _207903 = _207901, class_Rings_Olinordered__comm__semiring__strict(_207903)], (264 ^ _199745) ^ [_208196, _208198] : [-(class_Rings_Olinordered__semiring__strict(_208196)), _208198 = _208196, class_Rings_Olinordered__semiring__strict(_208198)], (274 ^ _199745) ^ [_208491, _208493] : [-(class_Groups_Oordered__ab__group__add__abs(_208491)), _208493 = _208491, class_Groups_Oordered__ab__group__add__abs(_208493)], (284 ^ _199745) ^ [_208786, _208788] : [-(class_Groups_Oordered__comm__monoid__add(_208786)), _208788 = _208786, class_Groups_Oordered__comm__monoid__add(_208788)], (294 ^ _199745) ^ [_209081, _209083] : [-(class_Groups_Olinordered__ab__group__add(_209081)), _209083 = _209081, class_Groups_Olinordered__ab__group__add(_209083)], (304 ^ _199745) ^ [_209376, _209378] : [-(class_Groups_Ocancel__ab__semigroup__add(_209376)), _209378 = _209376, class_Groups_Ocancel__ab__semigroup__add(_209378)], (314 ^ _199745) ^ [_209671, _209673] : [-(class_Rings_Oring__1__no__zero__divisors(_209671)), _209673 = _209671, class_Rings_Oring__1__no__zero__divisors(_209673)], (324 ^ _199745) ^ [_209966, _209968] : [-(class_Rings_Olinordered__ring__strict(_209966)), _209968 = _209966, class_Rings_Olinordered__ring__strict(_209968)], (334 ^ _199745) ^ [_210261, _210263] : [-(class_Rings_Oring__no__zero__divisors(_210261)), _210263 = _210261, class_Rings_Oring__no__zero__divisors(_210263)], (344 ^ _199745) ^ [_210556, _210558] : [-(class_Groups_Oordered__ab__group__add(_210556)), _210558 = _210556, class_Groups_Oordered__ab__group__add(_210558)], (354 ^ _199745) ^ [_210851, _210853] : [-(class_Groups_Ocancel__comm__monoid__add(_210851)), _210853 = _210851, class_Groups_Ocancel__comm__monoid__add(_210853)], (364 ^ _199745) ^ [_211146, _211148] : [-(class_Groups_Ocancel__semigroup__add(_211146)), _211148 = _211146, class_Groups_Ocancel__semigroup__add(_211148)], (374 ^ _199745) ^ [_211441, _211443] : [-(class_Rings_Olinordered__semiring(_211441)), _211443 = _211441, class_Rings_Olinordered__semiring(_211443)], (384 ^ _199745) ^ [_211736, _211738] : [-(class_Rings_Olinordered__semidom(_211736)), _211738 = _211736, class_Rings_Olinordered__semidom(_211738)], (394 ^ _199745) ^ [_212031, _212033] : [-(class_Groups_Oab__semigroup__mult(_212031)), _212033 = _212031, class_Groups_Oab__semigroup__mult(_212033)], (404 ^ _199745) ^ [_212326, _212328] : [-(class_Groups_Ocomm__monoid__mult(_212326)), _212328 = _212326, class_Groups_Ocomm__monoid__mult(_212328)], (414 ^ _199745) ^ [_212621, _212623] : [-(class_Groups_Oab__semigroup__add(_212621)), _212623 = _212621, class_Groups_Oab__semigroup__add(_212623)], (424 ^ _199745) ^ [_212916, _212918] : [-(class_Rings_Ono__zero__divisors(_212916)), _212918 = _212916, class_Rings_Ono__zero__divisors(_212918)], (434 ^ _199745) ^ [_213211, _213213] : [-(class_Rings_Olinordered__ring(_213211)), _213213 = _213211, class_Rings_Olinordered__ring(_213213)], (444 ^ _199745) ^ [_213506, _213508] : [-(class_Divides_Osemiring__div(_213506)), _213508 = _213506, class_Divides_Osemiring__div(_213508)], (454 ^ _199745) ^ [_213801, _213803] : [-(class_Rings_Ocomm__semiring(_213801)), _213803 = _213801, class_Rings_Ocomm__semiring(_213803)], (464 ^ _199745) ^ [_214096, _214098] : [-(class_Rings_Ozero__neq__one(_214096)), _214098 = _214096, class_Rings_Ozero__neq__one(_214098)], (474 ^ _199745) ^ [_214391, _214393] : [-(class_Rings_Oordered__ring(_214391)), _214393 = _214391, class_Rings_Oordered__ring(_214393)], (484 ^ _199745) ^ [_214686, _214688] : [-(class_Groups_Omonoid__mult(_214686)), _214688 = _214686, class_Groups_Omonoid__mult(_214688)], (494 ^ _199745) ^ [_214981, _214983] : [-(class_Groups_Ocomm__monoid__add(_214981)), _214983 = _214981, class_Groups_Ocomm__monoid__add(_214983)], (504 ^ _199745) ^ [_215276, _215278] : [-(class_Groups_Omonoid__add(_215276)), _215278 = _215276, class_Groups_Omonoid__add(_215278)], (514 ^ _199745) ^ [_215571, _215573] : [-(class_Rings_Osemiring__0(_215571)), _215573 = _215571, class_Rings_Osemiring__0(_215573)], (524 ^ _199745) ^ [_215866, _215868] : [-(class_Groups_Oab__group__add(_215866)), _215868 = _215866, class_Groups_Oab__group__add(_215868)], (534 ^ _199745) ^ [_216161, _216163] : [-(class_Groups_Ogroup__add(_216161)), _216163 = _216161, class_Groups_Ogroup__add(_216163)], (544 ^ _199745) ^ [_216456, _216458] : [-(class_Fields_Ofield(_216456)), _216458 = _216456, class_Fields_Ofield(_216458)], (554 ^ _199745) ^ [_216751, _216753] : [-(class_Divides_Oring__div(_216751)), _216753 = _216751, class_Divides_Oring__div(_216753)], (564 ^ _199745) ^ [_217046, _217048] : [-(class_Rings_Omult__zero(_217046)), _217048 = _217046, class_Rings_Omult__zero(_217048)], (574 ^ _199745) ^ [_217341, _217343] : [-(class_Int_Oring__char__0(_217341)), _217343 = _217341, class_Int_Oring__char__0(_217343)], (584 ^ _199745) ^ [_217636, _217638] : [-(class_Rings_Ocomm__semiring__0(_217636)), _217638 = _217636, class_Rings_Ocomm__semiring__0(_217638)], (594 ^ _199745) ^ [_217931, _217933] : [-(class_Rings_Osemiring(_217931)), _217933 = _217931, class_Rings_Osemiring(_217933)], (604 ^ _199745) ^ [_218226, _218228] : [-(class_Groups_Osgn__if(_218226)), _218228 = _218226, class_Groups_Osgn__if(_218228)], (614 ^ _199745) ^ [_218521, _218523] : [-(class_Rings_Olinordered__idom(_218521)), _218523 = _218521, class_Rings_Olinordered__idom(_218523)], (624 ^ _199745) ^ [_218816, _218818] : [-(class_Groups_Oabs__if(_218816)), _218818 = _218816, class_Groups_Oabs__if(_218818)], (634 ^ _199745) ^ [_219111, _219113] : [-(class_Rings_Ocomm__ring__1(_219111)), _219113 = _219111, class_Rings_Ocomm__ring__1(_219113)], (644 ^ _199745) ^ [_219406, _219408] : [-(class_Rings_Oring__1(_219406)), _219408 = _219406, class_Rings_Oring__1(_219408)], (654 ^ _199745) ^ [_219701, _219703] : [-(class_Power_Opower(_219701)), _219703 = _219701, class_Power_Opower(_219703)], (664 ^ _199745) ^ [_219996, _219998] : [-(class_Groups_Ozero(_219996)), _219998 = _219996, class_Groups_Ozero(_219998)], (674 ^ _199745) ^ [_220291, _220293] : [-(class_Rings_Ocomm__ring(_220291)), _220293 = _220291, class_Rings_Ocomm__ring(_220293)], (684 ^ _199745) ^ [_220586, _220588] : [-(class_Rings_Oring(_220586)), _220588 = _220586, class_Rings_Oring(_220588)], (694 ^ _199745) ^ [_220881, _220883] : [-(class_Groups_Oone(_220881)), _220883 = _220881, class_Groups_Oone(_220883)], (704 ^ _199745) ^ [_221176, _221178] : [-(class_Rings_Ocomm__semiring__1(_221176)), _221178 = _221176, class_Rings_Ocomm__semiring__1(_221178)], (714 ^ _199745) ^ [_221471, _221473] : [-(class_Rings_Odvd(_221471)), _221473 = _221471, class_Rings_Odvd(_221473)], (724 ^ _199745) ^ [_221766, _221768] : [-(hBOOL(_221766)), _221768 = _221766, hBOOL(_221768)], (734 ^ _199745) ^ [_222041, _222043] : [-(class_Rings_Oidom(_222041)), _222043 = _222041, class_Rings_Oidom(_222043)], (1162 ^ _199745) ^ [_238322, _238324] : [hAPP(_238322, 1163 ^ [_238322, _238324]) = hAPP(_238324, 1163 ^ [_238322, _238324]), -(_238322 = _238324)], (1169 ^ _199745) ^ [] : [class_Rings_Oidom(t_a), 1173 ^ _199745 : [(1174 ^ _199745) ^ [] : [1172 ^ [] = c_Groups_Ozero__class_Ozero(t_a)], (1176 ^ _199745) ^ [] : [hAPP(c_Polynomial_Opoly(t_a, c_Polynomial_OpCons(t_a, v_c____, v_cs____)), 1172 ^ []) = c_Groups_Ozero__class_Ozero(t_a)]]], (1178 ^ _199745) ^ [] : [class_Rings_Oidom(t_a), 1182 ^ _199745 : [(1183 ^ _199745) ^ [] : [1181 ^ [] = c_Groups_Ozero__class_Ozero(t_a)], (1185 ^ _199745) ^ [] : [hAPP(c_Polynomial_Opoly(t_a, v_p), 1181 ^ []) = c_Groups_Ozero__class_Ozero(t_a)]]], (1187 ^ _199745) ^ [] : [class_Rings_Oidom(t_a), -(v_c____ = c_Groups_Ozero__class_Ozero(t_a)), 1196 ^ _199745 : [(1197 ^ _199745) ^ [] : [1195 ^ [] = c_Groups_Ozero__class_Ozero(t_a)], (1200 ^ _199745) ^ [] : [c_Polynomial_OpCons(t_a, v_c____, v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)), -(c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_If(tc_Nat_Onat, c_fequal(1198 ^ [], c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(c_Polynomial_Odegree(t_a, 1198 ^ []))), 1194 ^ [])) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1212 ^ _199745) ^ [_239843] : [-(hAPP(c_Polynomial_Opoly(t_a, c_Polynomial_OpCons(t_a, v_c____, v_cs____)), _239843) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a), hAPP(hAPP(c_Power_Opower__class_Opower(t_a), _239843), 1194 ^ [])), hAPP(c_Polynomial_Opoly(t_a, c_Polynomial_OpCons(t_a, 1195 ^ [], 1198 ^ [])), _239843)))], (1206 ^ _199745) ^ [] : [-(c_Polynomial_OpCons(t_a, v_c____, v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), -(c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_If(tc_Nat_Onat, c_fequal(1198 ^ [], c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(c_Polynomial_Odegree(t_a, 1198 ^ []))), 1194 ^ [])) = c_Nat_OSuc(c_Polynomial_Odegree(t_a, c_Polynomial_OpCons(t_a, v_c____, v_cs____))))]]], (1214 ^ _199745) ^ [] : [class_Rings_Oidom(t_a), v_c____ = c_Groups_Ozero__class_Ozero(t_a), 1223 ^ _199745 : [(1224 ^ _199745) ^ [] : [1222 ^ [] = c_Groups_Ozero__class_Ozero(t_a)], (1227 ^ _199745) ^ [] : [c_Polynomial_OpCons(t_a, v_c____, v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)), -(c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_If(tc_Nat_Onat, c_fequal(1225 ^ [], c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(c_Polynomial_Odegree(t_a, 1225 ^ []))), 1221 ^ [])) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1239 ^ _199745) ^ [_240769] : [-(hAPP(c_Polynomial_Opoly(t_a, c_Polynomial_OpCons(t_a, v_c____, v_cs____)), _240769) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a), hAPP(hAPP(c_Power_Opower__class_Opower(t_a), _240769), 1221 ^ [])), hAPP(c_Polynomial_Opoly(t_a, c_Polynomial_OpCons(t_a, 1222 ^ [], 1225 ^ [])), _240769)))], (1233 ^ _199745) ^ [] : [-(c_Polynomial_OpCons(t_a, v_c____, v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), -(c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_If(tc_Nat_Onat, c_fequal(1225 ^ [], c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(c_Polynomial_Odegree(t_a, 1225 ^ []))), 1221 ^ [])) = c_Nat_OSuc(c_Polynomial_Odegree(t_a, c_Polynomial_OpCons(t_a, v_c____, v_cs____))))]]], (1241 ^ _199745) ^ [_240923, _240925, _240927] : [class_Groups_Ozero(_240923), 1244 ^ _199745 : [(1245 ^ _199745) ^ [] : [_240925 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_240923)), -(c_Polynomial_Odegree(_240923, c_Polynomial_OpCons(_240923, _240927, _240925)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1251 ^ _199745) ^ [] : [-(_240925 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_240923))), -(c_Polynomial_Odegree(_240923, c_Polynomial_OpCons(_240923, _240927, _240925)) = c_Nat_OSuc(c_Polynomial_Odegree(_240923, _240925)))]]], (1257 ^ _199745) ^ [_241471, _241473, _241475] : [class_Groups_Ozero(_241471), -(_241473 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_241471))), -(c_Polynomial_Odegree(_241471, c_Polynomial_OpCons(_241471, _241475, _241473)) = c_Nat_OSuc(c_Polynomial_Odegree(_241471, _241473)))], (1267 ^ _199745) ^ [_241813, _241815] : [class_Groups_Ozero(_241813), -(c_Polynomial_Odegree(_241813, c_Polynomial_OpCons(_241813, _241815, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_241813)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1273 ^ _199745) ^ [_242071, _242073, _242075, _242077] : [class_Rings_Ocomm__semiring__0(_242071), -(hAPP(c_Polynomial_Opoly(_242071, c_Polynomial_OpCons(_242071, _242073, _242075)), _242077) = c_Groups_Oplus__class_Oplus(_242071, _242073, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_242071), _242077), hAPP(c_Polynomial_Opoly(_242071, _242075), _242077))))], (1279 ^ _199745) ^ [_242347, _242349] : [class_Groups_Ozero(_242347), 1282 ^ _199745 : [(1283 ^ _199745) ^ [] : [_242349 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_242347)), -(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_242347, _242349) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1289 ^ _199745) ^ [] : [-(_242349 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_242347))), -(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_242347, _242349) = c_Nat_OSuc(c_Polynomial_Odegree(_242347, _242349)))]]], (1295 ^ _199745) ^ [] : [class_Rings_Oidom(t_a), 1300 ^ _199745 : [(1301 ^ _199745) ^ [_242927] : [-(_242927 = c_Groups_Ozero__class_Ozero(t_a)), -(hAPP(c_Polynomial_Opoly(t_a, v_cs____), _242927) = c_Groups_Ozero__class_Ozero(t_a))]], 1308 ^ _199745 : [(1309 ^ _199745) ^ [] : [1307 ^ [] = c_Groups_Ozero__class_Ozero(t_a)], (1312 ^ _199745) ^ [] : [v_cs____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)), -(c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_If(tc_Nat_Onat, c_fequal(1310 ^ [], c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(c_Polynomial_Odegree(t_a, 1310 ^ []))), 1306 ^ [])) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1324 ^ _199745) ^ [_243782] : [-(hAPP(c_Polynomial_Opoly(t_a, v_cs____), _243782) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a), hAPP(hAPP(c_Power_Opower__class_Opower(t_a), _243782), 1306 ^ [])), hAPP(c_Polynomial_Opoly(t_a, c_Polynomial_OpCons(t_a, 1307 ^ [], 1310 ^ [])), _243782)))], (1318 ^ _199745) ^ [] : [-(v_cs____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), -(c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_If(tc_Nat_Onat, c_fequal(1310 ^ [], c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(c_Polynomial_Odegree(t_a, 1310 ^ []))), 1306 ^ [])) = c_Nat_OSuc(c_Polynomial_Odegree(t_a, v_cs____)))]]], (1326 ^ _199745) ^ [_243923, _243925] : [class_Rings_Ocomm__semiring__0(_243923), -(hAPP(c_Polynomial_Opoly(_243923, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_243923))), _243925) = c_Groups_Ozero__class_Ozero(_243923))], (1332 ^ _199745) ^ [_244141] : [class_Groups_Ozero(_244141), -(c_Polynomial_Odegree(_244141, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_244141))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1338 ^ _199745) ^ [_244343] : [class_Groups_Ozero(_244343), -(c_Polynomial_OpCons(_244343, c_Groups_Ozero__class_Ozero(_244343), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_244343))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_244343)))], (1344 ^ _199745) ^ [_244587, _244589, _244591] : [class_Groups_Ozero(_244587), 1347 ^ _199745 : [(1348 ^ _199745) ^ [] : [c_Polynomial_OpCons(_244587, _244589, _244591) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_244587)), 1351 ^ _199745 : [(1352 ^ _199745) ^ [] : [-(_244589 = c_Groups_Ozero__class_Ozero(_244587))], (1354 ^ _199745) ^ [] : [-(_244591 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_244587)))]]], (1356 ^ _199745) ^ [] : [-(c_Polynomial_OpCons(_244587, _244589, _244591) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_244587))), _244589 = c_Groups_Ozero__class_Ozero(_244587), _244591 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_244587))]]], (1366 ^ _199745) ^ [_245267, _245269] : [class_Groups_Ocomm__monoid__add(_245267), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_245267), _245269, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_245267))) = _245269)], (1372 ^ _199745) ^ [_245495, _245497] : [class_Groups_Ocomm__monoid__add(_245495), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_245495), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_245495)), _245497) = _245497)], (1378 ^ _199745) ^ [_245723, _245725] : [class_Rings_Ocomm__semiring__0(_245723), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_245723)), _245725), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_245723))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_245723)))], (1384 ^ _199745) ^ [_245967, _245969] : [class_Rings_Ocomm__semiring__0(_245967), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_245967)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_245967))), _245969) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_245967)))], (1390 ^ _199745) ^ [_246225, _246227, _246229] : [class_Rings_Oidom(_246225), -(_246227 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_246225))), -(_246229 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_246225))), -(c_Polynomial_Odegree(_246225, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_246225)), _246227), _246229)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Polynomial_Odegree(_246225, _246227), c_Polynomial_Odegree(_246225, _246229)))], (1404 ^ _199745) ^ [_246735, _246737, _246739, _246741, _246743] : [class_Groups_Ozero(_246735), 1407 ^ _199745 : [(1408 ^ _199745) ^ [] : [c_Polynomial_OpCons(_246735, _246737, _246739) = c_Polynomial_OpCons(_246735, _246741, _246743), 1411 ^ _199745 : [(1412 ^ _199745) ^ [] : [-(_246737 = _246741)], (1414 ^ _199745) ^ [] : [-(_246739 = _246743)]]], (1416 ^ _199745) ^ [] : [-(c_Polynomial_OpCons(_246735, _246737, _246739) = c_Polynomial_OpCons(_246735, _246741, _246743)), _246737 = _246741, _246739 = _246743]]], (1426 ^ _199745) ^ [_247455, _247457, _247459] : [class_Int_Oring__char__0(_247455), class_Rings_Oidom(_247455), 1433 ^ _199745 : [(1434 ^ _199745) ^ [] : [c_Polynomial_Opoly(_247455, _247457) = c_Polynomial_Opoly(_247455, _247459), -(_247457 = _247459)], (1440 ^ _199745) ^ [] : [_247457 = _247459, -(c_Polynomial_Opoly(_247455, _247457) = c_Polynomial_Opoly(_247455, _247459))]]], (1446 ^ _199745) ^ [_248040, _248042] : [class_Groups_Ozero(_248040), 1449 ^ _199745 : [(1450 ^ _199745) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_248040, _248042) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_248042 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_248040)))], (1456 ^ _199745) ^ [] : [_248042 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_248040)), -(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_248040, _248042) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (1462 ^ _199745) ^ [_248561, _248563, _248565, _248567, _248569] : [class_Groups_Ocomm__monoid__add(_248561), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_248561), c_Polynomial_OpCons(_248561, _248563, _248565), c_Polynomial_OpCons(_248561, _248567, _248569)) = c_Polynomial_OpCons(_248561, c_Groups_Oplus__class_Oplus(_248561, _248563, _248567), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_248561), _248565, _248569)))], (1468 ^ _199745) ^ [_248871, _248873, _248875, _248877] : [class_Rings_Ocomm__semiring__0(_248871), -(hAPP(c_Polynomial_Opoly(_248871, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_248871)), _248873), _248875)), _248877) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_248871), hAPP(c_Polynomial_Opoly(_248871, _248873), _248877)), hAPP(c_Polynomial_Opoly(_248871, _248875), _248877)))], (1474 ^ _199745) ^ [_249191, _249193, _249195, _249197] : [class_Rings_Ocomm__semiring__0(_249191), -(hAPP(c_Polynomial_Opoly(_249191, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_249191), _249193, _249195)), _249197) = c_Groups_Oplus__class_Oplus(_249191, hAPP(c_Polynomial_Opoly(_249191, _249193), _249197), hAPP(c_Polynomial_Opoly(_249191, _249195), _249197)))], (1480 ^ _199745) ^ [_249495, _249497, _249499, _249501] : [class_Rings_Ocomm__semiring__1(_249495), -(hAPP(c_Polynomial_Opoly(_249495, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_249495)), _249497), _249499)), _249501) = hAPP(hAPP(c_Power_Opower__class_Opower(_249495), hAPP(c_Polynomial_Opoly(_249495, _249497), _249501)), _249499))], (1486 ^ _199745) ^ [_249775, _249777] : [class_Int_Oring__char__0(_249775), class_Rings_Oidom(_249775), 1493 ^ _199745 : [(1494 ^ _199745) ^ [] : [c_Polynomial_Opoly(_249775, _249777) = c_Polynomial_Opoly(_249775, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_249775))), -(_249777 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_249775)))], (1500 ^ _199745) ^ [] : [_249777 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_249775)), -(c_Polynomial_Opoly(_249775, _249777) = c_Polynomial_Opoly(_249775, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_249775))))]]], (1506 ^ _199745) ^ [_250393, _250395] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _250393, _250395) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 1511 ^ _199745 : [(1512 ^ _199745) ^ [] : [-(_250393 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (1514 ^ _199745) ^ [] : [-(_250395 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 1515 ^ _199745 : [(1516 ^ _199745) ^ [] : [-(_250393 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1518 ^ _199745) ^ [] : [-(_250395 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (1520 ^ _199745) ^ [_250803, _250805] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _250803, _250805) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 1521 ^ _199745 : [(1522 ^ _199745) ^ [] : [_250803 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _250805 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (1528 ^ _199745) ^ [] : [_250803 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _250805 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (1536 ^ _199745) ^ [_251304, _251306] : [c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _251304, _251306), 1541 ^ _199745 : [(1542 ^ _199745) ^ [] : [-(_251304 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (1544 ^ _199745) ^ [] : [-(_251306 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 1545 ^ _199745 : [(1546 ^ _199745) ^ [] : [-(_251304 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1548 ^ _199745) ^ [] : [-(_251306 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (1550 ^ _199745) ^ [_251714, _251716] : [-(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _251714, _251716)), 1551 ^ _199745 : [(1552 ^ _199745) ^ [] : [_251714 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _251716 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (1558 ^ _199745) ^ [] : [_251714 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _251716 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (1566 ^ _199745) ^ [_252214, _252216, _252218, _252220] : [class_Rings_Ocomm__semiring__1(_252214), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_252214), hAPP(hAPP(c_Power_Opower__class_Opower(_252214), _252216), _252218)), hAPP(hAPP(c_Power_Opower__class_Opower(_252214), _252216), _252220)) = hAPP(hAPP(c_Power_Opower__class_Opower(_252214), _252216), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _252218, _252220)))], (1572 ^ _199745) ^ [_252534, _252536, _252538, _252540] : [class_Groups_Omonoid__mult(_252534), -(hAPP(hAPP(c_Power_Opower__class_Opower(_252534), _252536), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _252538, _252540)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_252534), hAPP(hAPP(c_Power_Opower__class_Opower(_252534), _252536), _252538)), hAPP(hAPP(c_Power_Opower__class_Opower(_252534), _252536), _252540)))], (1578 ^ _199745) ^ [_252840, _252842, _252844] : [class_Rings_Ocomm__semiring__1(_252840), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_252840), hAPP(hAPP(c_Power_Opower__class_Opower(_252840), _252842), _252844)), _252842) = hAPP(hAPP(c_Power_Opower__class_Opower(_252840), _252842), c_Nat_OSuc(_252844)))], (1584 ^ _199745) ^ [_253120, _253122, _253124] : [class_Rings_Ocomm__semiring__1(_253120), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_253120), _253122), hAPP(hAPP(c_Power_Opower__class_Opower(_253120), _253122), _253124)) = hAPP(hAPP(c_Power_Opower__class_Opower(_253120), _253122), c_Nat_OSuc(_253124)))], (1590 ^ _199745) ^ [_253400, _253402, _253404] : [class_Groups_Omonoid__mult(_253400), -(hAPP(hAPP(c_Power_Opower__class_Opower(_253400), _253402), c_Nat_OSuc(_253404)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_253400), hAPP(hAPP(c_Power_Opower__class_Opower(_253400), _253402), _253404)), _253402))], (1596 ^ _199745) ^ [_253680, _253682, _253684] : [class_Rings_Ocomm__semiring__1(_253680), -(hAPP(hAPP(c_Power_Opower__class_Opower(_253680), _253682), c_Nat_OSuc(_253684)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_253680), _253682), hAPP(hAPP(c_Power_Opower__class_Opower(_253680), _253682), _253684)))], (1602 ^ _199745) ^ [_253960, _253962, _253964] : [class_Power_Opower(_253960), -(hAPP(hAPP(c_Power_Opower__class_Opower(_253960), _253962), c_Nat_OSuc(_253964)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_253960), _253962), hAPP(hAPP(c_Power_Opower__class_Opower(_253960), _253962), _253964)))], (1608 ^ _199745) ^ [_254226, _254228] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_254226), c_Groups_Ozero__class_Ozero(_254226)), c_Nat_OSuc(_254228)) = c_Groups_Ozero__class_Ozero(_254226)), class_Power_Opower(_254226), class_Rings_Osemiring__0(_254226)], (1618 ^ _199745) ^ [_254563, _254565, _254567] : [class_Power_Opower(_254563), class_Rings_Omult__zero(_254563), class_Rings_Ono__zero__divisors(_254563), class_Rings_Ozero__neq__one(_254563), 1633 ^ _199745 : [(1634 ^ _199745) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_254563), _254565), _254567) = c_Groups_Ozero__class_Ozero(_254563), 1637 ^ _199745 : [(1638 ^ _199745) ^ [] : [-(_254565 = c_Groups_Ozero__class_Ozero(_254563))], (1640 ^ _199745) ^ [] : [_254567 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (1642 ^ _199745) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_254563), _254565), _254567) = c_Groups_Ozero__class_Ozero(_254563)), _254565 = c_Groups_Ozero__class_Ozero(_254563), -(_254567 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (1652 ^ _199745) ^ [_255574, _255576, _255578, _255580, _255582, _255584] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_255574), -(_255576 = c_Groups_Ozero__class_Ozero(_255574)), c_Groups_Oplus__class_Oplus(_255574, _255578, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_255574), _255576), _255582)) = c_Groups_Oplus__class_Oplus(_255574, _255580, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_255574), _255576), _255584)), _255578 = _255580, -(_255582 = _255584)], (1670 ^ _199745) ^ [_256208, _256210, _256212, _256214] : [class_Rings_Ocomm__semiring__0(_256208), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_256208)), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_256208), _256210, _256212)), _256214) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_256208), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_256208)), _256210), _256214), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_256208)), _256212), _256214)))], (1676 ^ _199745) ^ [_256483] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _256483) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (1688 ^ _199745) ^ [_256886, _256888] : [1689 ^ _199745 : [(1690 ^ _199745) ^ [] : [_256888 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (1692 ^ _199745) ^ [] : [_256886 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _256886), _256888) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (1678 ^ _199745) ^ [_256622, _256624] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _256622), _256624) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_256624 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_256622 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (1696 ^ _199745) ^ [_257198, _257200, _257202] : [class_Rings_Ocomm__semiring__1(_257198), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_257198), _257200), _257202) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_257198), _257202), _257200))], (1702 ^ _199745) ^ [_257472, _257474, _257476, _257478] : [class_Rings_Ocomm__semiring__1(_257472), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_257472), _257474), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_257472), _257476), _257478)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_257472), _257476), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_257472), _257474), _257478)))], (1708 ^ _199745) ^ [_257784, _257786, _257788, _257790] : [class_Rings_Ocomm__semiring__1(_257784), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_257784), _257786), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_257784), _257788), _257790)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_257784), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_257784), _257786), _257788)), _257790))], (1714 ^ _199745) ^ [_258096, _258098, _258100, _258102] : [class_Rings_Ocomm__semiring__1(_258096), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_258096), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_258096), _258098), _258100)), _258102) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_258096), _258098), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_258096), _258100), _258102)))], (1720 ^ _199745) ^ [_258408, _258410, _258412, _258414] : [class_Rings_Ocomm__semiring__1(_258408), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_258408), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_258408), _258410), _258412)), _258414) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_258408), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_258408), _258410), _258414)), _258412))], (1726 ^ _199745) ^ [_258734, _258736, _258738, _258740, _258742] : [class_Rings_Ocomm__semiring__1(_258734), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_258734), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_258734), _258736), _258738)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_258734), _258740), _258742)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_258734), _258736), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_258734), _258738), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_258734), _258740), _258742))))], (1732 ^ _199745) ^ [_259098, _259100, _259102, _259104, _259106] : [class_Rings_Ocomm__semiring__1(_259098), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_259098), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_259098), _259100), _259102)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_259098), _259104), _259106)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_259098), _259104), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_259098), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_259098), _259100), _259102)), _259106)))], (1738 ^ _199745) ^ [_259462, _259464, _259466, _259468, _259470] : [class_Rings_Ocomm__semiring__1(_259462), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_259462), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_259462), _259464), _259466)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_259462), _259468), _259470)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_259462), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_259462), _259464), _259468)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_259462), _259466), _259470)))], (1744 ^ _199745) ^ [_259798, _259800, _259802] : [class_Rings_Ocomm__semiring__1(_259798), -(c_Groups_Oplus__class_Oplus(_259798, _259800, _259802) = c_Groups_Oplus__class_Oplus(_259798, _259802, _259800))], (1750 ^ _199745) ^ [_260056, _260058, _260060, _260062] : [class_Rings_Ocomm__semiring__1(_260056), -(c_Groups_Oplus__class_Oplus(_260056, _260058, c_Groups_Oplus__class_Oplus(_260056, _260060, _260062)) = c_Groups_Oplus__class_Oplus(_260056, _260060, c_Groups_Oplus__class_Oplus(_260056, _260058, _260062)))], (1756 ^ _199745) ^ [_260336, _260338, _260340, _260342] : [class_Rings_Ocomm__semiring__1(_260336), -(c_Groups_Oplus__class_Oplus(_260336, _260338, c_Groups_Oplus__class_Oplus(_260336, _260340, _260342)) = c_Groups_Oplus__class_Oplus(_260336, c_Groups_Oplus__class_Oplus(_260336, _260338, _260340), _260342))], (1762 ^ _199745) ^ [_260616, _260618, _260620, _260622] : [class_Rings_Ocomm__semiring__1(_260616), -(c_Groups_Oplus__class_Oplus(_260616, c_Groups_Oplus__class_Oplus(_260616, _260618, _260620), _260622) = c_Groups_Oplus__class_Oplus(_260616, _260618, c_Groups_Oplus__class_Oplus(_260616, _260620, _260622)))], (1768 ^ _199745) ^ [_260896, _260898, _260900, _260902] : [class_Rings_Ocomm__semiring__1(_260896), -(c_Groups_Oplus__class_Oplus(_260896, c_Groups_Oplus__class_Oplus(_260896, _260898, _260900), _260902) = c_Groups_Oplus__class_Oplus(_260896, c_Groups_Oplus__class_Oplus(_260896, _260898, _260902), _260900))], (1774 ^ _199745) ^ [_261190, _261192, _261194, _261196, _261198] : [class_Rings_Ocomm__semiring__1(_261190), -(c_Groups_Oplus__class_Oplus(_261190, c_Groups_Oplus__class_Oplus(_261190, _261192, _261194), c_Groups_Oplus__class_Oplus(_261190, _261196, _261198)) = c_Groups_Oplus__class_Oplus(_261190, c_Groups_Oplus__class_Oplus(_261190, _261192, _261196), c_Groups_Oplus__class_Oplus(_261190, _261194, _261198)))], (1780 ^ _199745) ^ [_261435] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _261435) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1782 ^ _199745) ^ [_261516] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _261516), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1794 ^ _199745) ^ [_261922, _261924] : [1795 ^ _199745 : [(1796 ^ _199745) ^ [] : [_261922 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (1798 ^ _199745) ^ [] : [_261924 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _261922), _261924) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1784 ^ _199745) ^ [_261658, _261660] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _261658), _261660) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_261658 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_261660 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1812 ^ _199745) ^ [_262549, _262551, _262553] : [1813 ^ _199745 : [(1814 ^ _199745) ^ [] : [_262551 = _262553], (1816 ^ _199745) ^ [] : [_262549 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _262549), _262551) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _262549), _262553))], (1802 ^ _199745) ^ [_262263, _262265, _262267] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _262263), _262265) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _262263), _262267), -(_262265 = _262267), -(_262263 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1830 ^ _199745) ^ [_263196, _263198, _263200] : [1831 ^ _199745 : [(1832 ^ _199745) ^ [] : [_263196 = _263200], (1834 ^ _199745) ^ [] : [_263198 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _263196), _263198) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _263200), _263198))], (1820 ^ _199745) ^ [_262910, _262912, _262914] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _262910), _262912) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _262914), _262912), -(_262910 = _262914), -(_262912 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1838 ^ _199745) ^ [_263542, _263544, _263546, _263548] : [class_Groups_Omonoid__mult(_263542), -(hAPP(hAPP(c_Power_Opower__class_Opower(_263542), _263544), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _263546), _263548)) = hAPP(hAPP(c_Power_Opower__class_Opower(_263542), hAPP(hAPP(c_Power_Opower__class_Opower(_263542), _263544), _263546)), _263548))], (1844 ^ _199745) ^ [_263850, _263852, _263854, _263856] : [class_Rings_Ocomm__semiring__1(_263850), -(hAPP(hAPP(c_Power_Opower__class_Opower(_263850), hAPP(hAPP(c_Power_Opower__class_Opower(_263850), _263852), _263854)), _263856) = hAPP(hAPP(c_Power_Opower__class_Opower(_263850), _263852), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _263854), _263856)))], (1850 ^ _199745) ^ [_264100] : [_264100 = c_Nat_OSuc(_264100)], (1852 ^ _199745) ^ [_264179] : [c_Nat_OSuc(_264179) = _264179], (1854 ^ _199745) ^ [_264317, _264319] : [c_Nat_OSuc(_264317) = c_Nat_OSuc(_264319), -(_264317 = _264319)], (1860 ^ _199745) ^ [_264487, _264489] : [_264487 = _264489, -(c_Nat_OSuc(_264487) = c_Nat_OSuc(_264489))], (1866 ^ _199745) ^ [_264707, _264709] : [c_Nat_OSuc(_264707) = c_Nat_OSuc(_264709), -(_264707 = _264709)], (1872 ^ _199745) ^ [_264968, _264970, _264972] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_264968)), _264970) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_264968)), _264972), -(_264970 = _264972)], (1878 ^ _199745) ^ [_265168, _265170, _265172] : [_265170 = _265172, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_265168)), _265170) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_265168)), _265172))], (1884 ^ _199745) ^ [_265403, _265405] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _265403, _265405) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _265405, _265403))], (1886 ^ _199745) ^ [_265519, _265521, _265523] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _265519, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _265521, _265523)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _265521, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _265519, _265523)))], (1888 ^ _199745) ^ [_265645, _265647, _265649] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _265645, _265647), _265649) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _265645, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _265647, _265649)))], (1890 ^ _199745) ^ [_265815, _265817, _265819] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _265815, _265817) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _265815, _265819), -(_265817 = _265819)], (1896 ^ _199745) ^ [_265999, _266001, _266003] : [_266001 = _266003, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _265999, _266001) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _265999, _266003))], (1902 ^ _199745) ^ [_266276, _266278, _266280] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _266276, _266278) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _266280, _266278), -(_266276 = _266280)], (1908 ^ _199745) ^ [_266460, _266462, _266464] : [_266460 = _266464, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _266460, _266462) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _266464, _266462))], (1914 ^ _199745) ^ [_266693, _266695, _266697] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _266693), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _266695, _266697)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _266693), _266695), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _266693), _266697)))], (1916 ^ _199745) ^ [_266829, _266831, _266833] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _266829, _266831)), _266833) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _266829), _266833), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _266831), _266833)))], (1918 ^ _199745) ^ [_266966, _266968] : [class_Rings_Ocomm__semiring__1(_266966), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_266966), c_Groups_Ozero__class_Ozero(_266966)), _266968) = c_Groups_Ozero__class_Ozero(_266966))], (1924 ^ _199745) ^ [_267198, _267200] : [class_Rings_Ocomm__semiring__1(_267198), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_267198), _267200), c_Groups_Ozero__class_Ozero(_267198)) = c_Groups_Ozero__class_Ozero(_267198))], (1930 ^ _199745) ^ [_267430, _267432] : [class_Rings_Ocomm__semiring__1(_267430), -(c_Groups_Oplus__class_Oplus(_267430, c_Groups_Ozero__class_Ozero(_267430), _267432) = _267432)], (1936 ^ _199745) ^ [_267650, _267652] : [class_Rings_Ocomm__semiring__1(_267650), -(c_Groups_Oplus__class_Oplus(_267650, _267652, c_Groups_Ozero__class_Ozero(_267650)) = _267652)], (1942 ^ _199745) ^ [_267884, _267886, _267888] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_267884), 1945 ^ _199745 : [(1946 ^ _199745) ^ [] : [_267886 = c_Groups_Oplus__class_Oplus(_267884, _267886, _267888), -(_267888 = c_Groups_Ozero__class_Ozero(_267884))], (1952 ^ _199745) ^ [] : [_267888 = c_Groups_Ozero__class_Ozero(_267884), -(_267886 = c_Groups_Oplus__class_Oplus(_267884, _267886, _267888))]]], (1958 ^ _199745) ^ [_268404, _268406, _268408, _268410] : [class_Rings_Ocomm__semiring__1(_268404), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_268404), _268406), c_Groups_Oplus__class_Oplus(_268404, _268408, _268410)) = c_Groups_Oplus__class_Oplus(_268404, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_268404), _268406), _268408), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_268404), _268406), _268410)))], (1964 ^ _199745) ^ [_268730, _268732, _268734, _268736, _268738] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_268730), 1967 ^ _199745 : [(1978 ^ _199745) ^ [] : [-(c_Groups_Oplus__class_Oplus(_268730, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_268730), _268732), _268736), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_268730), _268734), _268738)) = c_Groups_Oplus__class_Oplus(_268730, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_268730), _268732), _268738), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_268730), _268734), _268736))), 1981 ^ _199745 : [(1982 ^ _199745) ^ [] : [_268732 = _268734], (1984 ^ _199745) ^ [] : [_268736 = _268738]]], (1968 ^ _199745) ^ [] : [c_Groups_Oplus__class_Oplus(_268730, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_268730), _268732), _268736), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_268730), _268734), _268738)) = c_Groups_Oplus__class_Oplus(_268730, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_268730), _268732), _268738), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_268730), _268734), _268736)), -(_268732 = _268734), -(_268736 = _268738)]]], (1986 ^ _199745) ^ [_269566, _269568, _269570, _269572] : [class_Rings_Ocomm__semiring__1(_269566), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_269566), c_Groups_Oplus__class_Oplus(_269566, _269568, _269570)), _269572) = c_Groups_Oplus__class_Oplus(_269566, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_269566), _269568), _269572), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_269566), _269570), _269572)))], (1992 ^ _199745) ^ [_269878, _269880, _269882, _269884] : [class_Rings_Ocomm__semiring__1(_269878), -(c_Groups_Oplus__class_Oplus(_269878, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_269878), _269880), _269882), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_269878), _269884), _269882)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_269878), c_Groups_Oplus__class_Oplus(_269878, _269880, _269884)), _269882))], (1998 ^ _199745) ^ [_270204, _270206, _270208, _270210, _270212] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_270204), 2001 ^ _199745 : [(2012 ^ _199745) ^ [] : [2013 ^ _199745 : [(2014 ^ _199745) ^ [] : [_270206 = _270210], (2016 ^ _199745) ^ [] : [_270208 = _270212]], -(c_Groups_Oplus__class_Oplus(_270204, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_270204), _270206), _270208), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_270204), _270210), _270212)) = c_Groups_Oplus__class_Oplus(_270204, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_270204), _270206), _270212), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_270204), _270210), _270208)))], (2002 ^ _199745) ^ [] : [c_Groups_Oplus__class_Oplus(_270204, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_270204), _270206), _270208), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_270204), _270210), _270212)) = c_Groups_Oplus__class_Oplus(_270204, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_270204), _270206), _270212), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_270204), _270210), _270208)), -(_270206 = _270210), -(_270208 = _270212)]]], (2020 ^ _199745) ^ [_271020, _271022, _271024] : [class_Rings_Oring__1__no__zero__divisors(_271020), -(_271022 = c_Groups_Ozero__class_Ozero(_271020)), hAPP(hAPP(c_Power_Opower__class_Opower(_271020), _271022), _271024) = c_Groups_Ozero__class_Ozero(_271020)], (2030 ^ _199745) ^ [_271369, _271371, _271373] : [class_Groups_Omonoid__mult(_271369), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_271369), hAPP(hAPP(c_Power_Opower__class_Opower(_271369), _271371), _271373)), _271371) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_271369), _271371), hAPP(hAPP(c_Power_Opower__class_Opower(_271369), _271371), _271373)))], (2036 ^ _199745) ^ [_271675, _271677, _271679, _271681] : [class_Groups_Ocomm__monoid__mult(_271675), -(hAPP(hAPP(c_Power_Opower__class_Opower(_271675), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_271675), _271677), _271679)), _271681) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_271675), hAPP(hAPP(c_Power_Opower__class_Opower(_271675), _271677), _271681)), hAPP(hAPP(c_Power_Opower__class_Opower(_271675), _271679), _271681)))], (2042 ^ _199745) ^ [_272003, _272005, _272007, _272009] : [class_Rings_Ocomm__semiring__1(_272003), -(hAPP(hAPP(c_Power_Opower__class_Opower(_272003), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_272003), _272005), _272007)), _272009) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_272003), hAPP(hAPP(c_Power_Opower__class_Opower(_272003), _272005), _272009)), hAPP(hAPP(c_Power_Opower__class_Opower(_272003), _272007), _272009)))], (2048 ^ _199745) ^ [_272273] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_272273)], (2050 ^ _199745) ^ [_272352] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_272352)], (2052 ^ _199745) ^ [_272431] : [c_Nat_OSuc(_272431) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (2054 ^ _199745) ^ [_272510] : [c_Nat_OSuc(_272510) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (2056 ^ _199745) ^ [_272589] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_272589)], (2058 ^ _199745) ^ [_272668] : [c_Nat_OSuc(_272668) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (2060 ^ _199745) ^ [_272806, _272808] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _272806), _272808) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 2063 ^ _199745 : [(2064 ^ _199745) ^ [] : [-(_272806 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (2066 ^ _199745) ^ [] : [-(_272808 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (2068 ^ _199745) ^ [_273055, _273057] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _273055), _273057) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _273055 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _273057 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2078 ^ _199745) ^ [_273339] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _273339) = _273339)], (2080 ^ _199745) ^ [_273421] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _273421, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _273421)], (2082 ^ _199745) ^ [_273561, _273563] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _273561, _273563) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 2085 ^ _199745 : [(2086 ^ _199745) ^ [] : [-(_273561 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2088 ^ _199745) ^ [] : [-(_273563 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (2090 ^ _199745) ^ [_273806, _273808] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _273806, _273808) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _273806 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _273808 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (2100 ^ _199745) ^ [_274115, _274117] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _274115, _274117) = _274115, -(_274117 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2106 ^ _199745) ^ [_274318, _274320] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _274318, c_Nat_OSuc(_274320)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _274318, _274320)))], (2108 ^ _199745) ^ [_274424, _274426] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Nat_OSuc(_274424), _274426) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _274424, _274426)))], (2110 ^ _199745) ^ [_274530, _274532] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Nat_OSuc(_274530), _274532) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _274530, c_Nat_OSuc(_274532)))], (2112 ^ _199745) ^ [_274636, _274638] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _274636), c_Nat_OSuc(_274638)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _274636, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _274636), _274638)))], (2114 ^ _199745) ^ [_274748, _274750] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_274748)), _274750) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _274750, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _274748), _274750)))], (2116 ^ _199745) ^ [_274903, _274905, _274907, _274909] : [class_Rings_Ocomm__semiring__0(_274903), -(c_Polynomial_Opcompose(_274903, c_Polynomial_OpCons(_274903, _274905, _274907), _274909) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_274903), c_Polynomial_OpCons(_274903, _274905, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_274903))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_274903)), _274909), c_Polynomial_Opcompose(_274903, _274907, _274909))))], (2122 ^ _199745) ^ [_275209, _275211, _275213] : [class_Rings_Olinordered__ring__strict(_275209), 2125 ^ _199745 : [(2126 ^ _199745) ^ [] : [c_Groups_Oplus__class_Oplus(_275209, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_275209), _275211), _275211), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_275209), _275213), _275213)) = c_Groups_Ozero__class_Ozero(_275209), 2129 ^ _199745 : [(2130 ^ _199745) ^ [] : [-(_275211 = c_Groups_Ozero__class_Ozero(_275209))], (2132 ^ _199745) ^ [] : [-(_275213 = c_Groups_Ozero__class_Ozero(_275209))]]], (2134 ^ _199745) ^ [] : [-(c_Groups_Oplus__class_Oplus(_275209, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_275209), _275211), _275211), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_275209), _275213), _275213)) = c_Groups_Ozero__class_Ozero(_275209)), _275211 = c_Groups_Ozero__class_Ozero(_275209), _275213 = c_Groups_Ozero__class_Ozero(_275209)]]], (2144 ^ _199745) ^ [_275939, _275941, _275943] : [class_Rings_Oidom(_275939), 2147 ^ _199745 : [(2158 ^ _199745) ^ [] : [2159 ^ _199745 : [(2160 ^ _199745) ^ [] : [_275941 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_275939))], (2162 ^ _199745) ^ [] : [-(c_Polynomial_Oorder(_275939, _275943, _275941) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], -(hAPP(c_Polynomial_Opoly(_275939, _275941), _275943) = c_Groups_Ozero__class_Ozero(_275939))], (2148 ^ _199745) ^ [] : [hAPP(c_Polynomial_Opoly(_275939, _275941), _275943) = c_Groups_Ozero__class_Ozero(_275939), -(_275941 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_275939))), c_Polynomial_Oorder(_275939, _275943, _275941) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (2166 ^ _199745) ^ [_276655, _276657, _276659, _276661] : [class_RealVector_Oreal__normed__algebra(_276655), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_276655), _276657), c_Groups_Oplus__class_Oplus(_276655, _276659, _276661)) = c_Groups_Oplus__class_Oplus(_276655, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_276655), _276657), _276659), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_276655), _276657), _276661)))], (2172 ^ _199745) ^ [_276967, _276969, _276971, _276973] : [class_RealVector_Oreal__normed__algebra(_276967), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_276967), _276969), c_Groups_Oplus__class_Oplus(_276967, _276971, _276973)) = c_Groups_Oplus__class_Oplus(_276967, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_276967), _276969), _276971), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_276967), _276969), _276973)))], (2178 ^ _199745) ^ [_277279, _277281, _277283, _277285] : [class_Rings_Ocomm__semiring(_277279), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_277279), c_Groups_Oplus__class_Oplus(_277279, _277281, _277283)), _277285) = c_Groups_Oplus__class_Oplus(_277279, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_277279), _277281), _277285), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_277279), _277283), _277285)))], (2184 ^ _199745) ^ [_277591, _277593, _277595, _277597] : [class_RealVector_Oreal__normed__algebra(_277591), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_277591), c_Groups_Oplus__class_Oplus(_277591, _277593, _277595)), _277597) = c_Groups_Oplus__class_Oplus(_277591, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_277591), _277593), _277597), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_277591), _277595), _277597)))], (2190 ^ _199745) ^ [_277903, _277905, _277907, _277909] : [class_RealVector_Oreal__normed__algebra(_277903), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_277903), c_Groups_Oplus__class_Oplus(_277903, _277905, _277907)), _277909) = c_Groups_Oplus__class_Oplus(_277903, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_277903), _277905), _277909), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_277903), _277907), _277909)))], (2196 ^ _199745) ^ [_278229, _278231, _278233, _278235, _278237] : [class_Rings_Osemiring(_278229), -(c_Groups_Oplus__class_Oplus(_278229, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_278229), _278231), _278233), c_Groups_Oplus__class_Oplus(_278229, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_278229), _278235), _278233), _278237)) = c_Groups_Oplus__class_Oplus(_278229, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_278229), c_Groups_Oplus__class_Oplus(_278229, _278231, _278235)), _278233), _278237))], (2202 ^ _199745) ^ [_278535, _278537] : [class_Groups_Omonoid__add(_278535), -(c_Groups_Oplus__class_Oplus(_278535, c_Groups_Ozero__class_Ozero(_278535), _278537) = _278537)], (2208 ^ _199745) ^ [_278740, _278742] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _278740), _278742) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _278742), _278740))], (2210 ^ _199745) ^ [_278860, _278862, _278864] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _278860), _278862)), _278864) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _278860), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _278862), _278864)))], (2212 ^ _199745) ^ [_278995, _278997] : [class_Rings_Ocomm__semiring__0(_278995), -(c_Polynomial_Opcompose(_278995, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_278995)), _278997) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_278995)))], (2218 ^ _199745) ^ [_279255, _279257, _279259, _279261] : [class_Rings_Ocomm__semiring__0(_279255), -(hAPP(c_Polynomial_Opoly(_279255, c_Polynomial_Opcompose(_279255, _279257, _279259)), _279261) = hAPP(c_Polynomial_Opoly(_279255, _279257), hAPP(c_Polynomial_Opoly(_279255, _279259), _279261)))], (2224 ^ _199745) ^ [_279519, _279521] : [class_Groups_Ozero(_279519), 2227 ^ _199745 : [(2228 ^ _199745) ^ [] : [c_Groups_Ozero__class_Ozero(_279519) = _279521, -(_279521 = c_Groups_Ozero__class_Ozero(_279519))], (2234 ^ _199745) ^ [] : [_279521 = c_Groups_Ozero__class_Ozero(_279519), -(c_Groups_Ozero__class_Ozero(_279519) = _279521)]]], (2240 ^ _199745) ^ [_280017, _280019, _280021, _280023] : [class_Groups_Oab__semigroup__mult(_280017), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_280017), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_280017), _280019), _280021)), _280023) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_280017), _280019), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_280017), _280021), _280023)))], (2246 ^ _199745) ^ [_280329, _280331, _280333, _280335] : [class_Groups_Ocancel__semigroup__add(_280329), c_Groups_Oplus__class_Oplus(_280329, _280331, _280333) = c_Groups_Oplus__class_Oplus(_280329, _280335, _280333), -(_280331 = _280335)], (2256 ^ _199745) ^ [_280690, _280692, _280694, _280696] : [class_Groups_Ocancel__ab__semigroup__add(_280690), c_Groups_Oplus__class_Oplus(_280690, _280692, _280694) = c_Groups_Oplus__class_Oplus(_280690, _280692, _280696), -(_280694 = _280696)], (2266 ^ _199745) ^ [_281051, _281053, _281055, _281057] : [class_Groups_Ocancel__semigroup__add(_281051), c_Groups_Oplus__class_Oplus(_281051, _281053, _281055) = c_Groups_Oplus__class_Oplus(_281051, _281053, _281057), -(_281055 = _281057)], (2276 ^ _199745) ^ [_281412, _281414, _281416, _281418] : [class_Groups_Ocancel__semigroup__add(_281412), 2279 ^ _199745 : [(2280 ^ _199745) ^ [] : [c_Groups_Oplus__class_Oplus(_281412, _281414, _281416) = c_Groups_Oplus__class_Oplus(_281412, _281418, _281416), -(_281414 = _281418)], (2286 ^ _199745) ^ [] : [_281414 = _281418, -(c_Groups_Oplus__class_Oplus(_281412, _281414, _281416) = c_Groups_Oplus__class_Oplus(_281412, _281418, _281416))]]], (2292 ^ _199745) ^ [_281954, _281956, _281958, _281960] : [class_Groups_Ocancel__semigroup__add(_281954), 2295 ^ _199745 : [(2296 ^ _199745) ^ [] : [c_Groups_Oplus__class_Oplus(_281954, _281956, _281958) = c_Groups_Oplus__class_Oplus(_281954, _281956, _281960), -(_281958 = _281960)], (2302 ^ _199745) ^ [] : [_281958 = _281960, -(c_Groups_Oplus__class_Oplus(_281954, _281956, _281958) = c_Groups_Oplus__class_Oplus(_281954, _281956, _281960))]]], (2308 ^ _199745) ^ [_282496, _282498, _282500, _282502] : [class_Groups_Oab__semigroup__add(_282496), -(c_Groups_Oplus__class_Oplus(_282496, c_Groups_Oplus__class_Oplus(_282496, _282498, _282500), _282502) = c_Groups_Oplus__class_Oplus(_282496, _282498, c_Groups_Oplus__class_Oplus(_282496, _282500, _282502)))], (2314 ^ _199745) ^ [_282762, _282764, _282766] : [class_Rings_Ono__zero__divisors(_282762), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_282762), _282764), _282766) = c_Groups_Ozero__class_Ozero(_282762), -(_282764 = c_Groups_Ozero__class_Ozero(_282762)), -(_282766 = c_Groups_Ozero__class_Ozero(_282762))], (2328 ^ _199745) ^ [_283205, _283207, _283209] : [class_Rings_Ono__zero__divisors(_283205), -(_283207 = c_Groups_Ozero__class_Ozero(_283205)), -(_283209 = c_Groups_Ozero__class_Ozero(_283205)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_283205), _283207), _283209) = c_Groups_Ozero__class_Ozero(_283205)], (2342 ^ _199745) ^ [_283654, _283656, _283658] : [class_Rings_Oring__no__zero__divisors(_283654), 2345 ^ _199745 : [(2356 ^ _199745) ^ [] : [2357 ^ _199745 : [(2358 ^ _199745) ^ [] : [_283656 = c_Groups_Ozero__class_Ozero(_283654)], (2360 ^ _199745) ^ [] : [_283658 = c_Groups_Ozero__class_Ozero(_283654)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_283654), _283656), _283658) = c_Groups_Ozero__class_Ozero(_283654))], (2346 ^ _199745) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_283654), _283656), _283658) = c_Groups_Ozero__class_Ozero(_283654), -(_283656 = c_Groups_Ozero__class_Ozero(_283654)), -(_283658 = c_Groups_Ozero__class_Ozero(_283654))]]], (2364 ^ _199745) ^ [_284334, _284336] : [class_RealVector_Oreal__normed__algebra(_284334), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_284334), _284336), c_Groups_Ozero__class_Ozero(_284334)) = c_Groups_Ozero__class_Ozero(_284334))], (2370 ^ _199745) ^ [_284566, _284568] : [class_RealVector_Oreal__normed__algebra(_284566), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_284566), _284568), c_Groups_Ozero__class_Ozero(_284566)) = c_Groups_Ozero__class_Ozero(_284566))], (2376 ^ _199745) ^ [_284798, _284800] : [class_Rings_Omult__zero(_284798), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_284798), _284800), c_Groups_Ozero__class_Ozero(_284798)) = c_Groups_Ozero__class_Ozero(_284798))], (2382 ^ _199745) ^ [_285030, _285032] : [class_RealVector_Oreal__normed__algebra(_285030), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_285030), c_Groups_Ozero__class_Ozero(_285030)), _285032) = c_Groups_Ozero__class_Ozero(_285030))], (2388 ^ _199745) ^ [_285262, _285264] : [class_RealVector_Oreal__normed__algebra(_285262), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_285262), c_Groups_Ozero__class_Ozero(_285262)), _285264) = c_Groups_Ozero__class_Ozero(_285262))], (2394 ^ _199745) ^ [_285494, _285496] : [class_Rings_Omult__zero(_285494), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_285494), c_Groups_Ozero__class_Ozero(_285494)), _285496) = c_Groups_Ozero__class_Ozero(_285494))], (2400 ^ _199745) ^ [_285726, _285728] : [class_Groups_Ocomm__monoid__add(_285726), -(c_Groups_Oplus__class_Oplus(_285726, _285728, c_Groups_Ozero__class_Ozero(_285726)) = _285728)], (2406 ^ _199745) ^ [_285946, _285948] : [class_Groups_Omonoid__add(_285946), -(c_Groups_Oplus__class_Oplus(_285946, _285948, c_Groups_Ozero__class_Ozero(_285946)) = _285948)], (2412 ^ _199745) ^ [_286166, _286168] : [class_Groups_Olinordered__ab__group__add(_286166), 2415 ^ _199745 : [(2416 ^ _199745) ^ [] : [c_Groups_Ozero__class_Ozero(_286166) = c_Groups_Oplus__class_Oplus(_286166, _286168, _286168), -(_286168 = c_Groups_Ozero__class_Ozero(_286166))], (2422 ^ _199745) ^ [] : [_286168 = c_Groups_Ozero__class_Ozero(_286166), -(c_Groups_Ozero__class_Ozero(_286166) = c_Groups_Oplus__class_Oplus(_286166, _286168, _286168))]]], (2428 ^ _199745) ^ [_286648, _286650] : [class_Groups_Ocomm__monoid__add(_286648), -(c_Groups_Oplus__class_Oplus(_286648, c_Groups_Ozero__class_Ozero(_286648), _286650) = _286650)], (2434 ^ _199745) ^ [_286881, _286883, _286885, _286887] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _286881), _286883), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _286885), _286883), _286887)) = 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, _286881, _286885)), _286883), _286887))], (2446 ^ _199745) ^ [_287357, _287359, _287361] : [2447 ^ _199745 : [(2448 ^ _199745) ^ [] : [_287357 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (2450 ^ _199745) ^ [] : [_287359 = _287361]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _287357), _287359) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _287357), _287361))], (2436 ^ _199745) ^ [_287071, _287073, _287075] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _287071), _287073) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _287071), _287075), -(_287071 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_287073 = _287075)], (2454 ^ _199745) ^ [_287675, _287677] : [class_Groups_Olinordered__ab__group__add(_287675), 2457 ^ _199745 : [(2458 ^ _199745) ^ [] : [c_Groups_Oplus__class_Oplus(_287675, _287677, _287677) = c_Groups_Ozero__class_Ozero(_287675), -(_287677 = c_Groups_Ozero__class_Ozero(_287675))], (2464 ^ _199745) ^ [] : [_287677 = c_Groups_Ozero__class_Ozero(_287675), -(c_Groups_Oplus__class_Oplus(_287675, _287677, _287677) = c_Groups_Ozero__class_Ozero(_287675))]]], (2470 ^ _199745) ^ [_288213, _288215, _288217, _288219, _288221, _288223] : [class_Groups_Ozero(_288213), hAPP(hAPP(hAPP(_288215, c_Groups_Ozero__class_Ozero(_288213)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_288213))), _288217) = _288217, -(c_Polynomial_Opoly__rec(_288219, _288213, _288217, _288215, c_Polynomial_OpCons(_288213, _288221, _288223)) = hAPP(hAPP(hAPP(_288215, _288221), _288223), c_Polynomial_Opoly__rec(_288219, _288213, _288217, _288215, _288223)))], (2480 ^ _199745) ^ [_288644, _288646, _288648] : [class_Rings_Ocomm__semiring__0(_288644), 2483 ^ _199745 : [(2484 ^ _199745) ^ [] : [c_Polynomial_Osynthetic__div(_288644, _288646, _288648) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_288644)), -(c_Polynomial_Odegree(_288644, _288646) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2490 ^ _199745) ^ [] : [c_Polynomial_Odegree(_288644, _288646) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Polynomial_Osynthetic__div(_288644, _288646, _288648) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_288644)))]]], (2496 ^ _199745) ^ [_289165, _289167, _289169] : [class_Rings_Ocomm__semiring__1(_289165), -(c_Polynomial_Odegree(_289165, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_289165)), c_Polynomial_OpCons(_289165, _289167, c_Polynomial_OpCons(_289165, c_Groups_Oone__class_Oone(_289165), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_289165))))), _289169)) = _289169)], (2502 ^ _199745) ^ [_289404] : [-(c_Nat_Onat_Onat__size(c_Nat_OSuc(_289404)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Nat_Onat_Onat__size(_289404), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (2504 ^ _199745) ^ [_289577, _289579, _289581, _289583, _289585, _289587] : [class_Groups_Ozero(_289577), -(c_Polynomial_Opoly__rec(_289579, _289577, _289581, _289583, c_Polynomial_OpCons(_289577, _289585, _289587)) = hAPP(hAPP(hAPP(_289583, _289585), _289587), c_If(_289579, c_fequal(_289587, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_289577))), _289581, c_Polynomial_Opoly__rec(_289579, _289577, _289581, _289583, _289587))))], (2510 ^ _199745) ^ [_289911, _289913, _289915, _289917] : [class_Rings_Ocomm__semiring__0(_289911), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_289911)), c_Polynomial_OpCons(_289911, _289913, _289915)), _289917) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_289911), c_Polynomial_Osmult(_289911, _289913, _289917), c_Polynomial_OpCons(_289911, c_Groups_Ozero__class_Ozero(_289911), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_289911)), _289915), _289917))))], (2516 ^ _199745) ^ [_290211, _290213] : [class_Groups_Oone(_290211), 2519 ^ _199745 : [(2520 ^ _199745) ^ [] : [c_Groups_Oone__class_Oone(_290211) = _290213, -(_290213 = c_Groups_Oone__class_Oone(_290211))], (2526 ^ _199745) ^ [] : [_290213 = c_Groups_Oone__class_Oone(_290211), -(c_Groups_Oone__class_Oone(_290211) = _290213)]]], (2532 ^ _199745) ^ [_290681, _290683] : [class_Rings_Ocomm__semiring__1(_290681), -(hAPP(c_Polynomial_Opoly(_290681, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_290681))), _290683) = c_Groups_Oone__class_Oone(_290681))], (2538 ^ _199745) ^ [_290913, _290915] : [class_Rings_Ocomm__semiring__1(_290913), -(c_Polynomial_Osmult(_290913, c_Groups_Oone__class_Oone(_290913), _290915) = _290915)], (2544 ^ _199745) ^ [_291119] : [class_Rings_Ocomm__semiring__1(_291119), -(c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_291119)) = c_Polynomial_OpCons(_291119, c_Groups_Oone__class_Oone(_291119), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_291119))))], (2550 ^ _199745) ^ [_291377, _291379, _291381, _291383] : [class_Rings_Ocomm__semiring__0(_291377), -(c_Polynomial_Osmult(_291377, _291379, c_Polynomial_Osmult(_291377, _291381, _291383)) = c_Polynomial_Osmult(_291377, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_291377), _291379), _291381), _291383))], (2556 ^ _199745) ^ [_291623] : [class_Rings_Ozero__neq__one(_291623), c_Groups_Oone__class_Oone(_291623) = c_Groups_Ozero__class_Ozero(_291623)], (2562 ^ _199745) ^ [_291820] : [class_Rings_Ozero__neq__one(_291820), c_Groups_Ozero__class_Ozero(_291820) = c_Groups_Oone__class_Oone(_291820)], (2568 ^ _199745) ^ [_292031, _292033] : [class_Rings_Ocomm__semiring__1(_292031), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_292031), c_Groups_Oone__class_Oone(_292031)), _292033) = _292033)], (2574 ^ _199745) ^ [_292259, _292261] : [class_Rings_Ocomm__semiring__1(_292259), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_292259), _292261), c_Groups_Oone__class_Oone(_292259)) = _292261)], (2580 ^ _199745) ^ [_292487, _292489] : [class_Groups_Omonoid__mult(_292487), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_292487), c_Groups_Oone__class_Oone(_292487)), _292489) = _292489)], (2586 ^ _199745) ^ [_292715, _292717] : [class_Groups_Ocomm__monoid__mult(_292715), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_292715), c_Groups_Oone__class_Oone(_292715)), _292717) = _292717)], (2592 ^ _199745) ^ [_292943, _292945] : [class_Groups_Omonoid__mult(_292943), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_292943), _292945), c_Groups_Oone__class_Oone(_292943)) = _292945)], (2598 ^ _199745) ^ [_293171, _293173] : [class_Groups_Ocomm__monoid__mult(_293171), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_293171), _293173), c_Groups_Oone__class_Oone(_293171)) = _293173)], (2604 ^ _199745) ^ [_293399, _293401] : [class_Groups_Omonoid__mult(_293399), -(hAPP(hAPP(c_Power_Opower__class_Opower(_293399), c_Groups_Oone__class_Oone(_293399)), _293401) = c_Groups_Oone__class_Oone(_293399))], (2610 ^ _199745) ^ [_293631, _293633] : [class_Groups_Omonoid__mult(_293631), -(hAPP(hAPP(c_Power_Opower__class_Opower(_293631), _293633), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _293633)], (2616 ^ _199745) ^ [_293855, _293857] : [class_Rings_Ocomm__semiring__1(_293855), -(hAPP(hAPP(c_Power_Opower__class_Opower(_293855), _293857), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _293857)], (2622 ^ _199745) ^ [_294079, _294081] : [class_Rings_Ocomm__semiring__0(_294079), -(c_Polynomial_Osmult(_294079, _294081, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_294079))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_294079)))], (2628 ^ _199745) ^ [_294340, _294342] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _294340), _294342) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 2631 ^ _199745 : [(2632 ^ _199745) ^ [] : [-(_294340 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (2634 ^ _199745) ^ [] : [-(_294342 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (2636 ^ _199745) ^ [_294589, _294591] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _294589), _294591) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _294589 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _294591 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (2646 ^ _199745) ^ [_294873] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _294873), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _294873)], (2648 ^ _199745) ^ [_295015, _295017] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _295015), _295017), 2651 ^ _199745 : [(2652 ^ _199745) ^ [] : [-(_295015 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (2654 ^ _199745) ^ [] : [-(_295017 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (2656 ^ _199745) ^ [_295264, _295266] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _295264), _295266)), _295264 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _295266 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (2666 ^ _199745) ^ [_295548] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _295548) = _295548)], (2668 ^ _199745) ^ [_295686, _295688, _295690, _295692] : [class_Rings_Ocomm__semiring__0(_295686), -(c_Polynomial_Osmult(_295686, _295688, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_295686), _295690, _295692)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_295686), c_Polynomial_Osmult(_295686, _295688, _295690), c_Polynomial_Osmult(_295686, _295688, _295692)))], (2674 ^ _199745) ^ [_295982, _295984, _295986, _295988] : [class_Rings_Ocomm__semiring__0(_295982), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_295982)), _295984), c_Polynomial_Osmult(_295982, _295986, _295988)) = c_Polynomial_Osmult(_295982, _295986, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_295982)), _295984), _295988)))], (2680 ^ _199745) ^ [_296286, _296288, _296290, _296292] : [class_Rings_Ocomm__semiring__0(_296286), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_296286)), c_Polynomial_Osmult(_296286, _296288, _296290)), _296292) = c_Polynomial_Osmult(_296286, _296288, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_296286)), _296290), _296292)))], (2686 ^ _199745) ^ [] : [-(c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2688 ^ _199745) ^ [_296615, _296617] : [class_Rings_Ocomm__semiring__1(_296615), -(c_Groups_Oplus__class_Oplus(_296615, _296617, _296617) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_296615), c_Groups_Oplus__class_Oplus(_296615, c_Groups_Oone__class_Oone(_296615), c_Groups_Oone__class_Oone(_296615))), _296617))], (2694 ^ _199745) ^ [_296877, _296879, _296881] : [class_Rings_Ocomm__semiring__1(_296877), -(c_Groups_Oplus__class_Oplus(_296877, _296879, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_296877), _296881), _296879)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_296877), c_Groups_Oplus__class_Oplus(_296877, _296881, c_Groups_Oone__class_Oone(_296877))), _296879))], (2700 ^ _199745) ^ [_297157, _297159, _297161] : [class_Rings_Ocomm__semiring__1(_297157), -(c_Groups_Oplus__class_Oplus(_297157, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_297157), _297159), _297161), _297161) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_297157), c_Groups_Oplus__class_Oplus(_297157, _297159, c_Groups_Oone__class_Oone(_297157))), _297161))], (2706 ^ _199745) ^ [_297423, _297425] : [class_Rings_Ocomm__semiring__0(_297423), -(c_Polynomial_Osmult(_297423, c_Groups_Ozero__class_Ozero(_297423), _297425) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_297423)))], (2712 ^ _199745) ^ [_297665, _297667, _297669] : [class_Rings_Oidom(_297665), 2715 ^ _199745 : [(2726 ^ _199745) ^ [] : [2727 ^ _199745 : [(2728 ^ _199745) ^ [] : [_297667 = c_Groups_Ozero__class_Ozero(_297665)], (2730 ^ _199745) ^ [] : [_297669 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_297665))]], -(c_Polynomial_Osmult(_297665, _297667, _297669) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_297665)))], (2716 ^ _199745) ^ [] : [c_Polynomial_Osmult(_297665, _297667, _297669) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_297665)), -(_297667 = c_Groups_Ozero__class_Ozero(_297665)), -(_297669 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_297665)))]]], (2734 ^ _199745) ^ [_298345, _298347] : [class_Power_Opower(_298345), -(hAPP(hAPP(c_Power_Opower__class_Opower(_298345), _298347), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_298345))], (2740 ^ _199745) ^ [_298573, _298575] : [class_Rings_Ocomm__semiring__1(_298573), -(hAPP(hAPP(c_Power_Opower__class_Opower(_298573), _298575), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_298573))], (2746 ^ _199745) ^ [_298815, _298817, _298819] : [class_Rings_Ocomm__semiring__0(_298815), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_298815), _298817, c_Polynomial_Osmult(_298815, _298819, c_Polynomial_Osynthetic__div(_298815, _298817, _298819))) = c_Polynomial_OpCons(_298815, hAPP(c_Polynomial_Opoly(_298815, _298817), _298819), c_Polynomial_Osynthetic__div(_298815, _298817, _298819)))], (2752 ^ _199745) ^ [_299127, _299129, _299131, _299133, _299135] : [class_Rings_Ocomm__semiring__0(_299127), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_299127), _299129, c_Polynomial_Osmult(_299127, _299131, _299133)) = c_Polynomial_OpCons(_299127, _299135, _299133), 2759 ^ _199745 : [(2760 ^ _199745) ^ [] : [-(_299135 = hAPP(c_Polynomial_Opoly(_299127, _299129), _299131))], (2762 ^ _199745) ^ [] : [-(_299133 = c_Polynomial_Osynthetic__div(_299127, _299129, _299131))]]], (2764 ^ _199745) ^ [_299611, _299613, _299615, _299617] : [class_Rings_Ocomm__semiring__0(_299611), -(c_Polynomial_Osmult(_299611, _299613, c_Polynomial_OpCons(_299611, _299615, _299617)) = c_Polynomial_OpCons(_299611, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_299611), _299613), _299615), c_Polynomial_Osmult(_299611, _299613, _299617)))], (2770 ^ _199745) ^ [_299907, _299909, _299911, _299913] : [class_Rings_Ocomm__semiring__0(_299907), -(hAPP(c_Polynomial_Opoly(_299907, c_Polynomial_Osmult(_299907, _299909, _299911)), _299913) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_299907), _299909), hAPP(c_Polynomial_Opoly(_299907, _299911), _299913)))], (2776 ^ _199745) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (2778 ^ _199745) ^ [_300199] : [-(c_Nat_OSuc(_300199) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _300199))], (2780 ^ _199745) ^ [_300283] : [-(c_Nat_OSuc(_300283) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _300283, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (2782 ^ _199745) ^ [_300396, _300398] : [_300396 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _300396), _300398), -(_300398 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_300396 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2792 ^ _199745) ^ [_300694] : [class_Rings_Ocomm__semiring__1(_300694), -(c_Polynomial_Odegree(_300694, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_300694))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2798 ^ _199745) ^ [_300938, _300940, _300942, _300944] : [class_Rings_Ocomm__semiring__0(_300938), c_Polynomial_Osmult(_300938, _300940, _300942) = c_Polynomial_OpCons(_300938, _300944, _300942), -(_300942 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_300938)))], (2808 ^ _199745) ^ [_301307, _301309, _301311, _301313] : [class_Rings_Ocomm__semiring__0(_301307), -(c_Polynomial_Osmult(_301307, c_Groups_Oplus__class_Oplus(_301307, _301309, _301311), _301313) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_301307), c_Polynomial_Osmult(_301307, _301309, _301313), c_Polynomial_Osmult(_301307, _301311, _301313)))], (2814 ^ _199745) ^ [_301571, _301573] : [class_Rings_Ocomm__semiring__0(_301571), -(c_Polynomial_Osynthetic__div(_301571, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_301571)), _301573) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_301571)))], (2820 ^ _199745) ^ [_301803, _301805] : [class_Power_Opower(_301803), class_Rings_Osemiring__0(_301803), 2827 ^ _199745 : [(2828 ^ _199745) ^ [] : [_301805 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_301803), c_Groups_Ozero__class_Ozero(_301803)), _301805) = c_Groups_Oone__class_Oone(_301803))], (2834 ^ _199745) ^ [] : [-(_301805 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_301803), c_Groups_Ozero__class_Ozero(_301803)), _301805) = c_Groups_Ozero__class_Ozero(_301803))]]], (2840 ^ _199745) ^ [_302418, _302420, _302422] : [class_Rings_Oidom(_302418), 2843 ^ _199745 : [(2844 ^ _199745) ^ [] : [_302420 = c_Groups_Ozero__class_Ozero(_302418), -(c_Polynomial_Odegree(_302418, c_Polynomial_Osmult(_302418, _302420, _302422)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2850 ^ _199745) ^ [] : [-(_302420 = c_Groups_Ozero__class_Ozero(_302418)), -(c_Polynomial_Odegree(_302418, c_Polynomial_Osmult(_302418, _302420, _302422)) = c_Polynomial_Odegree(_302418, _302422))]]], (2856 ^ _199745) ^ [_302939, _302941, _302943] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _302939), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _302941, _302943)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _302939), _302941)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _302939), _302943)))], (2858 ^ _199745) ^ [_303106, _303108, _303110, _303112] : [class_Rings_Ocomm__semiring__0(_303106), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_303106), c_Polynomial_Osmult(_303106, _303108, _303110), c_Polynomial_OpCons(_303106, _303112, _303110)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_303106)), -(_303110 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_303106)))], (2868 ^ _199745) ^ [_303466, _303468, _303470] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _303466), _303468)), _303470) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _303466), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _303468), _303470)))], (2870 ^ _199745) ^ [_303629, _303631, _303633, _303635] : [class_Rings_Ocomm__semiring__0(_303629), -(c_Polynomial_Osynthetic__div(_303629, c_Polynomial_OpCons(_303629, _303631, _303633), _303635) = c_Polynomial_OpCons(_303629, hAPP(c_Polynomial_Opoly(_303629, _303633), _303635), c_Polynomial_Osynthetic__div(_303629, _303633, _303635)))], (2876 ^ _199745) ^ [_303921, _303923, _303925, _303927] : [class_Groups_Ozero(_303921), hAPP(hAPP(hAPP(_303923, c_Groups_Ozero__class_Ozero(_303921)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_303921))), _303925) = _303925, -(c_Polynomial_Opoly__rec(_303927, _303921, _303925, _303923, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_303921))) = _303925)], (2886 ^ _199745) ^ [_304316, _304318, _304320, _304322] : [class_Rings_Ocomm__semiring__0(_304316), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_304316)), _304318), c_Polynomial_OpCons(_304316, _304320, _304322)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_304316), c_Polynomial_Osmult(_304316, _304320, _304318), c_Polynomial_OpCons(_304316, c_Groups_Ozero__class_Ozero(_304316), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_304316)), _304318), _304322))))], (2892 ^ _199745) ^ [_304602] : [class_Power_Opower(_304602), -(c_Power_Opower__class_Opower(_304602) = c_Power_Opower_Opower(_304602, c_Groups_Oone__class_Oone(_304602), c_Groups_Otimes__class_Otimes(_304602)))], (2898 ^ _199745) ^ [_304838, _304840, _304842] : [class_Rings_Ocomm__ring__1(_304838), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_304838), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_304838)), c_Polynomial_OpCons(_304838, c_Groups_Ouminus__class_Ouminus(_304838, _304840), c_Polynomial_OpCons(_304838, c_Groups_Oone__class_Oone(_304838), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_304838))))), c_Polynomial_Osynthetic__div(_304838, _304842, _304840)), c_Polynomial_OpCons(_304838, hAPP(c_Polynomial_Opoly(_304838, _304842), _304840), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_304838)))) = _304842)], (2904 ^ _199745) ^ [_305125] : [-(c_Nat_Osize__class_Osize(tc_Nat_Onat, c_Nat_OSuc(_305125)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Nat_Osize__class_Osize(tc_Nat_Onat, _305125), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (2906 ^ _199745) ^ [_305272, _305274, _305276, _305278] : [class_Rings_Ocomm__ring__1(_305272), -(hAPP(c_Polynomial_Opoly(_305272, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_305272)), c_Polynomial_Omonom(_305272, c_Groups_Oone__class_Oone(_305272), _305274)), _305276)), _305278) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_305272), hAPP(hAPP(c_Power_Opower__class_Opower(_305272), _305278), _305274)), hAPP(c_Polynomial_Opoly(_305272, _305276), _305278)))], (2912 ^ _199745) ^ [_305608, _305610, _305612, _305614] : [class_Rings_Ocomm__semiring__0(_305608), -(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_305608, c_Polynomial_OpCons(_305608, _305610, _305612), _305614) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_305608), c_Polynomial_Osmult(_305608, _305614, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_305608, _305612, _305614)), c_Polynomial_OpCons(_305608, _305610, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_305608, _305612, _305614))))], (2918 ^ _199745) ^ [] : [-(c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2920 ^ _199745) ^ [] : [-(c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2922 ^ _199745) ^ [_306008, _306010, _306012] : [class_Rings_Ocomm__semiring__1(_306008), -(hAPP(c_Polynomial_Ocoeff(_306008, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_306008)), c_Polynomial_OpCons(_306008, _306010, c_Polynomial_OpCons(_306008, c_Groups_Oone__class_Oone(_306008), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_306008))))), _306012)), _306012) = c_Groups_Oone__class_Oone(_306008))], (2928 ^ _199745) ^ [_306257] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _306257) = _306257)], (2930 ^ _199745) ^ [_306338] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _306338), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _306338)], (2932 ^ _199745) ^ [_306436, _306438] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _306436), _306438) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _306438), _306436))], (2934 ^ _199745) ^ [_306556, _306558, _306560] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _306556), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _306558, _306560)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _306556), _306558), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _306556), _306560)))], (2936 ^ _199745) ^ [_306678, _306680] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _306678)), _306680) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _306678), _306680)))], (2938 ^ _199745) ^ [_306804, _306806, _306808] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _306804), _306806)), _306808) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _306804), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _306806), _306808)))], (2940 ^ _199745) ^ [_306938, _306940, _306942] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _306938, _306940)), _306942) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _306938), _306942), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _306940), _306942)))], (2942 ^ _199745) ^ [_307089, _307091, _307093] : [class_Rings_Ocomm__ring(_307089), -(c_Polynomial_Osmult(_307089, c_Groups_Ouminus__class_Ouminus(_307089, _307091), _307093) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_307089), c_Polynomial_Osmult(_307089, _307091, _307093)))], (2948 ^ _199745) ^ [_307363, _307365, _307367, _307369] : [class_Groups_Ozero(_307363), 2951 ^ _199745 : [(2952 ^ _199745) ^ [] : [c_Polynomial_Omonom(_307363, _307365, _307367) = c_Polynomial_Omonom(_307363, _307369, _307367), -(_307365 = _307369)], (2958 ^ _199745) ^ [] : [_307365 = _307369, -(c_Polynomial_Omonom(_307363, _307365, _307367) = c_Polynomial_Omonom(_307363, _307369, _307367))]]], (2964 ^ _199745) ^ [_307891, _307893, _307895] : [class_Groups_Ozero(_307891), 2967 ^ _199745 : [(2968 ^ _199745) ^ [] : [c_Polynomial_Ocoeff(_307891, _307893) = c_Polynomial_Ocoeff(_307891, _307895), -(_307893 = _307895)], (2974 ^ _199745) ^ [] : [_307893 = _307895, -(c_Polynomial_Ocoeff(_307891, _307893) = c_Polynomial_Ocoeff(_307891, _307895))]]], (2980 ^ _199745) ^ [_308397, _308399, _308401] : [class_Groups_Oab__group__add(_308397), -(hAPP(c_Polynomial_Ocoeff(_308397, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_308397), _308399)), _308401) = c_Groups_Ouminus__class_Ouminus(_308397, hAPP(c_Polynomial_Ocoeff(_308397, _308399), _308401)))], (2986 ^ _199745) ^ [_308665, _308667, _308669] : [class_Groups_Ozero(_308665), 2989 ^ _199745 : [(2990 ^ _199745) ^ [] : [_308667 = _308669, 2993 ^ _199745 : [(2994 ^ _199745) ^ [_308913] : [-(hAPP(c_Polynomial_Ocoeff(_308665, _308667), _308913) = hAPP(c_Polynomial_Ocoeff(_308665, _308669), _308913))]]], (2996 ^ _199745) ^ [] : [hAPP(c_Polynomial_Ocoeff(_308665, _308667), 2997 ^ [_308665, _308667, _308669]) = hAPP(c_Polynomial_Ocoeff(_308665, _308669), 2997 ^ [_308665, _308667, _308669]), -(_308667 = _308669)]]], (3003 ^ _199745) ^ [_309290, _309292, _309294] : [class_Groups_Oab__group__add(_309290), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_309290), c_Polynomial_Omonom(_309290, _309292, _309294)) = c_Polynomial_Omonom(_309290, c_Groups_Ouminus__class_Ouminus(_309290, _309292), _309294))], (3009 ^ _199745) ^ [_309564, _309566, _309568, _309570] : [class_Groups_Ozero(_309564), 3012 ^ _199745 : [(3013 ^ _199745) ^ [] : [_309566 = _309568, -(hAPP(c_Polynomial_Ocoeff(_309564, c_Polynomial_Omonom(_309564, _309570, _309566)), _309568) = _309570)], (3019 ^ _199745) ^ [] : [-(_309566 = _309568), -(hAPP(c_Polynomial_Ocoeff(_309564, c_Polynomial_Omonom(_309564, _309570, _309566)), _309568) = c_Groups_Ozero__class_Ozero(_309564))]]], (3025 ^ _199745) ^ [_310118, _310120, _310122] : [class_Rings_Ocomm__ring(_310118), -(hAPP(c_Polynomial_Opoly(_310118, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_310118), _310120)), _310122) = c_Groups_Ouminus__class_Ouminus(_310118, hAPP(c_Polynomial_Opoly(_310118, _310120), _310122)))], (3031 ^ _199745) ^ [_310386, _310388, _310390] : [class_Groups_Oab__group__add(_310386), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_310386), c_Polynomial_OpCons(_310386, _310388, _310390)) = c_Polynomial_OpCons(_310386, c_Groups_Ouminus__class_Ouminus(_310386, _310388), c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_310386), _310390)))], (3037 ^ _199745) ^ [_310656, _310658, _310660] : [class_Groups_Oab__group__add(_310656), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_310656), c_Polynomial_OpCons(_310656, _310658, _310660)) = c_Polynomial_OpCons(_310656, c_Groups_Ouminus__class_Ouminus(_310656, _310658), c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_310656), _310660)))], (3043 ^ _199745) ^ [_310926, _310928, _310930] : [class_Groups_Ogroup__add(_310926), 3046 ^ _199745 : [(3047 ^ _199745) ^ [] : [c_Groups_Ouminus__class_Ouminus(_310926, _310928) = c_Groups_Ouminus__class_Ouminus(_310926, _310930), -(_310928 = _310930)], (3053 ^ _199745) ^ [] : [_310928 = _310930, -(c_Groups_Ouminus__class_Ouminus(_310926, _310928) = c_Groups_Ouminus__class_Ouminus(_310926, _310930))]]], (3059 ^ _199745) ^ [_311432, _311434, _311436] : [class_Groups_Ogroup__add(_311432), 3062 ^ _199745 : [(3063 ^ _199745) ^ [] : [c_Groups_Ouminus__class_Ouminus(_311432, _311434) = _311436, -(c_Groups_Ouminus__class_Ouminus(_311432, _311436) = _311434)], (3069 ^ _199745) ^ [] : [c_Groups_Ouminus__class_Ouminus(_311432, _311436) = _311434, -(c_Groups_Ouminus__class_Ouminus(_311432, _311434) = _311436)]]], (3075 ^ _199745) ^ [_311938, _311940, _311942] : [class_Groups_Ogroup__add(_311938), 3078 ^ _199745 : [(3079 ^ _199745) ^ [] : [_311940 = c_Groups_Ouminus__class_Ouminus(_311938, _311942), -(_311942 = c_Groups_Ouminus__class_Ouminus(_311938, _311940))], (3085 ^ _199745) ^ [] : [_311942 = c_Groups_Ouminus__class_Ouminus(_311938, _311940), -(_311940 = c_Groups_Ouminus__class_Ouminus(_311938, _311942))]]], (3091 ^ _199745) ^ [_312430, _312432] : [class_Groups_Ogroup__add(_312430), -(c_Groups_Ouminus__class_Ouminus(_312430, c_Groups_Ouminus__class_Ouminus(_312430, _312432)) = _312432)], (3097 ^ _199745) ^ [_312621] : [-(c_Nat_Osize__class_Osize(tc_Nat_Onat, _312621) = _312621)], (3099 ^ _199745) ^ [_312731, _312733] : [class_Groups_Olinordered__ab__group__add(_312731), 3102 ^ _199745 : [(3103 ^ _199745) ^ [] : [c_Groups_Ouminus__class_Ouminus(_312731, _312733) = _312733, -(_312733 = c_Groups_Ozero__class_Ozero(_312731))], (3109 ^ _199745) ^ [] : [_312733 = c_Groups_Ozero__class_Ozero(_312731), -(c_Groups_Ouminus__class_Ouminus(_312731, _312733) = _312733)]]], (3115 ^ _199745) ^ [_313204, _313206] : [class_Groups_Ogroup__add(_313204), 3118 ^ _199745 : [(3119 ^ _199745) ^ [] : [c_Groups_Ouminus__class_Ouminus(_313204, _313206) = c_Groups_Ozero__class_Ozero(_313204), -(_313206 = c_Groups_Ozero__class_Ozero(_313204))], (3125 ^ _199745) ^ [] : [_313206 = c_Groups_Ozero__class_Ozero(_313204), -(c_Groups_Ouminus__class_Ouminus(_313204, _313206) = c_Groups_Ozero__class_Ozero(_313204))]]], (3131 ^ _199745) ^ [_313683, _313685] : [class_Groups_Olinordered__ab__group__add(_313683), 3134 ^ _199745 : [(3135 ^ _199745) ^ [] : [_313685 = c_Groups_Ouminus__class_Ouminus(_313683, _313685), -(_313685 = c_Groups_Ozero__class_Ozero(_313683))], (3141 ^ _199745) ^ [] : [_313685 = c_Groups_Ozero__class_Ozero(_313683), -(_313685 = c_Groups_Ouminus__class_Ouminus(_313683, _313685))]]], (3147 ^ _199745) ^ [_314156, _314158] : [class_Groups_Ogroup__add(_314156), 3150 ^ _199745 : [(3151 ^ _199745) ^ [] : [c_Groups_Ozero__class_Ozero(_314156) = c_Groups_Ouminus__class_Ouminus(_314156, _314158), -(c_Groups_Ozero__class_Ozero(_314156) = _314158)], (3157 ^ _199745) ^ [] : [c_Groups_Ozero__class_Ozero(_314156) = _314158, -(c_Groups_Ozero__class_Ozero(_314156) = c_Groups_Ouminus__class_Ouminus(_314156, _314158))]]], (3163 ^ _199745) ^ [_314621] : [class_Groups_Ogroup__add(_314621), -(c_Groups_Ouminus__class_Ouminus(_314621, c_Groups_Ozero__class_Ozero(_314621)) = c_Groups_Ozero__class_Ozero(_314621))], (3169 ^ _199745) ^ [_314851, _314853, _314855] : [class_Rings_Oidom(_314851), 3172 ^ _199745 : [(3183 ^ _199745) ^ [] : [3184 ^ _199745 : [(3185 ^ _199745) ^ [] : [_314853 = _314855], (3187 ^ _199745) ^ [] : [_314853 = c_Groups_Ouminus__class_Ouminus(_314851, _314855)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_314851), _314853), _314853) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_314851), _314855), _314855))], (3173 ^ _199745) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_314851), _314853), _314853) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_314851), _314855), _314855), -(_314853 = _314855), -(_314853 = c_Groups_Ouminus__class_Ouminus(_314851, _314855))]]], (3191 ^ _199745) ^ [_315560, _315562, _315564] : [class_Rings_Oring(_315560), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_315560), c_Groups_Ouminus__class_Ouminus(_315560, _315562)), c_Groups_Ouminus__class_Ouminus(_315560, _315564)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_315560), _315562), _315564))], (3197 ^ _199745) ^ [_315832, _315834, _315836] : [class_Rings_Oring(_315832), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_315832), c_Groups_Ouminus__class_Ouminus(_315832, _315834)), _315836) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_315832), _315834), c_Groups_Ouminus__class_Ouminus(_315832, _315836)))], (3203 ^ _199745) ^ [_316104, _316106, _316108] : [class_RealVector_Oreal__normed__algebra(_316104), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_316104), c_Groups_Ouminus__class_Ouminus(_316104, _316106)), _316108) = c_Groups_Ouminus__class_Ouminus(_316104, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_316104), _316106), _316108)))], (3209 ^ _199745) ^ [_316376, _316378, _316380] : [class_RealVector_Oreal__normed__algebra(_316376), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_316376), c_Groups_Ouminus__class_Ouminus(_316376, _316378)), _316380) = c_Groups_Ouminus__class_Ouminus(_316376, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_316376), _316378), _316380)))], (3215 ^ _199745) ^ [_316648, _316650, _316652] : [class_RealVector_Oreal__normed__algebra(_316648), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_316648), _316650), c_Groups_Ouminus__class_Ouminus(_316648, _316652)) = c_Groups_Ouminus__class_Ouminus(_316648, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_316648), _316650), _316652)))], (3221 ^ _199745) ^ [_316920, _316922, _316924] : [class_RealVector_Oreal__normed__algebra(_316920), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_316920), _316922), c_Groups_Ouminus__class_Ouminus(_316920, _316924)) = c_Groups_Ouminus__class_Ouminus(_316920, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_316920), _316922), _316924)))], (3227 ^ _199745) ^ [_317192, _317194, _317196] : [class_Rings_Oring(_317192), -(c_Groups_Ouminus__class_Ouminus(_317192, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_317192), _317194), _317196)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_317192), c_Groups_Ouminus__class_Ouminus(_317192, _317194)), _317196))], (3233 ^ _199745) ^ [_317464, _317466, _317468] : [class_Rings_Oring(_317464), -(c_Groups_Ouminus__class_Ouminus(_317464, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_317464), _317466), _317468)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_317464), _317466), c_Groups_Ouminus__class_Ouminus(_317464, _317468)))], (3239 ^ _199745) ^ [_317736, _317738, _317740] : [class_Groups_Ogroup__add(_317736), -(c_Groups_Oplus__class_Oplus(_317736, c_Groups_Ouminus__class_Ouminus(_317736, _317738), c_Groups_Oplus__class_Oplus(_317736, _317738, _317740)) = _317740)], (3245 ^ _199745) ^ [_317986, _317988, _317990] : [class_Groups_Ogroup__add(_317986), -(c_Groups_Oplus__class_Oplus(_317986, _317988, c_Groups_Oplus__class_Oplus(_317986, c_Groups_Ouminus__class_Ouminus(_317986, _317988), _317990)) = _317990)], (3251 ^ _199745) ^ [_318236, _318238, _318240] : [class_Groups_Ogroup__add(_318236), -(c_Groups_Ouminus__class_Ouminus(_318236, c_Groups_Oplus__class_Oplus(_318236, _318238, _318240)) = c_Groups_Oplus__class_Oplus(_318236, c_Groups_Ouminus__class_Ouminus(_318236, _318240), c_Groups_Ouminus__class_Ouminus(_318236, _318238)))], (3257 ^ _199745) ^ [_318498, _318500, _318502] : [class_Groups_Oab__group__add(_318498), -(c_Groups_Ouminus__class_Ouminus(_318498, c_Groups_Oplus__class_Oplus(_318498, _318500, _318502)) = c_Groups_Oplus__class_Oplus(_318498, c_Groups_Ouminus__class_Ouminus(_318498, _318500), c_Groups_Ouminus__class_Ouminus(_318498, _318502)))], (3263 ^ _199745) ^ [_318732] : [class_Groups_Oab__group__add(_318732), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_318732), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_318732))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_318732)))], (3269 ^ _199745) ^ [_318960, _318962] : [class_Groups_Oab__group__add(_318960), -(c_Polynomial_Odegree(_318960, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_318960), _318962)) = c_Polynomial_Odegree(_318960, _318962))], (3275 ^ _199745) ^ [_319204, _319206, _319208] : [class_Rings_Ocomm__ring(_319204), -(c_Polynomial_Osmult(_319204, _319206, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_319204), _319208)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_319204), c_Polynomial_Osmult(_319204, _319206, _319208)))], (3281 ^ _199745) ^ [_319468, _319470, _319472] : [class_Groups_Ogroup__add(_319468), c_Groups_Oplus__class_Oplus(_319468, _319470, _319472) = c_Groups_Ozero__class_Ozero(_319468), -(c_Groups_Ouminus__class_Ouminus(_319468, _319470) = _319472)], (3291 ^ _199745) ^ [_319793, _319795] : [class_Groups_Oab__group__add(_319793), -(c_Groups_Oplus__class_Oplus(_319793, c_Groups_Ouminus__class_Ouminus(_319793, _319795), _319795) = c_Groups_Ozero__class_Ozero(_319793))], (3297 ^ _199745) ^ [_320019, _320021] : [class_Groups_Ogroup__add(_320019), -(c_Groups_Oplus__class_Oplus(_320019, c_Groups_Ouminus__class_Ouminus(_320019, _320021), _320021) = c_Groups_Ozero__class_Ozero(_320019))], (3303 ^ _199745) ^ [_320259, _320261, _320263] : [class_Groups_Ogroup__add(_320259), 3306 ^ _199745 : [(3307 ^ _199745) ^ [] : [_320261 = c_Groups_Ouminus__class_Ouminus(_320259, _320263), -(c_Groups_Oplus__class_Oplus(_320259, _320261, _320263) = c_Groups_Ozero__class_Ozero(_320259))], (3313 ^ _199745) ^ [] : [c_Groups_Oplus__class_Oplus(_320259, _320261, _320263) = c_Groups_Ozero__class_Ozero(_320259), -(_320261 = c_Groups_Ouminus__class_Ouminus(_320259, _320263))]]], (3319 ^ _199745) ^ [_320760, _320762] : [class_Groups_Ogroup__add(_320760), -(c_Groups_Oplus__class_Oplus(_320760, _320762, c_Groups_Ouminus__class_Ouminus(_320760, _320762)) = c_Groups_Ozero__class_Ozero(_320760))], (3325 ^ _199745) ^ [_320986, _320988] : [class_Rings_Ocomm__ring__1(_320986), -(c_Groups_Ouminus__class_Ouminus(_320986, _320988) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_320986), c_Groups_Ouminus__class_Ouminus(_320986, c_Groups_Oone__class_Oone(_320986))), _320988))], (3331 ^ _199745) ^ [_321226, _321228] : [class_Rings_Oring__1__no__zero__divisors(_321226), 3334 ^ _199745 : [(3345 ^ _199745) ^ [] : [3346 ^ _199745 : [(3347 ^ _199745) ^ [] : [_321228 = c_Groups_Oone__class_Oone(_321226)], (3349 ^ _199745) ^ [] : [_321228 = c_Groups_Ouminus__class_Ouminus(_321226, c_Groups_Oone__class_Oone(_321226))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_321226), _321228), _321228) = c_Groups_Oone__class_Oone(_321226))], (3335 ^ _199745) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_321226), _321228), _321228) = c_Groups_Oone__class_Oone(_321226), -(_321228 = c_Groups_Oone__class_Oone(_321226)), -(_321228 = c_Groups_Ouminus__class_Ouminus(_321226, c_Groups_Oone__class_Oone(_321226)))]]], (3353 ^ _199745) ^ [_321893, _321895] : [class_Groups_Ozero(_321893), -(hAPP(c_Polynomial_Ocoeff(_321893, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_321893))), _321895) = c_Groups_Ozero__class_Ozero(_321893))], (3359 ^ _199745) ^ [_322139, _322141, _322143] : [class_Groups_Ozero(_322139), -(hAPP(c_Polynomial_Ocoeff(_322139, c_Polynomial_OpCons(_322139, _322141, _322143)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _322141)], (3365 ^ _199745) ^ [_322401, _322403, _322405, _322407] : [class_Groups_Ozero(_322401), -(hAPP(c_Polynomial_Ocoeff(_322401, c_Polynomial_OpCons(_322401, _322403, _322405)), c_Nat_OSuc(_322407)) = hAPP(c_Polynomial_Ocoeff(_322401, _322405), _322407))], (3371 ^ _199745) ^ [_322685, _322687, _322689, _322691] : [class_Rings_Ocomm__semiring__0(_322685), -(hAPP(c_Polynomial_Ocoeff(_322685, c_Polynomial_Osmult(_322685, _322687, _322689)), _322691) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_322685), _322687), hAPP(c_Polynomial_Ocoeff(_322685, _322689), _322691)))], (3377 ^ _199745) ^ [_322981, _322983, _322985, _322987] : [class_Groups_Ocomm__monoid__add(_322981), -(hAPP(c_Polynomial_Ocoeff(_322981, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_322981), _322983, _322985)), _322987) = c_Groups_Oplus__class_Oplus(_322981, hAPP(c_Polynomial_Ocoeff(_322981, _322983), _322987), hAPP(c_Polynomial_Ocoeff(_322981, _322985), _322987)))], (3383 ^ _199745) ^ [_323271, _323273, _323275] : [class_Rings_Ocomm__semiring__0(_323271), 3386 ^ _199745 : [(3387 ^ _199745) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_323271, _323273, _323275) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_323271)), -(_323273 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_323271)))], (3393 ^ _199745) ^ [] : [_323273 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_323271)), -(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_323271, _323273, _323275) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_323271)))]]], (3399 ^ _199745) ^ [_323781, _323783] : [class_Rings_Ocomm__semiring__0(_323781), -(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_323781, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_323781)), _323783) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_323781)))], (3405 ^ _199745) ^ [_324027, _324029, _324031] : [class_Rings_Ocomm__semiring__0(_324027), -(c_Polynomial_Odegree(_324027, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_324027, _324029, _324031)) = c_Polynomial_Odegree(_324027, _324029))], (3411 ^ _199745) ^ [_324275, _324277, _324279] : [class_Groups_Ozero(_324275), 3414 ^ _199745 : [(3415 ^ _199745) ^ [] : [c_Polynomial_Omonom(_324275, _324277, _324279) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_324275)), -(_324277 = c_Groups_Ozero__class_Ozero(_324275))], (3421 ^ _199745) ^ [] : [_324277 = c_Groups_Ozero__class_Ozero(_324275), -(c_Polynomial_Omonom(_324275, _324277, _324279) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_324275)))]]], (3427 ^ _199745) ^ [_324779, _324781] : [class_Groups_Ozero(_324779), -(c_Polynomial_Omonom(_324779, c_Groups_Ozero__class_Ozero(_324779), _324781) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_324779)))], (3433 ^ _199745) ^ [_325021, _325023, _325025] : [class_Groups_Ozero(_325021), -(_325023 = c_Groups_Ozero__class_Ozero(_325021)), -(c_Polynomial_Odegree(_325021, c_Polynomial_Omonom(_325021, _325023, _325025)) = _325025)], (3443 ^ _199745) ^ [_325377, _325379, _325381, _325383] : [class_Rings_Ocomm__semiring__0(_325377), -(c_Polynomial_Osmult(_325377, _325379, c_Polynomial_Omonom(_325377, _325381, _325383)) = c_Polynomial_Omonom(_325377, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_325377), _325379), _325381), _325383))], (3449 ^ _199745) ^ [_325665, _325667, _325669, _325671] : [class_Groups_Ocomm__monoid__add(_325665), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_325665), c_Polynomial_Omonom(_325665, _325667, _325669), c_Polynomial_Omonom(_325665, _325671, _325669)) = c_Polynomial_Omonom(_325665, c_Groups_Oplus__class_Oplus(_325665, _325667, _325671), _325669))], (3455 ^ _199745) ^ [] : [-(c_Nat_Osize__class_Osize(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3457 ^ _199745) ^ [_325996, _325998, _326000] : [class_Rings_Oring__1(_325996), -(hAPP(hAPP(c_Power_Opower__class_Opower(_325996), c_Groups_Ouminus__class_Ouminus(_325996, _325998)), _326000) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_325996), hAPP(hAPP(c_Power_Opower__class_Opower(_325996), c_Groups_Ouminus__class_Ouminus(_325996, c_Groups_Oone__class_Oone(_325996))), _326000)), hAPP(hAPP(c_Power_Opower__class_Opower(_325996), _325998), _326000)))], (3463 ^ _199745) ^ [_326290, _326292] : [class_Rings_Ocomm__semiring__1(_326290), 3466 ^ _199745 : [(3467 ^ _199745) ^ [] : [_326292 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Polynomial_Ocoeff(_326290, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_326290))), _326292) = c_Groups_Oone__class_Oone(_326290))], (3473 ^ _199745) ^ [] : [-(_326292 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_Polynomial_Ocoeff(_326290, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_326290))), _326292) = c_Groups_Ozero__class_Ozero(_326290))]]], (3479 ^ _199745) ^ [_326815, _326817, _326819, _326821] : [-(hAPP(hAPP(c_Power_Opower_Opower(_326815, _326817, _326819), _326821), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _326817)], (3481 ^ _199745) ^ [_326965, _326967, _326969, _326971, _326973] : [-(hAPP(hAPP(c_Power_Opower_Opower(_326965, _326967, _326969), _326971), c_Nat_OSuc(_326973)) = hAPP(hAPP(_326969, _326971), hAPP(hAPP(c_Power_Opower_Opower(_326965, _326967, _326969), _326971), _326973)))], (3483 ^ _199745) ^ [_327108, _327110] : [class_Groups_Ozero(_327108), -(_327110 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_327108))), hAPP(c_Polynomial_Ocoeff(_327108, _327110), c_Polynomial_Odegree(_327108, _327110)) = c_Groups_Ozero__class_Ozero(_327108)], (3493 ^ _199745) ^ [_327439, _327441] : [class_Groups_Ozero(_327439), 3496 ^ _199745 : [(3497 ^ _199745) ^ [] : [hAPP(c_Polynomial_Ocoeff(_327439, _327441), c_Polynomial_Odegree(_327439, _327441)) = c_Groups_Ozero__class_Ozero(_327439), -(_327441 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_327439)))], (3503 ^ _199745) ^ [] : [_327441 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_327439)), -(hAPP(c_Polynomial_Ocoeff(_327439, _327441), c_Polynomial_Odegree(_327439, _327441)) = c_Groups_Ozero__class_Ozero(_327439))]]], (3509 ^ _199745) ^ [_327956, _327958, _327960] : [class_Groups_Ozero(_327956), -(c_Polynomial_Omonom(_327956, _327958, c_Nat_OSuc(_327960)) = c_Polynomial_OpCons(_327956, c_Groups_Ozero__class_Ozero(_327956), c_Polynomial_Omonom(_327956, _327958, _327960)))], (3515 ^ _199745) ^ [_328230, _328232, _328234, _328236] : [class_Rings_Ocomm__semiring__1(_328230), -(hAPP(c_Polynomial_Opoly(_328230, c_Polynomial_Omonom(_328230, _328232, _328234)), _328236) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_328230), _328232), hAPP(hAPP(c_Power_Opower__class_Opower(_328230), _328236), _328234)))], (3521 ^ _199745) ^ [_328502, _328504] : [class_Groups_Ozero(_328502), -(c_Polynomial_Omonom(_328502, _328504, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(_328502, _328504, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_328502))))], (3527 ^ _199745) ^ [_328776, _328778, _328780, _328782, _328784] : [class_Rings_Ocomm__semiring__0(_328776), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_328776)), c_Polynomial_Omonom(_328776, _328778, _328780)), c_Polynomial_Omonom(_328776, _328782, _328784)) = c_Polynomial_Omonom(_328776, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_328776), _328778), _328782), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _328780, _328784)))], (3533 ^ _199745) ^ [_329098, _329100, _329102, _329104] : [class_Rings_Ocomm__semiring__0(_329098), -(hAPP(c_Polynomial_Opoly(_329098, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_329098, _329100, _329102)), _329104) = hAPP(c_Polynomial_Opoly(_329098, _329100), c_Groups_Oplus__class_Oplus(_329098, _329102, _329104)))], (3539 ^ _199745) ^ [_329372, _329374, _329376] : [class_Rings_Ocomm__semiring__0(_329372), -(hAPP(c_Polynomial_Ocoeff(_329372, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_329372)), _329374), _329376)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Polynomial_Odegree(_329372, _329374), c_Polynomial_Odegree(_329372, _329376))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_329372), hAPP(c_Polynomial_Ocoeff(_329372, _329374), c_Polynomial_Odegree(_329372, _329374))), hAPP(c_Polynomial_Ocoeff(_329372, _329376), c_Polynomial_Odegree(_329372, _329376))))], (3545 ^ _199745) ^ [_329704, _329706, _329708] : [class_Rings_Ocomm__semiring__0(_329704), -(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_329704, c_Polynomial_OpCons(_329704, _329706, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_329704))), _329708) = c_Polynomial_OpCons(_329704, _329706, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_329704))))], (3551 ^ _199745) ^ [_329972, _329974, _329976] : [class_Rings_Oidom(_329972), 3554 ^ _199745 : [(3565 ^ _199745) ^ [] : [3566 ^ _199745 : [(3567 ^ _199745) ^ [] : [_329974 = _329976], (3569 ^ _199745) ^ [] : [_329974 = c_Groups_Ouminus__class_Ouminus(_329972, _329976)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_329972), _329974), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(_329972), _329976), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (3555 ^ _199745) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_329972), _329974), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(_329972), _329976), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_329974 = _329976), -(_329974 = c_Groups_Ouminus__class_Ouminus(_329972, _329976))]]], (3573 ^ _199745) ^ [_330681, _330683, _330685] : [class_Groups_Ogroup__add(_330681), 3576 ^ _199745 : [(3577 ^ _199745) ^ [] : [c_Groups_Oplus__class_Oplus(_330681, _330683, _330685) = c_Groups_Ozero__class_Ozero(_330681), -(_330685 = c_Groups_Ouminus__class_Ouminus(_330681, _330683))], (3583 ^ _199745) ^ [] : [_330685 = c_Groups_Ouminus__class_Ouminus(_330681, _330683), -(c_Groups_Oplus__class_Oplus(_330681, _330683, _330685) = c_Groups_Ozero__class_Ozero(_330681))]]], (3589 ^ _199745) ^ [_331196, _331198, _331200] : [class_Rings_Oidom(_331196), -(_331198 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_331196))), 3596 ^ _199745 : [(3597 ^ _199745) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_331196), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_331196)), c_Polynomial_OpCons(_331196, c_Groups_Ouminus__class_Ouminus(_331196, _331200), c_Polynomial_OpCons(_331196, c_Groups_Oone__class_Oone(_331196), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_331196))))), c_Polynomial_Oorder(_331196, _331200, _331198)), _331198))], (3599 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_331196), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_331196)), c_Polynomial_OpCons(_331196, c_Groups_Ouminus__class_Ouminus(_331196, _331200), c_Polynomial_OpCons(_331196, c_Groups_Oone__class_Oone(_331196), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_331196))))), c_Nat_OSuc(c_Polynomial_Oorder(_331196, _331200, _331198))), _331198)]]], (3601 ^ _199745) ^ [_331746, _331748, _331750] : [class_Rings_Oidom(_331746), -(_331748 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_331746))), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_331746), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_331746)), c_Polynomial_OpCons(_331746, c_Groups_Ouminus__class_Ouminus(_331746, _331750), c_Polynomial_OpCons(_331746, c_Groups_Oone__class_Oone(_331746), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_331746))))), c_Nat_OSuc(c_Polynomial_Oorder(_331746, _331750, _331748))), _331748)], (3611 ^ _199745) ^ [_332151, _332153, _332155] : [class_Rings_Oidom(_332151), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_332151), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_332151)), c_Polynomial_OpCons(_332151, c_Groups_Ouminus__class_Ouminus(_332151, _332153), c_Polynomial_OpCons(_332151, c_Groups_Oone__class_Oone(_332151), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_332151))))), c_Polynomial_Oorder(_332151, _332153, _332155)), _332155))], (3617 ^ _199745) ^ [_332447, _332449, _332451] : [class_Fields_Ofield(_332447), 3620 ^ _199745 : [(3631 ^ _199745) ^ [] : [3632 ^ _199745 : [(3633 ^ _199745) ^ [] : [-(_332449 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_332447)))], (3635 ^ _199745) ^ [] : [-(_332451 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_332447)))]], -(hAPP(c_Polynomial_Ocoeff(_332447, c_Polynomial_Opoly__gcd(_332447, _332449, _332451)), c_Polynomial_Odegree(_332447, c_Polynomial_Opoly__gcd(_332447, _332449, _332451))) = c_Groups_Oone__class_Oone(_332447))], (3621 ^ _199745) ^ [] : [-(hAPP(c_Polynomial_Ocoeff(_332447, c_Polynomial_Opoly__gcd(_332447, _332449, _332451)), c_Polynomial_Odegree(_332447, c_Polynomial_Opoly__gcd(_332447, _332449, _332451))) = c_Groups_Ozero__class_Ozero(_332447)), _332449 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_332447)), _332451 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_332447))]]], (3639 ^ _199745) ^ [_333219, _333221, _333223] : [class_Rings_Oidom(_333219), 3642 ^ _199745 : [(3643 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_333219), c_Polynomial_OpCons(_333219, _333221, c_Polynomial_OpCons(_333219, c_Groups_Oone__class_Oone(_333219), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_333219)))), _333223), -(hAPP(c_Polynomial_Opoly(_333219, _333223), c_Groups_Ouminus__class_Ouminus(_333219, _333221)) = c_Groups_Ozero__class_Ozero(_333219))], (3649 ^ _199745) ^ [] : [hAPP(c_Polynomial_Opoly(_333219, _333223), c_Groups_Ouminus__class_Ouminus(_333219, _333221)) = c_Groups_Ozero__class_Ozero(_333219), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_333219), c_Polynomial_OpCons(_333219, _333221, c_Polynomial_OpCons(_333219, c_Groups_Oone__class_Oone(_333219), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_333219)))), _333223))]]], (3655 ^ _199745) ^ [_333777, _333779] : [class_Rings_Ocomm__semiring__1(_333777), -(c_Rings_Odvd__class_Odvd(_333777, _333779, c_Groups_Ozero__class_Ozero(_333777)))], (3661 ^ _199745) ^ [_334005, _334007, _334009] : [class_Fields_Ofield(_334005), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_334005), c_Polynomial_Opoly__gcd(_334005, _334007, _334009), _334007))], (3667 ^ _199745) ^ [_334247, _334249, _334251] : [class_Fields_Ofield(_334247), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_334247), c_Polynomial_Opoly__gcd(_334247, _334249, _334251), _334251))], (3673 ^ _199745) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (3675 ^ _199745) ^ [] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (3677 ^ _199745) ^ [_334551] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _334551)) = _334551)], (3679 ^ _199745) ^ [_334635] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _334635), _334635) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (3681 ^ _199745) ^ [_334734, _334736] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _334734, _334736)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _334734), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _334736)))], (3683 ^ _199745) ^ [_334830] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _334830), _334830) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (3685 ^ _199745) ^ [_334959, _334961, _334963] : [class_Fields_Ofield(_334959), -(c_Polynomial_Opoly__gcd(_334959, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_334959), _334961), _334963) = c_Polynomial_Opoly__gcd(_334959, _334961, _334963))], (3691 ^ _199745) ^ [_335213, _335215, _335217] : [class_Fields_Ofield(_335213), -(c_Polynomial_Opoly__gcd(_335213, _335215, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_335213), _335217)) = c_Polynomial_Opoly__gcd(_335213, _335215, _335217))], (3697 ^ _199745) ^ [_335453, _335455] : [class_Rings_Ocomm__semiring__1(_335453), -(c_Rings_Odvd__class_Odvd(_335453, _335455, _335455))], (3703 ^ _199745) ^ [_335691, _335693, _335695, _335697] : [class_Rings_Ocomm__semiring__1(_335691), c_Rings_Odvd__class_Odvd(_335691, _335693, _335695), c_Rings_Odvd__class_Odvd(_335691, _335695, _335697), -(c_Rings_Odvd__class_Odvd(_335691, _335693, _335697))], (3717 ^ _199745) ^ [_336125, _336127, _336129] : [class_Fields_Ofield(_336125), -(c_Polynomial_Opoly__gcd(_336125, _336127, _336129) = c_Polynomial_Opoly__gcd(_336125, _336129, _336127))], (3723 ^ _199745) ^ [_336383, _336385, _336387, _336389] : [class_Fields_Ofield(_336383), -(c_Polynomial_Opoly__gcd(_336383, _336385, c_Polynomial_Opoly__gcd(_336383, _336387, _336389)) = c_Polynomial_Opoly__gcd(_336383, _336387, c_Polynomial_Opoly__gcd(_336383, _336385, _336389)))], (3729 ^ _199745) ^ [_336663, _336665, _336667, _336669] : [class_Fields_Ofield(_336663), 3732 ^ _199745 : [(3733 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_336663), _336665, c_Polynomial_Opoly__gcd(_336663, _336667, _336669)), 3736 ^ _199745 : [(3737 ^ _199745) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_336663), _336665, _336667))], (3739 ^ _199745) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_336663), _336665, _336669))]]], (3741 ^ _199745) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_336663), _336665, c_Polynomial_Opoly__gcd(_336663, _336667, _336669))), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_336663), _336665, _336667), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_336663), _336665, _336669)]]], (3751 ^ _199745) ^ [_337390, _337392, _337394, _337396] : [class_Fields_Ofield(_337390), -(c_Polynomial_Opoly__gcd(_337390, c_Polynomial_Opoly__gcd(_337390, _337392, _337394), _337396) = c_Polynomial_Opoly__gcd(_337390, _337392, c_Polynomial_Opoly__gcd(_337390, _337394, _337396)))], (3757 ^ _199745) ^ [_337670, _337672, _337674, _337676] : [class_Fields_Ofield(_337670), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_337670), _337672, _337674), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_337670), _337672, _337676), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_337670), _337672, c_Polynomial_Opoly__gcd(_337670, _337674, _337676)))], (3771 ^ _199745) ^ [_338081] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _338081) = _338081)], (3773 ^ _199745) ^ [_338163] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _338163, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _338163)], (3775 ^ _199745) ^ [_338259, _338261] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _338259, _338261) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _338261, _338259))], (3777 ^ _199745) ^ [_338375, _338377, _338379] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _338375, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _338377, _338379)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _338377, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _338375, _338379)))], (3779 ^ _199745) ^ [_338501, _338503, _338505] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _338501, _338503), _338505) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _338501, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _338503, _338505)))], (3781 ^ _199745) ^ [_338628, _338630] : [class_Rings_Ocomm__semiring__1(_338628), c_Rings_Odvd__class_Odvd(_338628, c_Groups_Ozero__class_Ozero(_338628), _338630), -(_338630 = c_Groups_Ozero__class_Ozero(_338628))], (3791 ^ _199745) ^ [_338949, _338951, _338953] : [class_Rings_Ocomm__semiring__1(_338949), -(c_Rings_Odvd__class_Odvd(_338949, _338951, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_338949), _338951), _338953)))], (3797 ^ _199745) ^ [_339195, _339197, _339199] : [class_Rings_Ocomm__semiring__1(_339195), -(c_Rings_Odvd__class_Odvd(_339195, _339197, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339195), _339199), _339197)))], (3803 ^ _199745) ^ [_339455, _339457, _339459, _339461] : [class_Rings_Ocomm__semiring__1(_339455), c_Rings_Odvd__class_Odvd(_339455, _339457, _339459), -(c_Rings_Odvd__class_Odvd(_339455, _339457, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339455), _339459), _339461)))], (3813 ^ _199745) ^ [_339820, _339822, _339824, _339826] : [class_Rings_Ocomm__semiring__1(_339820), c_Rings_Odvd__class_Odvd(_339820, _339822, _339824), -(c_Rings_Odvd__class_Odvd(_339820, _339822, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339820), _339826), _339824)))], (3823 ^ _199745) ^ [_340199, _340201, _340203, _340205, _340207] : [class_Rings_Ocomm__semiring__1(_340199), c_Rings_Odvd__class_Odvd(_340199, _340201, _340203), c_Rings_Odvd__class_Odvd(_340199, _340205, _340207), -(c_Rings_Odvd__class_Odvd(_340199, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_340199), _340201), _340205), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_340199), _340203), _340207)))], (3837 ^ _199745) ^ [_340693, _340695, _340697, _340699] : [class_Rings_Odvd(_340693), _340695 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_340693), _340697), _340699), -(c_Rings_Odvd__class_Odvd(_340693, _340697, _340695))], (3847 ^ _199745) ^ [_341056, _341058, _341060, _341062] : [class_Rings_Ocomm__semiring__1(_341056), c_Rings_Odvd__class_Odvd(_341056, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_341056), _341058), _341060), _341062), -(c_Rings_Odvd__class_Odvd(_341056, _341058, _341062))], (3857 ^ _199745) ^ [_341421, _341423, _341425, _341427] : [class_Rings_Ocomm__semiring__1(_341421), c_Rings_Odvd__class_Odvd(_341421, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_341421), _341423), _341425), _341427), -(c_Rings_Odvd__class_Odvd(_341421, _341425, _341427))], (3867 ^ _199745) ^ [_341786, _341788, _341790, _341792] : [class_Rings_Ocomm__semiring__1(_341786), c_Rings_Odvd__class_Odvd(_341786, _341788, _341790), c_Rings_Odvd__class_Odvd(_341786, _341788, _341792), -(c_Rings_Odvd__class_Odvd(_341786, _341788, c_Groups_Oplus__class_Oplus(_341786, _341790, _341792)))], (3881 ^ _199745) ^ [_342214, _342216] : [class_Rings_Ocomm__semiring__1(_342214), -(c_Rings_Odvd__class_Odvd(_342214, c_Groups_Oone__class_Oone(_342214), _342216))], (3887 ^ _199745) ^ [_342442, _342444, _342446] : [class_Rings_Ocomm__ring__1(_342442), 3890 ^ _199745 : [(3891 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(_342442, _342444, c_Groups_Ouminus__class_Ouminus(_342442, _342446)), -(c_Rings_Odvd__class_Odvd(_342442, _342444, _342446))], (3897 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(_342442, _342444, _342446), -(c_Rings_Odvd__class_Odvd(_342442, _342444, c_Groups_Ouminus__class_Ouminus(_342442, _342446)))]]], (3903 ^ _199745) ^ [_342945, _342947, _342949] : [class_Rings_Ocomm__ring__1(_342945), 3906 ^ _199745 : [(3907 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(_342945, c_Groups_Ouminus__class_Ouminus(_342945, _342947), _342949), -(c_Rings_Odvd__class_Odvd(_342945, _342947, _342949))], (3913 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(_342945, _342947, _342949), -(c_Rings_Odvd__class_Odvd(_342945, c_Groups_Ouminus__class_Ouminus(_342945, _342947), _342949))]]], (3919 ^ _199745) ^ [_343462, _343464, _343466, _343468] : [class_Rings_Ocomm__semiring__1(_343462), c_Rings_Odvd__class_Odvd(_343462, _343464, _343466), -(c_Rings_Odvd__class_Odvd(_343462, hAPP(hAPP(c_Power_Opower__class_Opower(_343462), _343464), _343468), hAPP(hAPP(c_Power_Opower__class_Opower(_343462), _343466), _343468)))], (3929 ^ _199745) ^ [_343843, _343845, _343847, _343849] : [class_Rings_Ocomm__semiring__1(_343843), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_343843), _343845, _343847), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_343843), _343845, c_Polynomial_Osmult(_343843, _343849, _343847)))], (3939 ^ _199745) ^ [_344208, _344210, _344212, _344214] : [class_Rings_Ocomm__semiring__1(_344208), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_344208), c_Polynomial_Osmult(_344208, _344210, _344212), _344214), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_344208), _344212, _344214))], (3949 ^ _199745) ^ [_344531] : [class_Fields_Ofield(_344531), -(c_Polynomial_Opoly__gcd(_344531, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_344531)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_344531))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_344531)))], (3955 ^ _199745) ^ [_344779, _344781, _344783] : [class_Fields_Ofield(_344779), 3958 ^ _199745 : [(3959 ^ _199745) ^ [] : [c_Polynomial_Opoly__gcd(_344779, _344781, _344783) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_344779)), 3962 ^ _199745 : [(3963 ^ _199745) ^ [] : [-(_344781 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_344779)))], (3965 ^ _199745) ^ [] : [-(_344783 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_344779)))]]], (3967 ^ _199745) ^ [] : [-(c_Polynomial_Opoly__gcd(_344779, _344781, _344783) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_344779))), _344781 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_344779)), _344783 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_344779))]]], (3977 ^ _199745) ^ [_345493, _345495, _345497, _345499] : [class_Rings_Oidom(_345493), 3980 ^ _199745 : [(3991 ^ _199745) ^ [] : [3992 ^ _199745 : [(3993 ^ _199745) ^ [] : [_345497 = c_Groups_Ozero__class_Ozero(_345493)], (3995 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(_345493, _345495, _345499)]], -(c_Rings_Odvd__class_Odvd(_345493, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_345493), _345495), _345497), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_345493), _345499), _345497)))], (3981 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(_345493, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_345493), _345495), _345497), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_345493), _345499), _345497)), -(_345497 = c_Groups_Ozero__class_Ozero(_345493)), -(c_Rings_Odvd__class_Odvd(_345493, _345495, _345499))]]], (3999 ^ _199745) ^ [_346241, _346243, _346245, _346247] : [class_Rings_Oidom(_346241), 4002 ^ _199745 : [(4013 ^ _199745) ^ [] : [4014 ^ _199745 : [(4015 ^ _199745) ^ [] : [_346243 = c_Groups_Ozero__class_Ozero(_346241)], (4017 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(_346241, _346245, _346247)]], -(c_Rings_Odvd__class_Odvd(_346241, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_346241), _346243), _346245), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_346241), _346243), _346247)))], (4003 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(_346241, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_346241), _346243), _346245), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_346241), _346243), _346247)), -(_346243 = c_Groups_Ozero__class_Ozero(_346241)), -(c_Rings_Odvd__class_Odvd(_346241, _346245, _346247))]]], (4021 ^ _199745) ^ [_346961, _346963] : [class_Fields_Ofield(_346961), -(c_Polynomial_Opoly__gcd(_346961, _346963, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_346961))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_346961)))], (4027 ^ _199745) ^ [_347193, _347195] : [class_Fields_Ofield(_347193), -(c_Polynomial_Opoly__gcd(_347193, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_347193)), _347195) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_347193)))], (4033 ^ _199745) ^ [_347453, _347455, _347457, _347459] : [class_Fields_Ofield(_347453), -(_347455 = c_Groups_Ozero__class_Ozero(_347453)), 4040 ^ _199745 : [(4041 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_347453), _347457, c_Polynomial_Osmult(_347453, _347455, _347459)), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_347453), _347457, _347459))], (4047 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_347453), _347457, _347459), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_347453), _347457, c_Polynomial_Osmult(_347453, _347455, _347459)))]]], (4053 ^ _199745) ^ [_348105, _348107, _348109, _348111] : [class_Fields_Ofield(_348105), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_348105), _348107, _348109), -(_348111 = c_Groups_Ozero__class_Ozero(_348105)), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_348105), c_Polynomial_Osmult(_348105, _348111, _348107), _348109))], (4067 ^ _199745) ^ [_348574, _348576, _348578, _348580] : [class_Fields_Ofield(_348574), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_348574), _348576, c_Polynomial_Osmult(_348574, _348578, _348580)), -(_348578 = c_Groups_Ozero__class_Ozero(_348574)), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_348574), _348576, _348580))], (4081 ^ _199745) ^ [_349029, _349031, _349033] : [class_Rings_Oidom(_349029), hAPP(c_Polynomial_Ocoeff(_349029, _349031), c_Polynomial_Odegree(_349029, _349031)) = hAPP(c_Polynomial_Ocoeff(_349029, _349033), c_Polynomial_Odegree(_349029, _349033)), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_349029), _349031, _349033), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_349029), _349033, _349031), -(_349031 = _349033)], (4099 ^ _199745) ^ [_349598, _349600, _349602, _349604] : [class_Fields_Ofield(_349598), 4102 ^ _199745 : [(4119 ^ _199745) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_349598), c_Polynomial_Osmult(_349598, _349600, _349602), _349604)), 4122 ^ _199745 : [(4123 ^ _199745) ^ [] : [-(_349600 = c_Groups_Ozero__class_Ozero(_349598))], (4125 ^ _199745) ^ [] : [_349604 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_349598))]], 4126 ^ _199745 : [(4127 ^ _199745) ^ [] : [_349600 = c_Groups_Ozero__class_Ozero(_349598)], (4129 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_349598), _349602, _349604)]]], (4103 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_349598), c_Polynomial_Osmult(_349598, _349600, _349602), _349604), 4106 ^ _199745 : [(4107 ^ _199745) ^ [] : [_349600 = c_Groups_Ozero__class_Ozero(_349598), -(_349604 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_349598)))], (4113 ^ _199745) ^ [] : [-(_349600 = c_Groups_Ozero__class_Ozero(_349598)), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_349598), _349602, _349604))]]]]], (4133 ^ _199745) ^ [_350668, _350670, _350672] : [class_Rings_Oidom(_350668), 4136 ^ _199745 : [(4137 ^ _199745) ^ [] : [hAPP(c_Polynomial_Opoly(_350668, _350670), _350672) = c_Groups_Ozero__class_Ozero(_350668), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_350668), c_Polynomial_OpCons(_350668, c_Groups_Ouminus__class_Ouminus(_350668, _350672), c_Polynomial_OpCons(_350668, c_Groups_Oone__class_Oone(_350668), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_350668)))), _350670))], (4143 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_350668), c_Polynomial_OpCons(_350668, c_Groups_Ouminus__class_Ouminus(_350668, _350672), c_Polynomial_OpCons(_350668, c_Groups_Oone__class_Oone(_350668), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_350668)))), _350670), -(hAPP(c_Polynomial_Opoly(_350668, _350670), _350672) = c_Groups_Ozero__class_Ozero(_350668))]]], (4149 ^ _199745) ^ [_351240, _351242, _351244] : [class_Rings_Odvd(_351240), class_Rings_Osemiring__0(_351240), 4156 ^ _199745 : [(4157 ^ _199745) ^ [] : [4158 ^ _199745 : [(4159 ^ _199745) ^ [_351549] : [hBOOL(hAPP(_351242, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_351240), _351244), _351549)))]], 4161 ^ _199745 : [(4162 ^ _199745) ^ [] : [-(c_Rings_Odvd__class_Odvd(_351240, _351244, c_Groups_Oplus__class_Oplus(_351240, 4160 ^ [_351240, _351242, _351244], c_Groups_Ozero__class_Ozero(_351240))))], (4164 ^ _199745) ^ [] : [-(hBOOL(hAPP(_351242, 4160 ^ [_351240, _351242, _351244])))]]], (4166 ^ _199745) ^ [] : [-(hBOOL(hAPP(_351242, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_351240), _351244), 4173 ^ [_351240, _351242, _351244])))), 4167 ^ _199745 : [(4168 ^ _199745) ^ [_351889] : [c_Rings_Odvd__class_Odvd(_351240, _351244, c_Groups_Oplus__class_Oplus(_351240, _351889, c_Groups_Ozero__class_Ozero(_351240))), hBOOL(hAPP(_351242, _351889))]]]]], (4177 ^ _199745) ^ [_352302, _352304, _352306, _352308] : [class_Fields_Ofield(_352302), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_352302), _352304, _352306), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_352302), _352304, _352308), 4191 ^ _199745 : [(4192 ^ _199745) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_352302), 4190 ^ [_352302, _352304, _352306, _352308], _352306))], (4194 ^ _199745) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_352302), 4190 ^ [_352302, _352304, _352306, _352308], _352308))], (4196 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_352302), 4190 ^ [_352302, _352304, _352306, _352308], _352304)]], -(c_Polynomial_Opoly__gcd(_352302, _352306, _352308) = _352304), 4201 ^ _199745 : [(4202 ^ _199745) ^ [] : [-(_352306 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_352302)))], (4204 ^ _199745) ^ [] : [-(_352308 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_352302)))], (4206 ^ _199745) ^ [] : [hAPP(c_Polynomial_Ocoeff(_352302, _352304), c_Polynomial_Odegree(_352302, _352304)) = c_Groups_Ozero__class_Ozero(_352302)]], 4207 ^ _199745 : [(4214 ^ _199745) ^ [] : [hAPP(c_Polynomial_Ocoeff(_352302, _352304), c_Polynomial_Odegree(_352302, _352304)) = c_Groups_Oone__class_Oone(_352302)], (4208 ^ _199745) ^ [] : [_352306 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_352302)), _352308 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_352302))]]], (4218 ^ _199745) ^ [_353726, _353728] : [class_Fields_Ofield(_353726), -(c_Polynomial_Opoly__gcd(_353726, _353728, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_353726))) = c_Polynomial_Osmult(_353726, c_Rings_Oinverse__class_Oinverse(_353726, hAPP(c_Polynomial_Ocoeff(_353726, _353728), c_Polynomial_Odegree(_353726, _353728))), _353728))], (4224 ^ _199745) ^ [_353996, _353998, _354000] : [class_Rings_Ocomm__ring__1(_353996), -(c_Groups_Ominus__class_Ominus(_353996, hAPP(hAPP(c_Power_Opower__class_Opower(_353996), _353998), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(hAPP(c_Power_Opower__class_Opower(_353996), _354000), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_353996), c_Groups_Ominus__class_Ominus(_353996, _353998, _354000)), c_Groups_Oplus__class_Oplus(_353996, _353998, _354000)))], (4230 ^ _199745) ^ [_354302, _354304] : [_354302 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _354304), _354302) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (4236 ^ _199745) ^ [_354476, _354478] : [-(_354476 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _354478), _354476) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _354478), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _354478), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _354476, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (4242 ^ _199745) ^ [_354749, _354751, _354753] : [class_Groups_Ozero(_354749), -(c_Polynomial_Ocoeff(_354749, c_Polynomial_OpCons(_354749, _354751, _354753)) = c_Nat_Onat_Onat__case(_354749, _354751, c_Polynomial_Ocoeff(_354749, _354753)))], (4248 ^ _199745) ^ [_354962] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _354962))], (4250 ^ _199745) ^ [_355099, _355101] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _355099, _355101), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _355099, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _355101)))], (4256 ^ _199745) ^ [_355271, _355273] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _355271, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _355273)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _355271, _355273))], (4262 ^ _199745) ^ [_355522, _355524] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _355522, _355524), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _355522), _355524))], (4268 ^ _199745) ^ [_355694, _355696] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _355694), _355696), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _355694, _355696))], (4274 ^ _199745) ^ [_355930, _355932, _355934] : [-(_355930 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 4277 ^ _199745 : [(4278 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _355932, _355934), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _355930), _355932), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _355930), _355934)))], (4284 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _355930), _355932), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _355930), _355934)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _355932, _355934))]]], (4290 ^ _199745) ^ [_356465, _356467, _356469] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _356465, _356467), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _356465, _356469), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _356465, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _356467, _356469)))], (4300 ^ _199745) ^ [_356802, _356804, _356806] : [class_Rings_Odivision__ring(_356802), -(_356804 = c_Groups_Ozero__class_Ozero(_356802)), -(_356806 = c_Groups_Ozero__class_Ozero(_356802)), -(c_Groups_Ominus__class_Ominus(_356802, c_Rings_Oinverse__class_Oinverse(_356802, _356804), c_Rings_Oinverse__class_Oinverse(_356802, _356806)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_356802), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_356802), c_Rings_Oinverse__class_Oinverse(_356802, _356804)), c_Groups_Ominus__class_Ominus(_356802, _356806, _356804))), c_Rings_Oinverse__class_Oinverse(_356802, _356806)))], (4314 ^ _199745) ^ [_357316, _357318, _357320, _357322] : [class_Rings_Ocomm__ring(_357316), -(c_Polynomial_Osmult(_357316, c_Groups_Ominus__class_Ominus(_357316, _357318, _357320), _357322) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_357316), c_Polynomial_Osmult(_357316, _357318, _357322), c_Polynomial_Osmult(_357316, _357320, _357322)))], (4320 ^ _199745) ^ [_357579, _357581, _357583] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _357579, _357581), _357583) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _357579, _357583), _357581))], (4322 ^ _199745) ^ [_357734, _357736, _357738, _357740] : [class_Rings_Ocomm__ring(_357734), -(hAPP(c_Polynomial_Opoly(_357734, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_357734), _357736, _357738)), _357740) = c_Groups_Ominus__class_Ominus(_357734, hAPP(c_Polynomial_Opoly(_357734, _357736), _357740), hAPP(c_Polynomial_Opoly(_357734, _357738), _357740)))], (4328 ^ _199745) ^ [_358052, _358054, _358056, _358058, _358060] : [class_Groups_Oab__group__add(_358052), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_358052), c_Polynomial_OpCons(_358052, _358054, _358056), c_Polynomial_OpCons(_358052, _358058, _358060)) = c_Polynomial_OpCons(_358052, c_Groups_Ominus__class_Ominus(_358052, _358054, _358058), c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_358052), _358056, _358060)))], (4334 ^ _199745) ^ [_358376, _358378, _358380, _358382, _358384] : [class_Groups_Oab__group__add(_358376), c_Groups_Ominus__class_Ominus(_358376, _358378, _358380) = c_Groups_Ominus__class_Ominus(_358376, _358382, _358384), 4341 ^ _199745 : [(4342 ^ _199745) ^ [] : [_358378 = _358380, -(_358382 = _358384)], (4348 ^ _199745) ^ [] : [_358382 = _358384, -(_358378 = _358380)]]], (4354 ^ _199745) ^ [_359013, _359015, _359017] : [class_Rings_Odivision__ring__inverse__zero(_359013), c_Rings_Oinverse__class_Oinverse(_359013, _359015) = c_Rings_Oinverse__class_Oinverse(_359013, _359017), -(_359015 = _359017)], (4364 ^ _199745) ^ [_359346, _359348, _359350] : [class_Rings_Odivision__ring__inverse__zero(_359346), 4367 ^ _199745 : [(4368 ^ _199745) ^ [] : [c_Rings_Oinverse__class_Oinverse(_359346, _359348) = c_Rings_Oinverse__class_Oinverse(_359346, _359350), -(_359348 = _359350)], (4374 ^ _199745) ^ [] : [_359348 = _359350, -(c_Rings_Oinverse__class_Oinverse(_359346, _359348) = c_Rings_Oinverse__class_Oinverse(_359346, _359350))]]], (4380 ^ _199745) ^ [_359838, _359840] : [class_Rings_Odivision__ring__inverse__zero(_359838), -(c_Rings_Oinverse__class_Oinverse(_359838, c_Rings_Oinverse__class_Oinverse(_359838, _359840)) = _359840)], (4386 ^ _199745) ^ [_360086, _360088, _360090, _360092] : [class_Groups_Oab__group__add(_360086), -(hAPP(c_Polynomial_Ocoeff(_360086, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_360086), _360088, _360090)), _360092) = c_Groups_Ominus__class_Ominus(_360086, hAPP(c_Polynomial_Ocoeff(_360086, _360088), _360092), hAPP(c_Polynomial_Ocoeff(_360086, _360090), _360092)))], (4392 ^ _199745) ^ [_360390, _360392, _360394, _360396] : [class_Groups_Oab__group__add(_360390), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_360390), c_Polynomial_Omonom(_360390, _360392, _360394), c_Polynomial_Omonom(_360390, _360396, _360394)) = c_Polynomial_Omonom(_360390, c_Groups_Ominus__class_Ominus(_360390, _360392, _360396), _360394))], (4398 ^ _199745) ^ [_360668, _360670, _360672] : [class_Rings_Odivision__ring(_360668), c_Rings_Oinverse__class_Oinverse(_360668, _360670) = c_Rings_Oinverse__class_Oinverse(_360668, _360672), -(_360670 = c_Groups_Ozero__class_Ozero(_360668)), -(_360672 = c_Groups_Ozero__class_Ozero(_360668)), -(_360670 = _360672)], (4416 ^ _199745) ^ [_361187, _361189] : [class_Rings_Odivision__ring(_361187), c_Rings_Oinverse__class_Oinverse(_361187, _361189) = c_Groups_Ozero__class_Ozero(_361187), -(_361189 = c_Groups_Ozero__class_Ozero(_361187))], (4426 ^ _199745) ^ [_361498, _361500] : [class_Rings_Odivision__ring(_361498), -(_361500 = c_Groups_Ozero__class_Ozero(_361498)), -(c_Rings_Oinverse__class_Oinverse(_361498, c_Rings_Oinverse__class_Oinverse(_361498, _361500)) = _361500)], (4436 ^ _199745) ^ [_361814, _361816] : [class_Rings_Odivision__ring(_361814), -(_361816 = c_Groups_Ozero__class_Ozero(_361814)), c_Rings_Oinverse__class_Oinverse(_361814, _361816) = c_Groups_Ozero__class_Ozero(_361814)], (4446 ^ _199745) ^ [_362129, _362131] : [class_Rings_Odivision__ring__inverse__zero(_362129), 4449 ^ _199745 : [(4450 ^ _199745) ^ [] : [c_Rings_Oinverse__class_Oinverse(_362129, _362131) = c_Groups_Ozero__class_Ozero(_362129), -(_362131 = c_Groups_Ozero__class_Ozero(_362129))], (4456 ^ _199745) ^ [] : [_362131 = c_Groups_Ozero__class_Ozero(_362129), -(c_Rings_Oinverse__class_Oinverse(_362129, _362131) = c_Groups_Ozero__class_Ozero(_362129))]]], (4462 ^ _199745) ^ [_362594] : [class_Rings_Odivision__ring__inverse__zero(_362594), -(c_Rings_Oinverse__class_Oinverse(_362594, c_Groups_Ozero__class_Ozero(_362594)) = c_Groups_Ozero__class_Ozero(_362594))], (4468 ^ _199745) ^ [_362796] : [class_Rings_Odivision__ring(_362796), -(c_Rings_Oinverse__class_Oinverse(_362796, c_Groups_Oone__class_Oone(_362796)) = c_Groups_Oone__class_Oone(_362796))], (4474 ^ _199745) ^ [_363026, _363028, _363030] : [class_Groups_Ogroup__add(_363026), 4477 ^ _199745 : [(4478 ^ _199745) ^ [] : [c_Groups_Ominus__class_Ominus(_363026, _363028, _363030) = c_Groups_Ozero__class_Ozero(_363026), -(_363028 = _363030)], (4484 ^ _199745) ^ [] : [_363028 = _363030, -(c_Groups_Ominus__class_Ominus(_363026, _363028, _363030) = c_Groups_Ozero__class_Ozero(_363026))]]], (4490 ^ _199745) ^ [_363532, _363534, _363536] : [class_Groups_Oab__group__add(_363532), 4493 ^ _199745 : [(4494 ^ _199745) ^ [] : [_363534 = _363536, -(c_Groups_Ominus__class_Ominus(_363532, _363534, _363536) = c_Groups_Ozero__class_Ozero(_363532))], (4500 ^ _199745) ^ [] : [c_Groups_Ominus__class_Ominus(_363532, _363534, _363536) = c_Groups_Ozero__class_Ozero(_363532), -(_363534 = _363536)]]], (4506 ^ _199745) ^ [_364024, _364026] : [class_Groups_Ogroup__add(_364024), -(c_Groups_Ominus__class_Ominus(_364024, _364026, _364026) = c_Groups_Ozero__class_Ozero(_364024))], (4512 ^ _199745) ^ [_364244, _364246] : [class_Groups_Ogroup__add(_364244), -(c_Groups_Ominus__class_Ominus(_364244, _364246, c_Groups_Ozero__class_Ozero(_364244)) = _364246)], (4518 ^ _199745) ^ [_364464, _364466] : [class_Rings_Odivision__ring__inverse__zero(_364464), -(c_Rings_Oinverse__class_Oinverse(_364464, c_Groups_Ouminus__class_Ouminus(_364464, _364466)) = c_Groups_Ouminus__class_Ouminus(_364464, c_Rings_Oinverse__class_Oinverse(_364464, _364466)))], (4524 ^ _199745) ^ [_364710, _364712, _364714] : [class_Rings_Odivision__ring__inverse__zero(_364710), -(c_Rings_Oinverse__class_Oinverse(_364710, hAPP(hAPP(c_Power_Opower__class_Opower(_364710), _364712), _364714)) = hAPP(hAPP(c_Power_Opower__class_Opower(_364710), c_Rings_Oinverse__class_Oinverse(_364710, _364712)), _364714))], (4530 ^ _199745) ^ [_364996, _364998, _365000, _365002] : [class_RealVector_Oreal__normed__algebra(_364996), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_364996), c_Groups_Ominus__class_Ominus(_364996, _364998, _365000)), _365002) = c_Groups_Ominus__class_Ominus(_364996, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_364996), _364998), _365002), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_364996), _365000), _365002)))], (4536 ^ _199745) ^ [_365308, _365310, _365312, _365314] : [class_RealVector_Oreal__normed__algebra(_365308), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_365308), c_Groups_Ominus__class_Ominus(_365308, _365310, _365312)), _365314) = c_Groups_Ominus__class_Ominus(_365308, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_365308), _365310), _365314), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_365308), _365312), _365314)))], (4542 ^ _199745) ^ [_365620, _365622, _365624, _365626] : [class_RealVector_Oreal__normed__algebra(_365620), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_365620), _365622), c_Groups_Ominus__class_Ominus(_365620, _365624, _365626)) = c_Groups_Ominus__class_Ominus(_365620, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_365620), _365622), _365624), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_365620), _365622), _365626)))], (4548 ^ _199745) ^ [_365932, _365934, _365936, _365938] : [class_RealVector_Oreal__normed__algebra(_365932), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_365932), _365934), c_Groups_Ominus__class_Ominus(_365932, _365936, _365938)) = c_Groups_Ominus__class_Ominus(_365932, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_365932), _365934), _365936), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_365932), _365934), _365938)))], (4554 ^ _199745) ^ [_366230, _366232, _366234] : [class_Groups_Ogroup__add(_366230), -(c_Groups_Ominus__class_Ominus(_366230, c_Groups_Oplus__class_Oplus(_366230, _366232, _366234), _366234) = _366232)], (4560 ^ _199745) ^ [_366474, _366476, _366478] : [class_Groups_Ogroup__add(_366474), -(c_Groups_Oplus__class_Oplus(_366474, c_Groups_Ominus__class_Ominus(_366474, _366476, _366478), _366478) = _366476)], (4566 ^ _199745) ^ [_366718, _366720, _366722] : [class_Groups_Oab__group__add(_366718), -(c_Groups_Ouminus__class_Ouminus(_366718, c_Groups_Ominus__class_Ominus(_366718, _366720, _366722)) = c_Groups_Ominus__class_Ominus(_366718, _366722, _366720))], (4572 ^ _199745) ^ [_366982, _366984, _366986, _366988] : [class_Rings_Ocomm__ring__1(_366982), c_Rings_Odvd__class_Odvd(_366982, _366984, _366986), c_Rings_Odvd__class_Odvd(_366982, _366984, _366988), -(c_Rings_Odvd__class_Odvd(_366982, _366984, c_Groups_Ominus__class_Ominus(_366982, _366986, _366988)))], (4586 ^ _199745) ^ [_367424, _367426, _367428] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _367424), _367426), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _367424), _367428)), -(_367424 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _367426, _367428))], (4596 ^ _199745) ^ [_367764, _367766] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _367764, _367766) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _367766, _367764) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_367764 = _367766)], (4606 ^ _199745) ^ [_368050] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _368050, _368050) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4608 ^ _199745) ^ [_368132] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _368132, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _368132)], (4610 ^ _199745) ^ [_368214] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _368214) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4612 ^ _199745) ^ [_368324, _368326, _368328] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_368324), _368326), c_Nat_OSuc(_368328)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _368324, _368326), _368328))], (4614 ^ _199745) ^ [_368440, _368442] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_368440), c_Nat_OSuc(_368442)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _368440, _368442))], (4616 ^ _199745) ^ [_368590, _368592] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _368590, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _368592, _368590)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _368590, _368592))], (4622 ^ _199745) ^ [_368764, _368766] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _368764, _368766), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _368764, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _368766, _368764)))], (4628 ^ _199745) ^ [_368987, _368989, _368991] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _368987, _368989), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _368991, _368989)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _368987, _368991))], (4630 ^ _199745) ^ [_369113, _369115, _369117] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _369113, _369115), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _369113, _369117)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _369115, _369117))], (4632 ^ _199745) ^ [_369239, _369241, _369243] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _369239, _369241), _369243) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _369239, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _369241, _369243)))], (4634 ^ _199745) ^ [_369351, _369353] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _369351, _369353), _369351) = _369353)], (4636 ^ _199745) ^ [_369453, _369455] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _369453, _369455), _369455) = _369453)], (4638 ^ _199745) ^ [_369569, _369571, _369573] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _369569), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _369571, _369573)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _369569), _369571), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _369569), _369573)))], (4640 ^ _199745) ^ [_369705, _369707, _369709] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _369705, _369707)), _369709) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _369705), _369709), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _369707), _369709)))], (4642 ^ _199745) ^ [_369841, _369843, _369845] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _369841), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _369843, _369845)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _369841), _369843), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _369841), _369845)))], (4644 ^ _199745) ^ [_369977, _369979, _369981] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _369977, _369979)), _369981) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _369977), _369981), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _369979), _369981)))], (4646 ^ _199745) ^ [_370114, _370116] : [class_Groups_Oab__group__add(_370114), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_370114), _370116, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_370114))) = _370116)], (4652 ^ _199745) ^ [_370357] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _370357, c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_370357 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (4658 ^ _199745) ^ [_370515] : [_370515 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _370515, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (4664 ^ _199745) ^ [_370751, _370753, _370755, _370757] : [class_Rings_Ocomm__ring(_370751), -(c_Polynomial_Osmult(_370751, _370753, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_370751), _370755, _370757)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_370751), c_Polynomial_Osmult(_370751, _370753, _370755), c_Polynomial_Osmult(_370751, _370753, _370757)))], (4670 ^ _199745) ^ [_371033, _371035, _371037] : [class_Rings_Odivision__ring(_371033), -(_371035 = c_Groups_Ozero__class_Ozero(_371033)), -(_371037 = c_Groups_Ozero__class_Ozero(_371033)), -(c_Rings_Oinverse__class_Oinverse(_371033, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_371033), _371035), _371037)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_371033), c_Rings_Oinverse__class_Oinverse(_371033, _371037)), c_Rings_Oinverse__class_Oinverse(_371033, _371035)))], (4684 ^ _199745) ^ [_371497, _371499] : [class_Rings_Odivision__ring(_371497), -(_371499 = c_Groups_Ozero__class_Ozero(_371497)), -(c_Rings_Oinverse__class_Oinverse(_371497, c_Groups_Ouminus__class_Ouminus(_371497, _371499)) = c_Groups_Ouminus__class_Ouminus(_371497, c_Rings_Oinverse__class_Oinverse(_371497, _371499)))], (4694 ^ _199745) ^ [_371839, _371841, _371843] : [class_Rings_Odivision__ring(_371839), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_371839), _371841), _371843) = c_Groups_Oone__class_Oone(_371839), -(c_Rings_Oinverse__class_Oinverse(_371839, _371841) = _371843)], (4704 ^ _199745) ^ [_372186, _372188, _372190] : [class_Rings_Odivision__ring(_372186), -(_372188 = c_Groups_Ozero__class_Ozero(_372186)), -(c_Rings_Oinverse__class_Oinverse(_372186, hAPP(hAPP(c_Power_Opower__class_Opower(_372186), _372188), _372190)) = hAPP(hAPP(c_Power_Opower__class_Opower(_372186), c_Rings_Oinverse__class_Oinverse(_372186, _372188)), _372190))], (4714 ^ _199745) ^ [_372600, _372602, _372604, _372606, _372608, _372610] : [class_Rings_Oring(_372600), 4717 ^ _199745 : [(4718 ^ _199745) ^ [] : [c_Groups_Oplus__class_Oplus(_372600, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_372600), _372602), _372604), _372606) = c_Groups_Oplus__class_Oplus(_372600, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_372600), _372608), _372604), _372610), -(c_Groups_Oplus__class_Oplus(_372600, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_372600), c_Groups_Ominus__class_Ominus(_372600, _372602, _372608)), _372604), _372606) = _372610)], (4724 ^ _199745) ^ [] : [c_Groups_Oplus__class_Oplus(_372600, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_372600), c_Groups_Ominus__class_Ominus(_372600, _372602, _372608)), _372604), _372606) = _372610, -(c_Groups_Oplus__class_Oplus(_372600, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_372600), _372602), _372604), _372606) = c_Groups_Oplus__class_Oplus(_372600, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_372600), _372608), _372604), _372610))]]], (4730 ^ _199745) ^ [_373298, _373300, _373302, _373304, _373306, _373308] : [class_Rings_Oring(_373298), 4733 ^ _199745 : [(4734 ^ _199745) ^ [] : [c_Groups_Oplus__class_Oplus(_373298, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_373298), _373300), _373302), _373304) = c_Groups_Oplus__class_Oplus(_373298, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_373298), _373306), _373302), _373308), -(_373304 = c_Groups_Oplus__class_Oplus(_373298, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_373298), c_Groups_Ominus__class_Ominus(_373298, _373306, _373300)), _373302), _373308))], (4740 ^ _199745) ^ [] : [_373304 = c_Groups_Oplus__class_Oplus(_373298, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_373298), c_Groups_Ominus__class_Ominus(_373298, _373306, _373300)), _373302), _373308), -(c_Groups_Oplus__class_Oplus(_373298, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_373298), _373300), _373302), _373304) = c_Groups_Oplus__class_Oplus(_373298, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_373298), _373306), _373302), _373308))]]], (4746 ^ _199745) ^ [_373982, _373984, _373986, _373988, _373990] : [class_RealVector_Oreal__normed__algebra(_373982), -(c_Groups_Ominus__class_Ominus(_373982, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_373982), _373984), _373986), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_373982), _373988), _373990)) = c_Groups_Oplus__class_Oplus(_373982, c_Groups_Oplus__class_Oplus(_373982, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_373982), c_Groups_Ominus__class_Ominus(_373982, _373984, _373988)), c_Groups_Ominus__class_Ominus(_373982, _373986, _373990)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_373982), c_Groups_Ominus__class_Ominus(_373982, _373984, _373988)), _373990)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_373982), _373988), c_Groups_Ominus__class_Ominus(_373982, _373986, _373990))))], (4752 ^ _199745) ^ [_374386, _374388, _374390, _374392, _374394] : [class_Rings_Oring(_374386), -(c_Groups_Ominus__class_Ominus(_374386, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_374386), _374388), _374390), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_374386), _374392), _374394)) = c_Groups_Oplus__class_Oplus(_374386, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_374386), _374388), c_Groups_Ominus__class_Ominus(_374386, _374390, _374394)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_374386), c_Groups_Ominus__class_Ominus(_374386, _374388, _374392)), _374394)))], (4758 ^ _199745) ^ [_374736, _374738, _374740, _374742] : [class_Rings_Ocomm__ring(_374736), class_Rings_Odvd(_374736), c_Rings_Odvd__class_Odvd(_374736, _374738, _374740), 4769 ^ _199745 : [(4770 ^ _199745) ^ [_375139, _375141] : [c_Rings_Odvd__class_Odvd(_374736, _374738, c_Groups_Oplus__class_Oplus(_374736, _375141, _374742)), -(c_Rings_Odvd__class_Odvd(_374736, _374738, c_Groups_Oplus__class_Oplus(_374736, c_Groups_Ominus__class_Ominus(_374736, _375141, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_374736), _375139), _374740)), _374742)))], (4776 ^ _199745) ^ [_375377, _375379] : [c_Rings_Odvd__class_Odvd(_374736, _374738, c_Groups_Oplus__class_Oplus(_374736, c_Groups_Ominus__class_Ominus(_374736, _375379, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_374736), _375377), _374740)), _374742)), -(c_Rings_Odvd__class_Odvd(_374736, _374738, c_Groups_Oplus__class_Oplus(_374736, _375379, _374742)))]]], (4782 ^ _199745) ^ [_375704, _375706, _375708, _375710] : [class_Rings_Ocomm__ring(_375704), class_Rings_Odvd(_375704), c_Rings_Odvd__class_Odvd(_375704, _375706, _375708), 4793 ^ _199745 : [(4794 ^ _199745) ^ [_376107, _376109] : [c_Rings_Odvd__class_Odvd(_375704, _375706, c_Groups_Oplus__class_Oplus(_375704, _376109, _375710)), -(c_Rings_Odvd__class_Odvd(_375704, _375706, c_Groups_Oplus__class_Oplus(_375704, c_Groups_Ominus__class_Ominus(_375704, _376109, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_375704), _376107), _375708)), _375710)))], (4800 ^ _199745) ^ [_376345, _376347] : [c_Rings_Odvd__class_Odvd(_375704, _375706, c_Groups_Oplus__class_Oplus(_375704, c_Groups_Ominus__class_Ominus(_375704, _376347, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_375704), _376345), _375708)), _375710)), -(c_Rings_Odvd__class_Odvd(_375704, _375706, c_Groups_Oplus__class_Oplus(_375704, _376347, _375710)))]]], (4806 ^ _199745) ^ [_376644, _376646] : [class_Groups_Ogroup__add(_376644), -(c_Groups_Ominus__class_Ominus(_376644, c_Groups_Ozero__class_Ozero(_376644), _376646) = c_Groups_Ouminus__class_Ouminus(_376644, _376646))], (4812 ^ _199745) ^ [_376884, _376886, _376888] : [class_Rings_Ocomm__ring__1(_376884), -(c_Groups_Ominus__class_Ominus(_376884, _376886, _376888) = c_Groups_Oplus__class_Oplus(_376884, _376886, c_Groups_Ouminus__class_Ouminus(_376884, _376888)))], (4818 ^ _199745) ^ [_377134, _377136, _377138] : [class_Groups_Ogroup__add(_377134), -(c_Groups_Ominus__class_Ominus(_377134, _377136, c_Groups_Ouminus__class_Ouminus(_377134, _377138)) = c_Groups_Oplus__class_Oplus(_377134, _377136, _377138))], (4824 ^ _199745) ^ [_377384, _377386, _377388] : [class_Groups_Oab__group__add(_377384), -(c_Groups_Ominus__class_Ominus(_377384, _377386, _377388) = c_Groups_Oplus__class_Oplus(_377384, _377386, c_Groups_Ouminus__class_Ouminus(_377384, _377388)))], (4830 ^ _199745) ^ [_377634, _377636, _377638] : [class_Groups_Ogroup__add(_377634), -(c_Groups_Ominus__class_Ominus(_377634, _377636, _377638) = c_Groups_Oplus__class_Oplus(_377634, _377636, c_Groups_Ouminus__class_Ouminus(_377634, _377638)))], (4836 ^ _199745) ^ [_377913, _377915, _377917] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _377913, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _377915, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _377913), _377917))), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _377913, _377915))], (4842 ^ _199745) ^ [_378105, _378107, _378109] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _378105, _378107), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _378105, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _378107, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _378105), _378109))))], (4848 ^ _199745) ^ [_378389, _378391, _378393, _378395, _378397] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _378389, _378391), 4851 ^ _199745 : [(4852 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _378389, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _378393, _378395)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _378389, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _378393, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _378397), _378391)), _378395)))], (4858 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _378389, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _378393, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _378397), _378391)), _378395)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _378389, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _378393, _378395)))]]], (4864 ^ _199745) ^ [_378974] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _378974, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_378974 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (4870 ^ _199745) ^ [_379132] : [_379132 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _379132, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (4876 ^ _199745) ^ [_379325, _379327] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _379325, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _379325, _379327)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4888 ^ _199745) ^ [_379775, _379777, _379779] : [4889 ^ _199745 : [(4890 ^ _199745) ^ [] : [_379775 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (4892 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _379777, _379779)]], -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _379775), _379777), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _379775), _379779)))], (4878 ^ _199745) ^ [_379485, _379487, _379489] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _379485), _379487), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _379485), _379489)), -(_379485 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _379487, _379489))], (4896 ^ _199745) ^ [_380096, _380098, _380100] : [-(hAPP(c_Nat_Onat_Onat__case(_380096, _380098, _380100), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _380098)], (4898 ^ _199745) ^ [_380227, _380229, _380231, _380233] : [-(hAPP(c_Nat_Onat_Onat__case(_380227, _380229, _380231), c_Nat_OSuc(_380233)) = hAPP(_380231, _380233))], (4900 ^ _199745) ^ [_380323] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_380323), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _380323)], (4902 ^ _199745) ^ [_380421, _380423] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _380421, c_Nat_OSuc(_380423)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _380421, c_Groups_Oone__class_Oone(tc_Nat_Onat)), _380423))], (4904 ^ _199745) ^ [_380529, _380531] : [-(c_Groups_Ominus__class_Ominus(tc_Int_Oint, _380529, _380531) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _380529, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _380531)))], (4906 ^ _199745) ^ [_380634, _380636] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _380634, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _380636)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _380634, _380636))], (4908 ^ _199745) ^ [_380754, _380756] : [class_Groups_Oab__group__add(_380754), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_380754), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_380754)), _380756) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_380754), _380756))], (4914 ^ _199745) ^ [_381006, _381008, _381010] : [class_Rings_Odivision__ring(_381006), -(_381008 = c_Groups_Ozero__class_Ozero(_381006)), -(_381010 = c_Groups_Ozero__class_Ozero(_381006)), -(c_Groups_Oplus__class_Oplus(_381006, c_Rings_Oinverse__class_Oinverse(_381006, _381008), c_Rings_Oinverse__class_Oinverse(_381006, _381010)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_381006), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_381006), c_Rings_Oinverse__class_Oinverse(_381006, _381008)), c_Groups_Oplus__class_Oplus(_381006, _381008, _381010))), c_Rings_Oinverse__class_Oinverse(_381006, _381010)))], (4928 ^ _199745) ^ [_381492, _381494] : [class_Rings_Odivision__ring(_381492), -(_381494 = c_Groups_Ozero__class_Ozero(_381492)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_381492), c_Rings_Oinverse__class_Oinverse(_381492, _381494)), _381494) = c_Groups_Oone__class_Oone(_381492))], (4938 ^ _199745) ^ [_381822, _381824] : [class_Rings_Odivision__ring(_381822), -(_381824 = c_Groups_Ozero__class_Ozero(_381822)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_381822), _381824), c_Rings_Oinverse__class_Oinverse(_381822, _381824)) = c_Groups_Oone__class_Oone(_381822))], (4948 ^ _199745) ^ [_382152, _382154] : [class_Rings_Oring__1(_382152), -(c_Groups_Ominus__class_Ominus(_382152, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_382152), _382154), _382154), c_Groups_Oone__class_Oone(_382152)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_382152), c_Groups_Oplus__class_Oplus(_382152, _382154, c_Groups_Oone__class_Oone(_382152))), c_Groups_Ominus__class_Ominus(_382152, _382154, c_Groups_Oone__class_Oone(_382152))))], (4954 ^ _199745) ^ [_382442, _382444, _382446] : [class_Rings_Ocomm__semiring__0(_382442), -(c_Polynomial_Odegree(_382442, c_Polynomial_Osynthetic__div(_382442, _382444, _382446)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Polynomial_Odegree(_382442, _382444), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (4960 ^ _199745) ^ [_382704, _382706] : [_382704 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _382704, _382706) = _382706)], (4966 ^ _199745) ^ [_382874, _382876] : [-(_382874 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _382874, _382876) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _382874, c_Groups_Oone__class_Oone(tc_Nat_Onat)), _382876)))], (4972 ^ _199745) ^ [_383137, _383139] : [_383137 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _383137), _383139) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4978 ^ _199745) ^ [_383311, _383313] : [-(_383311 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _383311), _383313) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _383313, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _383311, c_Groups_Oone__class_Oone(tc_Nat_Onat))), _383313)))], (4984 ^ _199745) ^ [_383580, _383582, _383584] : [class_Power_Opower(_383580), 4987 ^ _199745 : [(4988 ^ _199745) ^ [] : [_383582 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_383580), _383584), _383582) = c_Groups_Oone__class_Oone(_383580))], (4994 ^ _199745) ^ [] : [-(_383582 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_383580), _383584), _383582) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_383580), _383584), hAPP(hAPP(c_Power_Opower__class_Opower(_383580), _383584), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _383582, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (5000 ^ _199745) ^ [_384150, _384152, _384154] : [class_Rings_Odivision__ring(_384150), -(_384152 = c_Groups_Ozero__class_Ozero(_384150)), -(_384154 = c_Groups_Ozero__class_Ozero(_384150)), -(c_Groups_Ominus__class_Ominus(_384150, c_Rings_Oinverse__class_Oinverse(_384150, _384152), c_Rings_Oinverse__class_Oinverse(_384150, _384154)) = c_Groups_Ouminus__class_Ouminus(_384150, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_384150), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_384150), c_Rings_Oinverse__class_Oinverse(_384150, _384152)), c_Groups_Ominus__class_Ominus(_384150, _384152, _384154))), c_Rings_Oinverse__class_Oinverse(_384150, _384154))))], (5014 ^ _199745) ^ [_384642, _384644] : [class_Fields_Ofield(_384642), -(_384644 = c_Groups_Ozero__class_Ozero(_384642)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_384642), c_Rings_Oinverse__class_Oinverse(_384642, _384644)), _384644) = c_Groups_Oone__class_Oone(_384642))], (5024 ^ _199745) ^ [_384986, _384988, _384990] : [class_Fields_Ofield(_384986), -(_384988 = c_Groups_Ozero__class_Ozero(_384986)), -(_384990 = c_Groups_Ozero__class_Ozero(_384986)), -(c_Groups_Oplus__class_Oplus(_384986, c_Rings_Oinverse__class_Oinverse(_384986, _384988), c_Rings_Oinverse__class_Oinverse(_384986, _384990)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_384986), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_384986), c_Groups_Oplus__class_Oplus(_384986, _384988, _384990)), c_Rings_Oinverse__class_Oinverse(_384986, _384988))), c_Rings_Oinverse__class_Oinverse(_384986, _384990)))], (5038 ^ _199745) ^ [_385486, _385488, _385490] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _385486), _385488), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _385490), _385488)), -(_385488 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _385486, _385490))], (5048 ^ _199745) ^ [_385797] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _385797, _385797))], (5050 ^ _199745) ^ [_385934, _385936] : [_385934 = _385936, 5053 ^ _199745 : [(5054 ^ _199745) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _385934, _385936))], (5056 ^ _199745) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _385936, _385934))]]], (5058 ^ _199745) ^ [_386175, _386177] : [-(_386175 = _386177), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _386175, _386177), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _386177, _386175)], (5068 ^ _199745) ^ [_386509, _386511] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _386509, _386511), 5073 ^ _199745 : [(5074 ^ _199745) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _386509, _386511))], (5076 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _386511, _386509)]], -(_386509 = _386511)], (5080 ^ _199745) ^ [_386843, _386845] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _386843, _386845)), 5081 ^ _199745 : [(5088 ^ _199745) ^ [] : [_386843 = _386845], (5082 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _386843, _386845), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _386845, _386843))]]], (5092 ^ _199745) ^ [_387256, _387258] : [5099 ^ _199745 : [(5100 ^ _199745) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _387256, _387258))], (5102 ^ _199745) ^ [] : [_387256 = _387258]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _387256, _387258), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _387258, _387256))], (5104 ^ _199745) ^ [_387592, _387594] : [5111 ^ _199745 : [(5112 ^ _199745) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _387592, _387594))], (5114 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _387594, _387592)]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _387592, _387594), -(_387592 = _387594)], (5116 ^ _199745) ^ [_387978, _387980] : [-(_387978 = _387980), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _387978, _387980), 5123 ^ _199745 : [(5124 ^ _199745) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _387978, _387980))], (5126 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _387980, _387978)]]], (5128 ^ _199745) ^ [_388362, _388364] : [_388362 = _388364, -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _388362, _388364))], (5134 ^ _199745) ^ [_388574, _388576] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _388574, _388576), 5137 ^ _199745 : [(5138 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _388576, _388574), -(_388576 = _388574)], (5144 ^ _199745) ^ [] : [_388576 = _388574, -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _388576, _388574))]]], (5150 ^ _199745) ^ [_389039, _389041] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _389039, _389041), 5155 ^ _199745 : [(5156 ^ _199745) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _389039, _389041))], (5158 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _389041, _389039)]], -(_389039 = _389041)], (5162 ^ _199745) ^ [_389421, _389423] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _389421, _389423), -(_389421 = _389423), 5169 ^ _199745 : [(5170 ^ _199745) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _389421, _389423))], (5172 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _389423, _389421)]]], (5174 ^ _199745) ^ [_389819, _389821, _389823] : [_389819 = _389821, c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _389821, _389823), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _389819, _389823))], (5184 ^ _199745) ^ [_390146, _390148, _390150] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _390146, _390148), _390148 = _390150, -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _390146, _390150))], (5194 ^ _199745) ^ [_390459, _390461] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _390459, _390461), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _390461, _390459), -(_390459 = _390461)], (5204 ^ _199745) ^ [_390762, _390764] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _390762, _390764), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _390764, _390762), -(_390762 = _390764)], (5214 ^ _199745) ^ [_391079, _391081, _391083] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _391079, _391081), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _391081, _391083), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _391079, _391083))], (5224 ^ _199745) ^ [_391408, _391410, _391412] : [_391408 = _391410, 5235 ^ _199745 : [(5236 ^ _199745) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _391408, _391412))], (5238 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _391412, _391408)]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _391410, _391412), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _391412, _391410))], (5240 ^ _199745) ^ [_391913, _391915, _391917] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _391913, _391915), 5251 ^ _199745 : [(5252 ^ _199745) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _391913, _391917))], (5254 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _391917, _391913)]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _391915, _391917), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _391917, _391915))], (5256 ^ _199745) ^ [_392406, _392408] : [_392406 = _392408, c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _392406, _392408), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _392408, _392406))], (5266 ^ _199745) ^ [_392713, _392715] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _392713, _392715), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _392715, _392713)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _392715, _392713), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _392713, _392715))], (5280 ^ _199745) ^ [_393118, _393120] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _393118, _393120)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _393118, _393120), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _393120, _393118))], (5290 ^ _199745) ^ [_393426, _393428] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _393426, _393428), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _393428, _393426)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _393428, _393426), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _393426, _393428))], (5304 ^ _199745) ^ [_393831, _393833] : [_393831 = _393833, c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _393831, _393833), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _393833, _393831))], (5314 ^ _199745) ^ [_394138, _394140] : [_394140 = _394138, c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _394138, _394140), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _394140, _394138))], (5324 ^ _199745) ^ [_394459, _394461, _394463] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _394459, _394461), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _394461, _394459)), _394461 = _394463, 5335 ^ _199745 : [(5336 ^ _199745) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _394459, _394463))], (5338 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _394463, _394459)]]], (5340 ^ _199745) ^ [_394966, _394968, _394970] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _394966, _394968), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _394968, _394966)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _394968, _394970), 5351 ^ _199745 : [(5352 ^ _199745) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _394966, _394970))], (5354 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _394970, _394966)]]], (5356 ^ _199745) ^ [_395461, _395463] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _395461, _395463), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _395463, _395461)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _395463, _395461), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _395461, _395463))], (5370 ^ _199745) ^ [_395880, _395882, _395884] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _395880, _395882), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _395882, _395880)), 5385 ^ _199745 : [(5386 ^ _199745) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _395880, _395884))], (5388 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _395884, _395880)]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _395882, _395884), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _395884, _395882))], (5390 ^ _199745) ^ [_396473, _396475] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _396473, _396475), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _396475, _396473)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _396475, _396473), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _396473, _396475))], (5404 ^ _199745) ^ [_396892, _396894, _396896] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _396892, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _396894, _396896)), c_Rings_Odvd__class_Odvd(tc_Int_Oint, _396892, _396896), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _396892, _396894))], (5414 ^ _199745) ^ [_397186] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _397186, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (5416 ^ _199745) ^ [_397265] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _397265))], (5418 ^ _199745) ^ [_397415, _397417, _397419, _397421, _397423] : [class_Groups_Oab__group__add(_397415), -(c_Groups_Ominus__class_Ominus(_397415, c_Groups_Oplus__class_Oplus(_397415, _397417, _397419), c_Groups_Oplus__class_Oplus(_397415, _397421, _397423)) = c_Groups_Oplus__class_Oplus(_397415, c_Groups_Ominus__class_Ominus(_397415, _397417, _397421), c_Groups_Ominus__class_Ominus(_397415, _397419, _397423)))], (5424 ^ _199745) ^ [_397675] : [class_Fields_Ofield__inverse__zero(_397675), -(c_Rings_Oinverse__class_Oinverse(_397675, c_Groups_Ozero__class_Ozero(_397675)) = c_Groups_Ozero__class_Ozero(_397675))], (5430 ^ _199745) ^ [_397905, _397907, _397909] : [class_Fields_Ofield__inverse__zero(_397905), -(c_Rings_Oinverse__class_Oinverse(_397905, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_397905), _397907), _397909)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_397905), c_Rings_Oinverse__class_Oinverse(_397905, _397907)), c_Rings_Oinverse__class_Oinverse(_397905, _397909)))], (5436 ^ _199745) ^ [_398169, _398171] : [class_Fields_Ofield__inverse__zero(_398169), 5439 ^ _199745 : [(5440 ^ _199745) ^ [] : [c_Rings_Oinverse__class_Oinverse(_398169, _398171) = c_Groups_Oone__class_Oone(_398169), -(_398171 = c_Groups_Oone__class_Oone(_398169))], (5446 ^ _199745) ^ [] : [_398171 = c_Groups_Oone__class_Oone(_398169), -(c_Rings_Oinverse__class_Oinverse(_398169, _398171) = c_Groups_Oone__class_Oone(_398169))]]], (5452 ^ _199745) ^ [_398662, _398664, _398666] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _398662), _398664), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _398666), _398664)), -(_398664 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _398662, _398666))], (5462 ^ _199745) ^ [_399016, _399018, _399020] : [-(_399016 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 5465 ^ _199745 : [(5466 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _399018), _399016), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _399020), _399016)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _399018, _399020))], (5472 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _399018, _399020), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _399018), _399016), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _399020), _399016)))]]], (5478 ^ _199745) ^ [_399551, _399553, _399555] : [-(_399551 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 5481 ^ _199745 : [(5482 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _399553), _399551), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _399555), _399551)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _399553, _399555))], (5488 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _399553, _399555), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _399553), _399551), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _399555), _399551)))]]], (5494 ^ _199745) ^ [_400086, _400088, _400090] : [class_Groups_Oab__group__add(_400086), -(c_Groups_Ominus__class_Ominus(_400086, c_Groups_Ouminus__class_Ouminus(_400086, _400088), c_Groups_Ouminus__class_Ouminus(_400086, _400090)) = c_Groups_Ouminus__class_Ouminus(_400086, c_Groups_Ominus__class_Ominus(_400086, _400088, _400090)))], (5500 ^ _199745) ^ [_400348, _400350, _400352] : [class_Fields_Ofield(_400348), 5503 ^ _199745 : [(5504 ^ _199745) ^ [] : [_400350 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_400348)), -(c_Polynomial_Opoly__gcd(_400348, _400352, _400350) = c_Polynomial_Osmult(_400348, c_Rings_Oinverse__class_Oinverse(_400348, hAPP(c_Polynomial_Ocoeff(_400348, _400352), c_Polynomial_Odegree(_400348, _400352))), _400352))], (5510 ^ _199745) ^ [] : [-(_400350 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_400348))), -(c_Polynomial_Opoly__gcd(_400348, _400352, _400350) = c_Polynomial_Opoly__gcd(_400348, _400350, c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(_400348), _400352, _400350)))]]], (5516 ^ _199745) ^ [_400926, _400928, _400930] : [class_Groups_Ozero(_400926), -(c_Polynomial_OpCons(_400926, _400928, _400930) = c_Polynomial_OAbs__poly(_400926, c_Nat_Onat_Onat__case(_400926, _400928, c_Polynomial_Ocoeff(_400926, _400930))))], (5522 ^ _199745) ^ [_401182, _401184, _401186] : [class_Groups_Omonoid__mult(_401182), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _401184), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_401182), hAPP(hAPP(c_Power_Opower__class_Opower(_401182), _401186), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _401184, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _401186) = hAPP(hAPP(c_Power_Opower__class_Opower(_401182), _401186), _401184))], (5532 ^ _199745) ^ [_401517] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _401517, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5534 ^ _199745) ^ [_401625, _401627] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _401625, _401627), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_401625), c_Nat_OSuc(_401627)))], (5540 ^ _199745) ^ [_401818] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _401818, c_Nat_OSuc(_401818)))], (5542 ^ _199745) ^ [_401899] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(_401899)))], (5544 ^ _199745) ^ [_402037, _402039, _402041, _402043] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_402037), 5547 ^ _199745 : [(5548 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_402037, c_Groups_Oplus__class_Oplus(_402037, _402039, _402041), c_Groups_Oplus__class_Oplus(_402037, _402043, _402041)), -(c_Orderings_Oord__class_Oless(_402037, _402039, _402043))], (5554 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_402037, _402039, _402043), -(c_Orderings_Oord__class_Oless(_402037, c_Groups_Oplus__class_Oplus(_402037, _402039, _402041), c_Groups_Oplus__class_Oplus(_402037, _402043, _402041)))]]], (5560 ^ _199745) ^ [_402585, _402587, _402589, _402591] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_402585), 5563 ^ _199745 : [(5564 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_402585, c_Groups_Oplus__class_Oplus(_402585, _402587, _402589), c_Groups_Oplus__class_Oplus(_402585, _402587, _402591)), -(c_Orderings_Oord__class_Oless(_402585, _402589, _402591))], (5570 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_402585, _402589, _402591), -(c_Orderings_Oord__class_Oless(_402585, c_Groups_Oplus__class_Oplus(_402585, _402587, _402589), c_Groups_Oplus__class_Oplus(_402585, _402587, _402591)))]]], (5576 ^ _199745) ^ [_403133, _403135, _403137, _403139] : [class_Groups_Oordered__cancel__ab__semigroup__add(_403133), c_Orderings_Oord__class_Oless(_403133, _403135, _403137), -(c_Orderings_Oord__class_Oless(_403133, c_Groups_Oplus__class_Oplus(_403133, _403135, _403139), c_Groups_Oplus__class_Oplus(_403133, _403137, _403139)))], (5586 ^ _199745) ^ [_403498, _403500, _403502, _403504] : [class_Groups_Oordered__cancel__ab__semigroup__add(_403498), c_Orderings_Oord__class_Oless(_403498, _403500, _403502), -(c_Orderings_Oord__class_Oless(_403498, c_Groups_Oplus__class_Oplus(_403498, _403504, _403500), c_Groups_Oplus__class_Oplus(_403498, _403504, _403502)))], (5596 ^ _199745) ^ [_403877, _403879, _403881, _403883, _403885] : [class_Groups_Oordered__cancel__ab__semigroup__add(_403877), c_Orderings_Oord__class_Oless(_403877, _403879, _403881), c_Orderings_Oord__class_Oless(_403877, _403883, _403885), -(c_Orderings_Oord__class_Oless(_403877, c_Groups_Oplus__class_Oplus(_403877, _403879, _403883), c_Groups_Oplus__class_Oplus(_403877, _403881, _403885)))], (5610 ^ _199745) ^ [_404355, _404357, _404359, _404361] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_404355), c_Orderings_Oord__class_Oless(_404355, c_Groups_Oplus__class_Oplus(_404355, _404357, _404359), c_Groups_Oplus__class_Oplus(_404355, _404361, _404359)), -(c_Orderings_Oord__class_Oless(_404355, _404357, _404361))], (5620 ^ _199745) ^ [_404720, _404722, _404724, _404726] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_404720), c_Orderings_Oord__class_Oless(_404720, c_Groups_Oplus__class_Oplus(_404720, _404722, _404724), c_Groups_Oplus__class_Oplus(_404720, _404722, _404726)), -(c_Orderings_Oord__class_Oless(_404720, _404724, _404726))], (5630 ^ _199745) ^ [_405099, _405101, _405103, _405105, _405107] : [class_Groups_Oordered__ab__group__add(_405099), c_Groups_Ominus__class_Ominus(_405099, _405101, _405103) = c_Groups_Ominus__class_Ominus(_405099, _405105, _405107), 5637 ^ _199745 : [(5638 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_405099, _405101, _405103), -(c_Orderings_Oord__class_Oless(_405099, _405105, _405107))], (5644 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_405099, _405105, _405107), -(c_Orderings_Oord__class_Oless(_405099, _405101, _405103))]]], (5650 ^ _199745) ^ [_405742, _405744, _405746] : [class_Groups_Oordered__ab__group__add(_405742), 5653 ^ _199745 : [(5654 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_405742, _405744, c_Groups_Ouminus__class_Ouminus(_405742, _405746)), -(c_Orderings_Oord__class_Oless(_405742, _405746, c_Groups_Ouminus__class_Ouminus(_405742, _405744)))], (5660 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_405742, _405746, c_Groups_Ouminus__class_Ouminus(_405742, _405744)), -(c_Orderings_Oord__class_Oless(_405742, _405744, c_Groups_Ouminus__class_Ouminus(_405742, _405746)))]]], (5666 ^ _199745) ^ [_406254, _406256, _406258] : [class_Groups_Oordered__ab__group__add(_406254), 5669 ^ _199745 : [(5670 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_406254, c_Groups_Ouminus__class_Ouminus(_406254, _406256), _406258), -(c_Orderings_Oord__class_Oless(_406254, c_Groups_Ouminus__class_Ouminus(_406254, _406258), _406256))], (5676 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_406254, c_Groups_Ouminus__class_Ouminus(_406254, _406258), _406256), -(c_Orderings_Oord__class_Oless(_406254, c_Groups_Ouminus__class_Ouminus(_406254, _406256), _406258))]]], (5682 ^ _199745) ^ [_406766, _406768, _406770] : [class_Groups_Oordered__ab__group__add(_406766), 5685 ^ _199745 : [(5686 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_406766, c_Groups_Ouminus__class_Ouminus(_406766, _406768), c_Groups_Ouminus__class_Ouminus(_406766, _406770)), -(c_Orderings_Oord__class_Oless(_406766, _406770, _406768))], (5692 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_406766, _406770, _406768), -(c_Orderings_Oord__class_Oless(_406766, c_Groups_Ouminus__class_Ouminus(_406766, _406768), c_Groups_Ouminus__class_Ouminus(_406766, _406770)))]]], (5698 ^ _199745) ^ [_407292, _407294, _407296, _407298] : [class_Fields_Ofield(_407292), -(c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(_407292), c_Polynomial_Osmult(_407292, _407294, _407296), _407298) = c_Polynomial_Osmult(_407292, _407294, c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(_407292), _407296, _407298)))], (5704 ^ _199745) ^ [_407522] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _407522, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5706 ^ _199745) ^ [_407645] : [-(_407645 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _407645))], (5712 ^ _199745) ^ [_407806] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _407806), _407806 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5718 ^ _199745) ^ [_407985] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _407985, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5720 ^ _199745) ^ [_408093, _408095] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _408093, _408095), _408095 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5726 ^ _199745) ^ [_408292] : [-(_408292 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _408292))], (5732 ^ _199745) ^ [_408530, _408532] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _408530, _408532)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _408532, c_Nat_OSuc(_408530)))], (5738 ^ _199745) ^ [_408703, _408705] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _408705, c_Nat_OSuc(_408703)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _408703, _408705)], (5754 ^ _199745) ^ [_409213, _409215] : [5755 ^ _199745 : [(5756 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _409213, _409215)], (5758 ^ _199745) ^ [] : [_409213 = _409215]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _409213, c_Nat_OSuc(_409215)))], (5744 ^ _199745) ^ [_408953, _408955] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _408953, c_Nat_OSuc(_408955)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _408953, _408955)), -(_408953 = _408955)], (5762 ^ _199745) ^ [_409536, _409538] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_409536), c_Nat_OSuc(_409538)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _409536, _409538))], (5768 ^ _199745) ^ [_409710, _409712] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _409710, _409712), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_409710), c_Nat_OSuc(_409712)))], (5774 ^ _199745) ^ [_409934, _409936] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _409934, _409936)), 5777 ^ _199745 : [(5778 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _409934, c_Nat_OSuc(_409936)), -(_409934 = _409936)], (5784 ^ _199745) ^ [] : [_409934 = _409936, -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _409934, c_Nat_OSuc(_409936)))]]], (5790 ^ _199745) ^ [_410408, _410410] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _410408, _410410)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _410408, c_Nat_OSuc(_410410)), -(_410410 = _410408)], (5800 ^ _199745) ^ [_410718, _410720] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _410718, _410720), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _410718, c_Nat_OSuc(_410720)))], (5806 ^ _199745) ^ [_410936, _410938] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _410936, _410938), -(c_Nat_OSuc(_410936) = _410938), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_410936), _410938))], (5816 ^ _199745) ^ [_411264, _411266, _411268] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _411264, _411266), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _411266, _411268), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_411264), _411268))], (5826 ^ _199745) ^ [_411583, _411585] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _411583, c_Nat_OSuc(_411585)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _411583, _411585)), -(_411583 = _411585)], (5836 ^ _199745) ^ [_411893, _411895] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_411893), _411895), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _411893, _411895))], (5842 ^ _199745) ^ [_412111, _412113] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_412111), c_Nat_OSuc(_412113)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _412111, _412113))], (5848 ^ _199745) ^ [_412317, _412319] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _412317, _412319), _412317)], (5850 ^ _199745) ^ [_412415, _412417] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _412415, _412417), _412417)], (5852 ^ _199745) ^ [_412572, _412574, _412576] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _412572, _412574), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _412572, _412576)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _412574, _412576))], (5858 ^ _199745) ^ [_412760, _412762, _412764] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _412762, _412764), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _412760, _412762), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _412760, _412764)))], (5864 ^ _199745) ^ [_413012, _413014, _413016] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _413012, _413014), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _413012, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _413014, _413016)))], (5870 ^ _199745) ^ [_413254, _413256, _413258] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _413254, _413256), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _413254, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _413258, _413256)))], (5876 ^ _199745) ^ [_413496, _413498, _413500] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _413496, _413498), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _413496, _413500), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _413498, _413500)))], (5882 ^ _199745) ^ [_413760, _413762, _413764, _413766] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _413760, _413762), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _413764, _413766), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _413760, _413764), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _413762, _413766)))], (5892 ^ _199745) ^ [_414129, _414131, _414133, _414135] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _414129, _414131), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _414133, _414131) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _414129, _414135), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _414133, _414135))], (5902 ^ _199745) ^ [_414482, _414484, _414486] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _414482, _414484), _414486), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _414482, _414486))], (5908 ^ _199745) ^ [_414724, _414726, _414728] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _414724, _414726), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _414724, _414728), _414726))], (5914 ^ _199745) ^ [_414966, _414968, _414970] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _414966, _414968), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _414966, _414970), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _414970, _414968), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _414970, _414966)))], (5924 ^ _199745) ^ [_415311, _415313, _415315] : [class_Fields_Ofield(_415311), -(c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(_415311), c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_415311), _415313), _415315) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_415311), c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(_415311), _415313, _415315)))], (5930 ^ _199745) ^ [_415583, _415585, _415587] : [class_Fields_Ofield(_415583), -(c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(_415583), _415585, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_415583), _415587)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(_415583), _415585, _415587))], (5936 ^ _199745) ^ [_415845, _415847, _415849] : [5937 ^ _199745 : [(5938 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _415845, _415847))], (5940 ^ _199745) ^ [] : [hBOOL(hAPP(hAPP(_415849, _415847), _415845))]], 5943 ^ _199745 : [(5944 ^ _199745) ^ [] : [-(_415845 = _415847)], (5946 ^ _199745) ^ [] : [hBOOL(hAPP(hAPP(_415849, _415847), _415845))]], 5949 ^ _199745 : [(5950 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _415847, _415845))], (5952 ^ _199745) ^ [] : [hBOOL(hAPP(hAPP(_415849, _415847), _415845))]], -(hBOOL(hAPP(hAPP(_415849, _415847), _415845)))], (5956 ^ _199745) ^ [_416522, _416524] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _416522, _416524), _416522 = _416524], (5962 ^ _199745) ^ [_416735, _416737] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _416735, _416737), _416737 = _416735], (5968 ^ _199745) ^ [_416918] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _416918, _416918)], (5970 ^ _199745) ^ [_417026, _417028] : [-(_417026 = _417028), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _417026, _417028)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _417028, _417026))], (5990 ^ _199745) ^ [_417623, _417625] : [5991 ^ _199745 : [(5992 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _417623, _417625)], (5994 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _417625, _417623)]], _417623 = _417625], (5980 ^ _199745) ^ [_417364, _417366] : [-(_417364 = _417366), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _417364, _417366)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _417366, _417364))], (5998 ^ _199745) ^ [_417884] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _417884, _417884)], (6000 ^ _199745) ^ [_418006, _418008, _418010] : [class_Fields_Ofield(_418006), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_418006, _418008), c_Polynomial_Odegree(_418006, _418010)), -(c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(_418006), _418008, _418010) = _418008)], (6010 ^ _199745) ^ [_418353, _418355, _418357] : [class_Rings_Olinordered__idom(_418353), -(_418355 = _418357), -(c_Orderings_Oord__class_Oless(_418353, _418355, _418357)), -(c_Orderings_Oord__class_Oless(_418353, _418357, _418355))], (6024 ^ _199745) ^ [_418777, _418779, _418781] : [class_Fields_Ofield(_418777), -(_418779 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_418777))), -(c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(_418777), _418781, _418779) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_418777))), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_418777, c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(_418777), _418781, _418779)), c_Polynomial_Odegree(_418777, _418779)))], (6038 ^ _199745) ^ [_419263, _419265, _419267, _419269] : [class_Rings_Olinordered__semidom(_419263), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _419265, _419267), c_Orderings_Oord__class_Oless(_419263, c_Groups_Oone__class_Oone(_419263), _419269), -(c_Orderings_Oord__class_Oless(_419263, hAPP(hAPP(c_Power_Opower__class_Opower(_419263), _419269), _419265), hAPP(hAPP(c_Power_Opower__class_Opower(_419263), _419269), _419267)))], (6052 ^ _199745) ^ [_419747, _419749, _419751, _419753] : [class_Rings_Olinordered__semidom(_419747), c_Orderings_Oord__class_Oless(_419747, c_Groups_Oone__class_Oone(_419747), _419749), c_Orderings_Oord__class_Oless(_419747, hAPP(hAPP(c_Power_Opower__class_Opower(_419747), _419749), _419751), hAPP(hAPP(c_Power_Opower__class_Opower(_419747), _419749), _419753)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _419751, _419753))], (6066 ^ _199745) ^ [_420231, _420233, _420235, _420237] : [class_Rings_Olinordered__semidom(_420231), c_Orderings_Oord__class_Oless(_420231, c_Groups_Oone__class_Oone(_420231), _420233), 6073 ^ _199745 : [(6074 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_420231, hAPP(hAPP(c_Power_Opower__class_Opower(_420231), _420233), _420235), hAPP(hAPP(c_Power_Opower__class_Opower(_420231), _420233), _420237)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _420235, _420237))], (6080 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _420235, _420237), -(c_Orderings_Oord__class_Oless(_420231, hAPP(hAPP(c_Power_Opower__class_Opower(_420231), _420233), _420235), hAPP(hAPP(c_Power_Opower__class_Opower(_420231), _420233), _420237)))]]], (6086 ^ _199745) ^ [_420906, _420908, _420910, _420912] : [class_Rings_Olinordered__semidom(_420906), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _420908, _420910), c_Orderings_Oord__class_Oless(_420906, c_Groups_Ozero__class_Ozero(_420906), _420912), c_Orderings_Oord__class_Oless(_420906, _420912, c_Groups_Oone__class_Oone(_420906)), -(c_Orderings_Oord__class_Oless(_420906, hAPP(hAPP(c_Power_Opower__class_Opower(_420906), _420912), _420910), hAPP(hAPP(c_Power_Opower__class_Opower(_420906), _420912), _420908)))], (6104 ^ _199745) ^ [_421479, _421481, _421483] : [class_Rings_Olinordered__semidom(_421479), c_Orderings_Oord__class_Oless(_421479, c_Groups_Oone__class_Oone(_421479), _421481), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _421483), -(c_Orderings_Oord__class_Oless(_421479, c_Groups_Oone__class_Oone(_421479), hAPP(hAPP(c_Power_Opower__class_Opower(_421479), _421481), _421483)))], (6118 ^ _199745) ^ [_421909, _421911] : [class_Groups_Ozero(_421909), -(c_Polynomial_OAbs__poly(_421909, c_Polynomial_Ocoeff(_421909, _421911)) = _421911)], (6124 ^ _199745) ^ [_422157, _422159, _422161, _422163] : [class_Fields_Ofield(_422157), -(_422159 = c_Groups_Ozero__class_Ozero(_422157)), -(c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(_422157), _422161, c_Polynomial_Osmult(_422157, _422159, _422163)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(_422157), _422161, _422163))], (6134 ^ _199745) ^ [_422541, _422543, _422545, _422547] : [class_Rings_Olinordered__ring__strict(_422541), c_Orderings_Oord__class_Oless(_422541, _422543, _422545), c_Orderings_Oord__class_Oless(_422541, _422547, c_Groups_Ozero__class_Ozero(_422541)), -(c_Orderings_Oord__class_Oless(_422541, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_422541), _422547), _422545), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_422541), _422547), _422543)))], (6148 ^ _199745) ^ [_423025, _423027, _423029, _423031] : [class_Rings_Olinordered__ring__strict(_423025), c_Orderings_Oord__class_Oless(_423025, _423027, _423029), c_Orderings_Oord__class_Oless(_423025, _423031, c_Groups_Ozero__class_Ozero(_423025)), -(c_Orderings_Oord__class_Oless(_423025, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_423025), _423029), _423031), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_423025), _423027), _423031)))], (6162 ^ _199745) ^ [_423509, _423511, _423513, _423515] : [class_Rings_Olinordered__comm__semiring__strict(_423509), c_Orderings_Oord__class_Oless(_423509, _423511, _423513), c_Orderings_Oord__class_Oless(_423509, c_Groups_Ozero__class_Ozero(_423509), _423515), -(c_Orderings_Oord__class_Oless(_423509, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_423509), _423515), _423511), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_423509), _423515), _423513)))], (6176 ^ _199745) ^ [_423993, _423995, _423997, _423999] : [class_Rings_Olinordered__semiring__strict(_423993), c_Orderings_Oord__class_Oless(_423993, _423995, _423997), c_Orderings_Oord__class_Oless(_423993, c_Groups_Ozero__class_Ozero(_423993), _423999), -(c_Orderings_Oord__class_Oless(_423993, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_423993), _423999), _423995), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_423993), _423999), _423997)))], (6190 ^ _199745) ^ [_424477, _424479, _424481, _424483] : [class_Rings_Olinordered__semiring__strict(_424477), c_Orderings_Oord__class_Oless(_424477, _424479, _424481), c_Orderings_Oord__class_Oless(_424477, c_Groups_Ozero__class_Ozero(_424477), _424483), -(c_Orderings_Oord__class_Oless(_424477, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_424477), _424479), _424483), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_424477), _424481), _424483)))], (6204 ^ _199745) ^ [_424947, _424949, _424951] : [class_Rings_Olinordered__ring__strict(_424947), c_Orderings_Oord__class_Oless(_424947, _424949, c_Groups_Ozero__class_Ozero(_424947)), c_Orderings_Oord__class_Oless(_424947, _424951, c_Groups_Ozero__class_Ozero(_424947)), -(c_Orderings_Oord__class_Oless(_424947, c_Groups_Ozero__class_Ozero(_424947), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_424947), _424949), _424951)))], (6218 ^ _199745) ^ [_425395, _425397, _425399] : [class_Rings_Olinordered__semiring__strict(_425395), c_Orderings_Oord__class_Oless(_425395, _425397, c_Groups_Ozero__class_Ozero(_425395)), c_Orderings_Oord__class_Oless(_425395, c_Groups_Ozero__class_Ozero(_425395), _425399), -(c_Orderings_Oord__class_Oless(_425395, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_425395), _425397), _425399), c_Groups_Ozero__class_Ozero(_425395)))], (6232 ^ _199745) ^ [_425857, _425859, _425861, _425863] : [class_Rings_Olinordered__ring__strict(_425857), c_Orderings_Oord__class_Oless(_425857, _425859, c_Groups_Ozero__class_Ozero(_425857)), 6239 ^ _199745 : [(6240 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_425857, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_425857), _425859), _425861), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_425857), _425859), _425863)), -(c_Orderings_Oord__class_Oless(_425857, _425863, _425861))], (6246 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_425857, _425863, _425861), -(c_Orderings_Oord__class_Oless(_425857, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_425857), _425859), _425861), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_425857), _425859), _425863)))]]], (6252 ^ _199745) ^ [_426518, _426520, _426522] : [class_Rings_Olinordered__semiring__strict(_426518), c_Orderings_Oord__class_Oless(_426518, c_Groups_Ozero__class_Ozero(_426518), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_426518), _426520), _426522)), c_Orderings_Oord__class_Oless(_426518, c_Groups_Ozero__class_Ozero(_426518), _426522), -(c_Orderings_Oord__class_Oless(_426518, c_Groups_Ozero__class_Ozero(_426518), _426520))], (6266 ^ _199745) ^ [_426966, _426968, _426970] : [class_Rings_Olinordered__semiring__strict(_426966), c_Orderings_Oord__class_Oless(_426966, c_Groups_Ozero__class_Ozero(_426966), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_426966), _426968), _426970)), c_Orderings_Oord__class_Oless(_426966, c_Groups_Ozero__class_Ozero(_426966), _426968), -(c_Orderings_Oord__class_Oless(_426966, c_Groups_Ozero__class_Ozero(_426966), _426970))], (6280 ^ _199745) ^ [_427414, _427416, _427418] : [class_Rings_Olinordered__semiring__strict(_427414), c_Orderings_Oord__class_Oless(_427414, c_Groups_Ozero__class_Ozero(_427414), _427416), c_Orderings_Oord__class_Oless(_427414, _427418, c_Groups_Ozero__class_Ozero(_427414)), -(c_Orderings_Oord__class_Oless(_427414, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_427414), _427418), _427416), c_Groups_Ozero__class_Ozero(_427414)))], (6294 ^ _199745) ^ [_427862, _427864, _427866] : [class_Rings_Olinordered__semiring__strict(_427862), c_Orderings_Oord__class_Oless(_427862, c_Groups_Ozero__class_Ozero(_427862), _427864), c_Orderings_Oord__class_Oless(_427862, _427866, c_Groups_Ozero__class_Ozero(_427862)), -(c_Orderings_Oord__class_Oless(_427862, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_427862), _427864), _427866), c_Groups_Ozero__class_Ozero(_427862)))], (6308 ^ _199745) ^ [_428310, _428312, _428314] : [class_Rings_Olinordered__semiring__strict(_428310), c_Orderings_Oord__class_Oless(_428310, c_Groups_Ozero__class_Ozero(_428310), _428312), c_Orderings_Oord__class_Oless(_428310, c_Groups_Ozero__class_Ozero(_428310), _428314), -(c_Orderings_Oord__class_Oless(_428310, c_Groups_Ozero__class_Ozero(_428310), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_428310), _428312), _428314)))], (6322 ^ _199745) ^ [_428772, _428774, _428776, _428778] : [class_Rings_Olinordered__ring__strict(_428772), c_Orderings_Oord__class_Oless(_428772, c_Groups_Ozero__class_Ozero(_428772), _428774), 