TSTP Solution File: SWW213+1 by nanoCoP---2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : nanoCoP---2.0
% Problem : SWW213+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : nanocop.sh %s %d
% Computer : n004.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 12:25:46 EDT 2023
% Result : Theorem 101.63s 98.80s
% Output : Proof 101.63s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW213+1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.13 % Command : nanocop.sh %s %d
% 0.13/0.34 % Computer : n004.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu May 18 22:35:39 EDT 2023
% 0.13/0.34 % CPUTime :
% 101.63/98.80
% 101.63/98.80 /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 101.63/98.80 Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 101.63/98.80 %-----------------------------------------------------
% 101.63/98.80 ncf(matrix, plain, [(12680 ^ _152310) ^ [] : [v_thesis____], (822 ^ _152310) ^ [_177738, _177740, _177742, _177744] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_177744, _177740) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_177742, _177738)), _177744 = _177742, _177740 = _177738], (832 ^ _152310) ^ [_178125, _178127, _178129, _178131, _178133, _178135] : [-(c_Polynomial_Opcompose(_178135, _178131, _178127) = c_Polynomial_Opcompose(_178133, _178129, _178125)), _178135 = _178133, _178131 = _178129, _178127 = _178125], (846 ^ _152310) ^ [_178641, _178643, _178645, _178647, _178649, _178651] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_178651, _178647, _178643) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_178649, _178645, _178641)), _178651 = _178649, _178647 = _178645, _178643 = _178641], (860 ^ _152310) ^ [_179157, _179159, _179161, _179163, _179165, _179167] : [-(c_Nat_Onat_Onat__case(_179167, _179163, _179159) = c_Nat_Onat_Onat__case(_179165, _179161, _179157)), _179167 = _179165, _179163 = _179161, _179159 = _179157], (874 ^ _152310) ^ [_179645, _179647, _179649, _179651] : [-(c_Polynomial_OAbs__poly(_179651, _179647) = c_Polynomial_OAbs__poly(_179649, _179645)), _179651 = _179649, _179647 = _179645], (884 ^ _152310) ^ [_180060, _180062, _180064, _180066, _180068, _180070, _180072, _180074] : [-(c_If(_180074, _180070, _180066, _180062) = c_If(_180072, _180068, _180064, _180060)), _180074 = _180072, _180070 = _180068, _180066 = _180064, _180062 = _180060], (902 ^ _152310) ^ [_180777, _180779, _180781, _180783, _180785, _180787, _180789, _180791, _180793, _180795] : [-(c_Polynomial_Opoly__rec(_180795, _180791, _180787, _180783, _180779) = c_Polynomial_Opoly__rec(_180793, _180789, _180785, _180781, _180777)), _180795 = _180793, _180791 = _180789, _180787 = _180785, _180783 = _180781, _180779 = _180777], (924 ^ _152310) ^ [_181599, _181601, _181603, _181605, _181607, _181609] : [-(c_Polynomial_Osynthetic__div(_181609, _181605, _181601) = c_Polynomial_Osynthetic__div(_181607, _181603, _181599)), _181609 = _181607, _181605 = _181603, _181601 = _181599], (938 ^ _152310) ^ [_182115, _182117, _182119, _182121, _182123, _182125] : [-(c_Polynomial_Omonom(_182125, _182121, _182117) = c_Polynomial_Omonom(_182123, _182119, _182115)), _182125 = _182123, _182121 = _182119, _182117 = _182115], (952 ^ _152310) ^ [_182631, _182633, _182635, _182637, _182639, _182641] : [-(c_Power_Opower_Opower(_182641, _182637, _182633) = c_Power_Opower_Opower(_182639, _182635, _182631)), _182641 = _182639, _182637 = _182635, _182633 = _182631], (966 ^ _152310) ^ [_183147, _183149, _183151, _183153, _183155, _183157] : [-(c_Polynomial_OpCons(_183157, _183153, _183149) = c_Polynomial_OpCons(_183155, _183151, _183147)), _183157 = _183155, _183153 = _183151, _183149 = _183147], (980 ^ _152310) ^ [_183663, _183665, _183667, _183669, _183671, _183673] : [-(c_Polynomial_Oorder(_183673, _183669, _183665) = c_Polynomial_Oorder(_183671, _183667, _183663)), _183673 = _183671, _183669 = _183667, _183665 = _183663], (994 ^ _152310) ^ [_184151, _184153, _184155, _184157] : [-(c_NthRoot_Oroot(_184157, _184153) = c_NthRoot_Oroot(_184155, _184151)), _184157 = _184155, _184153 = _184151], (1004 ^ _152310) ^ [_184482, _184484] : [_184484 = _184482, -(c_RComplete_Onatceiling(_184484) = c_RComplete_Onatceiling(_184482))], (1010 ^ _152310) ^ [_184700, _184702] : [_184702 = _184700, -(c_RComplete_Onatfloor(_184702) = c_RComplete_Onatfloor(_184700))], (1016 ^ _152310) ^ [_184918, _184920] : [_184920 = _184918, -(c_Power_Opower__class_Opower(_184920) = c_Power_Opower__class_Opower(_184918))], (1022 ^ _152310) ^ [_185164, _185166, _185168, _185170] : [-(c_RealDef_Oreal(_185170, _185166) = c_RealDef_Oreal(_185168, _185164)), _185170 = _185168, _185166 = _185164], (1032 ^ _152310) ^ [_185495, _185497] : [_185497 = _185495, -(c_Nat_OSuc(_185497) = c_Nat_OSuc(_185495))], (1038 ^ _152310) ^ [_185769, _185771, _185773, _185775, _185777, _185779] : [-(c_Polynomial_Osmult(_185779, _185775, _185771) = c_Polynomial_Osmult(_185777, _185773, _185769)), _185779 = _185777, _185775 = _185773, _185771 = _185769], (1052 ^ _152310) ^ [_186257, _186259, _186261, _186263] : [-(c_Rings_Oinverse__class_Oinverse(_186263, _186259) = c_Rings_Oinverse__class_Oinverse(_186261, _186257)), _186263 = _186261, _186259 = _186257], (1062 ^ _152310) ^ [_186616, _186618, _186620, _186622] : [-(c_Polynomial_Ocoeff(_186622, _186618) = c_Polynomial_Ocoeff(_186620, _186616)), _186622 = _186620, _186618 = _186616], (1072 ^ _152310) ^ [_187003, _187005, _187007, _187009, _187011, _187013] : [-(c_Polynomial_Opoly__gcd(_187013, _187009, _187005) = c_Polynomial_Opoly__gcd(_187011, _187007, _187003)), _187013 = _187011, _187009 = _187007, _187005 = _187003], (1086 ^ _152310) ^ [_187463, _187465] : [_187465 = _187463, -(c_Groups_Oone__class_Oone(_187465) = c_Groups_Oone__class_Oone(_187463))], (1092 ^ _152310) ^ [_187681, _187683] : [_187683 = _187681, -(c_Groups_Ozero__class_Ozero(_187683) = c_Groups_Ozero__class_Ozero(_187681))], (1098 ^ _152310) ^ [_187927, _187929, _187931, _187933] : [-(c_Groups_Ouminus__class_Ouminus(_187933, _187929) = c_Groups_Ouminus__class_Ouminus(_187931, _187927)), _187933 = _187931, _187929 = _187927], (1108 ^ _152310) ^ [_188258, _188260] : [_188260 = _188258, -(c_Groups_Otimes__class_Otimes(_188260) = c_Groups_Otimes__class_Otimes(_188258))], (1114 ^ _152310) ^ [_188532, _188534, _188536, _188538, _188540, _188542] : [-(c_Divides_Odiv__class_Omod(_188542, _188538, _188534) = c_Divides_Odiv__class_Omod(_188540, _188536, _188532)), _188542 = _188540, _188538 = _188536, _188534 = _188532], (1128 ^ _152310) ^ [_189020, _189022, _189024, _189026] : [-(tc_fun(_189026, _189022) = tc_fun(_189024, _189020)), _189026 = _189024, _189022 = _189020], (1138 ^ _152310) ^ [_189351, _189353] : [_189353 = _189351, -(tc_Polynomial_Opoly(_189353) = tc_Polynomial_Opoly(_189351))], (1144 ^ _152310) ^ [_189597, _189599, _189601, _189603] : [-(c_fequal(_189603, _189599) = c_fequal(_189601, _189597)), _189603 = _189601, _189599 = _189597], (1154 ^ _152310) ^ [_189956, _189958, _189960, _189962] : [-(c_Polynomial_Odegree(_189962, _189958) = c_Polynomial_Odegree(_189960, _189956)), _189962 = _189960, _189958 = _189956], (1164 ^ _152310) ^ [_190315, _190317, _190319, _190321] : [-(hAPP(_190321, _190317) = hAPP(_190319, _190315)), _190321 = _190319, _190317 = _190315], (1174 ^ _152310) ^ [_190674, _190676, _190678, _190680] : [-(c_Polynomial_Opoly(_190680, _190676) = c_Polynomial_Opoly(_190678, _190674)), _190680 = _190678, _190676 = _190674], (1184 ^ _152310) ^ [_191041, _191043, _191045, _191047, _191049, _191051] : [-(c_Groups_Oplus__class_Oplus(_191051, _191047, _191043) = c_Groups_Oplus__class_Oplus(_191049, _191045, _191041)), _191051 = _191049, _191047 = _191045, _191043 = _191041], (2 ^ _152310) ^ [_152454] : [-(_152454 = _152454)], (4 ^ _152310) ^ [_152561, _152563] : [_152563 = _152561, -(_152561 = _152563)], (10 ^ _152310) ^ [_152765, _152767, _152769] : [-(_152769 = _152765), _152769 = _152767, _152767 = _152765], (20 ^ _152310) ^ [_153106, _153108, _153110, _153112] : [-(c_Groups_Osemigroup(_153110, _153106)), c_Groups_Osemigroup(_153112, _153108), _153112 = _153110, _153108 = _153106], (34 ^ _152310) ^ [_153550, _153552, _153554, _153556] : [-(c_Polynomial_Opos__poly(_153554, _153550)), c_Polynomial_Opos__poly(_153556, _153552), _153556 = _153554, _153552 = _153550], (48 ^ _152310) ^ [_153966, _153968] : [-(class_Lattices_Oab__semigroup__idem__mult(_153966)), _153968 = _153966, class_Lattices_Oab__semigroup__idem__mult(_153968)], (58 ^ _152310) ^ [_154373, _154375, _154377, _154379, _154381, _154383, _154385, _154387, _154389, _154391] : [-(c_Polynomial_Opdivmod__rel(_154389, _154385, _154381, _154377, _154373)), c_Polynomial_Opdivmod__rel(_154391, _154387, _154383, _154379, _154375), _154391 = _154389, _154387 = _154385, _154383 = _154381, _154379 = _154377, _154375 = _154373], (84 ^ _152310) ^ [_155276, _155278, _155280, _155282] : [-(c_SEQ_Odecseq(_155280, _155276)), c_SEQ_Odecseq(_155282, _155278), _155282 = _155280, _155278 = _155276], (98 ^ _152310) ^ [_155748, _155750, _155752, _155754, _155756, _155758] : [-(c_Orderings_Oord__class_Oless__eq(_155756, _155752, _155748)), c_Orderings_Oord__class_Oless__eq(_155758, _155754, _155750), _155758 = _155756, _155754 = _155752, _155750 = _155748], (116 ^ _152310) ^ [_156357, _156359, _156361, _156363, _156365, _156367] : [-(c_Orderings_Oord__class_Oless(_156365, _156361, _156357)), c_Orderings_Oord__class_Oless(_156367, _156363, _156359), _156367 = _156365, _156363 = _156361, _156359 = _156357], (134 ^ _152310) ^ [_156966, _156968, _156970, _156972, _156974, _156976] : [-(c_Rings_Odvd__class_Odvd(_156974, _156970, _156966)), c_Rings_Odvd__class_Odvd(_156976, _156972, _156968), _156976 = _156974, _156972 = _156970, _156968 = _156966], (152 ^ _152310) ^ [_157519, _157521] : [-(class_Lattices_Oboolean__algebra(_157519)), _157521 = _157519, class_Lattices_Oboolean__algebra(_157521)], (162 ^ _152310) ^ [_157814, _157816] : [-(class_Fields_Olinordered__field__inverse__zero(_157814)), _157816 = _157814, class_Fields_Olinordered__field__inverse__zero(_157816)], (172 ^ _152310) ^ [_158109, _158111] : [-(class_Fields_Olinordered__field(_158109)), _158111 = _158109, class_Fields_Olinordered__field(_158111)], (182 ^ _152310) ^ [_158404, _158406] : [-(class_Rings_Odivision__ring__inverse__zero(_158404)), _158406 = _158404, class_Rings_Odivision__ring__inverse__zero(_158406)], (192 ^ _152310) ^ [_158699, _158701] : [-(class_RealVector_Oreal__normed__algebra(_158699)), _158701 = _158699, class_RealVector_Oreal__normed__algebra(_158701)], (202 ^ _152310) ^ [_158994, _158996] : [-(class_Fields_Ofield__inverse__zero(_158994)), _158996 = _158994, class_Fields_Ofield__inverse__zero(_158996)], (212 ^ _152310) ^ [_159289, _159291] : [-(class_Rings_Odivision__ring(_159289)), _159291 = _159289, class_Rings_Odivision__ring(_159291)], (222 ^ _152310) ^ [_159584, _159586] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_159584)), _159586 = _159584, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_159586)], (232 ^ _152310) ^ [_159879, _159881] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_159879)), _159881 = _159879, class_Groups_Oordered__cancel__ab__semigroup__add(_159881)], (242 ^ _152310) ^ [_160174, _160176] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_160174)), _160176 = _160174, class_Groups_Oordered__ab__semigroup__add__imp__le(_160176)], (252 ^ _152310) ^ [_160469, _160471] : [-(class_Rings_Olinordered__comm__semiring__strict(_160469)), _160471 = _160469, class_Rings_Olinordered__comm__semiring__strict(_160471)], (262 ^ _152310) ^ [_160764, _160766] : [-(class_Rings_Olinordered__semiring__1__strict(_160764)), _160766 = _160764, class_Rings_Olinordered__semiring__1__strict(_160766)], (272 ^ _152310) ^ [_161059, _161061] : [-(class_Rings_Olinordered__semiring__strict(_161059)), _161061 = _161059, class_Rings_Olinordered__semiring__strict(_161061)], (282 ^ _152310) ^ [_161354, _161356] : [-(class_Groups_Oordered__ab__semigroup__add(_161354)), _161356 = _161354, class_Groups_Oordered__ab__semigroup__add(_161356)], (292 ^ _152310) ^ [_161649, _161651] : [-(class_Groups_Oordered__comm__monoid__add(_161649)), _161651 = _161649, class_Groups_Oordered__comm__monoid__add(_161651)], (302 ^ _152310) ^ [_161944, _161946] : [-(class_Groups_Olinordered__ab__group__add(_161944)), _161946 = _161944, class_Groups_Olinordered__ab__group__add(_161946)], (312 ^ _152310) ^ [_162239, _162241] : [-(class_Groups_Ocancel__ab__semigroup__add(_162239)), _162241 = _162239, class_Groups_Ocancel__ab__semigroup__add(_162241)], (322 ^ _152310) ^ [_162534, _162536] : [-(class_Rings_Oring__1__no__zero__divisors(_162534)), _162536 = _162534, class_Rings_Oring__1__no__zero__divisors(_162536)], (332 ^ _152310) ^ [_162829, _162831] : [-(class_Rings_Oordered__cancel__semiring(_162829)), _162831 = _162829, class_Rings_Oordered__cancel__semiring(_162831)], (342 ^ _152310) ^ [_163124, _163126] : [-(class_Rings_Olinordered__ring__strict(_163124)), _163126 = _163124, class_Rings_Olinordered__ring__strict(_163126)], (352 ^ _152310) ^ [_163419, _163421] : [-(class_Rings_Oring__no__zero__divisors(_163419)), _163421 = _163419, class_Rings_Oring__no__zero__divisors(_163421)], (362 ^ _152310) ^ [_163714, _163716] : [-(class_Rings_Oordered__comm__semiring(_163714)), _163716 = _163714, class_Rings_Oordered__comm__semiring(_163716)], (372 ^ _152310) ^ [_164009, _164011] : [-(class_Rings_Olinordered__semiring__1(_164009)), _164011 = _164009, class_Rings_Olinordered__semiring__1(_164011)], (382 ^ _152310) ^ [_164304, _164306] : [-(class_Groups_Oordered__ab__group__add(_164304)), _164306 = _164304, class_Groups_Oordered__ab__group__add(_164306)], (392 ^ _152310) ^ [_164599, _164601] : [-(class_Groups_Ocancel__comm__monoid__add(_164599)), _164601 = _164599, class_Groups_Ocancel__comm__monoid__add(_164601)], (402 ^ _152310) ^ [_164894, _164896] : [-(class_Groups_Ocancel__semigroup__add(_164894)), _164896 = _164894, class_Groups_Ocancel__semigroup__add(_164896)], (412 ^ _152310) ^ [_165189, _165191] : [-(class_Rings_Olinordered__semiring(_165189)), _165191 = _165189, class_Rings_Olinordered__semiring(_165191)], (422 ^ _152310) ^ [_165484, _165486] : [-(class_Rings_Olinordered__semidom(_165484)), _165486 = _165484, class_Rings_Olinordered__semidom(_165486)], (432 ^ _152310) ^ [_165779, _165781] : [-(class_Groups_Oab__semigroup__mult(_165779)), _165781 = _165779, class_Groups_Oab__semigroup__mult(_165781)], (442 ^ _152310) ^ [_166074, _166076] : [-(class_Groups_Ocomm__monoid__mult(_166074)), _166076 = _166074, class_Groups_Ocomm__monoid__mult(_166076)], (452 ^ _152310) ^ [_166369, _166371] : [-(class_Groups_Oab__semigroup__add(_166369)), _166371 = _166369, class_Groups_Oab__semigroup__add(_166371)], (462 ^ _152310) ^ [_166664, _166666] : [-(class_Rings_Oordered__semiring(_166664)), _166666 = _166664, class_Rings_Oordered__semiring(_166666)], (472 ^ _152310) ^ [_166959, _166961] : [-(class_Rings_Ono__zero__divisors(_166959)), _166961 = _166959, class_Rings_Ono__zero__divisors(_166961)], (482 ^ _152310) ^ [_167254, _167256] : [-(class_Rings_Olinordered__ring(_167254)), _167256 = _167254, class_Rings_Olinordered__ring(_167256)], (492 ^ _152310) ^ [_167549, _167551] : [-(class_Divides_Osemiring__div(_167549)), _167551 = _167549, class_Divides_Osemiring__div(_167551)], (502 ^ _152310) ^ [_167844, _167846] : [-(class_Rings_Ocomm__semiring(_167844)), _167846 = _167844, class_Rings_Ocomm__semiring(_167846)], (512 ^ _152310) ^ [_168139, _168141] : [-(class_Rings_Ozero__neq__one(_168139)), _168141 = _168139, class_Rings_Ozero__neq__one(_168141)], (522 ^ _152310) ^ [_168434, _168436] : [-(class_Rings_Oordered__ring(_168434)), _168436 = _168434, class_Rings_Oordered__ring(_168436)], (532 ^ _152310) ^ [_168729, _168731] : [-(class_Orderings_Opreorder(_168729)), _168731 = _168729, class_Orderings_Opreorder(_168731)], (542 ^ _152310) ^ [_169024, _169026] : [-(class_Orderings_Olinorder(_169024)), _169026 = _169024, class_Orderings_Olinorder(_169026)], (552 ^ _152310) ^ [_169319, _169321] : [-(class_Groups_Omonoid__mult(_169319)), _169321 = _169319, class_Groups_Omonoid__mult(_169321)], (562 ^ _152310) ^ [_169614, _169616] : [-(class_Groups_Ocomm__monoid__add(_169614)), _169616 = _169614, class_Groups_Ocomm__monoid__add(_169616)], (572 ^ _152310) ^ [_169909, _169911] : [-(class_Groups_Omonoid__add(_169909)), _169911 = _169909, class_Groups_Omonoid__add(_169911)], (582 ^ _152310) ^ [_170204, _170206] : [-(class_Rings_Osemiring__0(_170204)), _170206 = _170204, class_Rings_Osemiring__0(_170206)], (592 ^ _152310) ^ [_170499, _170501] : [-(class_Groups_Ogroup__add(_170499)), _170501 = _170499, class_Groups_Ogroup__add(_170501)], (602 ^ _152310) ^ [_170794, _170796] : [-(class_Fields_Ofield(_170794)), _170796 = _170794, class_Fields_Ofield(_170796)], (612 ^ _152310) ^ [_171089, _171091] : [-(class_Divides_Oring__div(_171089)), _171091 = _171089, class_Divides_Oring__div(_171091)], (622 ^ _152310) ^ [_171384, _171386] : [-(class_Rings_Omult__zero(_171384)), _171386 = _171384, class_Rings_Omult__zero(_171386)], (632 ^ _152310) ^ [_171679, _171681] : [-(class_Orderings_Oorder(_171679)), _171681 = _171679, class_Orderings_Oorder(_171681)], (642 ^ _152310) ^ [_171974, _171976] : [-(class_Int_Oring__char__0(_171974)), _171976 = _171974, class_Int_Oring__char__0(_171976)], (652 ^ _152310) ^ [_172269, _172271] : [-(class_Rings_Ocomm__semiring__0(_172269)), _172271 = _172269, class_Rings_Ocomm__semiring__0(_172271)], (662 ^ _152310) ^ [_172564, _172566] : [-(class_Rings_Osemiring(_172564)), _172566 = _172564, class_Rings_Osemiring(_172566)], (672 ^ _152310) ^ [_172859, _172861] : [-(class_Rings_Olinordered__idom(_172859)), _172861 = _172859, class_Rings_Olinordered__idom(_172861)], (682 ^ _152310) ^ [_173154, _173156] : [-(class_Orderings_Oord(_173154)), _173156 = _173154, class_Orderings_Oord(_173156)], (692 ^ _152310) ^ [_173449, _173451] : [-(class_Groups_Oab__group__add(_173449)), _173451 = _173449, class_Groups_Oab__group__add(_173451)], (702 ^ _152310) ^ [_173744, _173746] : [-(class_Groups_Ouminus(_173744)), _173746 = _173744, class_Groups_Ouminus(_173746)], (712 ^ _152310) ^ [_174039, _174041] : [-(class_Rings_Ocomm__ring__1(_174039)), _174041 = _174039, class_Rings_Ocomm__ring__1(_174041)], (722 ^ _152310) ^ [_174334, _174336] : [-(class_Rings_Oring__1(_174334)), _174336 = _174334, class_Rings_Oring__1(_174336)], (732 ^ _152310) ^ [_174629, _174631] : [-(class_Power_Opower(_174629)), _174631 = _174629, class_Power_Opower(_174631)], (742 ^ _152310) ^ [_174924, _174926] : [-(class_Groups_Ozero(_174924)), _174926 = _174924, class_Groups_Ozero(_174926)], (752 ^ _152310) ^ [_175219, _175221] : [-(class_Rings_Ocomm__ring(_175219)), _175221 = _175219, class_Rings_Ocomm__ring(_175221)], (762 ^ _152310) ^ [_175514, _175516] : [-(class_Rings_Oring(_175514)), _175516 = _175514, class_Rings_Oring(_175516)], (772 ^ _152310) ^ [_175809, _175811] : [-(class_Rings_Oidom(_175809)), _175811 = _175809, class_Rings_Oidom(_175811)], (782 ^ _152310) ^ [_176104, _176106] : [-(class_Groups_Oone(_176104)), _176106 = _176104, class_Groups_Oone(_176106)], (792 ^ _152310) ^ [_176399, _176401] : [-(class_Rings_Ocomm__semiring__1(_176399)), _176401 = _176399, class_Rings_Ocomm__semiring__1(_176401)], (802 ^ _152310) ^ [_176694, _176696] : [-(class_Rings_Odvd(_176694)), _176696 = _176694, class_Rings_Odvd(_176696)], (812 ^ _152310) ^ [_176969, _176971] : [-(hBOOL(_176969)), _176971 = _176969, hBOOL(_176971)], (1198 ^ _152310) ^ [_191719, _191721] : [hAPP(_191719, 1199 ^ [_191719, _191721]) = hAPP(_191721, 1199 ^ [_191719, _191721]), -(_191719 = _191721)], (1205 ^ _152310) ^ [_192039, _192041, _192043, _192045] : [class_Rings_Ocomm__semiring__0(_192039), -(hAPP(c_Polynomial_Opoly(_192039, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_192039), _192041, _192043)), _192045) = c_Groups_Oplus__class_Oplus(_192039, hAPP(c_Polynomial_Opoly(_192039, _192041), _192045), hAPP(c_Polynomial_Opoly(_192039, _192043), _192045)))], (1211 ^ _152310) ^ [_192343, _192345, _192347, _192349] : [class_Rings_Ocomm__semiring__0(_192343), -(hAPP(c_Polynomial_Opoly(_192343, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_192343, _192345, _192347)), _192349) = hAPP(c_Polynomial_Opoly(_192343, _192345), c_Groups_Oplus__class_Oplus(_192343, _192347, _192349)))], (1217 ^ _152310) ^ [_192617, _192619, _192621] : [class_Int_Oring__char__0(_192617), class_Rings_Oidom(_192617), 1224 ^ _152310 : [(1225 ^ _152310) ^ [] : [c_Polynomial_Opoly(_192617, _192619) = c_Polynomial_Opoly(_192617, _192621), -(_192619 = _192621)], (1231 ^ _152310) ^ [] : [_192619 = _192621, -(c_Polynomial_Opoly(_192617, _192619) = c_Polynomial_Opoly(_192617, _192621))]]], (1237 ^ _152310) ^ [_193216, _193218, _193220] : [class_Rings_Ocomm__semiring__1(_193216), -(c_Groups_Oplus__class_Oplus(_193216, _193218, _193220) = c_Groups_Oplus__class_Oplus(_193216, _193220, _193218))], (1243 ^ _152310) ^ [_193474, _193476, _193478, _193480] : [class_Rings_Ocomm__semiring__1(_193474), -(c_Groups_Oplus__class_Oplus(_193474, _193476, c_Groups_Oplus__class_Oplus(_193474, _193478, _193480)) = c_Groups_Oplus__class_Oplus(_193474, _193478, c_Groups_Oplus__class_Oplus(_193474, _193476, _193480)))], (1249 ^ _152310) ^ [_193754, _193756, _193758, _193760] : [class_Rings_Ocomm__semiring__1(_193754), -(c_Groups_Oplus__class_Oplus(_193754, _193756, c_Groups_Oplus__class_Oplus(_193754, _193758, _193760)) = c_Groups_Oplus__class_Oplus(_193754, c_Groups_Oplus__class_Oplus(_193754, _193756, _193758), _193760))], (1255 ^ _152310) ^ [_194034, _194036, _194038, _194040] : [class_Rings_Ocomm__semiring__1(_194034), -(c_Groups_Oplus__class_Oplus(_194034, c_Groups_Oplus__class_Oplus(_194034, _194036, _194038), _194040) = c_Groups_Oplus__class_Oplus(_194034, _194036, c_Groups_Oplus__class_Oplus(_194034, _194038, _194040)))], (1261 ^ _152310) ^ [_194314, _194316, _194318, _194320] : [class_Groups_Oab__semigroup__add(_194314), -(c_Groups_Oplus__class_Oplus(_194314, c_Groups_Oplus__class_Oplus(_194314, _194316, _194318), _194320) = c_Groups_Oplus__class_Oplus(_194314, _194316, c_Groups_Oplus__class_Oplus(_194314, _194318, _194320)))], (1267 ^ _152310) ^ [_194594, _194596, _194598, _194600] : [class_Rings_Ocomm__semiring__1(_194594), -(c_Groups_Oplus__class_Oplus(_194594, c_Groups_Oplus__class_Oplus(_194594, _194596, _194598), _194600) = c_Groups_Oplus__class_Oplus(_194594, c_Groups_Oplus__class_Oplus(_194594, _194596, _194600), _194598))], (1273 ^ _152310) ^ [_194874, _194876, _194878, _194880] : [class_Groups_Ocancel__semigroup__add(_194874), 1276 ^ _152310 : [(1277 ^ _152310) ^ [] : [c_Groups_Oplus__class_Oplus(_194874, _194876, _194878) = c_Groups_Oplus__class_Oplus(_194874, _194876, _194880), -(_194878 = _194880)], (1283 ^ _152310) ^ [] : [_194878 = _194880, -(c_Groups_Oplus__class_Oplus(_194874, _194876, _194878) = c_Groups_Oplus__class_Oplus(_194874, _194876, _194880))]]], (1289 ^ _152310) ^ [_195416, _195418, _195420, _195422] : [class_Groups_Ocancel__semigroup__add(_195416), 1292 ^ _152310 : [(1293 ^ _152310) ^ [] : [c_Groups_Oplus__class_Oplus(_195416, _195418, _195420) = c_Groups_Oplus__class_Oplus(_195416, _195422, _195420), -(_195418 = _195422)], (1299 ^ _152310) ^ [] : [_195418 = _195422, -(c_Groups_Oplus__class_Oplus(_195416, _195418, _195420) = c_Groups_Oplus__class_Oplus(_195416, _195422, _195420))]]], (1305 ^ _152310) ^ [_195972, _195974, _195976, _195978, _195980] : [class_Rings_Ocomm__semiring__1(_195972), -(c_Groups_Oplus__class_Oplus(_195972, c_Groups_Oplus__class_Oplus(_195972, _195974, _195976), c_Groups_Oplus__class_Oplus(_195972, _195978, _195980)) = c_Groups_Oplus__class_Oplus(_195972, c_Groups_Oplus__class_Oplus(_195972, _195974, _195978), c_Groups_Oplus__class_Oplus(_195972, _195976, _195980)))], (1311 ^ _152310) ^ [_196260, _196262, _196264] : [class_Rings_Ocomm__semiring__0(_196260), -(c_Polynomial_Odegree(_196260, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_196260, _196262, _196264)) = c_Polynomial_Odegree(_196260, _196262))], (1317 ^ _152310) ^ [_196522, _196524, _196526, _196528] : [class_Groups_Ocancel__semigroup__add(_196522), c_Groups_Oplus__class_Oplus(_196522, _196524, _196526) = c_Groups_Oplus__class_Oplus(_196522, _196528, _196526), -(_196524 = _196528)], (1327 ^ _152310) ^ [_196883, _196885, _196887, _196889] : [class_Groups_Ocancel__ab__semigroup__add(_196883), c_Groups_Oplus__class_Oplus(_196883, _196885, _196887) = c_Groups_Oplus__class_Oplus(_196883, _196885, _196889), -(_196887 = _196889)], (1337 ^ _152310) ^ [_197244, _197246, _197248, _197250] : [class_Groups_Ocancel__semigroup__add(_197244), c_Groups_Oplus__class_Oplus(_197244, _197246, _197248) = c_Groups_Oplus__class_Oplus(_197244, _197246, _197250), -(_197248 = _197250)], (1347 ^ _152310) ^ [_197605, _197607, _197609, _197611] : [class_Rings_Ocomm__semiring__0(_197605), -(hAPP(c_Polynomial_Opoly(_197605, c_Polynomial_Opcompose(_197605, _197607, _197609)), _197611) = hAPP(c_Polynomial_Opoly(_197605, _197607), hAPP(c_Polynomial_Opoly(_197605, _197609), _197611)))], (1353 ^ _152310) ^ [_197897, _197899, _197901, _197903] : [class_Groups_Ocomm__monoid__add(_197897), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_197897), c_Polynomial_Omonom(_197897, _197899, _197901), c_Polynomial_Omonom(_197897, _197903, _197901)) = c_Polynomial_Omonom(_197897, c_Groups_Oplus__class_Oplus(_197897, _197899, _197903), _197901))], (1360 ^ _152310) ^ [_198240, _198242] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, 1358 ^ [_198240, _198242]) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex, _198240))], (1362 ^ _152310) ^ [_198313, _198315, _198317] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, 1358 ^ [_198315, _198317]), _198313) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, _198315), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, _198317, _198313)))], (1364 ^ _152310) ^ [_198477, _198479, _198481, _198483] : [class_Groups_Ocomm__monoid__add(_198477), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_198477, _198479), _198481), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_198477, _198483), _198481), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_198477, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_198477), _198479, _198483)), _198481))], (1378 ^ _152310) ^ [_198955, _198957, _198959, _198961] : [class_Groups_Ocomm__monoid__add(_198955), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_198955, _198957), _198959), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_198955, _198961), _198959), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_198955, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_198955), _198957, _198961)), _198959))], (1392 ^ _152310) ^ [_199419, _199421, _199423] : [class_Groups_Ocomm__monoid__add(_199419), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_199419, _199421), c_Polynomial_Odegree(_199419, _199423)), -(c_Polynomial_Odegree(_199419, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_199419), _199421, _199423)) = c_Polynomial_Odegree(_199419, _199423))], (1402 ^ _152310) ^ [_199778, _199780, _199782] : [class_Groups_Ocomm__monoid__add(_199778), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_199778, _199780), c_Polynomial_Odegree(_199778, _199782)), -(c_Polynomial_Odegree(_199778, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_199778), _199782, _199780)) = c_Polynomial_Odegree(_199778, _199782))], (1412 ^ _152310) ^ [_200137, _200139, _200141] : [class_Rings_Olinordered__idom(_200137), c_Polynomial_Opos__poly(_200137, _200139), c_Polynomial_Opos__poly(_200137, _200141), -(c_Polynomial_Opos__poly(_200137, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_200137), _200139, _200141)))], (1426 ^ _152310) ^ [_200577, _200579, _200581, _200583] : [class_Rings_Ocomm__semiring__0(_200577), -(c_Polynomial_Osmult(_200577, c_Groups_Oplus__class_Oplus(_200577, _200579, _200581), _200583) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_200577), c_Polynomial_Osmult(_200577, _200579, _200583), c_Polynomial_Osmult(_200577, _200581, _200583)))], (1432 ^ _152310) ^ [_200869, _200871, _200873, _200875] : [class_Groups_Ocomm__monoid__add(_200869), -(hAPP(c_Polynomial_Ocoeff(_200869, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_200869), _200871, _200873)), _200875) = c_Groups_Oplus__class_Oplus(_200869, hAPP(c_Polynomial_Ocoeff(_200869, _200871), _200875), hAPP(c_Polynomial_Ocoeff(_200869, _200873), _200875)))], (1438 ^ _152310) ^ [_201187, _201189, _201191, _201193, _201195] : [class_Groups_Ocomm__monoid__add(_201187), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_201187), c_Polynomial_OpCons(_201187, _201189, _201191), c_Polynomial_OpCons(_201187, _201193, _201195)) = c_Polynomial_OpCons(_201187, c_Groups_Oplus__class_Oplus(_201187, _201189, _201193), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_201187), _201191, _201195)))], (1444 ^ _152310) ^ [_201511, _201513, _201515, _201517, _201519] : [c_Groups_Osemigroup(_201511, _201513), -(hAPP(hAPP(_201513, hAPP(hAPP(_201513, _201515), _201517)), _201519) = hAPP(hAPP(_201513, _201515), hAPP(hAPP(_201513, _201517), _201519)))], (1450 ^ _152310) ^ [_201801, _201803, _201805] : [class_Groups_Ozero(_201801), 1453 ^ _152310 : [(1454 ^ _152310) ^ [] : [_201803 = _201805, 1457 ^ _152310 : [(1458 ^ _152310) ^ [_202049] : [-(hAPP(c_Polynomial_Ocoeff(_201801, _201803), _202049) = hAPP(c_Polynomial_Ocoeff(_201801, _201805), _202049))]]], (1460 ^ _152310) ^ [] : [hAPP(c_Polynomial_Ocoeff(_201801, _201803), 1461 ^ [_201801, _201803, _201805]) = hAPP(c_Polynomial_Ocoeff(_201801, _201805), 1461 ^ [_201801, _201803, _201805]), -(_201803 = _201805)]]], (1467 ^ _152310) ^ [_202426, _202428, _202430] : [class_Groups_Ozero(_202426), 1470 ^ _152310 : [(1471 ^ _152310) ^ [] : [c_Polynomial_Ocoeff(_202426, _202428) = c_Polynomial_Ocoeff(_202426, _202430), -(_202428 = _202430)], (1477 ^ _152310) ^ [] : [_202428 = _202430, -(c_Polynomial_Ocoeff(_202426, _202428) = c_Polynomial_Ocoeff(_202426, _202430))]]], (1483 ^ _152310) ^ [_202946, _202948, _202950, _202952] : [class_Groups_Ozero(_202946), 1486 ^ _152310 : [(1487 ^ _152310) ^ [] : [c_Polynomial_Omonom(_202946, _202948, _202950) = c_Polynomial_Omonom(_202946, _202952, _202950), -(_202948 = _202952)], (1493 ^ _152310) ^ [] : [_202948 = _202952, -(c_Polynomial_Omonom(_202946, _202948, _202950) = c_Polynomial_Omonom(_202946, _202952, _202950))]]], (1499 ^ _152310) ^ [_203502, _203504, _203506, _203508, _203510] : [class_Groups_Ozero(_203502), 1502 ^ _152310 : [(1503 ^ _152310) ^ [] : [c_Polynomial_OpCons(_203502, _203504, _203506) = c_Polynomial_OpCons(_203502, _203508, _203510), 1506 ^ _152310 : [(1507 ^ _152310) ^ [] : [-(_203504 = _203508)], (1509 ^ _152310) ^ [] : [-(_203506 = _203510)]]], (1511 ^ _152310) ^ [] : [-(c_Polynomial_OpCons(_203502, _203504, _203506) = c_Polynomial_OpCons(_203502, _203508, _203510)), _203504 = _203508, _203506 = _203510]]], (1521 ^ _152310) ^ [_204250, _204252, _204254, _204256, _204258] : [class_Groups_Oordered__cancel__ab__semigroup__add(_204250), c_Orderings_Oord__class_Oless__eq(_204250, _204252, _204254), c_Orderings_Oord__class_Oless(_204250, _204256, _204258), -(c_Orderings_Oord__class_Oless(_204250, c_Groups_Oplus__class_Oplus(_204250, _204252, _204256), c_Groups_Oplus__class_Oplus(_204250, _204254, _204258)))], (1535 ^ _152310) ^ [_204742, _204744, _204746, _204748, _204750] : [class_Groups_Oordered__cancel__ab__semigroup__add(_204742), c_Orderings_Oord__class_Oless(_204742, _204744, _204746), c_Orderings_Oord__class_Oless__eq(_204742, _204748, _204750), -(c_Orderings_Oord__class_Oless(_204742, c_Groups_Oplus__class_Oplus(_204742, _204744, _204748), c_Groups_Oplus__class_Oplus(_204742, _204746, _204750)))], (1549 ^ _152310) ^ [_205206, _205208, _205210] : [class_Rings_Ocomm__semiring__0(_205206), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_205206, c_Polynomial_Osmult(_205206, _205208, _205210)), c_Polynomial_Odegree(_205206, _205210)))], (1555 ^ _152310) ^ [_205456, _205458, _205460] : [class_Groups_Ozero(_205456), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_205456, c_Polynomial_Omonom(_205456, _205458, _205460)), _205460))], (1561 ^ _152310) ^ [_205714, _205716, _205718, _205720] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_205714), 1564 ^ _152310 : [(1565 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_205714, c_Groups_Oplus__class_Oplus(_205714, _205716, _205718), c_Groups_Oplus__class_Oplus(_205714, _205720, _205718)), -(c_Orderings_Oord__class_Oless(_205714, _205716, _205720))], (1571 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_205714, _205716, _205720), -(c_Orderings_Oord__class_Oless(_205714, c_Groups_Oplus__class_Oplus(_205714, _205716, _205718), c_Groups_Oplus__class_Oplus(_205714, _205720, _205718)))]]], (1577 ^ _152310) ^ [_206262, _206264, _206266, _206268] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_206262), 1580 ^ _152310 : [(1581 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_206262, c_Groups_Oplus__class_Oplus(_206262, _206264, _206266), c_Groups_Oplus__class_Oplus(_206262, _206264, _206268)), -(c_Orderings_Oord__class_Oless(_206262, _206266, _206268))], (1587 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_206262, _206266, _206268), -(c_Orderings_Oord__class_Oless(_206262, c_Groups_Oplus__class_Oplus(_206262, _206264, _206266), c_Groups_Oplus__class_Oplus(_206262, _206264, _206268)))]]], (1593 ^ _152310) ^ [_206810, _206812, _206814, _206816] : [class_Groups_Oordered__cancel__ab__semigroup__add(_206810), c_Orderings_Oord__class_Oless(_206810, _206812, _206814), -(c_Orderings_Oord__class_Oless(_206810, c_Groups_Oplus__class_Oplus(_206810, _206812, _206816), c_Groups_Oplus__class_Oplus(_206810, _206814, _206816)))], (1603 ^ _152310) ^ [_207175, _207177, _207179, _207181] : [class_Groups_Oordered__cancel__ab__semigroup__add(_207175), c_Orderings_Oord__class_Oless(_207175, _207177, _207179), -(c_Orderings_Oord__class_Oless(_207175, c_Groups_Oplus__class_Oplus(_207175, _207181, _207177), c_Groups_Oplus__class_Oplus(_207175, _207181, _207179)))], (1613 ^ _152310) ^ [_207554, _207556, _207558, _207560, _207562] : [class_Groups_Oordered__cancel__ab__semigroup__add(_207554), c_Orderings_Oord__class_Oless(_207554, _207556, _207558), c_Orderings_Oord__class_Oless(_207554, _207560, _207562), -(c_Orderings_Oord__class_Oless(_207554, c_Groups_Oplus__class_Oplus(_207554, _207556, _207560), c_Groups_Oplus__class_Oplus(_207554, _207558, _207562)))], (1627 ^ _152310) ^ [_208032, _208034, _208036, _208038] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_208032), c_Orderings_Oord__class_Oless(_208032, c_Groups_Oplus__class_Oplus(_208032, _208034, _208036), c_Groups_Oplus__class_Oplus(_208032, _208038, _208036)), -(c_Orderings_Oord__class_Oless(_208032, _208034, _208038))], (1637 ^ _152310) ^ [_208397, _208399, _208401, _208403] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_208397), c_Orderings_Oord__class_Oless(_208397, c_Groups_Oplus__class_Oplus(_208397, _208399, _208401), c_Groups_Oplus__class_Oplus(_208397, _208399, _208403)), -(c_Orderings_Oord__class_Oless(_208397, _208401, _208403))], (1647 ^ _152310) ^ [_208762, _208764, _208766, _208768] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_208762), 1650 ^ _152310 : [(1651 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_208762, c_Groups_Oplus__class_Oplus(_208762, _208764, _208766), c_Groups_Oplus__class_Oplus(_208762, _208768, _208766)), -(c_Orderings_Oord__class_Oless__eq(_208762, _208764, _208768))], (1657 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_208762, _208764, _208768), -(c_Orderings_Oord__class_Oless__eq(_208762, c_Groups_Oplus__class_Oplus(_208762, _208764, _208766), c_Groups_Oplus__class_Oplus(_208762, _208768, _208766)))]]], (1663 ^ _152310) ^ [_209310, _209312, _209314, _209316] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_209310), 1666 ^ _152310 : [(1667 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_209310, c_Groups_Oplus__class_Oplus(_209310, _209312, _209314), c_Groups_Oplus__class_Oplus(_209310, _209312, _209316)), -(c_Orderings_Oord__class_Oless__eq(_209310, _209314, _209316))], (1673 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_209310, _209314, _209316), -(c_Orderings_Oord__class_Oless__eq(_209310, c_Groups_Oplus__class_Oplus(_209310, _209312, _209314), c_Groups_Oplus__class_Oplus(_209310, _209312, _209316)))]]], (1679 ^ _152310) ^ [_209858, _209860, _209862, _209864] : [class_Groups_Oordered__ab__semigroup__add(_209858), c_Orderings_Oord__class_Oless__eq(_209858, _209860, _209862), -(c_Orderings_Oord__class_Oless__eq(_209858, c_Groups_Oplus__class_Oplus(_209858, _209860, _209864), c_Groups_Oplus__class_Oplus(_209858, _209862, _209864)))], (1689 ^ _152310) ^ [_210223, _210225, _210227, _210229] : [class_Groups_Oordered__ab__semigroup__add(_210223), c_Orderings_Oord__class_Oless__eq(_210223, _210225, _210227), -(c_Orderings_Oord__class_Oless__eq(_210223, c_Groups_Oplus__class_Oplus(_210223, _210229, _210225), c_Groups_Oplus__class_Oplus(_210223, _210229, _210227)))], (1699 ^ _152310) ^ [_210602, _210604, _210606, _210608, _210610] : [class_Groups_Oordered__ab__semigroup__add(_210602), c_Orderings_Oord__class_Oless__eq(_210602, _210604, _210606), c_Orderings_Oord__class_Oless__eq(_210602, _210608, _210610), -(c_Orderings_Oord__class_Oless__eq(_210602, c_Groups_Oplus__class_Oplus(_210602, _210604, _210608), c_Groups_Oplus__class_Oplus(_210602, _210606, _210610)))], (1713 ^ _152310) ^ [_211080, _211082, _211084, _211086] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_211080), c_Orderings_Oord__class_Oless__eq(_211080, c_Groups_Oplus__class_Oplus(_211080, _211082, _211084), c_Groups_Oplus__class_Oplus(_211080, _211086, _211084)), -(c_Orderings_Oord__class_Oless__eq(_211080, _211082, _211086))], (1723 ^ _152310) ^ [_211445, _211447, _211449, _211451] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_211445), c_Orderings_Oord__class_Oless__eq(_211445, c_Groups_Oplus__class_Oplus(_211445, _211447, _211449), c_Groups_Oplus__class_Oplus(_211445, _211447, _211451)), -(c_Orderings_Oord__class_Oless__eq(_211445, _211449, _211451))], (1733 ^ _152310) ^ [_211810, _211812, _211814, _211816] : [class_Rings_Ocomm__semiring__0(_211810), -(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_211810, c_Polynomial_OpCons(_211810, _211812, _211814), _211816) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_211810), c_Polynomial_Osmult(_211810, _211816, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_211810, _211814, _211816)), c_Polynomial_OpCons(_211810, _211812, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_211810, _211814, _211816))))], (1739 ^ _152310) ^ [_212118, _212120, _212122, _212124] : [class_Rings_Ocomm__semiring__0(_212118), -(c_Polynomial_Osmult(_212118, _212120, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_212118), _212122, _212124)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_212118), c_Polynomial_Osmult(_212118, _212120, _212122), c_Polynomial_Osmult(_212118, _212120, _212124)))], (1745 ^ _152310) ^ [_212386, _212388] : [class_Orderings_Opreorder(_212386), -(c_Orderings_Oord__class_Oless__eq(_212386, _212388, _212388))], (1751 ^ _152310) ^ [_212638, _212640, _212642, _212644, _212646] : [class_Rings_Ocomm__semiring__0(_212638), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_212638), _212640, c_Polynomial_Osmult(_212638, _212642, _212644)) = c_Polynomial_OpCons(_212638, _212646, _212644), 1758 ^ _152310 : [(1759 ^ _152310) ^ [] : [-(_212646 = hAPP(c_Polynomial_Opoly(_212638, _212640), _212642))], (1761 ^ _152310) ^ [] : [-(_212644 = c_Polynomial_Osynthetic__div(_212638, _212640, _212642))]]], (1763 ^ _152310) ^ [_213108, _213110, _213112] : [class_Rings_Ocomm__semiring__0(_213108), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_213108), _213110, c_Polynomial_Osmult(_213108, _213112, c_Polynomial_Osynthetic__div(_213108, _213110, _213112))) = c_Polynomial_OpCons(_213108, hAPP(c_Polynomial_Opoly(_213108, _213110), _213112), c_Polynomial_Osynthetic__div(_213108, _213110, _213112)))], (1769 ^ _152310) ^ [_213378, _213380] : [1770 ^ _152310 : [(1771 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _213378, _213380)], (1773 ^ _152310) ^ [] : [_213378 = _213380]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _213378, _213380))], (1777 ^ _152310) ^ [_213666, _213668] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _213666, _213668), -(_213666 = _213668), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _213666, _213668))], (1787 ^ _152310) ^ [_213972, _213974] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _213972, _213974), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _213972, _213974))], (1793 ^ _152310) ^ [_214186, _214188] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _214186, _214188), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _214186, _214188))], (1809 ^ _152310) ^ [_214685, _214687] : [1810 ^ _152310 : [(1811 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _214685, _214687)], (1813 ^ _152310) ^ [] : [_214685 = _214687]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _214685, _214687))], (1799 ^ _152310) ^ [_214429, _214431] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _214429, _214431), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _214429, _214431)), -(_214429 = _214431)], (1817 ^ _152310) ^ [_215004, _215006] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _215004, _215006), 1820 ^ _152310 : [(1821 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _215004, _215006))], (1823 ^ _152310) ^ [] : [_215004 = _215006]]], (1825 ^ _152310) ^ [_215246, _215248] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _215246, _215248)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _215246, _215248), -(_215246 = _215248)], (1835 ^ _152310) ^ [_215582, _215584, _215586, _215588] : [class_Orderings_Oorder(_215582), c_Orderings_Oord__class_Oless__eq(_215582, _215584, _215586), c_Orderings_Oord__class_Oless(_215582, _215588, _215584), -(c_Orderings_Oord__class_Oless(_215582, _215588, _215586))], (1849 ^ _152310) ^ [_216030, _216032, _216034, _216036] : [class_Orderings_Opreorder(_216030), c_Orderings_Oord__class_Oless__eq(_216030, _216032, _216034), c_Orderings_Oord__class_Oless(_216030, _216034, _216036), -(c_Orderings_Oord__class_Oless(_216030, _216032, _216036))], (1863 ^ _152310) ^ [_216478, _216480, _216482, _216484] : [class_Orderings_Oord(_216478), 1866 ^ _152310 : [(1867 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_216480, _216478), _216482, _216484), 1870 ^ _152310 : [(1871 ^ _152310) ^ [_216737] : [-(c_Orderings_Oord__class_Oless__eq(_216478, hAPP(_216482, _216737), hAPP(_216484, _216737)))]]], (1873 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_216478, hAPP(_216482, 1874 ^ [_216478, _216480, _216482, _216484]), hAPP(_216484, 1874 ^ [_216478, _216480, _216482, _216484])), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_216480, _216478), _216482, _216484))]]], (1880 ^ _152310) ^ [_217119, _217121, _217123] : [class_Orderings_Olinorder(_217119), -(c_Orderings_Oord__class_Oless__eq(_217119, _217121, _217123)), -(c_Orderings_Oord__class_Oless__eq(_217119, _217123, _217121))], (1890 ^ _152310) ^ [_217445, _217447, _217449] : [class_Orderings_Oorder(_217445), 1893 ^ _152310 : [(1894 ^ _152310) ^ [] : [_217447 = _217449, 1897 ^ _152310 : [(1898 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_217445, _217447, _217449))], (1900 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_217445, _217449, _217447))]]], (1902 ^ _152310) ^ [] : [-(_217447 = _217449), c_Orderings_Oord__class_Oless__eq(_217445, _217447, _217449), c_Orderings_Oord__class_Oless__eq(_217445, _217449, _217447)]]], (1912 ^ _152310) ^ [_218103, _218105, _218107] : [class_Orderings_Opreorder(_218103), _218105 = _218107, -(c_Orderings_Oord__class_Oless__eq(_218103, _218105, _218107))], (1922 ^ _152310) ^ [_218454, _218456, _218458, _218460, _218462] : [class_Orderings_Oord(_218454), c_Orderings_Oord__class_Oless__eq(tc_fun(_218456, _218454), _218458, _218460), -(c_Orderings_Oord__class_Oless__eq(_218454, hAPP(_218458, _218462), hAPP(_218460, _218462)))], (1932 ^ _152310) ^ [_218817, _218819, _218821] : [class_Orderings_Oorder(_218817), c_Orderings_Oord__class_Oless__eq(_218817, _218819, _218821), 1939 ^ _152310 : [(1940 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_218817, _218821, _218819), -(_218821 = _218819)], (1946 ^ _152310) ^ [] : [_218821 = _218819, -(c_Orderings_Oord__class_Oless__eq(_218817, _218821, _218819))]]], (1952 ^ _152310) ^ [_219417, _219419, _219421, _219423] : [class_Orderings_Oord(_219417), _219419 = _219421, c_Orderings_Oord__class_Oless__eq(_219417, _219421, _219423), -(c_Orderings_Oord__class_Oless__eq(_219417, _219419, _219423))], (1966 ^ _152310) ^ [_219863, _219865, _219867, _219869] : [class_Orderings_Oorder(_219863), _219865 = _219867, c_Orderings_Oord__class_Oless__eq(_219863, _219869, _219867), -(c_Orderings_Oord__class_Oless__eq(_219863, _219869, _219865))], (1980 ^ _152310) ^ [_220309, _220311, _220313, _220315] : [class_Orderings_Oord(_220309), c_Orderings_Oord__class_Oless__eq(_220309, _220311, _220313), _220313 = _220315, -(c_Orderings_Oord__class_Oless__eq(_220309, _220311, _220315))], (1994 ^ _152310) ^ [_220755, _220757, _220759, _220761] : [class_Orderings_Oorder(_220755), c_Orderings_Oord__class_Oless__eq(_220755, _220757, _220759), _220757 = _220761, -(c_Orderings_Oord__class_Oless__eq(_220755, _220761, _220759))], (2008 ^ _152310) ^ [_221187, _221189, _221191] : [class_Orderings_Oorder(_221187), c_Orderings_Oord__class_Oless__eq(_221187, _221189, _221191), c_Orderings_Oord__class_Oless__eq(_221187, _221191, _221189), -(_221189 = _221191)], (2022 ^ _152310) ^ [_221619, _221621, _221623, _221625] : [class_Orderings_Opreorder(_221619), c_Orderings_Oord__class_Oless__eq(_221619, _221621, _221623), c_Orderings_Oord__class_Oless__eq(_221619, _221623, _221625), -(c_Orderings_Oord__class_Oless__eq(_221619, _221621, _221625))], (2036 ^ _152310) ^ [_222053, _222055, _222057] : [class_Orderings_Oorder(_222053), c_Orderings_Oord__class_Oless__eq(_222053, _222055, _222057), c_Orderings_Oord__class_Oless__eq(_222053, _222057, _222055), -(_222057 = _222055)], (2050 ^ _152310) ^ [_222485, _222487, _222489, _222491] : [class_Orderings_Oorder(_222485), c_Orderings_Oord__class_Oless__eq(_222485, _222487, _222489), c_Orderings_Oord__class_Oless__eq(_222485, _222491, _222487), -(c_Orderings_Oord__class_Oless__eq(_222485, _222491, _222489))], (2064 ^ _152310) ^ [_222947, _222949, _222951, _222953, _222955] : [class_Orderings_Oord(_222947), c_Orderings_Oord__class_Oless__eq(tc_fun(_222949, _222947), _222951, _222953), -(c_Orderings_Oord__class_Oless__eq(_222947, hAPP(_222951, _222955), hAPP(_222953, _222955)))], (2074 ^ _152310) ^ [_223310, _223312, _223314] : [class_Orderings_Olinorder(_223310), -(c_Orderings_Oord__class_Oless__eq(_223310, _223312, _223314)), -(c_Orderings_Oord__class_Oless__eq(_223310, _223314, _223312))], (2084 ^ _152310) ^ [_223624, _223626] : [class_Orderings_Opreorder(_223624), c_Orderings_Oord__class_Oless(_223624, _223626, _223626)], (2090 ^ _152310) ^ [_223849, _223851, _223853] : [class_Orderings_Olinorder(_223849), 2093 ^ _152310 : [(2104 ^ _152310) ^ [] : [2105 ^ _152310 : [(2106 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_223849, _223851, _223853)], (2108 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_223849, _223853, _223851)]], _223851 = _223853], (2094 ^ _152310) ^ [] : [-(_223851 = _223853), -(c_Orderings_Oord__class_Oless(_223849, _223851, _223853)), -(c_Orderings_Oord__class_Oless(_223849, _223853, _223851))]]], (2112 ^ _152310) ^ [_224509, _224511, _224513] : [class_Orderings_Olinorder(_224509), 2115 ^ _152310 : [(2126 ^ _152310) ^ [] : [2127 ^ _152310 : [(2128 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_224509, _224513, _224511)], (2130 ^ _152310) ^ [] : [_224511 = _224513]], c_Orderings_Oord__class_Oless(_224509, _224511, _224513)], (2116 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(_224509, _224511, _224513)), -(c_Orderings_Oord__class_Oless(_224509, _224513, _224511)), -(_224511 = _224513)]]], (2134 ^ _152310) ^ [_225169, _225171, _225173] : [class_Orderings_Olinorder(_225169), -(c_Orderings_Oord__class_Oless(_225169, _225171, _225173)), -(_225171 = _225173), -(c_Orderings_Oord__class_Oless(_225169, _225173, _225171))], (2148 ^ _152310) ^ [_225589, _225591, _225593] : [class_Orderings_Olinorder(_225589), -(c_Orderings_Oord__class_Oless(_225589, _225591, _225593)), 2155 ^ _152310 : [(2156 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(_225589, _225593, _225591)), -(_225593 = _225591)], (2162 ^ _152310) ^ [] : [_225593 = _225591, c_Orderings_Oord__class_Oless(_225589, _225593, _225591)]]], (2168 ^ _152310) ^ [_226180, _226182, _226184] : [class_Orderings_Olinorder(_226180), -(_226182 = _226184), -(c_Orderings_Oord__class_Oless(_226180, _226182, _226184)), -(c_Orderings_Oord__class_Oless(_226180, _226184, _226182))], (2182 ^ _152310) ^ [_226604, _226606, _226608] : [class_Orderings_Oorder(_226604), c_Orderings_Oord__class_Oless(_226604, _226606, _226608), _226606 = _226608], (2192 ^ _152310) ^ [_226928, _226930, _226932] : [class_Orderings_Opreorder(_226928), c_Orderings_Oord__class_Oless(_226928, _226930, _226932), c_Orderings_Oord__class_Oless(_226928, _226932, _226930)], (2202 ^ _152310) ^ [_227254, _227256, _227258] : [class_Orderings_Opreorder(_227254), c_Orderings_Oord__class_Oless(_227254, _227256, _227258), c_Orderings_Oord__class_Oless(_227254, _227258, _227256)], (2212 ^ _152310) ^ [_227580, _227582, _227584] : [class_Orderings_Oorder(_227580), c_Orderings_Oord__class_Oless(_227580, _227582, _227584), _227582 = _227584], (2222 ^ _152310) ^ [_227904, _227906, _227908] : [class_Orderings_Oorder(_227904), c_Orderings_Oord__class_Oless(_227904, _227906, _227908), _227908 = _227906], (2232 ^ _152310) ^ [_228228, _228230, _228232] : [class_Orderings_Opreorder(_228228), c_Orderings_Oord__class_Oless(_228228, _228230, _228232), c_Orderings_Oord__class_Oless(_228228, _228232, _228230)], (2242 ^ _152310) ^ [_228554, _228556, _228558] : [class_Orderings_Oorder(_228554), c_Orderings_Oord__class_Oless(_228554, _228556, _228558), c_Orderings_Oord__class_Oless(_228554, _228558, _228556)], (2252 ^ _152310) ^ [_228894, _228896, _228898, _228900] : [class_Orderings_Oord(_228894), _228896 = _228898, c_Orderings_Oord__class_Oless(_228894, _228898, _228900), -(c_Orderings_Oord__class_Oless(_228894, _228896, _228900))], (2266 ^ _152310) ^ [_229340, _229342, _229344, _229346] : [class_Orderings_Oorder(_229340), _229342 = _229344, c_Orderings_Oord__class_Oless(_229340, _229346, _229344), -(c_Orderings_Oord__class_Oless(_229340, _229346, _229342))], (2280 ^ _152310) ^ [_229786, _229788, _229790, _229792] : [class_Orderings_Oord(_229786), c_Orderings_Oord__class_Oless(_229786, _229788, _229790), _229790 = _229792, -(c_Orderings_Oord__class_Oless(_229786, _229788, _229792))], (2294 ^ _152310) ^ [_230232, _230234, _230236, _230238] : [class_Orderings_Oorder(_230232), c_Orderings_Oord__class_Oless(_230232, _230234, _230236), _230234 = _230238, -(c_Orderings_Oord__class_Oless(_230232, _230238, _230236))], (2308 ^ _152310) ^ [_230678, _230680, _230682, _230684] : [class_Orderings_Opreorder(_230678), c_Orderings_Oord__class_Oless(_230678, _230680, _230682), c_Orderings_Oord__class_Oless(_230678, _230682, _230684), -(c_Orderings_Oord__class_Oless(_230678, _230680, _230684))], (2322 ^ _152310) ^ [_231126, _231128, _231130, _231132] : [class_Orderings_Oorder(_231126), c_Orderings_Oord__class_Oless(_231126, _231128, _231130), c_Orderings_Oord__class_Oless(_231126, _231132, _231128), -(c_Orderings_Oord__class_Oless(_231126, _231132, _231130))], (2336 ^ _152310) ^ [_231560, _231562, _231564] : [class_Orderings_Opreorder(_231560), c_Orderings_Oord__class_Oless(_231560, _231562, _231564), c_Orderings_Oord__class_Oless(_231560, _231564, _231562)], (2346 ^ _152310) ^ [_231886, _231888, _231890] : [class_Orderings_Olinorder(_231886), -(c_Orderings_Oord__class_Oless(_231886, _231888, _231890)), -(_231888 = _231890), -(c_Orderings_Oord__class_Oless(_231886, _231890, _231888))], (2360 ^ _152310) ^ [_232266] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _232266, _232266)], (2372 ^ _152310) ^ [_232662, _232664] : [2373 ^ _152310 : [(2374 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _232662, _232664)], (2376 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _232664, _232662)]], _232662 = _232664], (2362 ^ _152310) ^ [_232403, _232405] : [-(_232403 = _232405), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _232403, _232405)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _232405, _232403))], (2380 ^ _152310) ^ [_232953, _232955] : [-(_232953 = _232955), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _232953, _232955)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _232955, _232953))], (2390 ^ _152310) ^ [_233232] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _233232, _233232)], (2392 ^ _152310) ^ [_233340, _233342] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _233340, _233342), _233342 = _233340], (2398 ^ _152310) ^ [_233553, _233555] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _233553, _233555), _233553 = _233555], (2404 ^ _152310) ^ [_233780, _233782, _233784] : [2405 ^ _152310 : [(2406 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _233780, _233782))], (2408 ^ _152310) ^ [] : [hBOOL(hAPP(hAPP(_233784, _233782), _233780))]], 2411 ^ _152310 : [(2412 ^ _152310) ^ [] : [-(_233780 = _233782)], (2414 ^ _152310) ^ [] : [hBOOL(hAPP(hAPP(_233784, _233782), _233780))]], 2417 ^ _152310 : [(2418 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _233782, _233780))], (2420 ^ _152310) ^ [] : [hBOOL(hAPP(hAPP(_233784, _233782), _233780))]], -(hBOOL(hAPP(hAPP(_233784, _233782), _233780)))], (2424 ^ _152310) ^ [_234471, _234473, _234475] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _234471, _234473), _234475), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _234471, _234475))], (2430 ^ _152310) ^ [_234727, _234729, _234731, _234733] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _234727, _234729), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _234731, _234729) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _234727, _234733), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _234731, _234733))], (2440 ^ _152310) ^ [_235094, _235096, _235098, _235100] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _235094, _235096), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _235098, _235100), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _235094, _235098), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _235096, _235100)))], (2450 ^ _152310) ^ [_235449, _235451, _235453] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _235449, _235451), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _235449, _235453), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _235451, _235453)))], (2456 ^ _152310) ^ [_235699, _235701, _235703] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _235699, _235701), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _235699, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _235703, _235701)))], (2462 ^ _152310) ^ [_235941, _235943, _235945] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _235941, _235943), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _235941, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _235943, _235945)))], (2468 ^ _152310) ^ [_236183, _236185, _236187] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _236183, _236185), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _236183, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _236187, _236185)))], (2474 ^ _152310) ^ [_236425, _236427, _236429] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _236425, _236427), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _236425, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _236427, _236429)))], (2480 ^ _152310) ^ [_236696, _236698, _236700] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _236696, _236698), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _236696, _236700)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _236698, _236700))], (2486 ^ _152310) ^ [_236884, _236886, _236888] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _236886, _236888), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _236884, _236886), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _236884, _236888)))], (2492 ^ _152310) ^ [_237106, _237108] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _237106, _237108), _237108)], (2494 ^ _152310) ^ [_237204, _237206] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _237204, _237206), _237204)], (2496 ^ _152310) ^ [_237289] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _237289, _237289))], (2498 ^ _152310) ^ [_237397, _237399] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _237397, _237399)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _237399, _237397))], (2504 ^ _152310) ^ [_237612, _237614] : [_237612 = _237614, -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _237612, _237614))], (2510 ^ _152310) ^ [_237838, _237840, _237842] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _237838, _237840), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _237840, _237842), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _237838, _237842))], (2520 ^ _152310) ^ [_238153, _238155] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _238153, _238155), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _238155, _238153), -(_238153 = _238155)], (2530 ^ _152310) ^ [_238470, _238472, _238474] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _238470, _238472), _238474), 2533 ^ _152310 : [(2534 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _238470, _238474))], (2536 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _238472, _238474))]]], (2538 ^ _152310) ^ [_238795, _238797, _238799] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _238795, _238797), _238799), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _238795, _238799))], (2544 ^ _152310) ^ [_239037, _239039, _239041] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _239037, _239039), _239041), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _239039, _239041))], (2550 ^ _152310) ^ [_239293, _239295, _239297, _239299] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _239293, _239295), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _239297, _239299), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _239293, _239297), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _239295, _239299)))], (2560 ^ _152310) ^ [_239648, _239650, _239652] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _239648, _239650), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _239648, _239652), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _239650, _239652)))], (2566 ^ _152310) ^ [_239898, _239900, _239902] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _239898, _239900), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _239898, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _239902, _239900)))], (2572 ^ _152310) ^ [_240140, _240142, _240144] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _240140, _240142), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _240140, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _240142, _240144)))], (2578 ^ _152310) ^ [_240382, _240384, _240386] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _240382, _240384), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _240382, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _240386, _240384)))], (2584 ^ _152310) ^ [_240624, _240626, _240628] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _240624, _240626), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _240624, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _240626, _240628)))], (2590 ^ _152310) ^ [_240895, _240897, _240899] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _240895, _240897), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _240895, _240899)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _240897, _240899))], (2596 ^ _152310) ^ [_241083, _241085, _241087] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _241085, _241087), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _241083, _241085), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _241083, _241087)))], (2602 ^ _152310) ^ [_241350, _241352] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _241350, _241352), -(_241352 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _241350, 2605 ^ [_241350, _241352]))], (2609 ^ _152310) ^ [_241583, _241585] : [2610 ^ _152310 : [(2611 ^ _152310) ^ [_241658] : [_241585 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _241583, _241658)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _241583, _241585))], (2615 ^ _152310) ^ [_241812, _241814] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _241812, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _241812, _241814)))], (2617 ^ _152310) ^ [_241911, _241913] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _241911, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _241913, _241911)))], (2619 ^ _152310) ^ [_242053, _242055, _242057, _242059] : [class_Rings_Ocomm__semiring__0(_242053), -(c_Polynomial_Osynthetic__div(_242053, c_Polynomial_OpCons(_242053, _242055, _242057), _242059) = c_Polynomial_OpCons(_242053, hAPP(c_Polynomial_Opoly(_242053, _242057), _242059), c_Polynomial_Osynthetic__div(_242053, _242057, _242059)))], (2625 ^ _152310) ^ [_242331, _242333, _242335] : [class_Orderings_Olinorder(_242331), 2628 ^ _152310 : [(2629 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(_242331, _242333, _242335)), -(c_Orderings_Oord__class_Oless__eq(_242331, _242335, _242333))], (2635 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_242331, _242335, _242333), c_Orderings_Oord__class_Oless(_242331, _242333, _242335)]]], (2641 ^ _152310) ^ [_242827, _242829, _242831] : [class_Orderings_Olinorder(_242827), 2644 ^ _152310 : [(2645 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_242827, _242829, _242831)), -(c_Orderings_Oord__class_Oless(_242827, _242831, _242829))], (2651 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_242827, _242831, _242829), c_Orderings_Oord__class_Oless__eq(_242827, _242829, _242831)]]], (2657 ^ _152310) ^ [_243323, _243325, _243327] : [class_Orderings_Olinorder(_243323), -(c_Orderings_Oord__class_Oless__eq(_243323, _243325, _243327)), -(c_Orderings_Oord__class_Oless(_243323, _243327, _243325))], (2667 ^ _152310) ^ [_243649, _243651, _243653] : [class_Orderings_Oorder(_243649), 2670 ^ _152310 : [(2671 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_243649, _243651, _243653), 2674 ^ _152310 : [(2675 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_243649, _243651, _243653))], (2677 ^ _152310) ^ [] : [_243651 = _243653]]], (2679 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(_243649, _243651, _243653)), c_Orderings_Oord__class_Oless__eq(_243649, _243651, _243653), -(_243651 = _243653)]]], (2689 ^ _152310) ^ [_244309, _244311, _244313] : [class_Orderings_Opreorder(_244309), 2692 ^ _152310 : [(2693 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_244309, _244311, _244313), 2696 ^ _152310 : [(2697 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_244309, _244311, _244313))], (2699 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_244309, _244313, _244311)]]], (2701 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(_244309, _244311, _244313)), c_Orderings_Oord__class_Oless__eq(_244309, _244311, _244313), -(c_Orderings_Oord__class_Oless__eq(_244309, _244313, _244311))]]], (2711 ^ _152310) ^ [_244972, _244974, _244976] : [class_Orderings_Oorder(_244972), 2714 ^ _152310 : [(2725 ^ _152310) ^ [] : [2726 ^ _152310 : [(2727 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_244972, _244974, _244976)], (2729 ^ _152310) ^ [] : [_244974 = _244976]], -(c_Orderings_Oord__class_Oless__eq(_244972, _244974, _244976))], (2715 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_244972, _244974, _244976), -(c_Orderings_Oord__class_Oless(_244972, _244974, _244976)), -(_244974 = _244976)]]], (2733 ^ _152310) ^ [_245630, _245632, _245634] : [class_Orderings_Olinorder(_245630), -(c_Orderings_Oord__class_Oless(_245630, _245632, _245634)), -(c_Orderings_Oord__class_Oless__eq(_245630, _245634, _245632))], (2743 ^ _152310) ^ [_245958, _245960, _245962] : [class_Orderings_Olinorder(_245958), -(c_Orderings_Oord__class_Oless__eq(_245958, _245960, _245962)), -(c_Orderings_Oord__class_Oless(_245958, _245962, _245960))], (2753 ^ _152310) ^ [_246286, _246288, _246290] : [class_Orderings_Olinorder(_246286), -(c_Orderings_Oord__class_Oless(_246286, _246288, _246290)), 2760 ^ _152310 : [(2761 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_246286, _246288, _246290), -(_246288 = _246290)], (2767 ^ _152310) ^ [] : [_246288 = _246290, -(c_Orderings_Oord__class_Oless__eq(_246286, _246288, _246290))]]], (2773 ^ _152310) ^ [_246875, _246877, _246879] : [class_Orderings_Oorder(_246875), -(_246877 = _246879), c_Orderings_Oord__class_Oless__eq(_246875, _246877, _246879), -(c_Orderings_Oord__class_Oless(_246875, _246877, _246879))], (2787 ^ _152310) ^ [_247296, _247298, _247300] : [class_Orderings_Oorder(_247296), -(_247298 = _247300), c_Orderings_Oord__class_Oless__eq(_247296, _247300, _247298), -(c_Orderings_Oord__class_Oless(_247296, _247300, _247298))], (2801 ^ _152310) ^ [_247717, _247719, _247721] : [class_Orderings_Olinorder(_247717), c_Orderings_Oord__class_Oless__eq(_247717, _247719, _247721), c_Orderings_Oord__class_Oless(_247717, _247721, _247719)], (2811 ^ _152310) ^ [_248043, _248045, _248047] : [class_Orderings_Opreorder(_248043), c_Orderings_Oord__class_Oless(_248043, _248045, _248047), -(c_Orderings_Oord__class_Oless__eq(_248043, _248045, _248047))], (2821 ^ _152310) ^ [_248368, _248370, _248372] : [class_Orderings_Olinorder(_248368), c_Orderings_Oord__class_Oless__eq(_248368, _248370, _248372), 2828 ^ _152310 : [(2829 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(_248368, _248370, _248372)), -(_248370 = _248372)], (2835 ^ _152310) ^ [] : [_248370 = _248372, c_Orderings_Oord__class_Oless(_248368, _248370, _248372)]]], (2841 ^ _152310) ^ [_248956, _248958, _248960] : [class_Orderings_Oorder(_248956), c_Orderings_Oord__class_Oless__eq(_248956, _248958, _248960), -(c_Orderings_Oord__class_Oless(_248956, _248958, _248960)), -(_248958 = _248960)], (2855 ^ _152310) ^ [_249375, _249377, _249379] : [class_Orderings_Oorder(_249375), c_Orderings_Oord__class_Oless__eq(_249375, _249377, _249379), -(_249377 = _249379), -(c_Orderings_Oord__class_Oless(_249375, _249377, _249379))], (2869 ^ _152310) ^ [_249796, _249798, _249800] : [class_Orderings_Oorder(_249796), c_Orderings_Oord__class_Oless__eq(_249796, _249798, _249800), -(_249800 = _249798), -(c_Orderings_Oord__class_Oless(_249796, _249798, _249800))], (2883 ^ _152310) ^ [_250231, _250233, _250235, _250237] : [class_Orderings_Opreorder(_250231), c_Orderings_Oord__class_Oless(_250231, _250233, _250235), c_Orderings_Oord__class_Oless__eq(_250231, _250235, _250237), -(c_Orderings_Oord__class_Oless(_250231, _250233, _250237))], (2897 ^ _152310) ^ [_250679, _250681, _250683, _250685] : [class_Orderings_Oorder(_250679), c_Orderings_Oord__class_Oless(_250679, _250681, _250683), c_Orderings_Oord__class_Oless__eq(_250679, _250685, _250681), -(c_Orderings_Oord__class_Oless(_250679, _250685, _250683))], (2911 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), v_e))], (2913 ^ _152310) ^ [_251152, _251154] : [class_Rings_Olinordered__idom(_251152), 2916 ^ _152310 : [(2917 ^ _152310) ^ [] : [c_Polynomial_Opos__poly(_251152, _251154), -(c_Orderings_Oord__class_Oless(_251152, c_Groups_Ozero__class_Ozero(_251152), hAPP(c_Polynomial_Ocoeff(_251152, _251154), c_Polynomial_Odegree(_251152, _251154))))], (2923 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_251152, c_Groups_Ozero__class_Ozero(_251152), hAPP(c_Polynomial_Ocoeff(_251152, _251154), c_Polynomial_Odegree(_251152, _251154))), -(c_Polynomial_Opos__poly(_251152, _251154))]]], (2929 ^ _152310) ^ [_251660, _251662, _251664] : [class_Groups_Ozero(_251660), -(c_Polynomial_Ocoeff(_251660, c_Polynomial_OpCons(_251660, _251662, _251664)) = c_Nat_Onat_Onat__case(_251660, _251662, c_Polynomial_Ocoeff(_251660, _251664)))], (2935 ^ _152310) ^ [_251916, _251918, _251920] : [class_Rings_Ocomm__semiring__0(_251916), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_251916, c_Polynomial_Opcompose(_251916, _251918, _251920)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Polynomial_Odegree(_251916, _251918)), c_Polynomial_Odegree(_251916, _251920))))], (2941 ^ _152310) ^ [_252198, _252200, _252202, _252204] : [class_Rings_Ocomm__semiring__0(_252198), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_252198), c_Polynomial_Osmult(_252198, _252200, _252202), c_Polynomial_OpCons(_252198, _252204, _252202)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_252198)), -(_252202 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_252198)))], (2951 ^ _152310) ^ [_252573, _252575, _252577] : [class_Groups_Ozero(_252573), -(hAPP(c_Polynomial_Ocoeff(_252573, _252575), _252577) = c_Groups_Ozero__class_Ozero(_252573)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _252577, c_Polynomial_Odegree(_252573, _252575)))], (2961 ^ _152310) ^ [_252921, _252923, _252925] : [class_Groups_Ozero(_252921), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_252921, _252923), _252925), -(hAPP(c_Polynomial_Ocoeff(_252921, _252923), _252925) = c_Groups_Ozero__class_Ozero(_252921))], (2971 ^ _152310) ^ [_253281, _253283] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _253281, _253283), -(_253283 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _253281, 2974 ^ [_253281, _253283]))], (2978 ^ _152310) ^ [_253514, _253516] : [2979 ^ _152310 : [(2980 ^ _152310) ^ [_253589] : [_253516 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _253514, _253589)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _253514, _253516))], (2984 ^ _152310) ^ [_253786, _253788, _253790, _253792] : [class_Rings_Ocomm__semiring__0(_253786), -(hAPP(c_Polynomial_Opoly(_253786, c_Polynomial_OpCons(_253786, _253788, _253790)), _253792) = c_Groups_Oplus__class_Oplus(_253786, _253788, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_253786), _253792), hAPP(c_Polynomial_Opoly(_253786, _253790), _253792))))], (2990 ^ _152310) ^ [_254076, _254078, _254080] : [class_Groups_Ozero(_254076), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_254076, c_Polynomial_OpCons(_254076, _254078, _254080)), c_Nat_OSuc(c_Polynomial_Odegree(_254076, _254080))))], (2996 ^ _152310) ^ [_254286] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _254286, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2998 ^ _152310) ^ [_254365] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _254365))], (3000 ^ _152310) ^ [_254444] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(_254444)))], (3002 ^ _152310) ^ [_254554, _254556] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _254554, _254556), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_254554), c_Nat_OSuc(_254556)))], (3008 ^ _152310) ^ [_254747] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _254747, c_Nat_OSuc(_254747)))], (3010 ^ _152310) ^ [_254857, _254859] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _254857), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _254859), -(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), _254859), _254857)))], (3020 ^ _152310) ^ [_255174, _255176] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _255174), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _255176), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _255174, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _255174), _255176)))], (3030 ^ _152310) ^ [_255491, _255493] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _255491), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _255493), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _255491, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _255493), _255491)))], (3040 ^ _152310) ^ [_255837, _255839] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _255837), _255839)), 3043 ^ _152310 : [(3044 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _255837))], (3046 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _255839))]]], (3048 ^ _152310) ^ [_256092, _256094] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _256092), _256094))), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _256092), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _256094)], (3058 ^ _152310) ^ [_256439, _256441, _256443, _256445] : [class_Orderings_Oord(_256439), 3061 ^ _152310 : [(3062 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(tc_fun(_256441, _256439), _256443, _256445), 3065 ^ _152310 : [(3066 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_fun(_256441, _256439), _256443, _256445))], (3068 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_256441, _256439), _256445, _256443)]]], (3070 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_fun(_256441, _256439), _256443, _256445)), c_Orderings_Oord__class_Oless__eq(tc_fun(_256441, _256439), _256443, _256445), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_256441, _256439), _256445, _256443))]]], (3080 ^ _152310) ^ [_257107] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_257107)], (3082 ^ _152310) ^ [_257186] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_257186)], (3084 ^ _152310) ^ [_257265] : [_257265 = c_Nat_OSuc(_257265)], (3086 ^ _152310) ^ [_257344] : [c_Nat_OSuc(_257344) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3088 ^ _152310) ^ [_257423] : [c_Nat_OSuc(_257423) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3090 ^ _152310) ^ [_257502] : [c_Nat_OSuc(_257502) = _257502], (3092 ^ _152310) ^ [_257582] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _257582) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3094 ^ _152310) ^ [_257663] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _257663), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3096 ^ _152310) ^ [_257761, _257763] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _257761), _257763) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _257763), _257761))], (3098 ^ _152310) ^ [_257911, _257913] : [c_Nat_OSuc(_257911) = c_Nat_OSuc(_257913), -(_257911 = _257913)], (3104 ^ _152310) ^ [_258081, _258083] : [_258081 = _258083, -(c_Nat_OSuc(_258081) = c_Nat_OSuc(_258083))], (3120 ^ _152310) ^ [_258594, _258596] : [3121 ^ _152310 : [(3122 ^ _152310) ^ [] : [_258594 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3124 ^ _152310) ^ [] : [_258596 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _258594), _258596) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3110 ^ _152310) ^ [_258330, _258332] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _258330), _258332) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_258330 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_258332 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3128 ^ _152310) ^ [_258891, _258893, _258895] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _258891), _258893)), _258895) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _258891), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _258893), _258895)))], (3130 ^ _152310) ^ [_259055, _259057] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _259055), _259057) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 3133 ^ _152310 : [(3134 ^ _152310) ^ [] : [-(_259055 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (3136 ^ _152310) ^ [] : [-(_259057 