6329 ^ _199745 : [(6330 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_428772, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_428772), _428774), _428776), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_428772), _428774), _428778)), -(c_Orderings_Oord__class_Oless(_428772, _428776, _428778))], (6336 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_428772, _428776, _428778), -(c_Orderings_Oord__class_Oless(_428772, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_428772), _428774), _428776), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_428772), _428774), _428778)))]]], (6342 ^ _199745) ^ [_429447, _429449, _429451, _429453] : [class_Rings_Olinordered__ring__strict(_429447), 6345 ^ _199745 : [(6346 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_429447, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_429447), _429449), _429451), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_429447), _429449), _429453)), 6351 ^ _199745 : [(6352 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_429447, c_Groups_Ozero__class_Ozero(_429447), _429449))], (6354 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_429447, _429451, _429453))]], 6355 ^ _199745 : [(6356 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_429447, _429449, c_Groups_Ozero__class_Ozero(_429447)))], (6358 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_429447, _429453, _429451))]]], (6360 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_429447, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_429447), _429449), _429451), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_429447), _429449), _429453))), 6361 ^ _199745 : [(6362 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_429447, c_Groups_Ozero__class_Ozero(_429447), _429449), c_Orderings_Oord__class_Oless(_429447, _429451, _429453)], (6368 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_429447, _429449, c_Groups_Ozero__class_Ozero(_429447)), c_Orderings_Oord__class_Oless(_429447, _429453, _429451)]]]]], (6376 ^ _199745) ^ [_430550, _430552, _430554, _430556] : [class_Rings_Olinordered__ring__strict(_430550), 6379 ^ _199745 : [(6380 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_430550, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_430550), _430552), _430554), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_430550), _430556), _430554)), 6385 ^ _199745 : [(6386 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_430550, c_Groups_Ozero__class_Ozero(_430550), _430554))], (6388 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_430550, _430552, _430556))]], 6389 ^ _199745 : [(6390 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_430550, _430554, c_Groups_Ozero__class_Ozero(_430550)))], (6392 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_430550, _430556, _430552))]]], (6394 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_430550, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_430550), _430552), _430554), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_430550), _430556), _430554))), 6395 ^ _199745 : [(6396 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_430550, c_Groups_Ozero__class_Ozero(_430550), _430554), c_Orderings_Oord__class_Oless(_430550, _430552, _430556)], (6402 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_430550, _430554, c_Groups_Ozero__class_Ozero(_430550)), c_Orderings_Oord__class_Oless(_430550, _430556, _430552)]]]]], (6410 ^ _199745) ^ [_431625, _431627] : [class_Rings_Olinordered__ring(_431625), c_Orderings_Oord__class_Oless(_431625, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_431625), _431627), _431627), c_Groups_Ozero__class_Ozero(_431625))], (6416 ^ _199745) ^ [_431870, _431872, _431874] : [class_Groups_Oordered__comm__monoid__add(_431870), c_Orderings_Oord__class_Oless(_431870, _431872, c_Groups_Ozero__class_Ozero(_431870)), c_Orderings_Oord__class_Oless(_431870, _431874, c_Groups_Ozero__class_Ozero(_431870)), -(c_Orderings_Oord__class_Oless(_431870, c_Groups_Oplus__class_Oplus(_431870, _431872, _431874), c_Groups_Ozero__class_Ozero(_431870)))], (6430 ^ _199745) ^ [_432324, _432326, _432328, _432330] : [class_Rings_Olinordered__semidom(_432324), c_Orderings_Oord__class_Oless(_432324, c_Groups_Ozero__class_Ozero(_432324), _432326), c_Orderings_Oord__class_Oless(_432324, _432328, _432330), -(c_Orderings_Oord__class_Oless(_432324, _432328, c_Groups_Oplus__class_Oplus(_432324, _432326, _432330)))], (6444 ^ _199745) ^ [_432770, _432772, _432774] : [class_Groups_Oordered__comm__monoid__add(_432770), c_Orderings_Oord__class_Oless(_432770, c_Groups_Ozero__class_Ozero(_432770), _432772), c_Orderings_Oord__class_Oless(_432770, c_Groups_Ozero__class_Ozero(_432770), _432774), -(c_Orderings_Oord__class_Oless(_432770, c_Groups_Ozero__class_Ozero(_432770), c_Groups_Oplus__class_Oplus(_432770, _432772, _432774)))], (6458 ^ _199745) ^ [_433196, _433198] : [class_Groups_Olinordered__ab__group__add(_433196), 6461 ^ _199745 : [(6462 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_433196, c_Groups_Oplus__class_Oplus(_433196, _433198, _433198), c_Groups_Ozero__class_Ozero(_433196)), -(c_Orderings_Oord__class_Oless(_433196, _433198, c_Groups_Ozero__class_Ozero(_433196)))], (6468 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_433196, _433198, c_Groups_Ozero__class_Ozero(_433196)), -(c_Orderings_Oord__class_Oless(_433196, c_Groups_Oplus__class_Oplus(_433196, _433198, _433198), c_Groups_Ozero__class_Ozero(_433196)))]]], (6474 ^ _199745) ^ [_433684, _433686] : [class_Groups_Olinordered__ab__group__add(_433684), 6477 ^ _199745 : [(6478 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_433684, c_Groups_Ozero__class_Ozero(_433684), c_Groups_Oplus__class_Oplus(_433684, _433686, _433686)), -(c_Orderings_Oord__class_Oless(_433684, c_Groups_Ozero__class_Ozero(_433684), _433686))], (6484 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_433684, c_Groups_Ozero__class_Ozero(_433684), _433686), -(c_Orderings_Oord__class_Oless(_433684, c_Groups_Ozero__class_Ozero(_433684), c_Groups_Oplus__class_Oplus(_433684, _433686, _433686)))]]], (6490 ^ _199745) ^ [_434172, _434174] : [class_Rings_Olinordered__idom(_434172), 6493 ^ _199745 : [(6494 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_434172, c_Groups_Oplus__class_Oplus(_434172, _434174, _434174), c_Groups_Ozero__class_Ozero(_434172)), -(c_Orderings_Oord__class_Oless(_434172, _434174, c_Groups_Ozero__class_Ozero(_434172)))], (6500 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_434172, _434174, c_Groups_Ozero__class_Ozero(_434172)), -(c_Orderings_Oord__class_Oless(_434172, c_Groups_Oplus__class_Oplus(_434172, _434174, _434174), c_Groups_Ozero__class_Ozero(_434172)))]]], (6506 ^ _199745) ^ [_434674, _434676, _434678] : [class_Groups_Oordered__ab__group__add(_434674), 6509 ^ _199745 : [(6510 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_434674, _434676, _434678), -(c_Orderings_Oord__class_Oless(_434674, c_Groups_Ominus__class_Ominus(_434674, _434676, _434678), c_Groups_Ozero__class_Ozero(_434674)))], (6516 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_434674, c_Groups_Ominus__class_Ominus(_434674, _434676, _434678), c_Groups_Ozero__class_Ozero(_434674)), -(c_Orderings_Oord__class_Oless(_434674, _434676, _434678))]]], (6522 ^ _199745) ^ [_435158] : [class_Rings_Olinordered__semidom(_435158), c_Orderings_Oord__class_Oless(_435158, c_Groups_Oone__class_Oone(_435158), c_Groups_Ozero__class_Ozero(_435158))], (6528 ^ _199745) ^ [_435357] : [class_Rings_Olinordered__semidom(_435357), -(c_Orderings_Oord__class_Oless(_435357, c_Groups_Ozero__class_Ozero(_435357), c_Groups_Oone__class_Oone(_435357)))], (6534 ^ _199745) ^ [_435569, _435571] : [class_Groups_Oordered__ab__group__add(_435569), 6537 ^ _199745 : [(6538 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_435569, c_Groups_Ozero__class_Ozero(_435569), c_Groups_Ouminus__class_Ouminus(_435569, _435571)), -(c_Orderings_Oord__class_Oless(_435569, _435571, c_Groups_Ozero__class_Ozero(_435569)))], (6544 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_435569, _435571, c_Groups_Ozero__class_Ozero(_435569)), -(c_Orderings_Oord__class_Oless(_435569, c_Groups_Ozero__class_Ozero(_435569), c_Groups_Ouminus__class_Ouminus(_435569, _435571)))]]], (6550 ^ _199745) ^ [_436054, _436056] : [class_Rings_Olinordered__idom(_436054), 6553 ^ _199745 : [(6554 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_436054, _436056, c_Groups_Ouminus__class_Ouminus(_436054, _436056)), -(c_Orderings_Oord__class_Oless(_436054, _436056, c_Groups_Ozero__class_Ozero(_436054)))], (6560 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_436054, _436056, c_Groups_Ozero__class_Ozero(_436054)), -(c_Orderings_Oord__class_Oless(_436054, _436056, c_Groups_Ouminus__class_Ouminus(_436054, _436056)))]]], (6566 ^ _199745) ^ [_436533, _436535] : [class_Groups_Oordered__ab__group__add(_436533), 6569 ^ _199745 : [(6570 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_436533, c_Groups_Ouminus__class_Ouminus(_436533, _436535), c_Groups_Ozero__class_Ozero(_436533)), -(c_Orderings_Oord__class_Oless(_436533, c_Groups_Ozero__class_Ozero(_436533), _436535))], (6576 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_436533, c_Groups_Ozero__class_Ozero(_436533), _436535), -(c_Orderings_Oord__class_Oless(_436533, c_Groups_Ouminus__class_Ouminus(_436533, _436535), c_Groups_Ozero__class_Ozero(_436533)))]]], (6582 ^ _199745) ^ [_437018, _437020] : [class_Groups_Olinordered__ab__group__add(_437018), 6585 ^ _199745 : [(6586 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_437018, c_Groups_Ouminus__class_Ouminus(_437018, _437020), _437020), -(c_Orderings_Oord__class_Oless(_437018, c_Groups_Ozero__class_Ozero(_437018), _437020))], (6592 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_437018, c_Groups_Ozero__class_Ozero(_437018), _437020), -(c_Orderings_Oord__class_Oless(_437018, c_Groups_Ouminus__class_Ouminus(_437018, _437020), _437020))]]], (6598 ^ _199745) ^ [_437511, _437513, _437515] : [class_Rings_Olinordered__semidom(_437511), c_Orderings_Oord__class_Oless(_437511, c_Groups_Oone__class_Oone(_437511), _437513), c_Orderings_Oord__class_Oless(_437511, c_Groups_Oone__class_Oone(_437511), _437515), -(c_Orderings_Oord__class_Oless(_437511, c_Groups_Oone__class_Oone(_437511), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_437511), _437513), _437515)))], (6612 ^ _199745) ^ [_437959, _437961, _437963] : [class_Rings_Olinordered__semidom(_437959), c_Orderings_Oord__class_Oless(_437959, c_Groups_Ozero__class_Ozero(_437959), _437961), -(c_Orderings_Oord__class_Oless(_437959, c_Groups_Ozero__class_Ozero(_437959), hAPP(hAPP(c_Power_Opower__class_Opower(_437959), _437961), _437963)))], (6622 ^ _199745) ^ [_438294, _438296] : [class_Rings_Olinordered__semidom(_438294), -(c_Orderings_Oord__class_Oless(_438294, _438296, c_Groups_Oplus__class_Oplus(_438294, _438296, c_Groups_Oone__class_Oone(_438294))))], (6628 ^ _199745) ^ [_438544, _438546, _438548, _438550] : [class_Rings_Olinordered__semidom(_438544), c_Orderings_Oord__class_Oless(_438544, c_Groups_Oone__class_Oone(_438544), _438546), 6635 ^ _199745 : [(6636 ^ _199745) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_438544), _438546), _438548) = hAPP(hAPP(c_Power_Opower__class_Opower(_438544), _438546), _438550), -(_438548 = _438550)], (6642 ^ _199745) ^ [] : [_438548 = _438550, -(hAPP(hAPP(c_Power_Opower__class_Opower(_438544), _438546), _438548) = hAPP(hAPP(c_Power_Opower__class_Opower(_438544), _438546), _438550))]]], (6648 ^ _199745) ^ [_439199, _439201, _439203] : [class_Fields_Olinordered__field(_439199), c_Orderings_Oord__class_Oless(_439199, c_Rings_Oinverse__class_Oinverse(_439199, _439201), c_Rings_Oinverse__class_Oinverse(_439199, _439203)), c_Orderings_Oord__class_Oless(_439199, _439203, c_Groups_Ozero__class_Ozero(_439199)), -(c_Orderings_Oord__class_Oless(_439199, _439203, _439201))], (6662 ^ _199745) ^ [_439635, _439637, _439639] : [class_Fields_Olinordered__field(_439635), c_Orderings_Oord__class_Oless(_439635, c_Rings_Oinverse__class_Oinverse(_439635, _439637), c_Rings_Oinverse__class_Oinverse(_439635, _439639)), c_Orderings_Oord__class_Oless(_439635, c_Groups_Ozero__class_Ozero(_439635), _439637), -(c_Orderings_Oord__class_Oless(_439635, _439639, _439637))], (6676 ^ _199745) ^ [_440057, _440059] : [class_Fields_Olinordered__field(_440057), c_Orderings_Oord__class_Oless(_440057, c_Rings_Oinverse__class_Oinverse(_440057, _440059), c_Groups_Ozero__class_Ozero(_440057)), -(_440059 = c_Groups_Ozero__class_Ozero(_440057)), -(c_Orderings_Oord__class_Oless(_440057, _440059, c_Groups_Ozero__class_Ozero(_440057)))], (6690 ^ _199745) ^ [_440482, _440484, _440486] : [class_Fields_Olinordered__field(_440482), c_Orderings_Oord__class_Oless(_440482, _440484, _440486), c_Orderings_Oord__class_Oless(_440482, _440486, c_Groups_Ozero__class_Ozero(_440482)), -(c_Orderings_Oord__class_Oless(_440482, c_Rings_Oinverse__class_Oinverse(_440482, _440486), c_Rings_Oinverse__class_Oinverse(_440482, _440484)))], (6704 ^ _199745) ^ [_440918, _440920, _440922] : [class_Fields_Olinordered__field(_440918), c_Orderings_Oord__class_Oless(_440918, _440920, _440922), c_Orderings_Oord__class_Oless(_440918, c_Groups_Ozero__class_Ozero(_440918), _440920), -(c_Orderings_Oord__class_Oless(_440918, c_Rings_Oinverse__class_Oinverse(_440918, _440922), c_Rings_Oinverse__class_Oinverse(_440918, _440920)))], (6718 ^ _199745) ^ [_441340, _441342] : [class_Fields_Olinordered__field(_441340), c_Orderings_Oord__class_Oless(_441340, _441342, c_Groups_Ozero__class_Ozero(_441340)), -(c_Orderings_Oord__class_Oless(_441340, c_Rings_Oinverse__class_Oinverse(_441340, _441342), c_Groups_Ozero__class_Ozero(_441340)))], (6728 ^ _199745) ^ [_441655, _441657] : [class_Fields_Olinordered__field(_441655), c_Orderings_Oord__class_Oless(_441655, c_Groups_Ozero__class_Ozero(_441655), c_Rings_Oinverse__class_Oinverse(_441655, _441657)), -(_441657 = c_Groups_Ozero__class_Ozero(_441655)), -(c_Orderings_Oord__class_Oless(_441655, c_Groups_Ozero__class_Ozero(_441655), _441657))], (6742 ^ _199745) ^ [_442066, _442068] : [class_Fields_Olinordered__field(_442066), c_Orderings_Oord__class_Oless(_442066, c_Groups_Ozero__class_Ozero(_442066), _442068), -(c_Orderings_Oord__class_Oless(_442066, c_Groups_Ozero__class_Ozero(_442066), c_Rings_Oinverse__class_Oinverse(_442066, _442068)))], (6752 ^ _199745) ^ [_442381, _442383] : [class_Fields_Olinordered__field__inverse__zero(_442381), 6755 ^ _199745 : [(6756 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_442381, c_Rings_Oinverse__class_Oinverse(_442381, _442383), c_Groups_Ozero__class_Ozero(_442381)), -(c_Orderings_Oord__class_Oless(_442381, _442383, c_Groups_Ozero__class_Ozero(_442381)))], (6762 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_442381, _442383, c_Groups_Ozero__class_Ozero(_442381)), -(c_Orderings_Oord__class_Oless(_442381, c_Rings_Oinverse__class_Oinverse(_442381, _442383), c_Groups_Ozero__class_Ozero(_442381)))]]], (6768 ^ _199745) ^ [_442866, _442868] : [class_Fields_Olinordered__field__inverse__zero(_442866), 6771 ^ _199745 : [(6772 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_442866, c_Groups_Ozero__class_Ozero(_442866), c_Rings_Oinverse__class_Oinverse(_442866, _442868)), -(c_Orderings_Oord__class_Oless(_442866, c_Groups_Ozero__class_Ozero(_442866), _442868))], (6778 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_442866, c_Groups_Ozero__class_Ozero(_442866), _442868), -(c_Orderings_Oord__class_Oless(_442866, c_Groups_Ozero__class_Ozero(_442866), c_Rings_Oinverse__class_Oinverse(_442866, _442868)))]]], (6784 ^ _199745) ^ [_443380, _443382] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _443380, c_Nat_OSuc(_443382)), -(_443380 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 6792 ^ _199745 : [(6793 ^ _199745) ^ [] : [-(_443380 = c_Nat_OSuc(6791 ^ [_443380, _443382]))], (6795 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 6791 ^ [_443380, _443382], _443382))]]], (6797 ^ _199745) ^ [_443792, _443794] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _443792, c_Nat_OSuc(_443794))), 6798 ^ _199745 : [(6799 ^ _199745) ^ [] : [_443792 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (6801 ^ _199745) ^ [_443961] : [_443792 = c_Nat_OSuc(_443961), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _443961, _443794)]]], (6809 ^ _199745) ^ [_444259] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _444259, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_444259 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6815 ^ _199745) ^ [_444417] : [_444417 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _444417, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (6821 ^ _199745) ^ [_444640] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _444640), -(_444640 = c_Nat_OSuc(6824 ^ [_444640]))], (6828 ^ _199745) ^ [_444855] : [6829 ^ _199745 : [(6830 ^ _199745) ^ [_444926] : [_444855 = c_Nat_OSuc(_444926)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _444855))], (6834 ^ _199745) ^ [_445089, _445091] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _445089), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _445089, _445091), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _445091, _445089)], (6844 ^ _199745) ^ [_445395, _445397] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _445395), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _445397, _445395), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _445397))], (6864 ^ _199745) ^ [_445995, _445997] : [6865 ^ _199745 : [(6866 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _445995)], (6868 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _445997)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _445995, _445997)))], (6854 ^ _199745) ^ [_445729, _445731] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _445729, _445731)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _445729)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _445731))], (6872 ^ _199745) ^ [_446324, _446326] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _446324, _446326), -(_446326 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _446324, 6875 ^ [_446324, _446326])))], (6879 ^ _199745) ^ [_446563, _446565] : [6880 ^ _199745 : [(6881 ^ _199745) ^ [_446640] : [_446565 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _446563, _446640))]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _446563, _446565))], (6885 ^ _199745) ^ [_446796, _446798] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _446796, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _446798, _446796))))], (6887 ^ _199745) ^ [_446897, _446899] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _446897, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _446897, _446899))))], (6889 ^ _199745) ^ [_447027, _447029, _447031] : [class_Fields_Ofield(_447027), -(_447029 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_447027))), -(c_Polynomial_Opoly__gcd(_447027, _447031, _447029) = c_Polynomial_Opoly__gcd(_447027, _447029, c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(_447027), _447031, _447029)))], (6899 ^ _199745) ^ [_447402, _447404] : [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), _447402), _447404)), 6902 ^ _199745 : [(6903 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _447402))], (6905 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _447404))]]], (6907 ^ _199745) ^ [_447657, _447659] : [-(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), _447657), _447659))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _447657), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _447659)], (6917 ^ _199745) ^ [_448019, _448021, _448023] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _448019), _448021), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _448019), _448023)), 6920 ^ _199745 : [(6921 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _448019))], (6923 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _448021, _448023))]]], (6925 ^ _199745) ^ [_448294, _448296, _448298] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _448294), _448296), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _448294), _448298))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _448294), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _448296, _448298)], (6935 ^ _199745) ^ [_448678, _448680, _448682] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _448678), _448680), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _448682), _448680)), 6938 ^ _199745 : [(6939 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _448680))], (6941 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _448678, _448682))]]], (6943 ^ _199745) ^ [_448953, _448955, _448957] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _448953), _448955), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _448957), _448955))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _448955), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _448953, _448957)], (6953 ^ _199745) ^ [_449308, _449310, _449312] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _449308, _449310), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _449312), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _449308), _449312), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _449310), _449312)))], (6963 ^ _199745) ^ [_449661, _449663, _449665] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _449661, _449663), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _449665), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _449665), _449661), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _449665), _449663)))], (6973 ^ _199745) ^ [_450014, _450016, _450018] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _450014), 6976 ^ _199745 : [(6977 ^ _199745) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _450014), _450016) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _450014), _450018), -(_450016 = _450018)], (6983 ^ _199745) ^ [] : [_450016 = _450018, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _450014), _450016) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _450014), _450018))]]], (6989 ^ _199745) ^ [_450542, _450544, _450546] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _450542), 6992 ^ _199745 : [(6993 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _450542), _450544), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _450542), _450546)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _450544, _450546))], (6999 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _450544, _450546), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _450542), _450544), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _450542), _450546)))]]], (7005 ^ _199745) ^ [_451091, _451093] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _451091, _451093)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _451093, _451091))], (7011 ^ _199745) ^ [_451265, _451267] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _451267, _451265), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _451265, _451267)))], (7017 ^ _199745) ^ [_451489, _451491] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _451489), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _451491), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _451491, _451489), _451491))], (7027 ^ _199745) ^ [_451845, _451847, _451849] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_451845)), _451847), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_451845)), _451849)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _451847, _451849))], (7033 ^ _199745) ^ [_452049, _452051, _452053] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _452051, _452053), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_452049)), _452051), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_452049)), _452053)))], (7039 ^ _199745) ^ [_452288, _452290] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _452288, _452290), c_Nat_OSuc(_452288)))], (7041 ^ _199745) ^ [_452404, _452406] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _452404, _452406)), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _452406, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _452404, _452406)) = _452404)], (7047 ^ _199745) ^ [_452678, _452680, _452682] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _452678, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _452680, _452682)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _452678, _452682), _452680))], (7053 ^ _199745) ^ [_452866, _452868, _452870] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _452866, _452870), _452868), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _452866, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _452868, _452870)))], (7059 ^ _199745) ^ [_453118, _453120, _453122] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _453118), c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _453118), _453120), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _453118), _453122)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _453120, _453122))], (7079 ^ _199745) ^ [_453754, _453756] : [7080 ^ _199745 : [(7081 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _453754)], (7083 ^ _199745) ^ [] : [_453756 = 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), _453754), _453756)))], (7069 ^ _199745) ^ [_453486, _453488] : [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), _453486), _453488)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _453486)), -(_453488 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7087 ^ _199745) ^ [_454084, _454086, _454088, _454090] : [class_Groups_Ocomm__monoid__add(_454084), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_454084, _454086), _454088), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_454084, _454090), _454088), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_454084, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_454084), _454086, _454090)), _454088))], (7101 ^ _199745) ^ [_454548, _454550, _454552] : [class_Groups_Ocomm__monoid__add(_454548), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_454548, _454550), c_Polynomial_Odegree(_454548, _454552)), -(c_Polynomial_Odegree(_454548, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_454548), _454550, _454552)) = c_Polynomial_Odegree(_454548, _454552))], (7111 ^ _199745) ^ [_454907, _454909, _454911] : [class_Groups_Ocomm__monoid__add(_454907), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_454907, _454909), c_Polynomial_Odegree(_454907, _454911)), -(c_Polynomial_Odegree(_454907, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_454907), _454911, _454909)) = c_Polynomial_Odegree(_454907, _454911))], (7121 ^ _199745) ^ [_455280, _455282, _455284, _455286] : [class_Groups_Oab__group__add(_455280), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_455280, _455282), _455284), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_455280, _455286), _455284), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_455280, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_455280), _455282, _455286)), _455284))], (7135 ^ _199745) ^ [_455744, _455746, _455748] : [class_Rings_Olinordered__ring__strict(_455744), 7138 ^ _199745 : [(7149 ^ _199745) ^ [] : [7150 ^ _199745 : [(7151 ^ _199745) ^ [] : [-(_455746 = c_Groups_Ozero__class_Ozero(_455744))], (7153 ^ _199745) ^ [] : [-(_455748 = c_Groups_Ozero__class_Ozero(_455744))]], -(c_Orderings_Oord__class_Oless(_455744, c_Groups_Ozero__class_Ozero(_455744), c_Groups_Oplus__class_Oplus(_455744, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_455744), _455746), _455746), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_455744), _455748), _455748))))], (7139 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_455744, c_Groups_Ozero__class_Ozero(_455744), c_Groups_Oplus__class_Oplus(_455744, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_455744), _455746), _455746), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_455744), _455748), _455748))), _455746 = c_Groups_Ozero__class_Ozero(_455744), _455748 = c_Groups_Ozero__class_Ozero(_455744)]]], (7157 ^ _199745) ^ [_456481, _456483, _456485] : [class_Rings_Olinordered__ring(_456481), c_Orderings_Oord__class_Oless(_456481, c_Groups_Oplus__class_Oplus(_456481, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_456481), _456483), _456483), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_456481), _456485), _456485)), c_Groups_Ozero__class_Ozero(_456481))], (7163 ^ _199745) ^ [_456728] : [class_Rings_Olinordered__semidom(_456728), -(c_Orderings_Oord__class_Oless(_456728, c_Groups_Ozero__class_Ozero(_456728), c_Groups_Oplus__class_Oplus(_456728, c_Groups_Oone__class_Oone(_456728), c_Groups_Oone__class_Oone(_456728))))], (7169 ^ _199745) ^ [_457008, _457010, _457012, _457014, _457016, _457018] : [class_Rings_Oordered__ring(_457008), 7172 ^ _199745 : [(7173 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_457008, c_Groups_Oplus__class_Oplus(_457008, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_457008), _457010), _457012), _457014), c_Groups_Oplus__class_Oplus(_457008, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_457008), _457016), _457012), _457018)), -(c_Orderings_Oord__class_Oless(_457008, _457014, c_Groups_Oplus__class_Oplus(_457008, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_457008), c_Groups_Ominus__class_Ominus(_457008, _457016, _457010)), _457012), _457018)))], (7179 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_457008, _457014, c_Groups_Oplus__class_Oplus(_457008, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_457008), c_Groups_Ominus__class_Ominus(_457008, _457016, _457010)), _457012), _457018)), -(c_Orderings_Oord__class_Oless(_457008, c_Groups_Oplus__class_Oplus(_457008, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_457008), _457010), _457012), _457014), c_Groups_Oplus__class_Oplus(_457008, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_457008), _457016), _457012), _457018)))]]], (7185 ^ _199745) ^ [_457712, _457714, _457716, _457718, _457720, _457722] : [class_Rings_Oordered__ring(_457712), 7188 ^ _199745 : [(7189 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_457712, c_Groups_Oplus__class_Oplus(_457712, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_457712), _457714), _457716), _457718), c_Groups_Oplus__class_Oplus(_457712, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_457712), _457720), _457716), _457722)), -(c_Orderings_Oord__class_Oless(_457712, c_Groups_Oplus__class_Oplus(_457712, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_457712), c_Groups_Ominus__class_Ominus(_457712, _457714, _457720)), _457716), _457718), _457722))], (7195 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_457712, c_Groups_Oplus__class_Oplus(_457712, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_457712), c_Groups_Ominus__class_Ominus(_457712, _457714, _457720)), _457716), _457718), _457722), -(c_Orderings_Oord__class_Oless(_457712, c_Groups_Oplus__class_Oplus(_457712, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_457712), _457714), _457716), _457718), c_Groups_Oplus__class_Oplus(_457712, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_457712), _457720), _457716), _457722)))]]], (7201 ^ _199745) ^ [_458374, _458376, _458378] : [class_Rings_Olinordered__semidom(_458374), c_Orderings_Oord__class_Oless(_458374, c_Groups_Oone__class_Oone(_458374), _458376), -(c_Orderings_Oord__class_Oless(_458374, hAPP(hAPP(c_Power_Opower__class_Opower(_458374), _458376), _458378), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_458374), _458376), hAPP(hAPP(c_Power_Opower__class_Opower(_458374), _458376), _458378))))], (7211 ^ _199745) ^ [_458751, _458753, _458755] : [class_Rings_Olinordered__semidom(_458751), c_Orderings_Oord__class_Oless(_458751, c_Groups_Oone__class_Oone(_458751), _458753), -(c_Orderings_Oord__class_Oless(_458751, c_Groups_Oone__class_Oone(_458751), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_458751), _458753), hAPP(hAPP(c_Power_Opower__class_Opower(_458751), _458753), _458755))))], (7221 ^ _199745) ^ [_459102, _459104] : [class_Fields_Olinordered__field__inverse__zero(_459102), 7224 ^ _199745 : [(7225 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_459102, c_Groups_Oone__class_Oone(_459102), c_Rings_Oinverse__class_Oinverse(_459102, _459104)), 7228 ^ _199745 : [(7229 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_459102, c_Groups_Ozero__class_Ozero(_459102), _459104))], (7231 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_459102, _459104, c_Groups_Oone__class_Oone(_459102)))]]], (7233 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_459102, c_Groups_Oone__class_Oone(_459102), c_Rings_Oinverse__class_Oinverse(_459102, _459104))), c_Orderings_Oord__class_Oless(_459102, c_Groups_Ozero__class_Ozero(_459102), _459104), c_Orderings_Oord__class_Oless(_459102, _459104, c_Groups_Oone__class_Oone(_459102))]]], (7243 ^ _199745) ^ [_459754, _459756] : [class_Fields_Olinordered__field(_459754), c_Orderings_Oord__class_Oless(_459754, c_Groups_Ozero__class_Ozero(_459754), _459756), c_Orderings_Oord__class_Oless(_459754, _459756, c_Groups_Oone__class_Oone(_459754)), -(c_Orderings_Oord__class_Oless(_459754, c_Groups_Oone__class_Oone(_459754), c_Rings_Oinverse__class_Oinverse(_459754, _459756)))], (7257 ^ _199745) ^ [_460178, _460180, _460182] : [class_Rings_Olinordered__semidom(_460178), c_Orderings_Oord__class_Oless(_460178, c_Groups_Oone__class_Oone(_460178), _460180), -(c_Orderings_Oord__class_Oless(_460178, c_Groups_Oone__class_Oone(_460178), hAPP(hAPP(c_Power_Opower__class_Opower(_460178), _460180), c_Nat_OSuc(_460182))))], (7267 ^ _199745) ^ [_460517, _460519] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _460517), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _460519), -(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), _460519), _460517)))], (7277 ^ _199745) ^ [_460834, _460836] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _460834), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _460836), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _460834, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _460834), _460836)))], (7287 ^ _199745) ^ [_461151, _461153] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _461151), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _461153), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _461151, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _461153), _461151)))], (7297 ^ _199745) ^ [_461468, _461470] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _461468), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _461468, c_Nat_OSuc(_461470)), _461468))], (7303 ^ _199745) ^ [_461680] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _461680), -(c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _461680, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _461680)], (7309 ^ _199745) ^ [_461912, _461914, _461916] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _461912), _461914), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _461912), _461916)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _461912), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _461914, _461916))], (7319 ^ _199745) ^ [_462265, _462267, _462269] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _462265), 7322 ^ _199745 : [(7323 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _462265), _462267), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _462265), _462269)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _462267, _462269))], (7329 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _462267, _462269), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _462265), _462267), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _462265), _462269)))]]], (7351 ^ _199745) ^ [_463359, _463361, _463363] : [-(hBOOL(hAPP(_463359, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _463361, _463363)))), 7354 ^ _199745 : [(7355 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _463361, _463363))], (7357 ^ _199745) ^ [] : [hBOOL(hAPP(_463359, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 7359 ^ _199745 : [(7360 ^ _199745) ^ [] : [-(_463361 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _463363, 7358 ^ [_463359, _463361, _463363]))], (7362 ^ _199745) ^ [] : [hBOOL(hAPP(_463359, 7358 ^ [_463359, _463361, _463363]))]]], (7335 ^ _199745) ^ [_462828, _462830, _462832] : [hBOOL(hAPP(_462828, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _462830, _462832))), 7338 ^ _199745 : [(7339 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _462830, _462832), -(hBOOL(hAPP(_462828, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (7345 ^ _199745) ^ [_463160] : [_462830 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _462832, _463160), -(hBOOL(hAPP(_462828, _463160)))]]], (7382 ^ _199745) ^ [_464520, _464522, _464524] : [-(hBOOL(hAPP(_464520, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _464522, _464524)))), 7385 ^ _199745 : [(7386 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _464522, _464524))], (7388 ^ _199745) ^ [] : [hBOOL(hAPP(_464520, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 7390 ^ _199745 : [(7391 ^ _199745) ^ [] : [-(_464522 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _464524, 7389 ^ [_464520, _464522, _464524]))], (7393 ^ _199745) ^ [] : [hBOOL(hAPP(_464520, 7389 ^ [_464520, _464522, _464524]))]]], (7366 ^ _199745) ^ [_463981, _463983, _463985] : [hBOOL(hAPP(_463981, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _463983, _463985))), 7369 ^ _199745 : [(7370 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _463983, _463985), -(hBOOL(hAPP(_463981, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (7376 ^ _199745) ^ [_464319] : [_463983 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _463985, _464319), -(hBOOL(hAPP(_463981, _464319)))]]], (7397 ^ _199745) ^ [_465121, _465123, _465125] : [class_Groups_Ozero(_465121), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_465121, _465123), _465125), -(hAPP(c_Polynomial_Ocoeff(_465121, _465123), _465125) = c_Groups_Ozero__class_Ozero(_465121))], (7407 ^ _199745) ^ [_465466, _465468, _465470] : [class_Rings_Olinordered__semidom(_465466), c_Orderings_Oord__class_Oless(_465466, c_Groups_Ozero__class_Ozero(_465466), _465468), c_Orderings_Oord__class_Oless(_465466, _465468, c_Groups_Oone__class_Oone(_465466)), -(c_Orderings_Oord__class_Oless(_465466, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_465466), _465468), hAPP(hAPP(c_Power_Opower__class_Opower(_465466), _465468), _465470)), hAPP(hAPP(c_Power_Opower__class_Opower(_465466), _465468), _465470)))], (7421 ^ _199745) ^ [_465942, _465944, _465946] : [class_Rings_Olinordered__semidom(_465942), c_Orderings_Oord__class_Oless(_465942, c_Groups_Ozero__class_Ozero(_465942), _465944), c_Orderings_Oord__class_Oless(_465942, _465944, c_Groups_Oone__class_Oone(_465942)), -(c_Orderings_Oord__class_Oless(_465942, hAPP(hAPP(c_Power_Opower__class_Opower(_465942), _465944), c_Nat_OSuc(_465946)), c_Groups_Oone__class_Oone(_465942)))], (7435 ^ _199745) ^ [_466394, _466396, _466398] : [class_Rings_Ocomm__semiring__1(_466394), 7440 ^ _199745 : [(7441 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _466396)], (7443 ^ _199745) ^ [] : [_466398 = c_Groups_Oone__class_Oone(_466394)]], -(c_Rings_Odvd__class_Odvd(_466394, _466398, hAPP(hAPP(c_Power_Opower__class_Opower(_466394), _466398), _466396)))], (7447 ^ _199745) ^ [_466787] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _466787), -(_466787 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _466787, c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (7453 ^ _199745) ^ [_466991] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _466991), -(c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _466991, c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _466991)], (7459 ^ _199745) ^ [_467209, _467211] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _467209), 7462 ^ _199745 : [(7463 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _467209), _467211), _467209), -(_467211 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (7469 ^ _199745) ^ [] : [_467211 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _467209), _467211), _467209))]]], (7475 ^ _199745) ^ [_467692, _467694] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _467692), 7478 ^ _199745 : [(7479 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _467694), _467692), _467692), -(_467694 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (7485 ^ _199745) ^ [] : [_467694 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _467694), _467692), _467692))]]], (7501 ^ _199745) ^ [_468472, _468474] : [7502 ^ _199745 : [(7503 ^ _199745) ^ [] : [_468474 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (7505 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _468472)]], -(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), _468472), _468474)))], (7491 ^ _199745) ^ [_468204, _468206] : [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), _468204), _468206)), -(_468206 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _468204))], (7509 ^ _199745) ^ [_468760] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _468760, c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_468760 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_468760 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (7519 ^ _199745) ^ [_469066, _469068, _469070] : [class_Divides_Osemiring__div(_469066), 7522 ^ _199745 : [(7523 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(_469066, _469068, _469070), -(c_Divides_Odiv__class_Omod(_469066, _469070, _469068) = c_Groups_Ozero__class_Ozero(_469066))], (7529 ^ _199745) ^ [] : [c_Divides_Odiv__class_Omod(_469066, _469070, _469068) = c_Groups_Ozero__class_Ozero(_469066), -(c_Rings_Odvd__class_Odvd(_469066, _469068, _469070))]]], (7535 ^ _199745) ^ [_469575, _469577, _469579] : [class_Divides_Osemiring__div(_469575), c_Rings_Odvd__class_Odvd(_469575, _469577, _469579), -(c_Divides_Odiv__class_Omod(_469575, _469579, _469577) = c_Groups_Ozero__class_Ozero(_469575))], (7545 ^ _199745) ^ [_469910, _469912, _469914] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _469910, c_Divides_Odiv__class_Omod(tc_Int_Oint, _469912, _469914)), c_Rings_Odvd__class_Odvd(tc_Int_Oint, _469910, _469914), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _469910, _469912))], (7555 ^ _199745) ^ [_470247, _470249, _470251] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _470247, _470249), c_Rings_Odvd__class_Odvd(tc_Int_Oint, _470247, _470251), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _470247, c_Divides_Odiv__class_Omod(tc_Int_Oint, _470249, _470251)))], (7565 ^ _199745) ^ [_470590, _470592] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _470590, _470592), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _470590, _470592) = _470590)], (7571 ^ _199745) ^ [_470762, _470764] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _470762, _470764)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _470762, _470764) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _470762, _470764), _470764))], (7577 ^ _199745) ^ [_471002, _471004, _471006] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _471002, c_Divides_Odiv__class_Omod(tc_Int_Oint, _471004, _471006)), _471006) = c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _471002, _471004), _471006))], (7579 ^ _199745) ^ [_471132, _471134, _471136] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, c_Divides_Odiv__class_Omod(tc_Int_Oint, _471132, _471134), _471136), _471134) = c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _471132, _471136), _471134))], (7581 ^ _199745) ^ [_471263, _471265] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _471263, _471265)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _471263, _471265) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _471263, _471265), _471265))], (7587 ^ _199745) ^ [_471516, _471518, _471520] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _471516, _471518), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _471516, _471520), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _471518, _471520)))], (7593 ^ _199745) ^ [_471723] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _471723, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7595 ^ _199745) ^ [_471854, _471856] : [c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _471854, _471856)) = _471856, -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, c_Nat_OSuc(_471854), _471856) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7601 ^ _199745) ^ [_472040, _472042] : [-(c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _472040, _472042)) = _472042), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, c_Nat_OSuc(_472040), _472042) = c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _472040, _472042)))], (7607 ^ _199745) ^ [_472320, _472322] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _472320, _472322) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_472320 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _472322), 7610 ^ [_472320, _472322]))], (7614 ^ _199745) ^ [_472565, _472567] : [7615 ^ _199745 : [(7616 ^ _199745) ^ [_472645] : [_472565 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _472567), _472645)]], -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _472565, _472567) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7620 ^ _199745) ^ [_472848, _472850] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _472848, _472850) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_472848 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _472850), 7623 ^ [_472848, _472850]))], (7627 ^ _199745) ^ [_473093, _473095] : [7628 ^ _199745 : [(7629 ^ _199745) ^ [_473173] : [_473093 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _473095), _473173)]], -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _473093, _473095) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (7633 ^ _199745) ^ [_473346, _473348, _473350] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _473346), _473348), _473350), _473348) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _473350, _473348))], (7635 ^ _199745) ^ [_473475, _473477] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _473475, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _473477)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _473475, _473477) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (7641 ^ _199745) ^ [_473711, _473713] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _473711), _473713) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _473711, _473713) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (7647 ^ _199745) ^ [_473932, _473934] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _473932, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _473934)) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _473932), _473934)))], (7649 ^ _199745) ^ [_474043, _474045] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _474043), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _474045)) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Divides_Odiv__class_Omod(tc_Int_Oint, _474043, _474045)))], (7651 ^ _199745) ^ [_474154, _474156] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Divides_Odiv__class_Omod(tc_Int_Oint, _474154, _474156)), _474156) = c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _474154), _474156))], (7653 ^ _199745) ^ [_474281, _474283] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _474281, _474283), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _474281, _474283) = _474281)], (7659 ^ _199745) ^ [_474486, _474488] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, c_Nat_OSuc(_474486), _474488) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _474486, _474488)), _474488))], (7661 ^ _199745) ^ [_474610, _474612, _474614] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _474610), _474612), _474614) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _474610), c_Divides_Odiv__class_Omod(tc_Int_Oint, _474612, _474614)), _474614))], (7663 ^ _199745) ^ [_474744, _474746, _474748] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _474744), c_Divides_Odiv__class_Omod(tc_Int_Oint, _474746, _474748)), _474748) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _474744), _474746), _474748))], (7665 ^ _199745) ^ [_474878, _474880, _474882] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _474878, _474880)), _474882), _474880) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _474878), _474882), _474880))], (7667 ^ _199745) ^ [_475012, _475014, _475016] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _475012), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _475014, _475016)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _475012), _475014), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _475012), _475016)))], (7669 ^ _199745) ^ [_475148, _475150, _475152] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _475148, _475150)), _475152) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _475148), _475152), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _475150), _475152)))], (7671 ^ _199745) ^ [_475256] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _475256) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (7673 ^ _199745) ^ [_475338] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _475338, _475338) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (7675 ^ _199745) ^ [_475449, _475451] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _475449), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Omod(tc_Int_Oint, _475451, _475449), _475449))], (7681 ^ _199745) ^ [_475671, _475673] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _475671), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _475673, _475671), _475671))], (7687 ^ _199745) ^ [_475893, _475895] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _475893, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _475893, c_Divides_Odiv__class_Omod(tc_Int_Oint, _475895, _475893)))], (7693 ^ _199745) ^ [_476158, _476160, _476162] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _476158, _476160) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _476162, _476160), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _476160, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _476158, _476162)))], (7699 ^ _199745) ^ [_476352, _476354, _476356] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _476354, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _476352, _476356)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _476352, _476354) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _476356, _476354))], (7705 ^ _199745) ^ [_476595, _476597, _476599] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _476595), _476597), _476599)), _476597) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, c_Nat_OSuc(_476599), _476597))], (7707 ^ _199745) ^ [_476748, _476750] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _476748, _476750) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _476748, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _476750)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (7713 ^ _199745) ^ [_476932, _476934] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _476932, _476934) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _476932, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _476934)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, c_Divides_Odiv__class_Omod(tc_Int_Oint, _476932, _476934), _476934))], (7719 ^ _199745) ^ [_477205, _477207] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _477205, _477207) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _477205), _477207) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (7725 ^ _199745) ^ [_477389, _477391] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _477389, _477391) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _477389), _477391) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _477391, c_Divides_Odiv__class_Omod(tc_Int_Oint, _477389, _477391)))], (7731 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (7733 ^ _199745) ^ [_477709, _477711, _477713] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _477709, _477711), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _477713), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _477713), _477709), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _477713), _477711)))], (7753 ^ _199745) ^ [_478341, _478343] : [7754 ^ _199745 : [(7755 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _478341, _478343)], (7757 ^ _199745) ^ [] : [_478341 = _478343]], -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _478341, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _478343, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (7743 ^ _199745) ^ [_478077, _478079] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _478077, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _478079, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _478077, _478079)), -(_478077 = _478079)], (7761 ^ _199745) ^ [_478668, _478670] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _478668, _478670), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _478668, _478670), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (7767 ^ _199745) ^ [_478842, _478844] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _478842, _478844), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _478842, _478844))], (7773 ^ _199745) ^ [_479066, _479068] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _479066), c_Orderings_Oord__class_Oless(tc_Int_Oint, _479066, _479068), c_Rings_Odvd__class_Odvd(tc_Int_Oint, _479068, _479066)], (7783 ^ _199745) ^ [_479400, _479402, _479404, _479406] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _479400), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _479402, _479404), -(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), _479404), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _479406, _479400)), _479402), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _479404), _479400)))], (7817 ^ _199745) ^ [_480587, _480589, _480591] : [-(hBOOL(hAPP(_480587, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _480589, _480591)))), 7820 ^ _199745 : [(7821 ^ _199745) ^ [] : [-(_480591 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7823 ^ _199745) ^ [] : [hBOOL(hAPP(_480587, _480589))]], 7824 ^ _199745 : [(7825 ^ _199745) ^ [] : [_480591 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (7829 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 7827 ^ [_480587, _480589, _480591], _480591))], (7831 ^ _199745) ^ [] : [-(_480589 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _480591), 7826 ^ [_480587, _480589, _480591]), 7827 ^ [_480587, _480589, _480591]))], (7833 ^ _199745) ^ [] : [hBOOL(hAPP(_480587, 7827 ^ [_480587, _480589, _480591]))]]], (7793 ^ _199745) ^ [_479808, _479810, _479812] : [hBOOL(hAPP(_479808, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _479810, _479812))), 7796 ^ _199745 : [(7797 ^ _199745) ^ [] : [_479812 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_479808, _479810)))], (7803 ^ _199745) ^ [] : [-(_479812 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 7806 ^ _199745 : [(7807 ^ _199745) ^ [_480262, _480264] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _480262, _479812), _479810 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _479812), _480264), _480262), -(hBOOL(hAPP(_479808, _480262)))]]]]], (7837 ^ _199745) ^ [_481455, _481457] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _481455), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, c_Nat_OSuc(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _481455), _481457)), _481455) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (7843 ^ _199745) ^ [_481706] : [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), _481706), _481706), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _481706, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (7849 ^ _199745) ^ [_481882] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _481882, 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), _481882), _481882), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (7855 ^ _199745) ^ [_482108, _482110] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _482108), 7858 ^ _199745 : [(7859 ^ _199745) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _482108), _482110) = c_Groups_Oone__class_Oone(tc_Int_Oint), 7862 ^ _199745 : [(7863 ^ _199745) ^ [] : [-(_482108 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (7865 ^ _199745) ^ [] : [-(_482110 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (7867 ^ _199745) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _482108), _482110) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _482108 = c_Groups_Oone__class_Oone(tc_Int_Oint), _482110 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (7877 ^ _199745) ^ [_482760, _482762, _482764] : [class_Divides_Osemiring__div(_482760), -(c_Divides_Odiv__class_Omod(_482760, c_Divides_Odiv__class_Omod(_482760, _482762, _482764), _482764) = c_Divides_Odiv__class_Omod(_482760, _482762, _482764))], (7883 ^ _199745) ^ [_482998, _483000] : [class_Divides_Osemiring__div(_482998), -(c_Divides_Odiv__class_Omod(_482998, c_Groups_Ozero__class_Ozero(_482998), _483000) = c_Groups_Ozero__class_Ozero(_482998))], (7889 ^ _199745) ^ [_483222, _483224] : [class_Divides_Osemiring__div(_483222), -(c_Divides_Odiv__class_Omod(_483222, _483224, c_Groups_Ozero__class_Ozero(_483222)) = _483224)], (7895 ^ _199745) ^ [_483442, _483444] : [class_Divides_Osemiring__div(_483442), -(c_Divides_Odiv__class_Omod(_483442, _483444, _483444) = c_Groups_Ozero__class_Ozero(_483442))], (7901 ^ _199745) ^ [_483690, _483692, _483694, _483696] : [class_Divides_Osemiring__div(_483690), -(c_Divides_Odiv__class_Omod(_483690, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_483690), _483692), _483694), _483696) = c_Divides_Odiv__class_Omod(_483690, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_483690), _483692), c_Divides_Odiv__class_Omod(_483690, _483694, _483696)), _483696))], (7907 ^ _199745) ^ [_483994, _483996, _483998, _484000] : [class_Divides_Osemiring__div(_483994), -(c_Divides_Odiv__class_Omod(_483994, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_483994), _483996), _483998), _484000) = c_Divides_Odiv__class_Omod(_483994, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_483994), c_Divides_Odiv__class_Omod(_483994, _483996, _484000)), _483998), _484000))], (7913 ^ _199745) ^ [_484298, _484300, _484302, _484304] : [class_Divides_Osemiring__div(_484298), -(c_Divides_Odiv__class_Omod(_484298, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_484298), _484300), _484302), _484304) = c_Divides_Odiv__class_Omod(_484298, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_484298), c_Divides_Odiv__class_Omod(_484298, _484300, _484304)), c_Divides_Odiv__class_Omod(_484298, _484302, _484304)), _484304))], (7919 ^ _199745) ^ [_484610, _484612, _484614, _484616] : [class_Divides_Osemiring__div(_484610), -(c_Divides_Odiv__class_Omod(_484610, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_484610), _484612), _484614), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_484610), _484612), _484616)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_484610), _484612), c_Divides_Odiv__class_Omod(_484610, _484614, _484616)))], (7925 ^ _199745) ^ [_484922, _484924, _484926, _484928] : [class_Divides_Osemiring__div(_484922), -(c_Divides_Odiv__class_Omod(_484922, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_484922), _484924), _484926), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_484922), _484928), _484926)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_484922), c_Divides_Odiv__class_Omod(_484922, _484924, _484928)), _484926))], (7931 ^ _199745) ^ [_485234, _485236, _485238, _485240] : [class_Divides_Osemiring__div(_485234), -(c_Divides_Odiv__class_Omod(_485234, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_485234), c_Divides_Odiv__class_Omod(_485234, _485236, _485238)), _485240), _485238) = c_Divides_Odiv__class_Omod(_485234, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_485234), _485236), _485240), _485238))], (7937 ^ _199745) ^ [_485566, _485568, _485570, _485572, _485574, _485576] : [class_Divides_Osemiring__div(_485566), c_Divides_Odiv__class_Omod(_485566, _485568, _485570) = c_Divides_Odiv__class_Omod(_485566, _485572, _485570), c_Divides_Odiv__class_Omod(_485566, _485574, _485570) = c_Divides_Odiv__class_Omod(_485566, _485576, _485570), -(c_Divides_Odiv__class_Omod(_485566, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_485566), _485568), _485574), _485570) = c_Divides_Odiv__class_Omod(_485566, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_485566), _485572), _485576), _485570))], (7951 ^ _199745) ^ [_486102, _486104, _486106] : [class_Divides_Osemiring__div(_486102), -(c_Divides_Odiv__class_Omod(_486102, c_Groups_Oplus__class_Oplus(_486102, _486104, _486106), _486106) = c_Divides_Odiv__class_Omod(_486102, _486104, _486106))], (7957 ^ _199745) ^ [_486354, _486356, _486358] : [class_Divides_Osemiring__div(_486354), -(c_Divides_Odiv__class_Omod(_486354, c_Groups_Oplus__class_Oplus(_486354, _486356, _486358), _486356) = c_Divides_Odiv__class_Omod(_486354, _486358, _486356))], (7963 ^ _199745) ^ [_486620, _486622, _486624, _486626] : [class_Divides_Osemiring__div(_486620), -(c_Divides_Odiv__class_Omod(_486620, c_Groups_Oplus__class_Oplus(_486620, _486622, _486624), _486626) = c_Divides_Odiv__class_Omod(_486620, c_Groups_Oplus__class_Oplus(_486620, _486622, c_Divides_Odiv__class_Omod(_486620, _486624, _486626)), _486626))], (7969 ^ _199745) ^ [_486908, _486910, _486912, _486914] : [class_Divides_Osemiring__div(_486908), -(c_Divides_Odiv__class_Omod(_486908, c_Groups_Oplus__class_Oplus(_486908, _486910, _486912), _486914) = c_Divides_Odiv__class_Omod(_486908, c_Groups_Oplus__class_Oplus(_486908, c_Divides_Odiv__class_Omod(_486908, _486910, _486914), _486912), _486914))], (7975 ^ _199745) ^ [_487196, _487198, _487200, _487202] : [class_Divides_Osemiring__div(_487196), -(c_Divides_Odiv__class_Omod(_487196, c_Groups_Oplus__class_Oplus(_487196, _487198, _487200), _487202) = c_Divides_Odiv__class_Omod(_487196, c_Groups_Oplus__class_Oplus(_487196, c_Divides_Odiv__class_Omod(_487196, _487198, _487202), c_Divides_Odiv__class_Omod(_487196, _487200, _487202)), _487202))], (7981 ^ _199745) ^ [_487492, _487494, _487496, _487498] : [class_Divides_Osemiring__div(_487492), -(c_Divides_Odiv__class_Omod(_487492, c_Groups_Oplus__class_Oplus(_487492, _487494, c_Divides_Odiv__class_Omod(_487492, _487496, _487498)), _487498) = c_Divides_Odiv__class_Omod(_487492, c_Groups_Oplus__class_Oplus(_487492, _487494, _487496), _487498))], (7987 ^ _199745) ^ [_487780, _487782, _487784, _487786] : [class_Divides_Osemiring__div(_487780), -(c_Divides_Odiv__class_Omod(_487780, c_Groups_Oplus__class_Oplus(_487780, c_Divides_Odiv__class_Omod(_487780, _487782, _487784), _487786), _487784) = c_Divides_Odiv__class_Omod(_487780, c_Groups_Oplus__class_Oplus(_487780, _487782, _487786), _487784))], (7993 ^ _199745) ^ [_488096, _488098, _488100, _488102, _488104, _488106] : [class_Divides_Osemiring__div(_488096), c_Divides_Odiv__class_Omod(_488096, _488098, _488100) = c_Divides_Odiv__class_Omod(_488096, _488102, _488100), c_Divides_Odiv__class_Omod(_488096, _488104, _488100) = c_Divides_Odiv__class_Omod(_488096, _488106, _488100), -(c_Divides_Odiv__class_Omod(_488096, c_Groups_Oplus__class_Oplus(_488096, _488098, _488104), _488100) = c_Divides_Odiv__class_Omod(_488096, c_Groups_Oplus__class_Oplus(_488096, _488102, _488106), _488100))], (8007 ^ _199745) ^ [_488658, _488660, _488662, _488664, _488666, _488668] : [class_Divides_Oring__div(_488658), c_Divides_Odiv__class_Omod(_488658, _488660, _488662) = c_Divides_Odiv__class_Omod(_488658, _488664, _488662), c_Divides_Odiv__class_Omod(_488658, _488666, _488662) = c_Divides_Odiv__class_Omod(_488658, _488668, _488662), -(c_Divides_Odiv__class_Omod(_488658, c_Groups_Ominus__class_Ominus(_488658, _488660, _488666), _488662) = c_Divides_Odiv__class_Omod(_488658, c_Groups_Ominus__class_Ominus(_488658, _488664, _488668), _488662))], (8021 ^ _199745) ^ [_489192, _489194, _489196, _489198] : [class_Divides_Oring__div(_489192), -(c_Divides_Odiv__class_Omod(_489192, c_Groups_Ominus__class_Ominus(_489192, _489194, _489196), _489198) = c_Divides_Odiv__class_Omod(_489192, c_Groups_Ominus__class_Ominus(_489192, c_Divides_Odiv__class_Omod(_489192, _489194, _489198), c_Divides_Odiv__class_Omod(_489192, _489196, _489198)), _489198))], (8027 ^ _199745) ^ [_489488, _489490, _489492, _489494] : [class_Divides_Oring__div(_489488), -(c_Divides_Odiv__class_Omod(_489488, c_Groups_Ominus__class_Ominus(_489488, _489490, _489492), _489494) = c_Divides_Odiv__class_Omod(_489488, c_Groups_Ominus__class_Ominus(_489488, c_Divides_Odiv__class_Omod(_489488, _489490, _489494), _489492), _489494))], (8033 ^ _199745) ^ [_489776, _489778, _489780, _489782] : [class_Divides_Oring__div(_489776), -(c_Divides_Odiv__class_Omod(_489776, c_Groups_Ominus__class_Ominus(_489776, _489778, _489780), _489782) = c_Divides_Odiv__class_Omod(_489776, c_Groups_Ominus__class_Ominus(_489776, _489778, c_Divides_Odiv__class_Omod(_489776, _489780, _489782)), _489782))], (8039 ^ _199745) ^ [_490064, _490066, _490068, _490070] : [class_Divides_Oring__div(_490064), c_Divides_Odiv__class_Omod(_490064, _490066, _490068) = c_Divides_Odiv__class_Omod(_490064, _490070, _490068), -(c_Divides_Odiv__class_Omod(_490064, c_Groups_Ouminus__class_Ouminus(_490064, _490066), _490068) = c_Divides_Odiv__class_Omod(_490064, c_Groups_Ouminus__class_Ouminus(_490064, _490070), _490068))], (8049 ^ _199745) ^ [_490439, _490441, _490443] : [class_Divides_Oring__div(_490439), -(c_Divides_Odiv__class_Omod(_490439, c_Groups_Ouminus__class_Ouminus(_490439, _490441), _490443) = c_Divides_Odiv__class_Omod(_490439, c_Groups_Ouminus__class_Ouminus(_490439, c_Divides_Odiv__class_Omod(_490439, _490441, _490443)), _490443))], (8055 ^ _199745) ^ [_490717, _490719, _490721, _490723] : [class_Divides_Osemiring__div(_490717), c_Rings_Odvd__class_Odvd(_490717, _490719, _490721), 8062 ^ _199745 : [(8063 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(_490717, _490719, c_Divides_Odiv__class_Omod(_490717, _490723, _490721)), -(c_Rings_Odvd__class_Odvd(_490717, _490719, _490723))], (8069 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(_490717, _490719, _490723), -(c_Rings_Odvd__class_Odvd(_490717, _490719, c_Divides_Odiv__class_Omod(_490717, _490723, _490721)))]]], (8075 ^ _199745) ^ [_491352, _491354, _491356, _491358] : [class_Divides_Osemiring__div(_491352), c_Rings_Odvd__class_Odvd(_491352, _491354, _491356), -(c_Divides_Odiv__class_Omod(_491352, c_Divides_Odiv__class_Omod(_491352, _491358, _491356), _491354) = c_Divides_Odiv__class_Omod(_491352, _491358, _491354))], (8085 ^ _199745) ^ [_491723, _491725, _491727, _491729] : [class_Divides_Osemiring__div(_491723), c_Rings_Odvd__class_Odvd(_491723, _491725, _491727), c_Rings_Odvd__class_Odvd(_491723, _491725, _491729), -(c_Rings_Odvd__class_Odvd(_491723, _491725, c_Divides_Odiv__class_Omod(_491723, _491727, _491729)))], (8099 ^ _199745) ^ [_492179, _492181, _492183, _492185] : [class_Divides_Osemiring__div(_492179), c_Rings_Odvd__class_Odvd(_492179, _492181, c_Divides_Odiv__class_Omod(_492179, _492183, _492185)), c_Rings_Odvd__class_Odvd(_492179, _492181, _492185), -(c_Rings_Odvd__class_Odvd(_492179, _492181, _492183))], (8113 ^ _199745) ^ [_492621, _492623, _492625] : [class_Divides_Osemiring__div(_492621), -(c_Divides_Odiv__class_Omod(_492621, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_492621), _492623), _492625), _492623) = c_Groups_Ozero__class_Ozero(_492621))], (8119 ^ _199745) ^ [_492877, _492879, _492881] : [class_Divides_Osemiring__div(_492877), -(c_Divides_Odiv__class_Omod(_492877, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_492877), _492879), _492881), _492881) = c_Groups_Ozero__class_Ozero(_492877))], (8125 ^ _199745) ^ [_493119, _493121] : [class_Divides_Osemiring__div(_493119), -(c_Divides_Odiv__class_Omod(_493119, _493121, c_Groups_Oone__class_Oone(_493119)) = c_Groups_Ozero__class_Ozero(_493119))], (8131 ^ _199745) ^ [_493371, _493373, _493375, _493377] : [class_Divides_Osemiring__div(_493371), -(c_Divides_Odiv__class_Omod(_493371, c_Groups_Oplus__class_Oplus(_493371, _493373, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_493371), _493375), _493377)), _493377) = c_Divides_Odiv__class_Omod(_493371, _493373, _493377))], (8137 ^ _199745) ^ [_493659, _493661, _493663, _493665] : [class_Divides_Osemiring__div(_493659), -(c_Divides_Odiv__class_Omod(_493659, c_Groups_Oplus__class_Oplus(_493659, _493661, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_493659), _493663), _493665)), _493663) = c_Divides_Odiv__class_Omod(_493659, _493661, _493663))], (8143 ^ _199745) ^ [_493947, _493949, _493951, _493953] : [class_Fields_Ofield(_493947), -(_493949 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_493947))), -(c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(_493947), c_Polynomial_OpCons(_493947, _493951, _493953), _493949) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_493947), c_Polynomial_OpCons(_493947, _493951, c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(_493947), _493953, _493949)), c_Polynomial_Osmult(_493947, c_Rings_Oinverse__class_Odivide(_493947, hAPP(c_Polynomial_Ocoeff(_493947, c_Polynomial_OpCons(_493947, _493951, c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(_493947), _493953, _493949))), c_Polynomial_Odegree(_493947, _493949)), hAPP(c_Polynomial_Ocoeff(_493947, _493949), c_Polynomial_Odegree(_493947, _493949))), _493949)))], (8153 ^ _199745) ^ [_494441, _494443, _494445, _494447, _494449] : [class_Fields_Ofield(_494441), 8156 ^ _199745 : [(8179 ^ _199745) ^ [] : [-(c_Polynomial_Opdivmod__rel(_494441, _494443, _494445, _494447, _494449)), _494443 = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_494441), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_494441)), _494447), _494445), _494449), 8186 ^ _199745 : [(8187 ^ _199745) ^ [] : [-(_494445 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_494441)))], (8189 ^ _199745) ^ [] : [_494447 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_494441))]], 8190 ^ _199745 : [(8191 ^ _199745) ^ [] : [_494445 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_494441))], (8193 ^ _199745) ^ [] : [_494449 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_494441))], (8195 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_494441, _494449), c_Polynomial_Odegree(_494441, _494445))]]], (8157 ^ _199745) ^ [] : [c_Polynomial_Opdivmod__rel(_494441, _494443, _494445, _494447, _494449), 8160 ^ _199745 : [(8161 ^ _199745) ^ [] : [-(_494443 = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_494441), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_494441)), _494447), _494445), _494449))], (8163 ^ _199745) ^ [] : [_494445 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_494441)), -(_494447 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_494441)))], (8169 ^ _199745) ^ [] : [-(_494445 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_494441))), -(_494449 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_494441))), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_494441, _494449), c_Polynomial_Odegree(_494441, _494445)))]]]]], (8199 ^ _199745) ^ [_495967, _495969, _495971] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _495967, _495969), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _495967, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _495969, _495971)))], (8205 ^ _199745) ^ [_496195, _496197] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _496195, _496197)), -(_496195 = _496197), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _496197, _496195))], (8215 ^ _199745) ^ [_496528, _496530, _496532, _496534] : [class_Fields_Ofield(_496528), 8218 ^ _199745 : [(8219 ^ _199745) ^ [] : [c_Polynomial_Opdivmod__rel(_496528, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_496528)), _496530, _496532, _496534), 8222 ^ _199745 : [(8223 ^ _199745) ^ [] : [-(_496532 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_496528)))], (8225 ^ _199745) ^ [] : [-(_496534 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_496528)))]]], (8227 ^ _199745) ^ [] : [-(c_Polynomial_Opdivmod__rel(_496528, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_496528)), _496530, _496532, _496534)), _496532 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_496528)), _496534 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_496528))]]], (8237 ^ _199745) ^ [_497261, _497263, _497265, _497267] : [class_Fields_Ofield(_497261), 8240 ^ _199745 : [(8241 ^ _199745) ^ [] : [c_Polynomial_Opdivmod__rel(_497261, _497263, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_497261)), _497265, _497267), 8244 ^ _199745 : [(8245 ^ _199745) ^ [] : [-(_497265 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_497261)))], (8247 ^ _199745) ^ [] : [-(_497267 = _497263)]]], (8249 ^ _199745) ^ [] : [-(c_Polynomial_Opdivmod__rel(_497261, _497263, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_497261)), _497265, _497267)), _497265 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_497261)), _497267 = _497263]]], (8259 ^ _199745) ^ [_497954, _497956] : [class_Fields_Ofield(_497954), -(c_Polynomial_Opdivmod__rel(_497954, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_497954)), _497956, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_497954)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_497954))))], (8265 ^ _199745) ^ [_498192, _498194] : [class_Fields_Ofield(_498192), -(c_Polynomial_Opdivmod__rel(_498192, _498194, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_498192)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_498192)), _498194))], (8271 ^ _199745) ^ [_498478, _498480, _498482, _498484, _498486, _498488] : [class_Fields_Ofield(_498478), c_Polynomial_Opdivmod__rel(_498478, _498480, _498482, _498484, _498486), -(c_Polynomial_Opdivmod__rel(_498478, c_Polynomial_Osmult(_498478, _498488, _498480), _498482, c_Polynomial_Osmult(_498478, _498488, _498484), c_Polynomial_Osmult(_498478, _498488, _498486)))], (8281 ^ _199745) ^ [_498893, _498895, _498897, _498899, _498901] : [class_Fields_Ofield(_498893), c_Polynomial_Opdivmod__rel(_498893, _498895, _498897, _498899, _498901), -(c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(_498893), _498895, _498897) = _498901)], (8291 ^ _199745) ^ [_499252, _499254, _499256] : [class_Fields_Olinordered__field__inverse__zero(_499252), 8294 ^ _199745 : [(8295 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_499252, c_Groups_Ozero__class_Ozero(_499252), c_Rings_Oinverse__class_Odivide(_499252, _499254, _499256)), 8300 ^ _199745 : [(8301 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_499252, c_Groups_Ozero__class_Ozero(_499252), _499254))], (8303 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_499252, c_Groups_Ozero__class_Ozero(_499252), _499256))]], 8304 ^ _199745 : [(8305 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_499252, _499254, c_Groups_Ozero__class_Ozero(_499252)))], (8307 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_499252, _499256, c_Groups_Ozero__class_Ozero(_499252)))]]], (8309 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_499252, c_Groups_Ozero__class_Ozero(_499252), c_Rings_Oinverse__class_Odivide(_499252, _499254, _499256))), 8310 ^ _199745 : [(8311 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_499252, c_Groups_Ozero__class_Ozero(_499252), _499254), c_Orderings_Oord__class_Oless(_499252, c_Groups_Ozero__class_Ozero(_499252), _499256)], (8317 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_499252, _499254, c_Groups_Ozero__class_Ozero(_499252)), c_Orderings_Oord__class_Oless(_499252, _499256, c_Groups_Ozero__class_Ozero(_499252))]]]]], (8325 ^ _199745) ^ [_500289, _500291, _500293] : [class_Fields_Olinordered__field__inverse__zero(_500289), 8328 ^ _199745 : [(8329 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_500289, c_Rings_Oinverse__class_Odivide(_500289, _500291, _500293), c_Groups_Ozero__class_Ozero(_500289)), 8334 ^ _199745 : [(8335 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_500289, c_Groups_Ozero__class_Ozero(_500289), _500291))], (8337 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_500289, _500293, c_Groups_Ozero__class_Ozero(_500289)))]], 8338 ^ _199745 : [(8339 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_500289, _500291, c_Groups_Ozero__class_Ozero(_500289)))], (8341 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_500289, c_Groups_Ozero__class_Ozero(_500289), _500293))]]], (8343 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_500289, c_Rings_Oinverse__class_Odivide(_500289, _500291, _500293), c_Groups_Ozero__class_Ozero(_500289))), 8344 ^ _199745 : [(8345 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_500289, c_Groups_Ozero__class_Ozero(_500289), _500291), c_Orderings_Oord__class_Oless(_500289, _500293, c_Groups_Ozero__class_Ozero(_500289))], (8351 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_500289, _500291, c_Groups_Ozero__class_Ozero(_500289)), c_Orderings_Oord__class_Oless(_500289, c_Groups_Ozero__class_Ozero(_500289), _500293)]]]]], (8359 ^ _199745) ^ [_501326, _501328, _501330] : [class_Fields_Olinordered__field(_501326), c_Orderings_Oord__class_Oless(_501326, c_Groups_Ozero__class_Ozero(_501326), _501328), c_Orderings_Oord__class_Oless(_501326, c_Groups_Ozero__class_Ozero(_501326), _501330), -(c_Orderings_Oord__class_Oless(_501326, c_Groups_Ozero__class_Ozero(_501326), c_Rings_Oinverse__class_Odivide(_501326, _501328, _501330)))], (8373 ^ _199745) ^ [_501766, _501768, _501770] : [class_Fields_Olinordered__field(_501766), c_Orderings_Oord__class_Oless(_501766, c_Groups_Ozero__class_Ozero(_501766), _501768), c_Orderings_Oord__class_Oless(_501766, _501770, c_Groups_Ozero__class_Ozero(_501766)), -(c_Orderings_Oord__class_Oless(_501766, c_Rings_Oinverse__class_Odivide(_501766, _501768, _501770), c_Groups_Ozero__class_Ozero(_501766)))], (8387 ^ _199745) ^ [_502206, _502208, _502210] : [class_Fields_Olinordered__field(_502206), c_Orderings_Oord__class_Oless(_502206, _502208, c_Groups_Ozero__class_Ozero(_502206)), c_Orderings_Oord__class_Oless(_502206, c_Groups_Ozero__class_Ozero(_502206), _502210), -(c_Orderings_Oord__class_Oless(_502206, c_Rings_Oinverse__class_Odivide(_502206, _502208, _502210), c_Groups_Ozero__class_Ozero(_502206)))], (8401 ^ _199745) ^ [_502646, _502648, _502650] : [class_Fields_Olinordered__field(_502646), c_Orderings_Oord__class_Oless(_502646, _502648, c_Groups_Ozero__class_Ozero(_502646)), c_Orderings_Oord__class_Oless(_502646, _502650, c_Groups_Ozero__class_Ozero(_502646)), -(c_Orderings_Oord__class_Oless(_502646, c_Groups_Ozero__class_Ozero(_502646), c_Rings_Oinverse__class_Odivide(_502646, _502648, _502650)))], (8415 ^ _199745) ^ [_503100, _503102, _503104, _503106] : [class_Fields_Olinordered__field(_503100), c_Orderings_Oord__class_Oless(_503100, _503102, _503104), c_Orderings_Oord__class_Oless(_503100, c_Groups_Ozero__class_Ozero(_503100), _503106), -(c_Orderings_Oord__class_Oless(_503100, c_Rings_Oinverse__class_Odivide(_503100, _503102, _503106), c_Rings_Oinverse__class_Odivide(_503100, _503104, _503106)))], (8429 ^ _199745) ^ [_503568, _503570, _503572, _503574] : [class_Fields_Olinordered__field(_503568), c_Orderings_Oord__class_Oless(_503568, _503570, _503572), c_Orderings_Oord__class_Oless(_503568, _503574, c_Groups_Ozero__class_Ozero(_503568)), -(c_Orderings_Oord__class_Oless(_503568, c_Rings_Oinverse__class_Odivide(_503568, _503572, _503574), c_Rings_Oinverse__class_Odivide(_503568, _503570, _503574)))], (8443 ^ _199745) ^ [_504036, _504038, _504040, _504042] : [class_Fields_Ofield__inverse__zero(_504036), 8446 ^ _199745 : [(8463 ^ _199745) ^ [] : [-(_504038 = c_Rings_Oinverse__class_Odivide(_504036, _504040, _504042)), 8466 ^ _199745 : [(8467 ^ _199745) ^ [] : [_504042 = c_Groups_Ozero__class_Ozero(_504036)], (8469 ^ _199745) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_504036), _504038), _504042) = _504040]], 8470 ^ _199745 : [(8471 ^ _199745) ^ [] : [-(_504042 = c_Groups_Ozero__class_Ozero(_504036))], (8473 ^ _199745) ^ [] : [_504038 = c_Groups_Ozero__class_Ozero(_504036)]]], (8447 ^ _199745) ^ [] : [_504038 = c_Rings_Oinverse__class_Odivide(_504036, _504040, _504042), 8450 ^ _199745 : [(8451 ^ _199745) ^ [] : [-(_504042 = c_Groups_Ozero__class_Ozero(_504036)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_504036), _504038), _504042) = _504040)], (8457 ^ _199745) ^ [] : [_504042 = c_Groups_Ozero__class_Ozero(_504036), -(_504038 = c_Groups_Ozero__class_Ozero(_504036))]]]]], (8477 ^ _199745) ^ [_505120, _505122, _505124, _505126] : [class_Fields_Ofield__inverse__zero(_505120), 8480 ^ _199745 : [(8497 ^ _199745) ^ [] : [-(c_Rings_Oinverse__class_Odivide(_505120, _505122, _505124) = _505126), 8500 ^ _199745 : [(8501 ^ _199745) ^ [] : [_505124 = c_Groups_Ozero__class_Ozero(_505120)], (8503 ^ _199745) ^ [] : [_505122 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_505120), _505126), _505124)]], 8504 ^ _199745 : [(8505 ^ _199745) ^ [] : [-(_505124 = c_Groups_Ozero__class_Ozero(_505120))], (8507 ^ _199745) ^ [] : [_505126 = c_Groups_Ozero__class_Ozero(_505120)]]], (8481 ^ _199745) ^ [] : [c_Rings_Oinverse__class_Odivide(_505120, _505122, _505124) = _505126, 8484 ^ _199745 : [(8485 ^ _199745) ^ [] : [-(_505124 = c_Groups_Ozero__class_Ozero(_505120)), -(_505122 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_505120), _505126), _505124))], (8491 ^ _199745) ^ [] : [_505124 = c_Groups_Ozero__class_Ozero(_505120), -(_505126 = c_Groups_Ozero__class_Ozero(_505120))]]]]], (8511 ^ _199745) ^ [_506204, _506206, _506208, _506210] : [class_Fields_Ofield__inverse__zero(_506204), -(_506206 = c_Groups_Ozero__class_Ozero(_506204)), -(c_Rings_Oinverse__class_Odivide(_506204, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_506204), _506208), _506206), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_506204), _506210), _506206)) = c_Rings_Oinverse__class_Odivide(_506204, _506208, _506210))], (8521 ^ _199745) ^ [_506604, _506606, _506608, _506610] : [class_Fields_Ofield__inverse__zero(_506604), -(_506606 = c_Groups_Ozero__class_Ozero(_506604)), -(c_Rings_Oinverse__class_Odivide(_506604, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_506604), _506606), _506608), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_506604), _506606), _506610)) = c_Rings_Oinverse__class_Odivide(_506604, _506608, _506610))], (8531 ^ _199745) ^ [_507018, _507020, _507022, _507024, _507026] : [class_Fields_Ofield(_507018), -(_507020 = c_Groups_Ozero__class_Ozero(_507018)), -(_507022 = c_Groups_Ozero__class_Ozero(_507018)), 8542 ^ _199745 : [(8543 ^ _199745) ^ [] : [c_Rings_Oinverse__class_Odivide(_507018, _507024, _507020) = c_Rings_Oinverse__class_Odivide(_507018, _507026, _507022), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_507018), _507024), _507022) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_507018), _507026), _507020))], (8549 ^ _199745) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_507018), _507024), _507022) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_507018), _507026), _507020), -(c_Rings_Oinverse__class_Odivide(_507018, _507024, _507020) = c_Rings_Oinverse__class_Odivide(_507018, _507026, _507022))]]], (8555 ^ _199745) ^ [_507840, _507842, _507844, _507846] : [class_Rings_Odivision__ring(_507840), -(_507842 = c_Groups_Ozero__class_Ozero(_507840)), 8562 ^ _199745 : [(8563 ^ _199745) ^ [] : [_507844 = c_Rings_Oinverse__class_Odivide(_507840, _507846, _507842), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_507840), _507844), _507842) = _507846)], (8569 ^ _199745) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_507840), _507844), _507842) = _507846, -(_507844 = c_Rings_Oinverse__class_Odivide(_507840, _507846, _507842))]]], (8575 ^ _199745) ^ [_508498, _508500, _508502, _508504] : [class_Rings_Odivision__ring(_508498), -(_508500 = c_Groups_Ozero__class_Ozero(_508498)), 8582 ^ _199745 : [(8583 ^ _199745) ^ [] : [c_Rings_Oinverse__class_Odivide(_508498, _508502, _508500) = _508504, -(_508502 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_508498), _508504), _508500))], (8589 ^ _199745) ^ [] : [_508502 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_508498), _508504), _508500), -(c_Rings_Oinverse__class_Odivide(_508498, _508502, _508500) = _508504)]]], (8595 ^ _199745) ^ [_509156, _509158, _509160, _509162] : [class_Rings_Odivision__ring(_509156), -(_509158 = c_Groups_Ozero__class_Ozero(_509156)), _509160 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_509156), _509162), _509158), -(c_Rings_Oinverse__class_Odivide(_509156, _509160, _509158) = _509162)], (8609 ^ _199745) ^ [_509629, _509631, _509633, _509635] : [class_Rings_Odivision__ring(_509629), -(_509631 = c_Groups_Ozero__class_Ozero(_509629)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_509629), _509633), _509631) = _509635, -(_509633 = c_Rings_Oinverse__class_Odivide(_509629, _509635, _509631))], (8623 ^ _199745) ^ [_510088, _510090, _510092] : [class_Rings_Odivision__ring(_510088), -(_510090 = c_Groups_Ozero__class_Ozero(_510088)), 8630 ^ _199745 : [(8631 ^ _199745) ^ [] : [c_Rings_Oinverse__class_Odivide(_510088, _510092, _510090) = c_Groups_Oone__class_Oone(_510088), -(_510092 = _510090)], (8637 ^ _199745) ^ [] : [_510092 = _510090, -(c_Rings_Oinverse__class_Odivide(_510088, _510092, _510090) = c_Groups_Oone__class_Oone(_510088))]]], (8643 ^ _199745) ^ [_510680, _510682] : [class_Rings_Odivision__ring(_510680), -(_510682 = c_Groups_Ozero__class_Ozero(_510680)), -(c_Rings_Oinverse__class_Odivide(_510680, _510682, _510682) = c_Groups_Oone__class_Oone(_510680))], (8653 ^ _199745) ^ [_510996, _510998] : [class_Rings_Odivision__ring__inverse__zero(_510996), 8656 ^ _199745 : [(8657 ^ _199745) ^ [] : [_510998 = c_Groups_Ozero__class_Ozero(_510996), -(c_Rings_Oinverse__class_Odivide(_510996, _510998, _510998) = c_Groups_Ozero__class_Ozero(_510996))], (8663 ^ _199745) ^ [] : [-(_510998 = c_Groups_Ozero__class_Ozero(_510996)), -(c_Rings_Oinverse__class_Odivide(_510996, _510998, _510998) = c_Groups_Oone__class_Oone(_510996))]]], (8669 ^ _199745) ^ [_511506, _511508, _511510] : [class_Rings_Odivision__ring(_511506), -(_511508 = c_Groups_Ozero__class_Ozero(_511506)), -(c_Rings_Oinverse__class_Odivide(_511506, c_Groups_Ouminus__class_Ouminus(_511506, _511510), c_Groups_Ouminus__class_Ouminus(_511506, _511508)) = c_Rings_Oinverse__class_Odivide(_511506, _511510, _511508))], (8679 ^ _199745) ^ [_511862, _511864, _511866] : [class_Rings_Odivision__ring(_511862), -(_511864 = c_Groups_Ozero__class_Ozero(_511862)), -(c_Groups_Ouminus__class_Ouminus(_511862, c_Rings_Oinverse__class_Odivide(_511862, _511866, _511864)) = c_Rings_Oinverse__class_Odivide(_511862, _511866, c_Groups_Ouminus__class_Ouminus(_511862, _511864)))], (8689 ^ _199745) ^ [_512232, _512234, _512236, _512238] : [class_Fields_Ofield(_512232), -(_512234 = c_Groups_Ozero__class_Ozero(_512232)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_512232), c_Rings_Oinverse__class_Odivide(_512232, _512236, _512234)), _512238) = c_Rings_Oinverse__class_Odivide(_512232, hAPP(hAPP(c_Power_Opower__class_Opower(_512232), _512236), _512238), hAPP(hAPP(c_Power_Opower__class_Opower(_512232), _512234), _512238)))], (8699 ^ _199745) ^ [_512634, _512636, _512638] : [class_Fields_Ofield__inverse__zero(_512634), -(c_Rings_Oinverse__class_Odivide(_512634, c_Groups_Oone__class_Oone(_512634), hAPP(hAPP(c_Power_Opower__class_Opower(_512634), _512636), _512638)) = hAPP(hAPP(c_Power_Opower__class_Opower(_512634), c_Rings_Oinverse__class_Odivide(_512634, c_Groups_Oone__class_Oone(_512634), _512636)), _512638))], (8705 ^ _199745) ^ [_512918, _512920, _512922] : [class_Fields_Ofield__inverse__zero(_512918), -(c_Rings_Oinverse__class_Oinverse(_512918, c_Rings_Oinverse__class_Odivide(_512918, _512920, _512922)) = c_Rings_Oinverse__class_Odivide(_512918, _512922, _512920))], (8711 ^ _199745) ^ [_513182, _513184, _513186, _513188] : [class_RealVector_Oreal__normed__field(_513182), -(c_Rings_Oinverse__class_Odivide(_513182, c_Groups_Ominus__class_Ominus(_513182, _513184, _513186), _513188) = c_Groups_Ominus__class_Ominus(_513182, c_Rings_Oinverse__class_Odivide(_513182, _513184, _513188), c_Rings_Oinverse__class_Odivide(_513182, _513186, _513188)))], (8717 ^ _199745) ^ [_513470, _513472, _513474, _513476] : [class_Rings_Odivision__ring(_513470), -(c_Rings_Oinverse__class_Odivide(_513470, c_Groups_Ominus__class_Ominus(_513470, _513472, _513474), _513476) = c_Groups_Ominus__class_Ominus(_513470, c_Rings_Oinverse__class_Odivide(_513470, _513472, _513476), c_Rings_Oinverse__class_Odivide(_513470, _513474, _513476)))], (8723 ^ _199745) ^ [_513772, _513774, _513776, _513778, _513780] : [class_Fields_Ofield__inverse__zero(_513772), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_513772), c_Rings_Oinverse__class_Odivide(_513772, _513774, _513776)), c_Rings_Oinverse__class_Odivide(_513772, _513778, _513780)) = c_Rings_Oinverse__class_Odivide(_513772, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_513772), _513774), _513778), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_513772), _513776), _513780)))], (8729 ^ _199745) ^ [_514084, _514086, _514088] : [class_Fields_Ofield__inverse__zero(_514084), -(c_Rings_Oinverse__class_Odivide(_514084, c_Groups_Ouminus__class_Ouminus(_514084, _514086), c_Groups_Ouminus__class_Ouminus(_514084, _514088)) = c_Rings_Oinverse__class_Odivide(_514084, _514086, _514088))], (8735 ^ _199745) ^ [_514340, _514342, _514344] : [class_Fields_Ofield__inverse__zero(_514340), -(c_Groups_Ouminus__class_Ouminus(_514340, c_Rings_Oinverse__class_Odivide(_514340, _514342, _514344)) = c_Rings_Oinverse__class_Odivide(_514340, _514342, c_Groups_Ouminus__class_Ouminus(_514340, _514344)))], (8741 ^ _199745) ^ [_514582, _514584] : [class_Rings_Odivision__ring(_514582), -(c_Rings_Oinverse__class_Odivide(_514582, _514584, c_Groups_Oone__class_Oone(_514582)) = _514584)], (8747 ^ _199745) ^ [_514816, _514818, _514820] : [class_Rings_Odivision__ring(_514816), -(c_Groups_Ouminus__class_Ouminus(_514816, c_Rings_Oinverse__class_Odivide(_514816, _514818, _514820)) = c_Rings_Oinverse__class_Odivide(_514816, c_Groups_Ouminus__class_Ouminus(_514816, _514818), _514820))], (8753 ^ _199745) ^ [_515072, _515074, _515076] : [class_RealVector_Oreal__normed__field(_515072), -(c_Rings_Oinverse__class_Odivide(_515072, c_Groups_Ouminus__class_Ouminus(_515072, _515074), _515076) = c_Groups_Ouminus__class_Ouminus(_515072, c_Rings_Oinverse__class_Odivide(_515072, _515074, _515076)))], (8759 ^ _199745) ^ [_515342, _515344, _515346, _515348] : [class_Fields_Ofield__inverse__zero(_515342), -(hAPP(hAPP(c_Power_Opower__class_Opower(_515342), c_Rings_Oinverse__class_Odivide(_515342, _515344, _515346)), _515348) = c_Rings_Oinverse__class_Odivide(_515342, hAPP(hAPP(c_Power_Opower__class_Opower(_515342), _515344), _515348), hAPP(hAPP(c_Power_Opower__class_Opower(_515342), _515346), _515348)))], (8765 ^ _199745) ^ [_515696, _515698, _515700, _515702, _515704, _515706, _515708] : [class_Fields_Ofield(_515696), c_Polynomial_Opdivmod__rel(_515696, _515698, _515700, _515702, _515704), c_Polynomial_Opdivmod__rel(_515696, _515698, _515700, _515706, _515708), 8776 ^ _199745 : [(8777 ^ _199745) ^ [] : [-(_515702 = _515706)], (8779 ^ _199745) ^ [] : [-(_515704 = _515708)]]], (8781 ^ _199745) ^ [_516319, _516321, _516323, _516325, _516327, _516329, _516331] : [class_Fields_Ofield(_516319), c_Polynomial_Opdivmod__rel(_516319, _516321, _516323, _516325, _516327), c_Polynomial_Opdivmod__rel(_516319, _516321, _516323, _516329, _516331), -(_516327 = _516331)], (8795 ^ _199745) ^ [_516857, _516859, _516861, _516863, _516865, _516867, _516869] : [class_Fields_Ofield(_516857), c_Polynomial_Opdivmod__rel(_516857, _516859, _516861, _516863, _516865), c_Polynomial_Opdivmod__rel(_516857, _516859, _516861, _516867, _516869), -(_516863 = _516867)], (8809 ^ _199745) ^ [_517353, _517355, _517357, _517359] : [class_Rings_Odivision__ring(_517353), -(c_Rings_Oinverse__class_Odivide(_517353, c_Groups_Oplus__class_Oplus(_517353, _517355, _517357), _517359) = c_Groups_Oplus__class_Oplus(_517353, c_Rings_Oinverse__class_Odivide(_517353, _517355, _517359), c_Rings_Oinverse__class_Odivide(_517353, _517357, _517359)))], (8815 ^ _199745) ^ [_517641, _517643, _517645, _517647] : [class_RealVector_Oreal__normed__field(_517641), -(c_Rings_Oinverse__class_Odivide(_517641, c_Groups_Oplus__class_Oplus(_517641, _517643, _517645), _517647) = c_Groups_Oplus__class_Oplus(_517641, c_Rings_Oinverse__class_Odivide(_517641, _517643, _517647), c_Rings_Oinverse__class_Odivide(_517641, _517645, _517647)))], (8821 ^ _199745) ^ [_517929, _517931, _517933, _517935] : [class_Rings_Odivision__ring(_517929), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_517929), _517931), c_Rings_Oinverse__class_Odivide(_517929, _517933, _517935)) = c_Rings_Oinverse__class_Odivide(_517929, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_517929), _517931), _517933), _517935))], (8827 ^ _199745) ^ [_518197, _518199] : [class_Rings_Odivision__ring(_518197), -(c_Rings_Oinverse__class_Odivide(_518197, c_Groups_Ozero__class_Ozero(_518197), _518199) = c_Groups_Ozero__class_Ozero(_518197))], (8833 ^ _199745) ^ [_518421, _518423] : [class_RealVector_Oreal__normed__field(_518421), -(c_Rings_Oinverse__class_Odivide(_518421, c_Groups_Ozero__class_Ozero(_518421), _518423) = c_Groups_Ozero__class_Ozero(_518421))], (8839 ^ _199745) ^ [_518645, _518647] : [class_Rings_Odivision__ring__inverse__zero(_518645), -(c_Rings_Oinverse__class_Odivide(_518645, _518647, c_Groups_Ozero__class_Ozero(_518645)) = c_Groups_Ozero__class_Ozero(_518645))], (8845 ^ _199745) ^ [_518883, _518885, _518887] : [class_Rings_Odivision__ring(_518883), -(c_Rings_Oinverse__class_Odivide(_518883, _518885, _518887) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_518883), _518885), c_Rings_Oinverse__class_Oinverse(_518883, _518887)))], (8851 ^ _199745) ^ [_519141, _519143, _519145] : [class_Fields_Ofield(_519141), -(c_Rings_Oinverse__class_Odivide(_519141, _519143, _519145) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_519141), _519143), c_Rings_Oinverse__class_Oinverse(_519141, _519145)))], (8857 ^ _199745) ^ [_519385, _519387] : [class_Rings_Odivision__ring(_519385), -(c_Rings_Oinverse__class_Oinverse(_519385, _519387) = c_Rings_Oinverse__class_Odivide(_519385, c_Groups_Oone__class_Oone(_519385), _519387))], (8863 ^ _199745) ^ [_519611, _519613] : [class_Fields_Ofield(_519611), -(c_Rings_Oinverse__class_Oinverse(_519611, _519613) = c_Rings_Oinverse__class_Odivide(_519611, c_Groups_Oone__class_Oone(_519611), _519613))], (8869 ^ _199745) ^ [_519865, _519867, _519869, _519871] : [class_Fields_Olinordered__field(_519865), c_Orderings_Oord__class_Oless(_519865, _519867, _519869), c_Orderings_Oord__class_Oless(_519865, _519871, c_Groups_Ozero__class_Ozero(_519865)), c_Orderings_Oord__class_Oless(_519865, c_Groups_Ozero__class_Ozero(_519865), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_519865), _519867), _519869)), -(c_Orderings_Oord__class_Oless(_519865, c_Rings_Oinverse__class_Odivide(_519865, _519871, _519867), c_Rings_Oinverse__class_Odivide(_519865, _519871, _519869)))], (8887 ^ _199745) ^ [_520452, _520454, _520456, _520458] : [class_Fields_Olinordered__field(_520452), c_Orderings_Oord__class_Oless(_520452, _520454, _520456), c_Orderings_Oord__class_Oless(_520452, c_Groups_Ozero__class_Ozero(_520452), _520458), c_Orderings_Oord__class_Oless(_520452, c_Groups_Ozero__class_Ozero(_520452), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_520452), _520456), _520454)), -(c_Orderings_Oord__class_Oless(_520452, c_Rings_Oinverse__class_Odivide(_520452, _520458, _520456), c_Rings_Oinverse__class_Odivide(_520452, _520458, _520454)))], (8905 ^ _199745) ^ [_521039, _521041, _521043, _521045] : [class_Fields_Olinordered__field(_521039), c_Orderings_Oord__class_Oless(_521039, _521041, c_Groups_Ozero__class_Ozero(_521039)), 8912 ^ _199745 : [(8913 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_521039, c_Rings_Oinverse__class_Odivide(_521039, _521043, _521041), _521045), -(c_Orderings_Oord__class_Oless(_521039, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_521039), _521045), _521041), _521043))], (8919 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_521039, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_521039), _521045), _521041), _521043), -(c_Orderings_Oord__class_Oless(_521039, c_Rings_Oinverse__class_Odivide(_521039, _521043, _521041), _521045))]]], (8925 ^ _199745) ^ [_521702, _521704, _521706, _521708] : [class_Fields_Olinordered__field(_521702), c_Orderings_Oord__class_Oless(_521702, _521704, c_Groups_Ozero__class_Ozero(_521702)), 8932 ^ _199745 : [(8933 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_521702, _521706, c_Rings_Oinverse__class_Odivide(_521702, _521708, _521704)), -(c_Orderings_Oord__class_Oless(_521702, _521708, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_521702), _521706), _521704)))], (8939 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_521702, _521708, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_521702), _521706), _521704)), -(c_Orderings_Oord__class_Oless(_521702, _521706, c_Rings_Oinverse__class_Odivide(_521702, _521708, _521704)))]]], (8945 ^ _199745) ^ [_522365, _522367, _522369, _522371] : [class_Fields_Olinordered__field(_522365), c_Orderings_Oord__class_Oless(_522365, c_Groups_Ozero__class_Ozero(_522365), _522367), c_Orderings_Oord__class_Oless(_522365, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_522365), _522369), _522367), _522371), -(c_Orderings_Oord__class_Oless(_522365, _522369, c_Rings_Oinverse__class_Odivide(_522365, _522371, _522367)))], (8959 ^ _199745) ^ [_522841, _522843, _522845, _522847] : [class_Fields_Olinordered__field(_522841), c_Orderings_Oord__class_Oless(_522841, c_Groups_Ozero__class_Ozero(_522841), _522843), c_Orderings_Oord__class_Oless(_522841, _522845, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_522841), _522847), _522843)), -(c_Orderings_Oord__class_Oless(_522841, c_Rings_Oinverse__class_Odivide(_522841, _522845, _522843), _522847))], (8973 ^ _199745) ^ [_523317, _523319, _523321, _523323] : [class_Fields_Olinordered__field(_523317), c_Orderings_Oord__class_Oless(_523317, c_Groups_Ozero__class_Ozero(_523317), _523319), 8980 ^ _199745 : [(8981 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_523317, c_Rings_Oinverse__class_Odivide(_523317, _523321, _523319), _523323), -(c_Orderings_Oord__class_Oless(_523317, _523321, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_523317), _523323), _523319)))], (8987 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_523317, _523321, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_523317), _523323), _523319)), -(c_Orderings_Oord__class_Oless(_523317, c_Rings_Oinverse__class_Odivide(_523317, _523321, _523319), _523323))]]], (8993 ^ _199745) ^ [_523980, _523982, _523984, _523986] : [class_Fields_Olinordered__field(_523980), c_Orderings_Oord__class_Oless(_523980, c_Groups_Ozero__class_Ozero(_523980), _523982), 9000 ^ _199745 : [(9001 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_523980, _523984, c_Rings_Oinverse__class_Odivide(_523980, _523986, _523982)), -(c_Orderings_Oord__class_Oless(_523980, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_523980), _523984), _523982), _523986))], (9007 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_523980, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_523980), _523984), _523982), _523986), -(c_Orderings_Oord__class_Oless(_523980, _523984, c_Rings_Oinverse__class_Odivide(_523980, _523986, _523982)))]]], (9013 ^ _199745) ^ [_524643, _524645, _524647, _524649] : [class_Fields_Olinordered__field__inverse__zero(_524643), 9016 ^ _199745 : [(9043 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_524643, c_Rings_Oinverse__class_Odivide(_524643, _524645, _524647), _524649)), 9046 ^ _199745 : [(9047 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_524643, c_Groups_Ozero__class_Ozero(_524643), _524647))], (9049 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_524643, _524645, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_524643), _524649), _524647))]], 9050 ^ _199745 : [(9051 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_524643, c_Groups_Ozero__class_Ozero(_524643), _524647)], (9053 ^ _199745) ^ [] : [9054 ^ _199745 : [(9055 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_524643, _524647, c_Groups_Ozero__class_Ozero(_524643)))], (9057 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_524643, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_524643), _524649), _524647), _524645)]], 9058 ^ _199745 : [(9059 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_524643, _524647, c_Groups_Ozero__class_Ozero(_524643))], (9061 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_524643, c_Groups_Ozero__class_Ozero(_524643), _524649)]]]]], (9017 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_524643, c_Rings_Oinverse__class_Odivide(_524643, _524645, _524647), _524649), 9020 ^ _199745 : [(9021 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_524643, c_Groups_Ozero__class_Ozero(_524643), _524647), -(c_Orderings_Oord__class_Oless(_524643, _524645, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_524643), _524649), _524647)))], (9027 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_524643, c_Groups_Ozero__class_Ozero(_524643), _524647)), 9030 ^ _199745 : [(9031 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_524643, _524647, c_Groups_Ozero__class_Ozero(_524643)), -(c_Orderings_Oord__class_Oless(_524643, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_524643), _524649), _524647), _524645))], (9037 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_524643, _524647, c_Groups_Ozero__class_Ozero(_524643))), -(c_Orderings_Oord__class_Oless(_524643, c_Groups_Ozero__class_Ozero(_524643), _524649))]]]]]]], (9065 ^ _199745) ^ [_526299, _526301, _526303, _526305] : [class_Fields_Olinordered__field__inverse__zero(_526299), 9068 ^ _199745 : [(9095 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_526299, _526301, c_Rings_Oinverse__class_Odivide(_526299, _526303, _526305))), 9098 ^ _199745 : [(9099 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_526299, c_Groups_Ozero__class_Ozero(_526299), _526305))], (9101 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_526299, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_526299), _526301), _526305), _526303)]], 9102 ^ _199745 : [(9103 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_526299, c_Groups_Ozero__class_Ozero(_526299), _526305)], (9105 ^ _199745) ^ [] : [9106 ^ _199745 : [(9107 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_526299, _526305, c_Groups_Ozero__class_Ozero(_526299)))], (9109 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_526299, _526303, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_526299), _526301), _526305))]], 9110 ^ _199745 : [(9111 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_526299, _526305, c_Groups_Ozero__class_Ozero(_526299))], (9113 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_526299, _526301, c_Groups_Ozero__class_Ozero(_526299))]]]]], (9069 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_526299, _526301, c_Rings_Oinverse__class_Odivide(_526299, _526303, _526305)), 9072 ^ _199745 : [(9073 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_526299, c_Groups_Ozero__class_Ozero(_526299), _526305), -(c_Orderings_Oord__class_Oless(_526299, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_526299), _526301), _526305), _526303))], (9079 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_526299, c_Groups_Ozero__class_Ozero(_526299), _526305)), 9082 ^ _199745 : [(9083 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_526299, _526305, c_Groups_Ozero__class_Ozero(_526299)), -(c_Orderings_Oord__class_Oless(_526299, _526303, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_526299), _526301), _526305)))], (9089 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_526299, _526305, c_Groups_Ozero__class_Ozero(_526299))), -(c_Orderings_Oord__class_Oless(_526299, _526301, c_Groups_Ozero__class_Ozero(_526299)))]]]]]]], (9117 ^ _199745) ^ [_527969, _527971, _527973, _527975, _527977] : [class_Fields_Ofield(_527969), -(_527971 = c_Groups_Ozero__class_Ozero(_527969)), -(_527973 = c_Groups_Ozero__class_Ozero(_527969)), -(c_Groups_Oplus__class_Oplus(_527969, c_Rings_Oinverse__class_Odivide(_527969, _527975, _527971), c_Rings_Oinverse__class_Odivide(_527969, _527977, _527973)) = c_Rings_Oinverse__class_Odivide(_527969, c_Groups_Oplus__class_Oplus(_527969, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_527969), _527975), _527973), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_527969), _527977), _527971)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_527969), _527971), _527973)))], (9131 ^ _199745) ^ [_528527, _528529, _528531, _528533] : [class_Fields_Ofield(_528527), -(_528529 = c_Groups_Ozero__class_Ozero(_528527)), -(c_Groups_Oplus__class_Oplus(_528527, c_Rings_Oinverse__class_Odivide(_528527, _528531, _528529), _528533) = c_Rings_Oinverse__class_Odivide(_528527, c_Groups_Oplus__class_Oplus(_528527, _528531, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_528527), _528529), _528533)), _528529))], (9141 ^ _199745) ^ [_528927, _528929, _528931, _528933] : [class_Fields_Ofield__inverse__zero(_528927), -(_528929 = c_Groups_Ozero__class_Ozero(_528927)), -(c_Groups_Oplus__class_Oplus(_528927, c_Rings_Oinverse__class_Odivide(_528927, _528931, _528929), _528933) = c_Rings_Oinverse__class_Odivide(_528927, c_Groups_Oplus__class_Oplus(_528927, _528931, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_528927), _528933), _528929)), _528929))], (9151 ^ _199745) ^ [_529327, _529329, _529331, _529333] : [class_Fields_Ofield(_529327), -(_529329 = c_Groups_Ozero__class_Ozero(_529327)), -(c_Groups_Oplus__class_Oplus(_529327, _529331, c_Rings_Oinverse__class_Odivide(_529327, _529333, _529329)) = c_Rings_Oinverse__class_Odivide(_529327, c_Groups_Oplus__class_Oplus(_529327, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_529327), _529329), _529331), _529333), _529329))], (9161 ^ _199745) ^ [_529727, _529729, _529731, _529733] : [class_Fields_Ofield__inverse__zero(_529727), -(_529729 = c_Groups_Ozero__class_Ozero(_529727)), -(c_Groups_Oplus__class_Oplus(_529727, _529731, c_Rings_Oinverse__class_Odivide(_529727, _529733, _529729)) = c_Rings_Oinverse__class_Odivide(_529727, c_Groups_Oplus__class_Oplus(_529727, _529733, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_529727), _529731), _529729)), _529729))], (9171 ^ _199745) ^ [_530141, _530143, _530145, _530147, _530149] : [class_Fields_Ofield(_530141), -(_530143 = c_Groups_Ozero__class_Ozero(_530141)), -(_530145 = c_Groups_Ozero__class_Ozero(_530141)), -(c_Groups_Ominus__class_Ominus(_530141, c_Rings_Oinverse__class_Odivide(_530141, _530147, _530143), c_Rings_Oinverse__class_Odivide(_530141, _530149, _530145)) = c_Rings_Oinverse__class_Odivide(_530141, c_Groups_Ominus__class_Ominus(_530141, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_530141), _530147), _530145), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_530141), _530149), _530143)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_530141), _530143), _530145)))], (9185 ^ _199745) ^ [_530699, _530701, _530703, _530705] : [class_Fields_Ofield(_530699), -(_530701 = c_Groups_Ozero__class_Ozero(_530699)), -(c_Groups_Ominus__class_Ominus(_530699, c_Rings_Oinverse__class_Odivide(_530699, _530703, _530701), _530705) = c_Rings_Oinverse__class_Odivide(_530699, c_Groups_Ominus__class_Ominus(_530699, _530703, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_530699), _530701), _530705)), _530701))], (9195 ^ _199745) ^ [_531099, _531101, _531103, _531105] : [class_Fields_Ofield(_531099), -(_531101 = c_Groups_Ozero__class_Ozero(_531099)), -(c_Groups_Ominus__class_Ominus(_531099, _531103, c_Rings_Oinverse__class_Odivide(_531099, _531105, _531101)) = c_Rings_Oinverse__class_Odivide(_531099, c_Groups_Ominus__class_Ominus(_531099, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_531099), _531101), _531103), _531105), _531101))], (9205 ^ _199745) ^ [_531485, _531487, _531489] : [class_Fields_Olinordered__field(_531485), c_Orderings_Oord__class_Oless(_531485, _531487, _531489), -(c_Orderings_Oord__class_Oless(_531485, _531487, c_Rings_Oinverse__class_Odivide(_531485, c_Groups_Oplus__class_Oplus(_531485, _531487, _531489), c_Groups_Oplus__class_Oplus(_531485, c_Groups_Oone__class_Oone(_531485), c_Groups_Oone__class_Oone(_531485)))))], (9215 ^ _199745) ^ [_531842, _531844, _531846] : [class_Fields_Olinordered__field(_531842), c_Orderings_Oord__class_Oless(_531842, _531844, _531846), -(c_Orderings_Oord__class_Oless(_531842, c_Rings_Oinverse__class_Odivide(_531842, c_Groups_Oplus__class_Oplus(_531842, _531844, _531846), c_Groups_Oplus__class_Oplus(_531842, c_Groups_Oone__class_Oone(_531842), c_Groups_Oone__class_Oone(_531842))), _531846))], (9225 ^ _199745) ^ [_532241, _532243, _532245, _532247, _532249, _532251] : [class_RealVector_Oreal__field(_532241), -(c_Rings_Oinverse__class_Odivide(_532241, c_Groups_Ominus__class_Ominus(_532241, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_532241), _532243), _532245), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_532241), _532247), _532249)), _532251) = c_Groups_Oplus__class_Oplus(_532241, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_532241), _532243), c_Rings_Oinverse__class_Odivide(_532241, c_Groups_Ominus__class_Ominus(_532241, _532245, _532249), _532251)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_532241), c_Rings_Oinverse__class_Odivide(_532241, c_Groups_Ominus__class_Ominus(_532241, _532243, _532247), _532251)), _532249)))], (9231 ^ _199745) ^ [_532593, _532595] : [class_Rings_Odivision__ring(_532593), -(_532595 = c_Groups_Ozero__class_Ozero(_532593)), -(c_Rings_Oinverse__class_Oinverse(_532593, _532595) = c_Rings_Oinverse__class_Odivide(_532593, c_Groups_Oone__class_Oone(_532593), _532595))], (9241 ^ _199745) ^ [_532999, _533001, _533003, _533005, _533007, _533009, _533011, _533013] : [class_Fields_Ofield(_532999), c_Polynomial_Opdivmod__rel(_532999, _533001, _533003, _533005, _533007), c_Polynomial_Opdivmod__rel(_532999, _533005, _533009, _533011, _533013), -(c_Polynomial_Opdivmod__rel(_532999, _533001, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_532999)), _533003), _533009), _533011, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_532999), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_532999)), _533003), _533013), _533007)))], (9255 ^ _199745) ^ [_533609, _533611, _533613, _533615, _533617, _533619, _533621] : [class_Fields_Ofield(_533609), c_Polynomial_Opdivmod__rel(_533609, _533611, _533613, _533615, _533617), -(_533613 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_533609))), _533619 = c_Rings_Oinverse__class_Odivide(_533609, hAPP(c_Polynomial_Ocoeff(_533609, c_Polynomial_OpCons(_533609, _533621, _533617)), c_Polynomial_Odegree(_533609, _533613)), hAPP(c_Polynomial_Ocoeff(_533609, _533613), c_Polynomial_Odegree(_533609, _533613))), -(c_Polynomial_Opdivmod__rel(_533609, c_Polynomial_OpCons(_533609, _533621, _533611), _533613, c_Polynomial_OpCons(_533609, _533619, _533615), c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_533609), c_Polynomial_OpCons(_533609, _533621, _533617), c_Polynomial_Osmult(_533609, _533619, _533613))))], (9273 ^ _199745) ^ [_534349, _534351, _534353, _534355, _534357, _534359] : [class_Fields_Ofield(_534349), -(_534351 = c_Groups_Ozero__class_Ozero(_534349)), c_Polynomial_Opdivmod__rel(_534349, _534353, _534355, _534357, _534359), -(c_Polynomial_Opdivmod__rel(_534349, _534353, c_Polynomial_Osmult(_534349, _534351, _534355), c_Polynomial_Osmult(_534349, c_Rings_Oinverse__class_Oinverse(_534349, _534351), _534357), _534359))], (9287 ^ _199745) ^ [_534860, _534862, _534864, _534866] : [class_RealVector_Oreal__normed__field(_534860), -(_534862 = c_Groups_Ozero__class_Ozero(_534860)), -(_534864 = c_Groups_Ozero__class_Ozero(_534860)), -(c_Rings_Oinverse__class_Odivide(_534860, c_Groups_Ominus__class_Ominus(_534860, c_Rings_Oinverse__class_Oinverse(_534860, _534862), c_Rings_Oinverse__class_Oinverse(_534860, _534864)), _534866) = c_Groups_Ouminus__class_Ouminus(_534860, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_534860), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_534860), c_Rings_Oinverse__class_Oinverse(_534860, _534862)), c_Rings_Oinverse__class_Odivide(_534860, c_Groups_Ominus__class_Ominus(_534860, _534862, _534864), _534866))), c_Rings_Oinverse__class_Oinverse(_534860, _534864))))], (9301 ^ _199745) ^ [_535396, _535398, _535400] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _535396, _535398), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _535396, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _535400, _535398)))], (9307 ^ _199745) ^ [_535624, _535626] : [class_Rings_Olinordered__idom(_535624), 9310 ^ _199745 : [(9311 ^ _199745) ^ [] : [c_Polynomial_Opos__poly(_535624, _535626), -(c_Orderings_Oord__class_Oless(_535624, c_Groups_Ozero__class_Ozero(_535624), hAPP(c_Polynomial_Ocoeff(_535624, _535626), c_Polynomial_Odegree(_535624, _535626))))], (9317 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_535624, c_Groups_Ozero__class_Ozero(_535624), hAPP(c_Polynomial_Ocoeff(_535624, _535626), c_Polynomial_Odegree(_535624, _535626))), -(c_Polynomial_Opos__poly(_535624, _535626))]]], (9323 ^ _199745) ^ [_536132, _536134, _536136] : [class_Rings_Olinordered__idom(_536132), 9326 ^ _199745 : [(9327 ^ _199745) ^ [] : [c_Polynomial_Opos__poly(_536132, c_Polynomial_OpCons(_536132, _536134, _536136)), -(c_Polynomial_Opos__poly(_536132, _536136)), 9334 ^ _199745 : [(9335 ^ _199745) ^ [] : [-(_536136 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_536132)))], (9337 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_536132, c_Groups_Ozero__class_Ozero(_536132), _536134))]]], (9339 ^ _199745) ^ [] : [-(c_Polynomial_Opos__poly(_536132, c_Polynomial_OpCons(_536132, _536134, _536136))), 9340 ^ _199745 : [(9341 ^ _199745) ^ [] : [c_Polynomial_Opos__poly(_536132, _536136)], (9343 ^ _199745) ^ [] : [_536136 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_536132)), c_Orderings_Oord__class_Oless(_536132, c_Groups_Ozero__class_Ozero(_536132), _536134)]]]]], (9351 ^ _199745) ^ [_536953] : [class_Rings_Olinordered__idom(_536953), c_Polynomial_Opos__poly(_536953, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_536953)))], (9357 ^ _199745) ^ [_537178, _537180, _537182] : [class_Rings_Olinordered__idom(_537178), c_Polynomial_Opos__poly(_537178, _537180), c_Polynomial_Opos__poly(_537178, _537182), -(c_Polynomial_Opos__poly(_537178, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_537178), _537180, _537182)))], (9371 ^ _199745) ^ [_537604, _537606, _537608] : [class_Rings_Olinordered__idom(_537604), c_Polynomial_Opos__poly(_537604, _537606), c_Polynomial_Opos__poly(_537604, _537608), -(c_Polynomial_Opos__poly(_537604, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_537604)), _537606), _537608)))], (9385 ^ _199745) ^ [_538038, _538040, _538042] : [class_Rings_Olinordered__idom(_538038), 9388 ^ _199745 : [(9389 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_538038), _538040, _538042), -(c_Polynomial_Opos__poly(_538038, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_538038), _538042, _538040)))], (9395 ^ _199745) ^ [] : [c_Polynomial_Opos__poly(_538038, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_538038), _538042, _538040)), -(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_538038), _538040, _538042))]]], (9401 ^ _199745) ^ [_538539, _538541] : [class_Rings_Olinordered__idom(_538539), -(_538541 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_538539))), -(c_Polynomial_Opos__poly(_538539, _538541)), -(c_Polynomial_Opos__poly(_538539, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_538539), _538541)))], (9415 ^ _199745) ^ [_538945, _538947] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _538945), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _538947), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _538947), _538945), _538947) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _538947), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _538945, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (9425 ^ _199745) ^ [_539302, _539304, _539306] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _539302), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _539304, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oabs__class_Oabs(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _539304, _539306)), c_Groups_Oone__class_Oone(tc_Int_Oint))), _539302)), _539306))], (9431 ^ _199745) ^ [_539564, _539566] : [class_Divides_Osemiring__div(_539564), -(c_Divides_Odiv__class_Odiv(_539564, c_Groups_Ozero__class_Ozero(_539564), _539566) = c_Groups_Ozero__class_Ozero(_539564))], (9437 ^ _199745) ^ [_539788, _539790] : [class_Divides_Osemiring__div(_539788), -(c_Divides_Odiv__class_Odiv(_539788, _539790, c_Groups_Ozero__class_Ozero(_539788)) = c_Groups_Ozero__class_Ozero(_539788))], (9443 ^ _199745) ^ [_539983] : [-(c_Divides_Odiv__class_Odiv(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _539983) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (9445 ^ _199745) ^ [_540079, _540081] : [-(c_Divides_Odiv__class_Odiv(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _540079), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _540081)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint, _540079, _540081))], (9447 ^ _199745) ^ [_540187, _540189] : [-(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _540187, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _540189)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _540187), _540189))], (9449 ^ _199745) ^ [_540310, _540312] : [class_Divides_Osemiring__div(_540310), -(c_Divides_Odiv__class_Odiv(_540310, _540312, c_Groups_Oone__class_Oone(_540310)) = _540312)], (9455 ^ _199745) ^ [_540516] : [-(_540516 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _540516, _540516) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (9461 ^ _199745) ^ [_540731, _540733] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _540731, _540733), -(c_Groups_Oabs__class_Oabs(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _540733, _540731)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint, c_Groups_Oabs__class_Oabs(tc_Int_Oint, _540733), c_Groups_Oabs__class_Oabs(tc_Int_Oint, _540731)))], (9467 ^ _199745) ^ [_541005, _541007, _541009, _541011] : [class_Divides_Osemiring__div(_541005), c_Rings_Odvd__class_Odvd(_541005, _541007, _541009), c_Rings_Odvd__class_Odvd(_541005, _541007, _541011), 9478 ^ _199745 : [(9479 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(_541005, c_Divides_Odiv__class_Odiv(_541005, _541009, _541007), c_Divides_Odiv__class_Odiv(_541005, _541011, _541007)), -(c_Rings_Odvd__class_Odvd(_541005, _541009, _541011))], (9485 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(_541005, _541009, _541011), -(c_Rings_Odvd__class_Odvd(_541005, c_Divides_Odiv__class_Odiv(_541005, _541009, _541007), c_Divides_Odiv__class_Odiv(_541005, _541011, _541007)))]]], (9491 ^ _199745) ^ [_541723, _541725] : [class_Fields_Olinordered__field(_541723), -(_541725 = c_Groups_Ozero__class_Ozero(_541723)), -(c_Groups_Oabs__class_Oabs(_541723, c_Rings_Oinverse__class_Oinverse(_541723, _541725)) = c_Rings_Oinverse__class_Oinverse(_541723, c_Groups_Oabs__class_Oabs(_541723, _541725)))], (9501 ^ _199745) ^ [_542065, _542067, _542069] : [class_Rings_Olinordered__idom(_542065), -(c_Groups_Oabs__class_Oabs(_542065, hAPP(hAPP(c_Power_Opower__class_Opower(_542065), c_Groups_Ouminus__class_Ouminus(_542065, _542067)), _542069)) = c_Groups_Oabs__class_Oabs(_542065, hAPP(hAPP(c_Power_Opower__class_Opower(_542065), _542067), _542069)))], (9507 ^ _199745) ^ [_542329, _542331] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _542329, _542331), c_Rings_Odvd__class_Odvd(tc_Int_Oint, _542331, _542329), -(c_Groups_Oabs__class_Oabs(tc_Int_Oint, _542329) = c_Groups_Oabs__class_Oabs(tc_Int_Oint, _542331))], (9517 ^ _199745) ^ [_542644, _542646] : [class_Fields_Olinordered__field__inverse__zero(_542644), -(c_Groups_Oabs__class_Oabs(_542644, c_Rings_Oinverse__class_Oinverse(_542644, _542646)) = c_Rings_Oinverse__class_Oinverse(_542644, c_Groups_Oabs__class_Oabs(_542644, _542646)))], (9523 ^ _199745) ^ [_542890, _542892, _542894] : [class_Groups_Oordered__ab__group__add__abs(_542890), -(c_Groups_Oabs__class_Oabs(_542890, c_Groups_Ominus__class_Ominus(_542890, _542892, _542894)) = c_Groups_Oabs__class_Oabs(_542890, c_Groups_Ominus__class_Ominus(_542890, _542894, _542892)))], (9529 ^ _199745) ^ [_543146, _543148, _543150] : [class_Rings_Olinordered__idom(_543146), c_Groups_Oabs__class_Oabs(_543146, _543148) = c_Groups_Oabs__class_Oabs(_543146, _543150), -(c_Rings_Odvd__class_Odvd(_543146, _543148, _543150))], (9539 ^ _199745) ^ [_543481, _543483, _543485] : [class_Rings_Olinordered__idom(_543481), 9542 ^ _199745 : [(9543 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(_543481, c_Groups_Oabs__class_Oabs(_543481, _543483), _543485), -(c_Rings_Odvd__class_Odvd(_543481, _543483, _543485))], (9549 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(_543481, _543483, _543485), -(c_Rings_Odvd__class_Odvd(_543481, c_Groups_Oabs__class_Oabs(_543481, _543483), _543485))]]], (9555 ^ _199745) ^ [_543984, _543986, _543988] : [class_Rings_Olinordered__idom(_543984), 9558 ^ _199745 : [(9559 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(_543984, _543986, c_Groups_Oabs__class_Oabs(_543984, _543988)), -(c_Rings_Odvd__class_Odvd(_543984, _543986, _543988))], (9565 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(_543984, _543986, _543988), -(c_Rings_Odvd__class_Odvd(_543984, _543986, c_Groups_Oabs__class_Oabs(_543984, _543988)))]]], (9571 ^ _199745) ^ [_544473, _544475] : [class_Groups_Oordered__ab__group__add__abs(_544473), -(c_Groups_Oabs__class_Oabs(_544473, c_Groups_Oabs__class_Oabs(_544473, _544475)) = c_Groups_Oabs__class_Oabs(_544473, _544475))], (9577 ^ _199745) ^ [_544713, _544715, _544717] : [class_Rings_Olinordered__idom(_544713), -(c_Groups_Oabs__class_Oabs(_544713, hAPP(hAPP(c_Power_Opower__class_Opower(_544713), _544715), _544717)) = hAPP(hAPP(c_Power_Opower__class_Opower(_544713), c_Groups_Oabs__class_Oabs(_544713, _544715)), _544717))], (9583 ^ _199745) ^ [_544971, _544973] : [class_Groups_Oordered__ab__group__add__abs(_544971), -(c_Groups_Oabs__class_Oabs(_544971, c_Groups_Ouminus__class_Ouminus(_544971, _544973)) = c_Groups_Oabs__class_Oabs(_544971, _544973))], (9589 ^ _199745) ^ [_545183] : [class_Rings_Olinordered__idom(_545183), -(c_Groups_Oabs__class_Oabs(_545183, c_Groups_Oone__class_Oone(_545183)) = c_Groups_Oone__class_Oone(_545183))], (9595 ^ _199745) ^ [_545413, _545415, _545417] : [class_Groups_Oordered__ab__group__add__abs(_545413), -(c_Groups_Oabs__class_Oabs(_545413, c_Groups_Oplus__class_Oplus(_545413, c_Groups_Oabs__class_Oabs(_545413, _545415), c_Groups_Oabs__class_Oabs(_545413, _545417))) = c_Groups_Oplus__class_Oplus(_545413, c_Groups_Oabs__class_Oabs(_545413, _545415), c_Groups_Oabs__class_Oabs(_545413, _545417)))], (9601 ^ _199745) ^ [_545687, _545689, _545691] : [class_Rings_Olinordered__idom(_545687), -(c_Groups_Oabs__class_Oabs(_545687, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_545687), _545689), _545691)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_545687), c_Groups_Oabs__class_Oabs(_545687, _545689)), c_Groups_Oabs__class_Oabs(_545687, _545691)))], (9607 ^ _199745) ^ [_545951, _545953] : [class_Rings_Olinordered__idom(_545951), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_545951), c_Groups_Oabs__class_Oabs(_545951, _545953)), c_Groups_Oabs__class_Oabs(_545951, _545953)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_545951), _545953), _545953))], (9613 ^ _199745) ^ [_546189] : [class_Groups_Oordered__ab__group__add__abs(_546189), -(c_Groups_Oabs__class_Oabs(_546189, c_Groups_Ozero__class_Ozero(_546189)) = c_Groups_Ozero__class_Ozero(_546189))], (9619 ^ _199745) ^ [_546405, _546407] : [class_Groups_Oordered__ab__group__add__abs(_546405), 9622 ^ _199745 : [(9623 ^ _199745) ^ [] : [c_Groups_Oabs__class_Oabs(_546405, _546407) = c_Groups_Ozero__class_Ozero(_546405), -(_546407 = c_Groups_Ozero__class_Ozero(_546405))], (9629 ^ _199745) ^ [] : [_546407 = c_Groups_Ozero__class_Ozero(_546405), -(c_Groups_Oabs__class_Oabs(_546405, _546407) = c_Groups_Ozero__class_Ozero(_546405))]]], (9635 ^ _199745) ^ [_546912, _546914, _546916, _546918] : [class_Divides_Osemiring__div(_546912), c_Rings_Odvd__class_Odvd(_546912, _546914, _546916), -(hAPP(hAPP(c_Power_Opower__class_Opower(_546912), c_Divides_Odiv__class_Odiv(_546912, _546916, _546914)), _546918) = c_Divides_Odiv__class_Odiv(_546912, hAPP(hAPP(c_Power_Opower__class_Opower(_546912), _546916), _546918), hAPP(hAPP(c_Power_Opower__class_Opower(_546912), _546914), _546918)))], (9645 ^ _199745) ^ [_547309, _547311, _547313] : [class_Divides_Oring__div(_547309), c_Rings_Odvd__class_Odvd(_547309, _547311, _547313), -(c_Divides_Odiv__class_Odiv(_547309, c_Groups_Ouminus__class_Ouminus(_547309, _547313), _547311) = c_Groups_Ouminus__class_Ouminus(_547309, c_Divides_Odiv__class_Odiv(_547309, _547313, _547311)))], (9655 ^ _199745) ^ [_547660, _547662, _547664] : [class_Divides_Oring__div(_547660), c_Rings_Odvd__class_Odvd(_547660, _547662, _547664), -(c_Divides_Odiv__class_Odiv(_547660, _547664, c_Groups_Ouminus__class_Ouminus(_547660, _547662)) = c_Groups_Ouminus__class_Ouminus(_547660, c_Divides_Odiv__class_Odiv(_547660, _547664, _547662)))], (9665 ^ _199745) ^ [_548011, _548013, _548015] : [class_Divides_Osemiring__div(_548011), -(c_Divides_Odiv__class_Odiv(_548011, c_Divides_Odiv__class_Omod(_548011, _548013, _548015), _548015) = c_Groups_Ozero__class_Ozero(_548011))], (9671 ^ _199745) ^ [_548273, _548275, _548277, _548279] : [class_Divides_Osemiring__div(_548273), c_Rings_Odvd__class_Odvd(_548273, _548275, _548277), c_Rings_Odvd__class_Odvd(_548273, _548275, _548279), -(c_Divides_Odiv__class_Odiv(_548273, c_Groups_Oplus__class_Oplus(_548273, _548277, _548279), _548275) = c_Groups_Oplus__class_Oplus(_548273, c_Divides_Odiv__class_Odiv(_548273, _548277, _548275), c_Divides_Odiv__class_Odiv(_548273, _548279, _548275)))], (9685 ^ _199745) ^ [_548745, _548747, _548749] : [class_Divides_Osemiring__div(_548745), c_Rings_Odvd__class_Odvd(_548745, _548747, _548749), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_548745), _548747), c_Divides_Odiv__class_Odiv(_548745, _548749, _548747)) = _548749)], (9695 ^ _199745) ^ [_549106, _549108, _549110, _549112] : [class_Divides_Osemiring__div(_549106), c_Rings_Odvd__class_Odvd(_549106, _549108, _549110), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_549106), _549112), c_Divides_Odiv__class_Odiv(_549106, _549110, _549108)) = c_Divides_Odiv__class_Odiv(_549106, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_549106), _549112), _549110), _549108))], (9705 ^ _199745) ^ [_549487, _549489, _549491] : [class_Divides_Osemiring__div(_549487), c_Rings_Odvd__class_Odvd(_549487, _549489, _549491), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_549487), c_Divides_Odiv__class_Odiv(_549487, _549491, _549489)), _549489) = _549491)], (9715 ^ _199745) ^ [_549848, _549850, _549852, _549854] : [class_Divides_Osemiring__div(_549848), c_Rings_Odvd__class_Odvd(_549848, _549850, _549852), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_549848), c_Divides_Odiv__class_Odiv(_549848, _549852, _549850)), _549854) = c_Divides_Odiv__class_Odiv(_549848, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_549848), _549852), _549854), _549850))], (9725 ^ _199745) ^ [_550257, _550259, _550261, _550263, _550265] : [class_Divides_Osemiring__div(_550257), c_Rings_Odvd__class_Odvd(_550257, _550259, _550261), c_Rings_Odvd__class_Odvd(_550257, _550263, _550265), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_550257), c_Divides_Odiv__class_Odiv(_550257, _550261, _550259)), c_Divides_Odiv__class_Odiv(_550257, _550265, _550263)) = c_Divides_Odiv__class_Odiv(_550257, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_550257), _550261), _550265), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_550257), _550259), _550263)))], (9739 ^ _199745) ^ [_550761, _550763] : [class_Divides_Osemiring__div(_550761), -(_550763 = c_Groups_Ozero__class_Ozero(_550761)), -(c_Divides_Odiv__class_Odiv(_550761, _550763, _550763) = c_Groups_Oone__class_Oone(_550761))], (9749 ^ _199745) ^ [_551105, _551107, _551109, _551111] : [class_Divides_Osemiring__div(_551105), -(_551107 = c_Groups_Ozero__class_Ozero(_551105)), -(c_Divides_Odiv__class_Odiv(_551105, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_551105), _551107), _551109), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_551105), _551107), _551111)) = c_Divides_Odiv__class_Odiv(_551105, _551109, _551111))], (9759 ^ _199745) ^ [_551505, _551507, _551509, _551511] : [class_Divides_Osemiring__div(_551505), -(_551507 = c_Groups_Ozero__class_Ozero(_551505)), -(c_Divides_Odiv__class_Odiv(_551505, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_551505), _551509), _551507), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_551505), _551511), _551507)) = c_Divides_Odiv__class_Odiv(_551505, _551509, _551511))], (9769 ^ _199745) ^ [_551891, _551893, _551895] : [class_Divides_Osemiring__div(_551891), -(_551893 = c_Groups_Ozero__class_Ozero(_551891)), -(c_Divides_Odiv__class_Odiv(_551891, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_551891), _551893), _551895), _551893) = _551895)], (9779 ^ _199745) ^ [_552243, _552245, _552247] : [class_Divides_Osemiring__div(_552243), -(_552245 = c_Groups_Ozero__class_Ozero(_552243)), -(c_Divides_Odiv__class_Odiv(_552243, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_552243), _552247), _552245), _552245) = _552247)], (9789 ^ _199745) ^ [_552609, _552611, _552613, _552615] : [class_Divides_Osemiring__div(_552609), 9792 ^ _199745 : [(9793 ^ _199745) ^ [] : [_552611 = c_Groups_Ozero__class_Ozero(_552609), -(c_Divides_Odiv__class_Odiv(_552609, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_552609), _552611), _552613), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_552609), _552611), _552615)) = c_Groups_Ozero__class_Ozero(_552609))], (9799 ^ _199745) ^ [] : [-(_552611 = c_Groups_Ozero__class_Ozero(_552609)), -(c_Divides_Odiv__class_Odiv(_552609, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_552609), _552611), _552613), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_552609), _552611), _552615)) = c_Divides_Odiv__class_Odiv(_552609, _552613, _552615))]]], (9805 ^ _199745) ^ [_553220] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _553220, c_Groups_Oone__class_Oone(tc_Int_Oint)), -(c_Groups_Oabs__class_Oabs(tc_Int_Oint, _553220) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (9811 ^ _199745) ^ [_553384] : [c_Groups_Oabs__class_Oabs(tc_Int_Oint, _553384) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _553384, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (9817 ^ _199745) ^ [_553598, _553600] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _553598, _553600), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _553598), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _553600, _553598)) = _553600)], (9823 ^ _199745) ^ [_553830, _553832] : [c_Groups_Oabs__class_Oabs(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _553830), _553832)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(c_Groups_Oabs__class_Oabs(tc_Int_Oint, _553830) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (9829 ^ _199745) ^ [_554078, _554080, _554082] : [class_Fields_Olinordered__field__inverse__zero(_554078), -(c_Groups_Oabs__class_Oabs(_554078, c_Rings_Oinverse__class_Odivide(_554078, _554080, _554082)) = c_Rings_Oinverse__class_Odivide(_554078, c_Groups_Oabs__class_Oabs(_554078, _554080), c_Groups_Oabs__class_Oabs(_554078, _554082)))], (9835 ^ _199745) ^ [_554340, _554342, _554344] : [class_Fields_Olinordered__field(_554340), -(_554342 = c_Groups_Ozero__class_Ozero(_554340)), -(c_Groups_Oabs__class_Oabs(_554340, c_Rings_Oinverse__class_Odivide(_554340, _554344, _554342)) = c_Rings_Oinverse__class_Odivide(_554340, c_Groups_Oabs__class_Oabs(_554340, _554344), c_Groups_Oabs__class_Oabs(_554340, _554342)))], (9845 ^ _199745) ^ [_554702, _554704, _554706] : [class_Rings_Olinordered__idom(_554702), 9848 ^ _199745 : [(9849 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_554702, c_Groups_Oabs__class_Oabs(_554702, _554704), _554706), 9852 ^ _199745 : [(9853 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_554702, _554704, _554706))], (9855 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_554702, c_Groups_Ouminus__class_Ouminus(_554702, _554704), _554706))]]], (9857 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_554702, c_Groups_Oabs__class_Oabs(_554702, _554704), _554706)), c_Orderings_Oord__class_Oless(_554702, _554704, _554706), c_Orderings_Oord__class_Oless(_554702, c_Groups_Ouminus__class_Ouminus(_554702, _554704), _554706)]]], (9867 ^ _199745) ^ [_555409, _555411, _555413, _555415, _555417] : [class_Rings_Olinordered__idom(_555409), c_Orderings_Oord__class_Oless(_555409, c_Groups_Oabs__class_Oabs(_555409, _555411), _555413), c_Orderings_Oord__class_Oless(_555409, c_Groups_Oabs__class_Oabs(_555409, _555415), _555417), -(c_Orderings_Oord__class_Oless(_555409, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_555409), c_Groups_Oabs__class_Oabs(_555409, _555411)), c_Groups_Oabs__class_Oabs(_555409, _555415)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_555409), _555413), _555417)))], (9881 ^ _199745) ^ [_555899, _555901] : [class_Groups_Oordered__ab__group__add__abs(_555899), c_Orderings_Oord__class_Oless(_555899, c_Groups_Ozero__class_Ozero(_555899), _555901), -(c_Groups_Oabs__class_Oabs(_555899, _555901) = _555901)], (9891 ^ _199745) ^ [_556208, _556210] : [class_Groups_Oordered__ab__group__add__abs(_556208), 9894 ^ _199745 : [(9895 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_556208, c_Groups_Ozero__class_Ozero(_556208), c_Groups_Oabs__class_Oabs(_556208, _556210)), _556210 = c_Groups_Ozero__class_Ozero(_556208)], (9901 ^ _199745) ^ [] : [-(_556210 = c_Groups_Ozero__class_Ozero(_556208)), -(c_Orderings_Oord__class_Oless(_556208, c_Groups_Ozero__class_Ozero(_556208), c_Groups_Oabs__class_Oabs(_556208, _556210)))]]], (9907 ^ _199745) ^ [_556692, _556694] : [class_Groups_Oordered__ab__group__add__abs(_556692), c_Orderings_Oord__class_Oless(_556692, c_Groups_Oabs__class_Oabs(_556692, _556694), c_Groups_Ozero__class_Ozero(_556692))], (9913 ^ _199745) ^ [_556913, _556915] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _556913, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _556915), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _556913, _556915), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9923 ^ _199745) ^ [_557226, _557228] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _557226, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 9926 ^ _199745 : [(9927 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _557228, _557226), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _557228))], (9933 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _557228), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _557228, _557226), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (9939 ^ _199745) ^ [_557706, _557708] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _557706), 9942 ^ _199745 : [(9943 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _557708, _557706), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _557708, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9949 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _557708, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _557708, _557706), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (9955 ^ _199745) ^ [_558171, _558173] : [-(c_Divides_Odiv__class_Odiv(tc_Int_Oint, c_Divides_Odiv__class_Omod(tc_Int_Oint, _558171, _558173), _558173) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (9957 ^ _199745) ^ [_558279] : [-(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _558279, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (9959 ^ _199745) ^ [_558327] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _558327, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _558327)], (9961 ^ _199745) ^ [_558439, _558441, _558443] : [-(c_Divides_Odiv__class_Odiv(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _558439, _558441), _558443) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _558439, _558443), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _558441, _558443)), c_Divides_Odiv__class_Odiv(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Divides_Odiv__class_Omod(tc_Int_Oint, _558439, _558443), c_Divides_Odiv__class_Omod(tc_Int_Oint, _558441, _558443)), _558443)))], (9963 ^ _199745) ^ [_558590, _558592] : [class_Groups_Oabs__if(_558590), 9966 ^ _199745 : [(9967 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_558590, _558592, c_Groups_Ozero__class_Ozero(_558590)), -(c_Groups_Oabs__class_Oabs(_558590, _558592) = c_Groups_Ouminus__class_Ouminus(_558590, _558592))], (9973 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_558590, _558592, c_Groups_Ozero__class_Ozero(_558590))), -(c_Groups_Oabs__class_Oabs(_558590, _558592) = _558592)]]], (9979 ^ _199745) ^ [_559084, _559086] : [class_Groups_Oordered__ab__group__add__abs(_559084), c_Orderings_Oord__class_Oless(_559084, _559086, c_Groups_Ozero__class_Ozero(_559084)), -(c_Groups_Oabs__class_Oabs(_559084, _559086) = c_Groups_Ouminus__class_Ouminus(_559084, _559086))], (9989 ^ _199745) ^ [_559413, _559415, _559417] : [class_Fields_Olinordered__field__inverse__zero(_559413), c_Orderings_Oord__class_Oless(_559413, c_Groups_Ozero__class_Ozero(_559413), _559415), -(c_Rings_Oinverse__class_Odivide(_559413, c_Groups_Oabs__class_Oabs(_559413, _559417), _559415) = c_Groups_Oabs__class_Oabs(_559413, c_Rings_Oinverse__class_Odivide(_559413, _559417, _559415)))], (9999 ^ _199745) ^ [_559754, _559756] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _559754), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _559756), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _559754, _559756), _559754))], (10009 ^ _199745) ^ [_560081, _560083, _560085] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _560081), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _560083, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _560085), _560081)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _560083, _560085), _560081))], (10015 ^ _199745) ^ [_560350] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oabs__class_Oabs(tc_Int_Oint, _560350), c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_560350 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (10021 ^ _199745) ^ [_560514] : [_560514 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oabs__class_Oabs(tc_Int_Oint, _560514), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (10027 ^ _199745) ^ [_560734] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _560734, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Groups_Oabs__class_Oabs(tc_Int_Oint, _560734) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _560734))], (10033 ^ _199745) ^ [_560904] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _560904, c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Groups_Oabs__class_Oabs(tc_Int_Oint, _560904) = _560904)], (10039 ^ _199745) ^ [_561106, _561108] : [-(_561106 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _561108), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _561106, _561108)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _561106, _561108)))], (10041 ^ _199745) ^ [_561232, _561234, _561236] : [-(c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _561232), _561234), _561236) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _561232), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _561234, _561236)), c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _561232), c_Divides_Odiv__class_Omod(tc_Int_Oint, _561234, _561236)), _561236)))], (10043 ^ _199745) ^ [_561380, _561382, _561384] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _561380), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _561382, _561380)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _561382, _561380)), _561384) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _561382, _561384))], (10045 ^ _199745) ^ [_561516, _561518, _561520] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _561516, _561518)), _561518), c_Divides_Odiv__class_Omod(tc_Int_Oint, _561516, _561518)), _561520) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _561516, _561520))], (10047 ^ _199745) ^ [_561638, _561640] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _561638), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _561640, _561638)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _561640, c_Divides_Odiv__class_Omod(tc_Int_Oint, _561640, _561638)))], (10049 ^ _199745) ^ [_561750, _561752] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _561750, _561752) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _561750, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _561750, _561752)), _561752)))], (10051 ^ _199745) ^ [_561905, _561907, _561909, _561911] : [class_Divides_Osemiring__div(_561905), -(_561907 = c_Groups_Ozero__class_Ozero(_561905)), -(c_Divides_Odiv__class_Odiv(_561905, c_Groups_Oplus__class_Oplus(_561905, _561909, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_561905), _561911), _561907)), _561907) = c_Groups_Oplus__class_Oplus(_561905, _561911, c_Divides_Odiv__class_Odiv(_561905, _561909, _561907)))], (10061 ^ _199745) ^ [_562305, _562307, _562309, _562311] : [class_Divides_Osemiring__div(_562305), -(_562307 = c_Groups_Ozero__class_Ozero(_562305)), -(c_Divides_Odiv__class_Odiv(_562305, c_Groups_Oplus__class_Oplus(_562305, _562309, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_562305), _562307), _562311)), _562307) = c_Groups_Oplus__class_Oplus(_562305, _562311, c_Divides_Odiv__class_Odiv(_562305, _562309, _562307)))], (10071 ^ _199745) ^ [_562691, _562693, _562695] : [class_Divides_Osemiring__div(_562691), -(_562693 = c_Groups_Ozero__class_Ozero(_562691)), -(c_Divides_Odiv__class_Odiv(_562691, c_Groups_Oplus__class_Oplus(_562691, _562693, _562695), _562693) = c_Groups_Oplus__class_Oplus(_562691, c_Divides_Odiv__class_Odiv(_562691, _562695, _562693), c_Groups_Oone__class_Oone(_562691)))], (10081 ^ _199745) ^ [_563055, _563057, _563059] : [class_Divides_Osemiring__div(_563055), -(_563057 = c_Groups_Ozero__class_Ozero(_563055)), -(c_Divides_Odiv__class_Odiv(_563055, c_Groups_Oplus__class_Oplus(_563055, _563059, _563057), _563057) = c_Groups_Oplus__class_Oplus(_563055, c_Divides_Odiv__class_Odiv(_563055, _563059, _563057), c_Groups_Oone__class_Oone(_563055)))], (10091 ^ _199745) ^ [_563433, _563435, _563437, _563439] : [class_Divides_Osemiring__div(_563433), -(_563435 = c_Groups_Ozero__class_Ozero(_563433)), c_Rings_Odvd__class_Odvd(_563433, _563435, _563437), 10102 ^ _199745 : [(10103 ^ _199745) ^ [] : [c_Divides_Odiv__class_Odiv(_563433, _563437, _563435) = _563439, -(_563437 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_563433), _563439), _563435))], (10109 ^ _199745) ^ [] : [_563437 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_563433), _563439), _563435), -(c_Divides_Odiv__class_Odiv(_563433, _563437, _563435) = _563439)]]], (10115 ^ _199745) ^ [_564204, _564206, _564208, _564210, _564212] : [class_Divides_Osemiring__div(_564204), -(_564206 = c_Groups_Ozero__class_Ozero(_564204)), -(_564208 = c_Groups_Ozero__class_Ozero(_564204)), c_Rings_Odvd__class_Odvd(_564204, _564206, _564210), c_Rings_Odvd__class_Odvd(_564204, _564208, _564212), 10134 ^ _199745 : [(10135 ^ _199745) ^ [] : [c_Divides_Odiv__class_Odiv(_564204, _564210, _564206) = c_Divides_Odiv__class_Odiv(_564204, _564212, _564208), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_564204), _564210), _564208) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_564204), _564206), _564212))], (10141 ^ _199745) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_564204), _564210), _564208) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_564204), _564206), _564212), -(c_Divides_Odiv__class_Odiv(_564204, _564210, _564206) = c_Divides_Odiv__class_Odiv(_564204, _564212, _564208))]]], (10147 ^ _199745) ^ [_565218, _565220, _565222] : [class_Divides_Osemiring__div(_565218), -(c_Groups_Oplus__class_Oplus(_565218, c_Divides_Odiv__class_Omod(_565218, _565220, _565222), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_565218), c_Divides_Odiv__class_Odiv(_565218, _565220, _565222)), _565222)) = _565220)], (10153 ^ _199745) ^ [_565486, _565488, _565490] : [class_Divides_Osemiring__div(_565486), -(c_Groups_Oplus__class_Oplus(_565486, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_565486), _565488), c_Divides_Odiv__class_Odiv(_565486, _565490, _565488)), c_Divides_Odiv__class_Omod(_565486, _565490, _565488)) = _565490)], (10159 ^ _199745) ^ [_565754, _565756, _565758] : [class_Divides_Osemiring__div(_565754), -(c_Groups_Oplus__class_Oplus(_565754, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_565754), c_Divides_Odiv__class_Odiv(_565754, _565756, _565758)), _565758), c_Divides_Odiv__class_Omod(_565754, _565756, _565758)) = _565756)], (10165 ^ _199745) ^ [_566036, _566038, _566040, _566042] : [class_Divides_Osemiring__div(_566036), -(c_Groups_Oplus__class_Oplus(_566036, c_Groups_Oplus__class_Oplus(_566036, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_566036), _566038), c_Divides_Odiv__class_Odiv(_566036, _566040, _566038)), c_Divides_Odiv__class_Omod(_566036, _566040, _566038)), _566042) = c_Groups_Oplus__class_Oplus(_566036, _566040, _566042))], (10171 ^ _199745) ^ [_566340, _566342, _566344, _566346] : [class_Divides_Osemiring__div(_566340), -(c_Groups_Oplus__class_Oplus(_566340, c_Groups_Oplus__class_Oplus(_566340, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_566340), c_Divides_Odiv__class_Odiv(_566340, _566342, _566344)), _566344), c_Divides_Odiv__class_Omod(_566340, _566342, _566344)), _566346) = c_Groups_Oplus__class_Oplus(_566340, _566342, _566346))], (10177 ^ _199745) ^ [_566616, _566618] : [-(_566616 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 10180 ^ _199745 : [(10181 ^ _199745) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _566616), _566618), _566616), -(c_Groups_Oabs__class_Oabs(tc_Int_Oint, _566618) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (10187 ^ _199745) ^ [] : [c_Groups_Oabs__class_Oabs(tc_Int_Oint, _566618) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _566616), _566618), _566616))]]], (10203 ^ _199745) ^ [_567411, _567413] : [10204 ^ _199745 : [(10205 ^ _199745) ^ [] : [-(_567411 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (10207 ^ _199745) ^ [] : [_567413 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), c_Groups_Oabs__class_Oabs(tc_Int_Oint, _567411)), _567413)))], (10193 ^ _199745) ^ [_567138, _567140] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), c_Groups_Oabs__class_Oabs(tc_Int_Oint, _567138)), _567140)), _567138 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_567140 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10211 ^ _199745) ^ [_567734, _567736, _567738] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _567734), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _567736, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _567738), _567734)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _567738), c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _567736, _567738), _567734)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _567736, _567738)))], (10217 ^ _199745) ^ [_568016, _568018] : [-(_568016 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 10220 ^ _199745 : [(10221 ^ _199745) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _568018, _568016) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _568018), _568016) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _568018, _568016)))], (10227 ^ _199745) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _568018, _568016) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _568018), _568016) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _568018, _568016)), c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (10233 ^ _199745) ^ [_568565, _568567] : [-(_568565 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 10236 ^ _199745 : [(10237 ^ _199745) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _568567, _568565) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _568567, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _568565)) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _568567, _568565)))], (10243 ^ _199745) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _568567, _568565) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _568567, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _568565)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _568567, _568565)), c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (10249 ^ _199745) ^ [_569128, _569130, _569132] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _569128), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _569130, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _569132, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oabs__class_Oabs(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _569132, _569130)), c_Groups_Oone__class_Oone(tc_Int_Oint))), _569128))))], (10255 ^ _199745) ^ [_569418, _569420, _569422, _569424] : [class_Rings_Olinordered__idom(_569418), 10258 ^ _199745 : [(10259 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_569418, c_Groups_Oabs__class_Oabs(_569418, c_Groups_Ominus__class_Ominus(_569418, _569420, _569422)), _569424), 10262 ^ _199745 : [(10263 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_569418, c_Groups_Ominus__class_Ominus(_569418, _569422, _569424), _569420))], (10265 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_569418, _569420, c_Groups_Oplus__class_Oplus(_569418, _569422, _569424)))]]], (10267 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_569418, c_Groups_Oabs__class_Oabs(_569418, c_Groups_Ominus__class_Ominus(_569418, _569420, _569422)), _569424)), c_Orderings_Oord__class_Oless(_569418, c_Groups_Ominus__class_Ominus(_569418, _569422, _569424), _569420), c_Orderings_Oord__class_Oless(_569418, _569420, c_Groups_Oplus__class_Oplus(_569418, _569422, _569424))]]], (10277 ^ _199745) ^ [_570132, _570134] : [class_Rings_Olinordered__idom(_570132), 10280 ^ _199745 : [(10281 ^ _199745) ^ [] : [_570134 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_570132)), -(c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(_570132), _570134) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_570132)))], (10287 ^ _199745) ^ [] : [-(_570134 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_570132))), 10290 ^ _199745 : [(10291 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_570132), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_570132)), _570134), -(c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(_570132), _570134) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_570132)))], (10297 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_570132), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_570132)), _570134)), -(c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(_570132), _570134) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_570132), c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_570132))))]]]]], (10303 ^ _199745) ^ [_570960, _570962] : [class_Rings_Olinordered__idom(_570960), 10306 ^ _199745 : [(10307 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_570960, c_Groups_Ozero__class_Ozero(_570960), c_Groups_Osgn__class_Osgn(_570960, _570962)), -(c_Orderings_Oord__class_Oless(_570960, c_Groups_Ozero__class_Ozero(_570960), _570962))], (10313 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_570960, c_Groups_Ozero__class_Ozero(_570960), _570962), -(c_Orderings_Oord__class_Oless(_570960, c_Groups_Ozero__class_Ozero(_570960), c_Groups_Osgn__class_Osgn(_570960, _570962)))]]], (10319 ^ _199745) ^ [_571445, _571447] : [class_Rings_Olinordered__idom(_571445), 10322 ^ _199745 : [(10323 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_571445, c_Groups_Osgn__class_Osgn(_571445, _571447), c_Groups_Ozero__class_Ozero(_571445)), -(c_Orderings_Oord__class_Oless(_571445, _571447, c_Groups_Ozero__class_Ozero(_571445)))], (10329 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_571445, _571447, c_Groups_Ozero__class_Ozero(_571445)), -(c_Orderings_Oord__class_Oless(_571445, c_Groups_Osgn__class_Osgn(_571445, _571447), c_Groups_Ozero__class_Ozero(_571445)))]]], (10335 ^ _199745) ^ [_571944, _571946, _571948] : [class_Fields_Ofield(_571944), -(c_Polynomial_Opdivmod__rel(_571944, _571946, _571948, c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_571944), _571946, _571948), c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(_571944), _571946, _571948)))], (10341 ^ _199745) ^ [_572187, _572189, _572191] : [-(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _572187, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _572189), _572191)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _572187, _572189), _572191))], (10343 ^ _199745) ^ [_572287] : [-(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _572287, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _572287)], (10345 ^ _199745) ^ [_572432, _572434, _572436] : [_572432 = 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), _572432), _572434), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _572432), _572436)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10351 ^ _199745) ^ [_572632, _572634, _572636] : [-(_572632 = 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), _572632), _572634), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _572632), _572636)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _572634, _572636))], (10357 ^ _199745) ^ [_572921, _572923, _572925, _572927] : [class_Fields_Ofield(_572921), -(c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_572921), c_Polynomial_Osmult(_572921, _572923, _572925), _572927) = c_Polynomial_Osmult(_572921, _572923, c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_572921), _572925, _572927)))], (10363 ^ _199745) ^ [_573181, _573183] : [class_Rings_Olinordered__idom(_573181), -(c_Groups_Oabs__class_Oabs(_573181, _573183) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_573181), _573183), c_Groups_Osgn__class_Osgn(_573181, _573183)))], (10369 ^ _199745) ^ [_573417, _573419] : [class_Rings_Olinordered__idom(_573417), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_573417), c_Groups_Osgn__class_Osgn(_573417, _573419)), c_Groups_Oabs__class_Oabs(_573417, _573419)) = _573419)], (10375 ^ _199745) ^ [_573667, _573669, _573671] : [class_Fields_Ofield(_573667), -(c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_573667), c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_573667), _573669), _573671) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_573667), c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_573667), _573669, _573671)))], (10381 ^ _199745) ^ [_573939, _573941, _573943] : [class_Fields_Ofield(_573939), -(c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_573939), _573941, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_573939), _573943)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_573939), c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_573939), _573941, _573943)))], (10387 ^ _199745) ^ [_574225, _574227, _574229, _574231] : [class_Fields_Ofield(_574225), -(c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_574225), _574227, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_574225)), _574229), _574231)) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_574225), c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_574225), _574227, _574229), _574231))], (10393 ^ _199745) ^ [_574543, _574545, _574547, _574549, _574551] : [class_Fields_Ofield(_574543), c_Polynomial_Opdivmod__rel(_574543, _574545, _574547, _574549, _574551), -(c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_574543), _574545, _574547) = _574549)], (10403 ^ _199745) ^ [_574888, _574890] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _574888, _574890), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _574888, _574890) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10409 ^ _199745) ^ [_575107, _575109, _575111] : [-(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _575107, _575109), _575111) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _575107, _575111), c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _575109, _575111)), c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _575107, _575111), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _575109, _575111)), _575111)))], (10411 ^ _199745) ^ [_575258, _575260] : [class_RealVector_Oreal__normed__vector(_575258), 10414 ^ _199745 : [(10415 ^ _199745) ^ [] : [c_Groups_Osgn__class_Osgn(_575258, _575260) = c_Groups_Ozero__class_Ozero(_575258), -(_575260 = c_Groups_Ozero__class_Ozero(_575258))], (10421 ^ _199745) ^ [] : [_575260 = c_Groups_Ozero__class_Ozero(_575258), -(c_Groups_Osgn__class_Osgn(_575258, _575260) = c_Groups_Ozero__class_Ozero(_575258))]]], (10427 ^ _199745) ^ [_575737, _575739] : [class_Rings_Olinordered__idom(_575737), 10430 ^ _199745 : [(10431 ^ _199745) ^ [] : [c_Groups_Osgn__class_Osgn(_575737, _575739) = c_Groups_Ozero__class_Ozero(_575737), -(_575739 = c_Groups_Ozero__class_Ozero(_575737))], (10437 ^ _199745) ^ [] : [_575739 = c_Groups_Ozero__class_Ozero(_575737), -(c_Groups_Osgn__class_Osgn(_575737, _575739) = c_Groups_Ozero__class_Ozero(_575737))]]], (10443 ^ _199745) ^ [_576202] : [class_RealVector_Oreal__normed__vector(_576202), -(c_Groups_Osgn__class_Osgn(_576202, c_Groups_Ozero__class_Ozero(_576202)) = c_Groups_Ozero__class_Ozero(_576202))], (10449 ^ _199745) ^ [_576404] : [class_Groups_Osgn__if(_576404), -(c_Groups_Osgn__class_Osgn(_576404, c_Groups_Ozero__class_Ozero(_576404)) = c_Groups_Ozero__class_Ozero(_576404))], (10455 ^ _199745) ^ [_576634, _576636, _576638] : [class_RealVector_Oreal__normed__div__algebra(_576634), -(c_Groups_Osgn__class_Osgn(_576634, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_576634), _576636), _576638)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_576634), c_Groups_Osgn__class_Osgn(_576634, _576636)), c_Groups_Osgn__class_Osgn(_576634, _576638)))], (10461 ^ _199745) ^ [_576912, _576914, _576916] : [class_Rings_Olinordered__idom(_576912), -(c_Groups_Osgn__class_Osgn(_576912, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_576912), _576914), _576916)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_576912), c_Groups_Osgn__class_Osgn(_576912, _576914)), c_Groups_Osgn__class_Osgn(_576912, _576916)))], (10467 ^ _199745) ^ [_577162] : [class_RealVector_Oreal__normed__algebra__1(_577162), -(c_Groups_Osgn__class_Osgn(_577162, c_Groups_Oone__class_Oone(_577162)) = c_Groups_Oone__class_Oone(_577162))], (10473 ^ _199745) ^ [_577378, _577380] : [class_RealVector_Oreal__normed__vector(_577378), -(c_Groups_Osgn__class_Osgn(_577378, c_Groups_Ouminus__class_Ouminus(_577378, _577380)) = c_Groups_Ouminus__class_Ouminus(_577378, c_Groups_Osgn__class_Osgn(_577378, _577380)))], (10479 ^ _199745) ^ [_577610, _577612] : [class_Rings_Olinordered__idom(_577610), -(c_Groups_Osgn__class_Osgn(_577610, c_Groups_Osgn__class_Osgn(_577610, _577612)) = c_Groups_Osgn__class_Osgn(_577610, _577612))], (10485 ^ _199745) ^ [_577836, _577838] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _577836), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _577836), _577838), _577836) = _577838)], (10491 ^ _199745) ^ [_578068, _578070] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _578068), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _578070), _578068), _578068) = _578070)], (10497 ^ _199745) ^ [_578314, _578316, _578318] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _578314), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _578314), _578316), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _578314), _578318)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _578316, _578318))], (10503 ^ _199745) ^ [_578572, _578574] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _578572), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _578574), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _578574, _578572), _578574))], (10513 ^ _199745) ^ [_578884, _578886, _578888] : [-(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _578884), _578886), _578888) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _578884), c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _578886, _578888)), c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _578884), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _578886, _578888)), _578888)))], (10515 ^ _199745) ^ [_579032, _579034, _579036] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _579032, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _579034), _579036)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _579034), c_Divides_Odiv__class_Omod(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _579032, _579034), _579036)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _579032, _579034)))], (10517 ^ _199745) ^ [_579160, _579162] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _579160, _579162) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _579160, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _579160, _579162)), _579162)))], (10519 ^ _199745) ^ [_579272, _579274] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _579272), c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _579274, _579272)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _579274, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _579274, _579272)))], (10521 ^ _199745) ^ [_579384, _579386] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _579384, _579386)), _579386) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _579384, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _579384, _579386)))], (10523 ^ _199745) ^ [_579539, _579541, _579543, _579545] : [class_Fields_Ofield(_579539), -(_579541 = c_Groups_Ozero__class_Ozero(_579539)), -(c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_579539), _579543, c_Polynomial_Osmult(_579539, _579541, _579545)) = c_Polynomial_Osmult(_579539, c_Rings_Oinverse__class_Oinverse(_579539, _579541), c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_579539), _579543, _579545)))], (10533 ^ _199745) ^ [_579923, _579925, _579927] : [class_Fields_Ofield(_579923), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_579923, _579925), c_Polynomial_Odegree(_579923, _579927)), -(c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_579923), _579925, _579927) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_579923)))], (10543 ^ _199745) ^ [_580264, _580266] : [class_Rings_Olinordered__idom(_580264), 10546 ^ _199745 : [(10547 ^ _199745) ^ [] : [c_Groups_Osgn__class_Osgn(_580264, _580266) = c_Groups_Oone__class_Oone(_580264), -(c_Orderings_Oord__class_Oless(_580264, c_Groups_Ozero__class_Ozero(_580264), _580266))], (10553 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_580264, c_Groups_Ozero__class_Ozero(_580264), _580266), -(c_Groups_Osgn__class_Osgn(_580264, _580266) = c_Groups_Oone__class_Oone(_580264))]]], (10559 ^ _199745) ^ [_580746, _580748] : [class_Rings_Olinordered__idom(_580746), c_Orderings_Oord__class_Oless(_580746, c_Groups_Ozero__class_Ozero(_580746), _580748), -(c_Groups_Osgn__class_Osgn(_580746, _580748) = c_Groups_Oone__class_Oone(_580746))], (10569 ^ _199745) ^ [_581087, _581089, _581091, _581093] : [class_Fields_Ofield(_581087), -(c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(_581087), _581089, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_581087)), _581091), _581093)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_581087), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_581087)), _581091), c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(_581087), c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_581087), _581089, _581091), _581093)), c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(_581087), _581089, _581091)))], (10575 ^ _199745) ^ [_581407, _581409] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _581407), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _581409, _581407)), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _581409, _581407) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _581409, _581407), _581407)))], (10585 ^ _199745) ^ [_581741, _581743] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _581741), 10588 ^ _199745 : [(10589 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _581743, _581741), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _581743, _581741) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10595 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _581743, _581741)), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _581743, _581741) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _581743, _581741), _581741)))]]], (10625 ^ _199745) ^ [_583071, _583073, _583075] : [-(hBOOL(hAPP(_583071, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _583073, _583075)))), 10628 ^ _199745 : [(10629 ^ _199745) ^ [] : [-(_583075 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10631 ^ _199745) ^ [] : [hBOOL(hAPP(_583071, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 10632 ^ _199745 : [(10633 ^ _199745) ^ [] : [_583075 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10637 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 10635 ^ [_583071, _583073, _583075], _583075))], (10639 ^ _199745) ^ [] : [-(_583073 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _583075), 10634 ^ [_583071, _583073, _583075]), 10635 ^ [_583071, _583073, _583075]))], (10641 ^ _199745) ^ [] : [hBOOL(hAPP(_583071, 10634 ^ [_583071, _583073, _583075]))]]], (10601 ^ _199745) ^ [_582292, _582294, _582296] : [hBOOL(hAPP(_582292, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _582294, _582296))), 10604 ^ _199745 : [(10605 ^ _199745) ^ [] : [_582296 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_582292, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (10611 ^ _199745) ^ [] : [-(_582296 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 10614 ^ _199745 : [(10615 ^ _199745) ^ [_582746, _582748] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _582746, _582296), _582294 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _582296), _582748), _582746), -(hBOOL(hAPP(_582292, _582748)))]]]]], (10645 ^ _199745) ^ [_583948, _583950] : [class_Rings_Olinordered__idom(_583948), 10648 ^ _199745 : [(10649 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_583948), _583950, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_583948))), -(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(_583948), _583950) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_583948), _583950))], (10655 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_583948), _583950, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_583948)))), -(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(_583948), _583950) = _583950)]]], (10661 ^ _199745) ^ [_584455, _584457] : [-(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Nat_OSuc(_584455), _584457) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _584455, _584457), c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _584457)), c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _584455, _584457), c_Divides_Odiv__class_Omod(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _584457)), _584457)))], (10663 ^ _199745) ^ [_584602, _584604] : [class_Groups_Osgn__if(_584602), 10666 ^ _199745 : [(10667 ^ _199745) ^ [] : [_584604 = c_Groups_Ozero__class_Ozero(_584602), -(c_Groups_Osgn__class_Osgn(_584602, _584604) = c_Groups_Ozero__class_Ozero(_584602))], (10673 ^ _199745) ^ [] : [-(_584604 = c_Groups_Ozero__class_Ozero(_584602)), 10676 ^ _199745 : [(10677 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_584602, c_Groups_Ozero__class_Ozero(_584602), _584604), -(c_Groups_Osgn__class_Osgn(_584602, _584604) = c_Groups_Oone__class_Oone(_584602))], (10683 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(_584602, c_Groups_Ozero__class_Ozero(_584602), _584604)), -(c_Groups_Osgn__class_Osgn(_584602, _584604) = c_Groups_Ouminus__class_Ouminus(_584602, c_Groups_Oone__class_Oone(_584602)))]]]]], (10689 ^ _199745) ^ [_585378, _585380] : [class_Rings_Olinordered__idom(_585378), 10692 ^ _199745 : [(10693 ^ _199745) ^ [] : [c_Groups_Osgn__class_Osgn(_585378, _585380) = c_Groups_Ouminus__class_Ouminus(_585378, c_Groups_Oone__class_Oone(_585378)), -(c_Orderings_Oord__class_Oless(_585378, _585380, c_Groups_Ozero__class_Ozero(_585378)))], (10699 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless(_585378, _585380, c_Groups_Ozero__class_Ozero(_585378)), -(c_Groups_Osgn__class_Osgn(_585378, _585380) = c_Groups_Ouminus__class_Ouminus(_585378, c_Groups_Oone__class_Oone(_585378)))]]], (10705 ^ _199745) ^ [_585869, _585871] : [class_Rings_Olinordered__idom(_585869), c_Orderings_Oord__class_Oless(_585869, _585871, c_Groups_Ozero__class_Ozero(_585869)), -(c_Groups_Osgn__class_Osgn(_585869, _585871) = c_Groups_Ouminus__class_Ouminus(_585869, c_Groups_Oone__class_Oone(_585869)))], (10715 ^ _199745) ^ [_586202, _586204, _586206] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _586202), 10718 ^ _199745 : [(10737 ^ _199745) ^ [] : [10740 ^ _199745 : [(10741 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), 10739 ^ [_586202, _586204, _586206]))], (10743 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, 10739 ^ [_586202, _586204, _586206], _586202))], (10745 ^ _199745) ^ [] : [-(_586206 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _586202), 10738 ^ [_586202, _586204, _586206]), 10739 ^ [_586202, _586204, _586206]))], (10747 ^ _199745) ^ [] : [hBOOL(hAPP(hAPP(_586204, 10738 ^ [_586202, _586204, _586206]), 10739 ^ [_586202, _586204, _586206]))]], -(hBOOL(hAPP(hAPP(_586204, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _586206, _586202)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _586206, _586202))))], (10719 ^ _199745) ^ [] : [hBOOL(hAPP(hAPP(_586204, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _586206, _586202)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _586206, _586202))), 10722 ^ _199745 : [(10723 ^ _199745) ^ [_586537, _586539] : [-(hBOOL(hAPP(hAPP(_586204, _586539), _586537))), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _586537), c_Orderings_Oord__class_Oless(tc_Int_Oint, _586537, _586202), _586206 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _586202), _586539), _586537)]]]]], (10751 ^ _199745) ^ [_587658, _587660, _587662] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _587658, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 10754 ^ _199745 : [(10773 ^ _199745) ^ [] : [10776 ^ _199745 : [(10777 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _587658, 10775 ^ [_587658, _587660, _587662]))], (10779 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, 10775 ^ [_587658, _587660, _587662], c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (10781 ^ _199745) ^ [] : [-(_587662 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _587658), 10774 ^ [_587658, _587660, _587662]), 10775 ^ [_587658, _587660, _587662]))], (10783 ^ _199745) ^ [] : [hBOOL(hAPP(hAPP(_587660, 10774 ^ [_587658, _587660, _587662]), 10775 ^ [_587658, _587660, _587662]))]], -(hBOOL(hAPP(hAPP(_587660, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _587662, _587658)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _587662, _587658))))], (10755 ^ _199745) ^ [] : [hBOOL(hAPP(hAPP(_587660, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _587662, _587658)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _587662, _587658))), 10758 ^ _199745 : [(10759 ^ _199745) ^ [_587993, _587995] : [-(hBOOL(hAPP(hAPP(_587660, _587995), _587993))), c_Orderings_Oord__class_Oless(tc_Int_Oint, _587658, _587993), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _587993, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _587662 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _587658), _587995), _587993)]]]]], (10787 ^ _199745) ^ [_589100, _589102] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _589100), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _589102), -(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, _589100, _589102)))], (10797 ^ _199745) ^ [_589427, _589429, _589431] : [class_Groups_Oordered__ab__group__add__abs(_589427), -(c_Orderings_Oord__class_Oless__eq(_589427, c_Groups_Ominus__class_Ominus(_589427, c_Groups_Oabs__class_Oabs(_589427, _589429), c_Groups_Oabs__class_Oabs(_589427, _589431)), c_Groups_Oabs__class_Oabs(_589427, c_Groups_Ominus__class_Ominus(_589427, _589431, _589429))))], (10803 ^ _199745) ^ [_589691, _589693, _589695] : [class_Groups_Oordered__ab__group__add__abs(_589691), -(c_Orderings_Oord__class_Oless__eq(_589691, c_Groups_Ominus__class_Ominus(_589691, c_Groups_Oabs__class_Oabs(_589691, _589693), c_Groups_Oabs__class_Oabs(_589691, _589695)), c_Groups_Oabs__class_Oabs(_589691, c_Groups_Ominus__class_Ominus(_589691, _589693, _589695))))], (10809 ^ _199745) ^ [_589955, _589957, _589959] : [class_Groups_Oordered__ab__group__add__abs(_589955), -(c_Orderings_Oord__class_Oless__eq(_589955, c_Groups_Oabs__class_Oabs(_589955, c_Groups_Ominus__class_Ominus(_589955, c_Groups_Oabs__class_Oabs(_589955, _589957), c_Groups_Oabs__class_Oabs(_589955, _589959))), c_Groups_Oabs__class_Oabs(_589955, c_Groups_Ominus__class_Ominus(_589955, _589957, _589959))))], (10815 ^ _199745) ^ [_590225, _590227, _590229] : [class_Groups_Oordered__ab__group__add__abs(_590225), c_Orderings_Oord__class_Oless__eq(_590225, c_Groups_Oabs__class_Oabs(_590225, _590227), _590229), -(c_Orderings_Oord__class_Oless__eq(_590225, c_Groups_Ouminus__class_Ouminus(_590225, _590227), _590229))], (10825 ^ _199745) ^ [_590562, _590564, _590566] : [class_Groups_Oordered__ab__group__add__abs(_590562), c_Orderings_Oord__class_Oless__eq(_590562, _590564, _590566), c_Orderings_Oord__class_Oless__eq(_590562, c_Groups_Ouminus__class_Ouminus(_590562, _590564), _590566), -(c_Orderings_Oord__class_Oless__eq(_590562, c_Groups_Oabs__class_Oabs(_590562, _590564), _590566))], (10839 ^ _199745) ^ [_590994, _590996, _590998] : [class_Groups_Oordered__ab__group__add__abs(_590994), 10842 ^ _199745 : [(10843 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless__eq(_590994, c_Groups_Oabs__class_Oabs(_590994, _590996), _590998), 10846 ^ _199745 : [(10847 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_590994, _590996, _590998))], (10849 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_590994, c_Groups_Ouminus__class_Ouminus(_590994, _590996), _590998))]]], (10851 ^ _199745) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_590994, c_Groups_Oabs__class_Oabs(_590994, _590996), _590998)), c_Orderings_Oord__class_Oless__eq(_590994, _590996, _590998), c_Orderings_Oord__class_Oless__eq(_590994, c_Groups_Ouminus__class_Ouminus(_590994, _590996), _590998)]]], (10861 ^ _199745) ^ [_591659, _591661] : [class_Groups_Oordered__ab__group__add__abs(_591659), -(c_Orderings_Oord__class_Oless__eq(_591659, c_Groups_Ouminus__class_Ouminus(_591659, _591661), c_Groups_Oabs__class_Oabs(_591659, _591661)))], (10867 ^ _199745) ^ [_591895, _591897, _591899] : [class_Groups_Oordered__ab__group__add__abs(_591895), -(c_Orderings_Oord__class_Oless__eq(_591895, c_Groups_Oabs__class_Oabs(_591895, c_Groups_Oplus__class_Oplus(_591895, _591897, _591899)), c_Groups_Oplus__class_Oplus(_591895, c_Groups_Oabs__class_Oabs(_591895, _591897), c_Groups_Oabs__class_Oabs(_591895, _591899))))], (10873 ^ _199745) ^ [_592159, _592161, _592163] : [class_Groups_Oordered__ab__group__add__abs(_592159), c_Orderings_Oord__class_Oless__eq(_592159, c_Groups_Oabs__class_Oabs(_592159, _592161), _592163), -(c_Orderings_Oord__class_Oless__eq(_592159, _592161, _592163))], (10883 ^ _199745) ^ [_592476, _592478] : [class_Groups_Oordered__ab__group__add__abs(_592476), -(c_Orderings_Oord__class_Oless__eq(_592476, _592478, c_Groups_Oabs__class_Oabs(_592476, _592478)))], (10889 ^ _199745) ^ [_592692, _592694] : [class_Groups_Oordered__ab__group__add__abs(_592692), c_Orderings_Oord__class_Oless__eq(_592692, c_Groups_Ozero__class_Ozero(_592692), _592694), -(c_Groups_Oabs__class_Oabs(_592692, _592694) = _592694)], (10899 ^ _199745) ^ [_593001, _593003] : [class_Groups_Oordered__ab__group__add__abs(_593001), 10902 ^ _199745 : [(10903 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless__eq(_593001, c_Groups_Oabs__class_Oabs(_593001, _593003), c_Groups_Ozero__class_Ozero(_593001)), -(_593003 = c_Groups_Ozero__class_Ozero(_593001))], (10909 ^ _199745) ^ [] : [_593003 = c_Groups_Ozero__class_Ozero(_593001), -(c_Orderings_Oord__class_Oless__eq(_593001, c_Groups_Oabs__class_Oabs(_593001, _593003), c_Groups_Ozero__class_Ozero(_593001)))]]], (10915 ^ _199745) ^ [_593483, _593485] : [class_Groups_Oordered__ab__group__add__abs(_593483), -(c_Orderings_Oord__class_Oless__eq(_593483, c_Groups_Ozero__class_Ozero(_593483), c_Groups_Oabs__class_Oabs(_593483, _593485)))], (10921 ^ _199745) ^ [_593731, _593733, _593735, _593737] : [class_Rings_Olinordered__ring__strict(_593731), c_Orderings_Oord__class_Oless(_593731, c_Groups_Ozero__class_Ozero(_593731), _593733), 10928 ^ _199745 : [(10929 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless__eq(_593731, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_593731), _593733), _593735), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_593731), _593733), _593737)), -(c_Orderings_Oord__class_Oless__eq(_593731, _593735, _593737))], (10935 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless__eq(_593731, _593735, _593737), -(c_Orderings_Oord__class_Oless__eq(_593731, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_593731), _593733), _593735), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_593731), _593733), _593737)))]]], (10941 ^ _199745) ^ [_594406, _594408, _594410, _594412] : [class_Rings_Olinordered__ring__strict(_594406), c_Orderings_Oord__class_Oless(_594406, _594408, c_Groups_Ozero__class_Ozero(_594406)), 10948 ^ _199745 : [(10949 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless__eq(_594406, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_594406), _594408), _594410), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_594406), _594408), _594412)), -(c_Orderings_Oord__class_Oless__eq(_594406, _594412, _594410))], (10955 ^ _199745) ^ [] : [c_Orderings_Oord__class_Oless__eq(_594406, _594412, _594410), -(c_Orderings_Oord__class_Oless__eq(_594406, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_594406), _594408), _594410), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_594406), _594408), _594412)))]]], (10961 ^ _199745) ^ [_595095, _595097, _595099, _595101, _595103] : [class_Rings_Olinordered__semiring__strict(_595095), c_Orderings_Oord__class_Oless(_595095, _595097, _595099), c_Orderings_Oord__class_Oless(_595095, _595101, _595103), c_Orderings_Oord__class_Oless(_595095, c_Groups_Ozero__class_Ozero(_595095), _595099), c_Orderings_Oord__class_Oless__eq(_595095, c_Groups_Ozero__class_Ozero(_595095), _595101), -(c_Orderings_Oord__class_Oless(_595095, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_595095), _595097), _595101), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_595095), _595099), _595103)))], (10983 ^ _199745) ^ [_595817, _595819, _595821, _595823, _595825] : [class_Rings_Olinordered__semiring__strict(_595817), c_Orderings_Oord__class_Oless(_595817, _595819, _595821), c_Orderings_Oord__class_Oless(_595817, _595823, _595825), c_Orderings_Oord__class_Oless__eq(_595817, c_Groups_Ozero__class_Ozero(_595817), _595819), c_Orderings_Oord__class_Oless__eq(_595817, c_Groups_Ozero__class_Ozero(_595817), _595823), -(c_Orderings_Oord__class_Oless(_595817, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_595817), _595819), _595823), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_595817), _595821), _595825)))], (11005 ^ _199745) ^ [_596539, _596541, _596543, _596545, _596547] : [class_Rings_Olinordered__semiring__strict(_596539), c_Orderings_Oord__class_Oless(_596539, _596541, _596543), c_Orderings_Oord__class_Oless__eq(_596539, _596545, _596547), c_Orderings_Oord__class_Oless__eq(_596539, c_Groups_Ozero__class_Ozero(_596539), _596541), c_Orderings_Oord__class_Oless(_596539, c_Groups_Ozero__class_Ozero(_596539), _596545), -(c_Orderings_Oord__class_Oless(_596539, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_596539), _596541), _596545), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_596539), _596543), _596547)))], (11027 ^ _199745) ^ [_597261, _597263, _597265, _597267, _597269] : [class_Rings_Olinordered__semiring__strict(_597261), c_Orderings_Oord__class_Oless__eq(_597261, _597263, _597265), c_Orderings_Oord__class_Oless(_597261, _597267, _597269), c_Orderings_Oord__class_Oless(_597261, c_Groups_Ozero__class_Ozero(_597261), _597263), c_Orderings_Oord__class_Oless__eq(_597261, c_Groups_Ozero__class_Ozero(_597261), _597267), -(c_Orderings_Oord__class_Oless(_597261, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_597261), _597263), _597267), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_597261), _597265), _597269)))], (11049 ^ _199745) ^ [_597969, _597971, _597973, _597975] : [class_Rings_Olinordered__semiring(_597969), c_Orderings_Oord__class_Oless(_597969, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_597969), _597971), _597973), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_597969), _597975), _597973)), c_Orderings_Oord__class_Oless__eq(_597969, c_Groups_Ozero__class_Ozero(_597969), _597973), -(c_Orderings_Oord__class_Oless(_597969, _597971, _597975))], (11063 ^ _199745) ^ [_598453, _598455, _598457, _598459] : [class_Rings_Olinordered__semiring__strict(_598453), c_Orderings_Oord__class_Oless(_598453, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_598453), _598455), _598457), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_598453), _598459), _598457)), c_Orderings_Oord__class_Oless__eq(_598453, c_Groups_Ozero__class_Ozero(_598453), _598457), -(c_Orderings_Oord__class_Oless(_598453, _598455, _598459))], (11077 ^ _199745) ^ [_598937, _598939, _598941, _598943] : [class_Rings_Olinordered__semiring(_598937), c_Orderings_Oord__class_Oless(_598937, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_598937), _598939), _598941), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_598937), _598939), _598943)), c_Orderings_Oord__class_Oless__eq(_598937, 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_599911))], (11119 ^ _199745) ^ [_600389, _600391, _600393, _600395] : [class_Rings_Olinordered__semiring__strict(_600389), c_Orderings_Oord__class_Oless__eq(_600389, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_600389), _600391), _600393), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_600389), _600391), _600395)), c_Orderings_Oord__class_Oless(_600389, c_Groups_Ozero__class_Ozero(_600389), _600391), -(c_Orderings_Oord__class_Oless__eq(_600389, _600393, _600395))], (11133 ^ _199745) ^ [_600859, _600861, _600863] : [class_Groups_Oordered__comm__monoid__add(_600859), c_Orderings_Oord__class_Oless(_600859, c_Groups_Ozero__class_Ozero(_600859), _600861), c_Orderings_Oord__class_Oless__eq(_600859, c_Groups_Ozero__class_Ozero(_600859), _600863), -(c_Orderings_Oord__class_Oless(_600859, c_Groups_Ozero__class_Ozero(_600859), c_Groups_Oplus__class_Oplus(_600859, _600861, _600863)))], (11147 ^ _199745) ^ [_601299, _601301, _601303] : [class_Groups_Oordered__comm__monoid__add(_601299), c_Orderings_Oord__class_Oless__eq(_601299, c_Groups_Ozero__class_Ozero(_601299), _601301), c_Orderings_Oord__class_Oless(_601299, c_Groups_Ozero__class_Ozero(_601299), _601303), -(c_Orderings_Oord__class_Oless(_601299, c_Groups_Ozero__class_Ozero(_601299), c_Groups_Oplus__class_Oplus(_601299, _601301, _601303)))], (11161 ^ _199745) ^ [_601753, _601755, _601757, _601759] : [class_Groups_Oordered__comm__monoid__add(_601753), c_Orderings_Oord__class_Oless(_601753, c_Groups_Ozero__class_Ozero(_601753), _601755), c_Orderings_Oord__class_Oless__eq(_601753, _601757, _601759), -(c_Orderings_Oord__class_Oless(_601753, _601757, c_Groups_Oplus__class_Oplus(_601753, _601755, _601759)))], (11175 ^ _199745) ^ [_602213, _602215, _602217, _602219] : [class_Groups_Oordered__comm__monoid__add(_602213), c_Orderings_Oord__class_Oless__eq(_602213, c_Groups_Ozero__class_Ozero(_602213), _602215), c_Orderings_Oord__class_Oless(_602213, _602217, _602219), -(c_Orderings_Oord__class_Oless(_602213, _602217, 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[_604901] : [class_Rings_Oidom(_604901), -(class_Groups_Ocomm__monoid__mult(_604901))], (11265 ^ _199745) ^ [_605087] : [class_Rings_Oidom(_605087), -(class_Groups_Oab__semigroup__add(_605087))], (11271 ^ _199745) ^ [_605273] : [class_Rings_Oidom(_605273), -(class_Rings_Ono__zero__divisors(_605273))], (11277 ^ _199745) ^ [_605459] : [class_Rings_Oidom(_605459), -(class_Groups_Ocomm__monoid__add(_605459))], (11283 ^ _199745) ^ [_605645] : [class_Rings_Oidom(_605645), -(class_Rings_Ocomm__semiring__1(_605645))], (11289 ^ _199745) ^ [_605831] : [class_Rings_Oidom(_605831), -(class_Rings_Ocomm__semiring__0(_605831))], (11295 ^ _199745) ^ [_606017] : [class_Rings_Oidom(_606017), -(class_Rings_Ocomm__semiring(_606017))], (11301 ^ _199745) ^ [_606203] : [class_Rings_Oidom(_606203), -(class_Groups_Oab__group__add(_606203))], (11307 ^ _199745) ^ [_606389] : [class_Rings_Oidom(_606389), -(class_Rings_Ozero__neq__one(_606389))], (11313 ^ _199745) ^ [_606575] : [class_Rings_Oidom(_606575), 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[-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (11419 ^ _199745) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (11421 ^ _199745) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (11423 ^ _199745) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (11425 ^ _199745) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (11427 ^ _199745) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (11429 ^ _199745) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (11431 ^ _199745) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (11433 ^ _199745) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (11435 ^ _199745) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (11437 ^ _199745) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (11439 ^ _199745) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (11441 ^ _199745) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (11443 ^ _199745) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (11445 ^ _199745) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (11447 ^ _199745) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (11449 ^ _199745) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (11451 ^ _199745) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (11453 ^ _199745) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (11455 ^ _199745) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (11457 ^ _199745) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (11459 ^ _199745) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (11461 ^ _199745) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Int_Oint))], (11463 ^ _199745) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (11465 ^ _199745) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (11467 ^ _199745) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (11469 ^ _199745) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (11471 ^ _199745) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (11473 ^ _199745) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (11475 ^ _199745) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (11477 ^ _199745) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (11479 ^ _199745) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (11481 ^ _199745) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (11483 ^ _199745) ^ [] : [-(class_Divides_Oring__div(tc_Int_Oint))], (11485 ^ _199745) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (11487 ^ _199745) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (11489 ^ _199745) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (11491 ^ _199745) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (11493 ^ _199745) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (11495 ^ _199745) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (11497 ^ _199745) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (11499 ^ _199745) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (11501 ^ _199745) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (11503 ^ _199745) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (11505 ^ _199745) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (11507 ^ _199745) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (11509 ^ _199745) ^ [] : [-(class_Rings_Odvd(tc_Int_Oint))], (11511 ^ _199745) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (11513 ^ _199745) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (11515 ^ _199745) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (11517 ^ _199745) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (11519 ^ _199745) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (11521 ^ _199745) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (11523 ^ _199745) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (11525 ^ _199745) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (11527 ^ _199745) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (11529 ^ _199745) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (11531 ^ _199745) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (11533 ^ _199745) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (11535 ^ _199745) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (11537 ^ _199745) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (11539 ^ _199745) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (11541 ^ _199745) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (11543 ^ _199745) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Nat_Onat))], (11545 ^ _199745) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (11547 ^ _199745) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (11549 ^ _199745) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (11551 ^ _199745) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (11553 ^ _199745) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (11555 ^ _199745) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (11557 ^ _199745) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (11559 ^ _199745) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (11561 ^ _199745) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (11563 ^ _199745) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (11565 ^ _199745) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (11567 ^ _199745) ^ [] : [-(class_Rings_Odvd(tc_Nat_Onat))], (11569 ^ _199745) ^ [_613795] : [class_Rings_Oidom(_613795), -(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(_613795)))], (11575 ^ _199745) ^ [_613985] : [class_Rings_Olinordered__idom(_613985), -(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(_613985)))], (11581 ^ _199745) ^ [_614175] : [class_Rings_Olinordered__idom(_614175), -(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(_614175)))], (11587 ^ _199745) ^ [_614365] : [class_Rings_Olinordered__idom(_614365), -(class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(_614365)))], (11593 ^ _199745) ^ [_614555] : [class_Rings_Olinordered__idom(_614555), -(class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(_614555)))], (11599 ^ _199745) ^ [_614745] : [class_Rings_Olinordered__idom(_614745), -(class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(_614745)))], (11605 ^ _199745) ^ [_614935] : [class_Rings_Olinordered__idom(_614935), -(class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(_614935)))], (11611 ^ _199745) ^ [_615125] : [class_Rings_Olinordered__idom(_615125), -(class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(_615125)))], (11617 ^ _199745) ^ [_615315] : [class_Groups_Ocancel__comm__monoid__add(_615315), -(class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(_615315)))], (11623 ^ _199745) ^ [_615505] : [class_Rings_Oidom(_615505), -(class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(_615505)))], (11629 ^ _199745) ^ [_615695] : [class_Rings_Olinordered__idom(_615695), -(class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(_615695)))], (11635 ^ _199745) ^ [_615885] : [class_Rings_Oidom(_615885), -(class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(_615885)))], (11641 ^ _199745) ^ [_616075] : [class_Rings_Olinordered__idom(_616075), -(class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(_616075)))], (11647 ^ _199745) ^ [_616265] : [class_Groups_Ocancel__comm__monoid__add(_616265), -(class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(_616265)))], (11653 ^ _199745) ^ [_616455] : [class_Rings_Olinordered__idom(_616455), -(class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(_616455)))], (11659 ^ _199745) ^ [_616645] : [class_Rings_Olinordered__idom(_616645), -(class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(_616645)))], (11665 ^ _199745) ^ [_616835] : [class_Rings_Ocomm__semiring__0(_616835), -(class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(_616835)))], (11671 ^ _199745) ^ [_617025] : [class_Rings_Ocomm__semiring__1(_617025), -(class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(_617025)))], (11677 ^ _199745) ^ [_617215] : [class_Groups_Ocomm__monoid__add(_617215), -(class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(_617215)))], (11683 ^ _199745) ^ [_617405] : [class_Rings_Oidom(_617405), -(class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(_617405)))], (11689 ^ _199745) ^ [_617595] : [class_Groups_Ocomm__monoid__add(_617595), -(class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(_617595)))], (11695 ^ _199745) ^ [_617785] : [class_Rings_Olinordered__idom(_617785), -(class_Rings_Olinordered__ring(tc_Polynomial_Opoly(_617785)))], (11701 ^ _199745) ^ [_617975] : [class_Rings_Olinordered__idom(_617975), -(class_Rings_Olinordered__idom(tc_Polynomial_Opoly(_617975)))], (11707 ^ _199745) ^ [_618165] : [class_Rings_Ocomm__semiring__1(_618165), -(class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(_618165)))], (11713 ^ _199745) ^ [_618355] : [class_Rings_Ocomm__semiring__0(_618355), -(class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(_618355)))], (11719 ^ _199745) ^ [_618545] : [class_Fields_Ofield(_618545), -(class_Divides_Osemiring__div(tc_Polynomial_Opoly(_618545)))], (11725 ^ _199745) ^ [_618735] : [class_Rings_Ocomm__semiring__0(_618735), -(class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(_618735)))], (11731 ^ _199745) ^ [_618925] : [class_Groups_Oab__group__add(_618925), -(class_Groups_Oab__group__add(tc_Polynomial_Opoly(_618925)))], (11737 ^ _199745) ^ [_619115] : [class_Rings_Ocomm__semiring__1(_619115), -(class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(_619115)))], (11743 ^ _199745) ^ [_619305] : [class_Rings_Olinordered__idom(_619305), -(class_Rings_Oordered__ring(tc_Polynomial_Opoly(_619305)))], (11749 ^ _199745) ^ [_619495] : [class_Rings_Ocomm__semiring__1(_619495), -(class_Groups_Omonoid__mult(tc_Polynomial_Opoly(_619495)))], (11755 ^ _199745) ^ [_619685] : [class_Rings_Ocomm__ring__1(_619685), -(class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(_619685)))], (11761 ^ _199745) ^ [_619875] : [class_Groups_Ocomm__monoid__add(_619875), -(class_Groups_Omonoid__add(tc_Polynomial_Opoly(_619875)))], (11767 ^ _199745) ^ [_620065] : [class_Rings_Ocomm__semiring__0(_620065), -(class_Rings_Osemiring__0(tc_Polynomial_Opoly(_620065)))], (11773 ^ _199745) ^ [_620255] : [class_Groups_Oab__group__add(_620255), -(class_Groups_Ogroup__add(tc_Polynomial_Opoly(_620255)))], (11779 ^ _199745) ^ [_620445] : [class_Fields_Ofield(_620445), -(class_Divides_Oring__div(tc_Polynomial_Opoly(_620445)))], (11785 ^ _199745) ^ [_620635] : [class_Rings_Ocomm__semiring__0(_620635), -(class_Rings_Omult__zero(tc_Polynomial_Opoly(_620635)))], (11791 ^ _199745) ^ [_620825] : [class_Rings_Ocomm__ring(_620825), -(class_Rings_Ocomm__ring(tc_Polynomial_Opoly(_620825)))], (11797 ^ _199745) ^ [_621015] : [class_Rings_Olinordered__idom(_621015), -(class_Int_Oring__char__0(tc_Polynomial_Opoly(_621015)))], (11803 ^ _199745) ^ [_621205] : [class_Rings_Ocomm__semiring__0(_621205), -(class_Rings_Osemiring(tc_Polynomial_Opoly(_621205)))], (11809 ^ _199745) ^ [_621395] : [class_Rings_Olinordered__idom(_621395), -(class_Groups_Osgn__if(tc_Polynomial_Opoly(_621395)))], (11815 ^ _199745) ^ [_621585] : [class_Rings_Olinordered__idom(_621585), -(class_Groups_Oabs__if(tc_Polynomial_Opoly(_621585)))], (11821 ^ _199745) ^ [_621775] : [class_Rings_Ocomm__ring__1(_621775), -(class_Rings_Oring__1(tc_Polynomial_Opoly(_621775)))], (11827 ^ _199745) ^ [_621965] : [class_Rings_Ocomm__semiring__1(_621965), -(class_Power_Opower(tc_Polynomial_Opoly(_621965)))], (11833 ^ _199745) ^ [_622155] : [class_Groups_Ozero(_622155), -(class_Groups_Ozero(tc_Polynomial_Opoly(_622155)))], (11839 ^ _199745) ^ [_622345] : [class_Rings_Ocomm__ring(_622345), -(class_Rings_Oring(tc_Polynomial_Opoly(_622345)))], (11845 ^ _199745) ^ [_622535] : [class_Rings_Oidom(_622535), -(class_Rings_Oidom(tc_Polynomial_Opoly(_622535)))], (11851 ^ _199745) ^ [_622725] : [class_Rings_Ocomm__semiring__1(_622725), -(class_Groups_Oone(tc_Polynomial_Opoly(_622725)))], (11857 ^ _199745) ^ [_622915] : [class_Rings_Ocomm__semiring__1(_622915), -(class_Rings_Odvd(tc_Polynomial_Opoly(_622915)))], (11863 ^ _199745) ^ [_623119, _623121] : [hBOOL(c_fequal(_623119, _623121)), -(_623119 = _623121)], (11875 ^ _199745) ^ [] : [hBOOL(c_fFalse)], (11877 ^ _199745) ^ [] : [-(hBOOL(c_fTrue))], (11879 ^ _199745) ^ [] : [-(class_Rings_Oidom(t_a))], (11869 ^ _199745) ^ [_623335, _623337] : [_623335 = _623337, -(hBOOL(c_fequal(_623335, _623337)))]], input).
% 40.29/39.73  ncf('1',plain,[class_Rings_Oidom(t_a), v_c____ = c_Groups_Ozero__class_Ozero(t_a), 1224 : 1222 ^ [] = c_Groups_Ozero__class_Ozero(t_a)],start(1214 ^ 0)).
% 40.29/39.73  ncf('1.1',plain,[-(class_Rings_Oidom(t_a))],extension(11879 ^ 1)).
% 40.29/39.73  ncf('1.2',plain,[-(v_c____ = c_Groups_Ozero__class_Ozero(t_a)), class_Rings_Oidom(t_a), 1212 : -(hAPP(c_Polynomial_Opoly(t_a, c_Polynomial_OpCons(t_a, v_c____, v_cs____)), 11896 ^ [1195 ^ [], 1194 ^ [], 1198 ^ []]) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a), hAPP(hAPP(c_Power_Opower__class_Opower(t_a), 11896 ^ [1195 ^ [], 1194 ^ [], 1198 ^ []]), 1194 ^ [])), hAPP(c_Polynomial_Opoly(t_a, c_Polynomial_OpCons(t_a, 1195 ^ [], 1198 ^ [])), 11896 ^ [1195 ^ [], 1194 ^ [], 1198 ^ []])))],extension(1187 ^ 1,bind([[_239843], [11896 ^ [1195 ^ [], 1194 ^ [], 1198 ^ []]]]))).
% 40.29/39.73  ncf('1.2.1',plain,[-(class_Rings_Oidom(t_a))],lemmata('x')).
% 40.29/39.73  ncf('1.2.2',plain,[hAPP(c_Polynomial_Opoly(t_a, c_Polynomial_OpCons(t_a, v_c____, v_cs____)), 11896 ^ [1195 ^ [], 1194 ^ [], 1198 ^ []]) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a), hAPP(hAPP(c_Power_Opower__class_Opower(t_a), 11896 ^ [1195 ^ [], 1194 ^ [], 1198 ^ []]), 1194 ^ [])), hAPP(c_Polynomial_Opoly(t_a, c_Polynomial_OpCons(t_a, 1195 ^ [], 1198 ^ [])), 11896 ^ [1195 ^ [], 1194 ^ [], 1198 ^ []])), 11887 : -(c_Polynomial_OpCons(t_a, v_c____, v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), 11893 : c_Polynomial_OpCons(t_a, v_c____, v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)), 11885 : -(1195 ^ [] = c_Groups_Ozero__class_Ozero(t_a))],extension(11881 ^ 4,bind([[_643470, _643472, _643690], [1195 ^ [], 1194 ^ [], 1198 ^ []]]))).
% 40.29/39.73  ncf('1.2.2.1',plain,[c_Polynomial_OpCons(t_a, v_c____, v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)), 11889 : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_If(tc_Nat_Onat, c_fequal(1198 ^ [], c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(c_Polynomial_Odegree(t_a, 1198 ^ []))), 1194 ^ [])) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 11889 : hAPP(c_Polynomial_Opoly(t_a, c_Polynomial_OpCons(t_a, v_c____, v_cs____)), 11896 ^ [1195 ^ [], 1194 ^ [], 1198 ^ []]) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a), hAPP(hAPP(c_Power_Opower__class_Opower(t_a), 11896 ^ [1195 ^ [], 1194 ^ [], 1198 ^ []]), 1194 ^ [])), hAPP(c_Polynomial_Opoly(t_a, c_Polynomial_OpCons(t_a, 1195 ^ [], 1198 ^ [])), 11896 ^ [1195 ^ [], 1194 ^ [], 1198 ^ []]))],extension(11885 ^ 9,bind([[_643690], [1198 ^ []]]))).
% 40.29/39.73  ncf('1.2.2.1.1',plain,[-(c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_If(tc_Nat_Onat, c_fequal(1198 ^ [], c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(c_Polynomial_Odegree(t_a, 1198 ^ []))), 1194 ^ [])) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Polynomial_OpCons(t_a, v_c____, v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))],extension(1200 ^ 12)).
% 40.29/39.73  ncf('1.2.2.1.1.1',plain,[-(c_Polynomial_OpCons(t_a, v_c____, v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))],reduction('1.2.2')).
% 40.29/39.73  ncf('1.2.2.1.2',plain,[-(hAPP(c_Polynomial_Opoly(t_a, c_Polynomial_OpCons(t_a, v_c____, v_cs____)), 11896 ^ [1195 ^ [], 1194 ^ [], 1198 ^ []]) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a), hAPP(hAPP(c_Power_Opower__class_Opower(t_a), 11896 ^ [1195 ^ [], 1194 ^ [], 1198 ^ []]), 1194 ^ [])), hAPP(c_Polynomial_Opoly(t_a, c_Polynomial_OpCons(t_a, 1195 ^ [], 1198 ^ [])), 11896 ^ [1195 ^ [], 1194 ^ [], 1198 ^ []])))],reduction('1.2')).
% 40.29/39.73  ncf('1.2.2.2',plain,[-(c_Polynomial_OpCons(t_a, v_c____, v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), 11895 : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_If(tc_Nat_Onat, c_fequal(1198 ^ [], c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(c_Polynomial_Odegree(t_a, 1198 ^ []))), 1194 ^ [])) = c_Nat_OSuc(c_Polynomial_Odegree(t_a, c_Polynomial_OpCons(t_a, v_c____, v_cs____))), 11895 : hAPP(c_Polynomial_Opoly(t_a, c_Polynomial_OpCons(t_a, v_c____, v_cs____)), 11896 ^ [1195 ^ [], 1194 ^ [], 1198 ^ []]) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a), hAPP(hAPP(c_Power_Opower__class_Opower(t_a), 11896 ^ [1195 ^ [], 1194 ^ [], 1198 ^ []]), 1194 ^ [])), hAPP(c_Polynomial_Opoly(t_a, c_Polynomial_OpCons(t_a, 1195 ^ [], 1198 ^ [])), 11896 ^ [1195 ^ [], 1194 ^ [], 1198 ^ []]))],extension(11885 ^ 9,bind([[_643690], [1198 ^ []]]))).
% 40.29/39.73  ncf('1.2.2.2.1',plain,[-(c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_If(tc_Nat_Onat, c_fequal(1198 ^ [], c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(c_Polynomial_Odegree(t_a, 1198 ^ []))), 1194 ^ [])) = c_Nat_OSuc(c_Polynomial_Odegree(t_a, c_Polynomial_OpCons(t_a, v_c____, v_cs____)))), -(c_Polynomial_OpCons(t_a, v_c____, v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))],extension(1206 ^ 12)).
% 40.29/39.73  ncf('1.2.2.2.1.1',plain,[c_Polynomial_OpCons(t_a, v_c____, v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))],reduction('1.2.2')).
% 40.29/39.73  ncf('1.2.2.2.2',plain,[-(hAPP(c_Polynomial_Opoly(t_a, c_Polynomial_OpCons(t_a, v_c____, v_cs____)), 11896 ^ [1195 ^ [], 1194 ^ [], 1198 ^ []]) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a), hAPP(hAPP(c_Power_Opower__class_Opower(t_a), 11896 ^ [1195 ^ [], 1194 ^ [], 1198 ^ []]), 1194 ^ [])), hAPP(c_Polynomial_Opoly(t_a, c_Polynomial_OpCons(t_a, 1195 ^ [], 1198 ^ [])), 11896 ^ [1195 ^ [], 1194 ^ [], 1198 ^ []])))],reduction('1.2')).
% 40.29/39.73  ncf('1.2.2.3',plain,[1195 ^ [] = c_Groups_Ozero__class_Ozero(t_a)],extension(1197 ^ 5)).
% 40.29/39.73  ncf('1.3',plain,[-(1222 ^ [] = c_Groups_Ozero__class_Ozero(t_a)), 11887 : -(c_Polynomial_OpCons(t_a, v_c____, v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), 11895 : c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_If(tc_Nat_Onat, c_fequal(1225 ^ [], c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(c_Polynomial_Odegree(t_a, 1225 ^ []))), 1221 ^ [])) = c_Nat_OSuc(c_Polynomial_Odegree(t_a, c_Polynomial_OpCons(t_a, v_c____, v_cs____))), 11895 : hAPP(c_Polynomial_Opoly(t_a, c_Polynomial_OpCons(t_a, v_c____, v_cs____)), 11896 ^ [1222 ^ [], 1221 ^ [], 1225 ^ []]) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a), hAPP(hAPP(c_Power_Opower__class_Opower(t_a), 11896 ^ [1222 ^ [], 1221 ^ [], 1225 ^ []]), 1221 ^ [])), hAPP(c_Polynomial_Opoly(t_a, c_Polynomial_OpCons(t_a, 1222 ^ [], 1225 ^ [])), 11896 ^ [1222 ^ [], 1221 ^ [], 1225 ^ []]))],extension(11881 ^ 3,bind([[_643470, _643472, _643690], [1222 ^ [], 1221 ^ [], 1225 ^ []]]))).
% 40.29/39.73  ncf('1.3.1',plain,[c_Polynomial_OpCons(t_a, v_c____, v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)), 2158 : -(hAPP(c_Polynomial_Opoly(t_a, c_Polynomial_OpCons(t_a, v_c____, v_cs____)), 1172 ^ []) = c_Groups_Ozero__class_Ozero(t_a)), 2158 : class_Rings_Oidom(t_a)],extension(2144 ^ 8,bind([[_275939, _275941, _275943], [t_a, c_Polynomial_OpCons(t_a, v_c____, v_cs____), 1172 ^ []]]))).
% 40.29/39.73  ncf('1.3.1.1',plain,[hAPP(c_Polynomial_Opoly(t_a, c_Polynomial_OpCons(t_a, v_c____, v_cs____)), 1172 ^ []) = c_Groups_Ozero__class_Ozero(t_a), class_Rings_Oidom(t_a)],extension(1169 ^ 11)).
% 40.29/39.73  ncf('1.3.1.1.1',plain,[-(class_Rings_Oidom(t_a))],lemmata('x')).
% 40.29/39.73  ncf('1.3.1.2',plain,[-(class_Rings_Oidom(t_a))],lemmata('x')).
% 40.29/39.73  ncf('1.3.2',plain,[-(c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_If(tc_Nat_Onat, c_fequal(1225 ^ [], c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(c_Polynomial_Odegree(t_a, 1225 ^ []))), 1221 ^ [])) = c_Nat_OSuc(c_Polynomial_Odegree(t_a, c_Polynomial_OpCons(t_a, v_c____, v_cs____)))), -(c_Polynomial_OpCons(t_a, v_c____, v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))],extension(1233 ^ 8)).
% 40.29/39.73  ncf('1.3.2.1',plain,[c_Polynomial_OpCons(t_a, v_c____, v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))],extension(11893 ^ 9)).
% 40.29/39.73  ncf('1.3.3',plain,[-(hAPP(c_Polynomial_Opoly(t_a, c_Polynomial_OpCons(t_a, v_c____, v_cs____)), 11896 ^ [1222 ^ [], 1221 ^ [], 1225 ^ []]) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(t_a), hAPP(hAPP(c_Power_Opower__class_Opower(t_a), 11896 ^ [1222 ^ [], 1221 ^ [], 1225 ^ []]), 1221 ^ [])), hAPP(c_Polynomial_Opoly(t_a, c_Polynomial_OpCons(t_a, 1222 ^ [], 1225 ^ [])), 11896 ^ [1222 ^ [], 1221 ^ [], 1225 ^ []])))],extension(1239 ^ 6,bind([[_240769], [11896 ^ [1222 ^ [], 1221 ^ [], 1225 ^ []]]]))).
% 40.29/39.73  %-----------------------------------------------------
% 40.29/39.73  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------