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (3138 ^ _152310) ^ [_259304, _259306] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _259304), _259306) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _259304 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _259306 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3158 ^ _152310) ^ [_259946, _259948, _259950] : [3159 ^ _152310 : [(3160 ^ _152310) ^ [] : [_259948 = _259950], (3162 ^ _152310) ^ [] : [_259946 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _259946), _259948) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _259946), _259950))], (3148 ^ _152310) ^ [_259660, _259662, _259664] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _259660), _259662) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _259660), _259664), -(_259662 = _259664), -(_259660 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3176 ^ _152310) ^ [_260593, _260595, _260597] : [3177 ^ _152310 : [(3178 ^ _152310) ^ [] : [_260593 = _260597], (3180 ^ _152310) ^ [] : [_260595 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _260593), _260595) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _260597), _260595))], (3166 ^ _152310) ^ [_260307, _260309, _260311] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _260307), _260309) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _260311), _260309), -(_260307 = _260311), -(_260309 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3184 ^ _152310) ^ [_260954, _260956, _260958] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_260954)), _260956) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_260954)), _260958), -(_260956 = _260958)], (3190 ^ _152310) ^ [_261154, _261156, _261158] : [_261156 = _261158, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_261154)), _261156) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_261154)), _261158))], (3196 ^ _152310) ^ [_261403, _261405, _261407] : [-(hAPP(c_Nat_Onat_Onat__case(_261403, _261405, _261407), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _261405)], (3198 ^ _152310) ^ [_261534, _261536, _261538, _261540] : [-(hAPP(c_Nat_Onat_Onat__case(_261534, _261536, _261538), c_Nat_OSuc(_261540)) = hAPP(_261538, _261540))], (3200 ^ _152310) ^ [_261629] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_261629)], (3202 ^ _152310) ^ [_261708] : [c_Nat_OSuc(_261708) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3204 ^ _152310) ^ [_261817, _261819] : [c_Nat_OSuc(_261817) = c_Nat_OSuc(_261819), -(_261817 = _261819)], (3210 ^ _152310) ^ [_262035, _262037] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _262035, _262037) = _262035, -(_262037 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3216 ^ _152310) ^ [_262296, _262298, _262300] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _262296, _262298) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _262300, _262298), -(_262296 = _262300)], (3222 ^ _152310) ^ [_262480, _262482, _262484] : [_262480 = _262484, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _262480, _262482) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _262484, _262482))], (3228 ^ _152310) ^ [_262757, _262759, _262761] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _262757, _262759) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _262757, _262761), -(_262759 = _262761)], (3234 ^ _152310) ^ [_262941, _262943, _262945] : [_262943 = _262945, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _262941, _262943) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _262941, _262945))], (3240 ^ _152310) ^ [_263204, _263206] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _263204, _263206) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 3245 ^ _152310 : [(3246 ^ _152310) ^ [] : [-(_263204 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (3248 ^ _152310) ^ [] : [-(_263206 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 3249 ^ _152310 : [(3250 ^ _152310) ^ [] : [-(_263204 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3252 ^ _152310) ^ [] : [-(_263206 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (3254 ^ _152310) ^ [_263614, _263616] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _263614, _263616) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 3255 ^ _152310 : [(3256 ^ _152310) ^ [] : [_263614 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _263616 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3262 ^ _152310) ^ [] : [_263614 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _263616 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (3270 ^ _152310) ^ [_264085, _264087, _264089] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _264085, _264087)), _264089) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _264085), _264089), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _264087), _264089)))], (3272 ^ _152310) ^ [_264221, _264223, _264225] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _264221, _264223), _264225) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _264221, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _264223, _264225)))], (3274 ^ _152310) ^ [_264377, _264379] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _264377, _264379) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 3277 ^ _152310 : [(3278 ^ _152310) ^ [] : [-(_264377 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3280 ^ _152310) ^ [] : [-(_264379 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (3282 ^ _152310) ^ [_264622, _264624] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _264622, _264624) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _264622 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _264624 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3292 ^ _152310) ^ [_264916, _264918] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_264916)), _264918) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _264918, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _264916), _264918)))], (3294 ^ _152310) ^ [_265028, _265030] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Nat_OSuc(_265028), _265030) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _265028, c_Nat_OSuc(_265030)))], (3296 ^ _152310) ^ [_265134, _265136] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Nat_OSuc(_265134), _265136) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _265134, _265136)))], (3298 ^ _152310) ^ [_265284, _265286] : [c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _265284, _265286), 3303 ^ _152310 : [(3304 ^ _152310) ^ [] : [-(_265284 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (3306 ^ _152310) ^ [] : [-(_265286 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 3307 ^ _152310 : [(3308 ^ _152310) ^ [] : [-(_265284 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3310 ^ _152310) ^ [] : [-(_265286 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (3312 ^ _152310) ^ [_265694, _265696] : [-(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _265694, _265696)), 3313 ^ _152310 : [(3314 ^ _152310) ^ [] : [_265694 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _265696 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3320 ^ _152310) ^ [] : [_265694 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _265696 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (3328 ^ _152310) ^ [_266165, _266167, _266169] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _266165), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _266167, _266169)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _266165), _266167), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _266165), _266169)))], (3330 ^ _152310) ^ [_266301, _266303, _266305] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _266301, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _266303, _266305)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _266303, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _266301, _266305)))], (3332 ^ _152310) ^ [_266413, _266415] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _266413), c_Nat_OSuc(_266415)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _266413, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _266413), _266415)))], (3334 ^ _152310) ^ [_266525, _266527] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _266525, c_Nat_OSuc(_266527)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _266525, _266527)))], (3336 ^ _152310) ^ [_266631, _266633] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _266631, _266633) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _266633, _266631))], (3338 ^ _152310) ^ [_266719] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _266719, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _266719)], (3340 ^ _152310) ^ [_266801] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _266801) = _266801)], (3342 ^ _152310) ^ [_266912, _266914] : [class_Rings_Ocomm__semiring__1(_266912), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_266912), c_Groups_Ozero__class_Ozero(_266912)), _266914) = c_Groups_Ozero__class_Ozero(_266912))], (3348 ^ _152310) ^ [_267144, _267146] : [class_Rings_Ocomm__semiring__0(_267144), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_267144)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_267144))), _267146) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_267144)))], (3354 ^ _152310) ^ [_267388, _267390] : [class_Groups_Ozero(_267388), 3357 ^ _152310 : [(3358 ^ _152310) ^ [] : [c_Groups_Ozero__class_Ozero(_267388) = _267390, -(_267390 = c_Groups_Ozero__class_Ozero(_267388))], (3364 ^ _152310) ^ [] : [_267390 = c_Groups_Ozero__class_Ozero(_267388), -(c_Groups_Ozero__class_Ozero(_267388) = _267390)]]], (3370 ^ _152310) ^ [_267858, _267860] : [class_Rings_Ocomm__semiring__1(_267858), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_267858), _267860), c_Groups_Ozero__class_Ozero(_267858)) = c_Groups_Ozero__class_Ozero(_267858))], (3376 ^ _152310) ^ [_268090, _268092] : [class_Rings_Ocomm__semiring__0(_268090), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_268090)), _268092), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_268090))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_268090)))], (3382 ^ _152310) ^ [_268348, _268350, _268352] : [class_Rings_Ocomm__semiring__1(_268348), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_268348), _268350), _268352) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_268348), _268352), _268350))], (3388 ^ _152310) ^ [_268622, _268624, _268626, _268628] : [class_Rings_Ocomm__semiring__1(_268622), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_268622), _268624), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_268622), _268626), _268628)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_268622), _268626), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_268622), _268624), _268628)))], (3394 ^ _152310) ^ [_268934, _268936, _268938, _268940] : [class_Rings_Ocomm__semiring__1(_268934), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_268934), _268936), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_268934), _268938), _268940)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_268934), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_268934), _268936), _268938)), _268940))], (3400 ^ _152310) ^ [_269246, _269248, _269250, _269252] : [class_Groups_Oab__semigroup__mult(_269246), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_269246), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_269246), _269248), _269250)), _269252) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_269246), _269248), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_269246), _269250), _269252)))], (3406 ^ _152310) ^ [_269558, _269560, _269562, _269564] : [class_Rings_Ocomm__semiring__1(_269558), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_269558), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_269558), _269560), _269562)), _269564) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_269558), _269560), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_269558), _269562), _269564)))], (3412 ^ _152310) ^ [_269870, _269872, _269874, _269876] : [class_Rings_Ocomm__semiring__1(_269870), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_269870), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_269870), _269872), _269874)), _269876) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_269870), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_269870), _269872), _269876)), _269874))], (3418 ^ _152310) ^ [_270196, _270198, _270200, _270202, _270204] : [class_Rings_Ocomm__semiring__1(_270196), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_270196), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_270196), _270198), _270200)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_270196), _270202), _270204)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_270196), _270198), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_270196), _270200), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_270196), _270202), _270204))))], (3424 ^ _152310) ^ [_270560, _270562, _270564, _270566, _270568] : [class_Rings_Ocomm__semiring__1(_270560), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_270560), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_270560), _270562), _270564)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_270560), _270566), _270568)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_270560), _270566), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_270560), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_270560), _270562), _270564)), _270568)))], (3430 ^ _152310) ^ [_270924, _270926, _270928, _270930, _270932] : [class_Rings_Ocomm__semiring__1(_270924), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_270924), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_270924), _270926), _270928)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_270924), _270930), _270932)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_270924), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_270924), _270926), _270930)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_270924), _270928), _270932)))], (3436 ^ _152310) ^ [_271289, _271291, _271293] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_271289)), _271291), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_271289)), _271293)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _271291, _271293))], (3442 ^ _152310) ^ [_271493, _271495, _271497] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _271495, _271497), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_271493)), _271495), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_271493)), _271497)))], (3448 ^ _152310) ^ [_271803, _271805, _271807, _271809, _271811, _271813] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_271803), -(_271805 = c_Groups_Ozero__class_Ozero(_271803)), c_Groups_Oplus__class_Oplus(_271803, _271807, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_271803), _271805), _271811)) = c_Groups_Oplus__class_Oplus(_271803, _271809, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_271803), _271805), _271813)), _271807 = _271809, -(_271811 = _271813)], (3466 ^ _152310) ^ [_272452, _272454, _272456] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_272452)), _272454), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_272452)), _272456)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _272454, _272456))], (3472 ^ _152310) ^ [_272656, _272658, _272660] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _272658, _272660), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_272656)), _272658), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_272656)), _272660)))], (3478 ^ _152310) ^ [_272925] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _272925), -(_272925 = c_Nat_OSuc(3481 ^ [_272925]))], (3485 ^ _152310) ^ [_273140] : [3486 ^ _152310 : [(3487 ^ _152310) ^ [_273211] : [_273140 = c_Nat_OSuc(_273211)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _273140))], (3491 ^ _152310) ^ [_273389] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _273389, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_273389 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3497 ^ _152310) ^ [_273547] : [_273547 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _273547, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (3503 ^ _152310) ^ [_273784, _273786] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _273784, c_Nat_OSuc(_273786)), -(_273784 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 3511 ^ _152310 : [(3512 ^ _152310) ^ [] : [-(_273784 = c_Nat_OSuc(3510 ^ [_273784, _273786]))], (3514 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 3510 ^ [_273784, _273786], _273786))]]], (3516 ^ _152310) ^ [_274196, _274198] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _274196, c_Nat_OSuc(_274198))), 3517 ^ _152310 : [(3518 ^ _152310) ^ [] : [_274196 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3520 ^ _152310) ^ [_274365] : [_274196 = c_Nat_OSuc(_274365), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _274365, _274198)]]], (3528 ^ _152310) ^ [_274677, _274679] : [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), _274677), _274679)), 3531 ^ _152310 : [(3532 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _274677))], (3534 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _274679))]]], (3536 ^ _152310) ^ [_274932, _274934] : [-(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), _274932), _274934))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _274932), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _274934)], (3546 ^ _152310) ^ [_275294, _275296, _275298] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _275294), _275296), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _275294), _275298)), 3549 ^ _152310 : [(3550 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _275294))], (3552 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _275296, _275298))]]], (3554 ^ _152310) ^ [_275569, _275571, _275573] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _275569), _275571), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _275569), _275573))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _275569), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _275571, _275573)], (3564 ^ _152310) ^ [_275953, _275955, _275957] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _275953), _275955), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _275957), _275955)), 3567 ^ _152310 : [(3568 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _275955))], (3570 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _275953, _275957))]]], (3572 ^ _152310) ^ [_276228, _276230, _276232] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _276228), _276230), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _276232), _276230))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _276230), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _276228, _276232)], (3582 ^ _152310) ^ [_276583, _276585, _276587] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _276583, _276585), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _276587), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _276583), _276587), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _276585), _276587)))], (3592 ^ _152310) ^ [_276936, _276938, _276940] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _276936, _276938), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _276940), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _276940), _276936), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _276940), _276938)))], (3602 ^ _152310) ^ [_277289, _277291, _277293] : [class_Rings_Oidom(_277289), -(_277291 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_277289))), -(_277293 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_277289))), -(c_Polynomial_Odegree(_277289, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_277289)), _277291), _277293)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Polynomial_Odegree(_277289, _277291), c_Polynomial_Odegree(_277289, _277293)))], (3616 ^ _152310) ^ [_277785, _277787, _277789, _277791] : [class_Rings_Ocomm__semiring__0(_277785), -(hAPP(c_Polynomial_Opoly(_277785, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_277785)), _277787), _277789)), _277791) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_277785), hAPP(c_Polynomial_Opoly(_277785, _277787), _277791)), hAPP(c_Polynomial_Opoly(_277785, _277789), _277791)))], (3622 ^ _152310) ^ [_278063] : [class_Groups_Ozero(_278063), -(c_Polynomial_OpCons(_278063, c_Groups_Ozero__class_Ozero(_278063), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_278063))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_278063)))], (3628 ^ _152310) ^ [_278307, _278309, _278311] : [class_Groups_Ozero(_278307), 3631 ^ _152310 : [(3632 ^ _152310) ^ [] : [c_Polynomial_OpCons(_278307, _278309, _278311) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_278307)), 3635 ^ _152310 : [(3636 ^ _152310) ^ [] : [-(_278309 = c_Groups_Ozero__class_Ozero(_278307))], (3638 ^ _152310) ^ [] : [-(_278311 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_278307)))]]], (3640 ^ _152310) ^ [] : [-(c_Polynomial_OpCons(_278307, _278309, _278311) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_278307))), _278309 = c_Groups_Ozero__class_Ozero(_278307), _278311 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_278307))]]], (3650 ^ _152310) ^ [_278973] : [class_Groups_Ozero(_278973), -(c_Polynomial_Odegree(_278973, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_278973))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3656 ^ _152310) ^ [_279189, _279191] : [class_Groups_Ozero(_279189), -(hAPP(c_Polynomial_Ocoeff(_279189, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_279189))), _279191) = c_Groups_Ozero__class_Ozero(_279189))], (3662 ^ _152310) ^ [_279421, _279423] : [class_Rings_Ocomm__semiring__0(_279421), -(c_Polynomial_Osmult(_279421, c_Groups_Ozero__class_Ozero(_279421), _279423) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_279421)))], (3668 ^ _152310) ^ [_279663, _279665, _279667] : [class_Rings_Oidom(_279663), 3671 ^ _152310 : [(3682 ^ _152310) ^ [] : [3683 ^ _152310 : [(3684 ^ _152310) ^ [] : [_279665 = c_Groups_Ozero__class_Ozero(_279663)], (3686 ^ _152310) ^ [] : [_279667 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_279663))]], -(c_Polynomial_Osmult(_279663, _279665, _279667) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_279663)))], (3672 ^ _152310) ^ [] : [c_Polynomial_Osmult(_279663, _279665, _279667) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_279663)), -(_279665 = c_Groups_Ozero__class_Ozero(_279663)), -(_279667 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_279663)))]]], (3690 ^ _152310) ^ [_280385, _280387, _280389, _280391, _280393] : [class_Rings_Ocomm__semiring__0(_280385), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_280385)), c_Polynomial_Omonom(_280385, _280387, _280389)), c_Polynomial_Omonom(_280385, _280391, _280393)) = c_Polynomial_Omonom(_280385, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_280385), _280387), _280391), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _280389, _280393)))], (3696 ^ _152310) ^ [_280679, _280681] : [class_Rings_Ocomm__semiring__0(_280679), -(hAPP(c_Polynomial_Opoly(_280679, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_280679))), _280681) = c_Groups_Ozero__class_Ozero(_280679))], (3702 ^ _152310) ^ [_280911, _280913] : [class_Groups_Ozero(_280911), -(c_Polynomial_Omonom(_280911, c_Groups_Ozero__class_Ozero(_280911), _280913) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_280911)))], (3708 ^ _152310) ^ [_281153, _281155, _281157] : [class_Groups_Ozero(_281153), 3711 ^ _152310 : [(3712 ^ _152310) ^ [] : [c_Polynomial_Omonom(_281153, _281155, _281157) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_281153)), -(_281155 = c_Groups_Ozero__class_Ozero(_281153))], (3718 ^ _152310) ^ [] : [_281155 = c_Groups_Ozero__class_Ozero(_281153), -(c_Polynomial_Omonom(_281153, _281155, _281157) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_281153)))]]], (3724 ^ _152310) ^ [_281671, _281673, _281675] : [class_Groups_Ozero(_281671), 3727 ^ _152310 : [(3728 ^ _152310) ^ [] : [_281673 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_281671)), -(c_Polynomial_Odegree(_281671, c_Polynomial_OpCons(_281671, _281675, _281673)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3734 ^ _152310) ^ [] : [-(_281673 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_281671))), -(c_Polynomial_Odegree(_281671, c_Polynomial_OpCons(_281671, _281675, _281673)) = c_Nat_OSuc(c_Polynomial_Odegree(_281671, _281673)))]]], (3740 ^ _152310) ^ [_282205, _282207] : [class_Groups_Ozero(_282205), 3743 ^ _152310 : [(3744 ^ _152310) ^ [] : [_282207 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_282205)), -(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_282205, _282207) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3750 ^ _152310) ^ [] : [-(_282207 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_282205))), -(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_282205, _282207) = c_Nat_OSuc(c_Polynomial_Odegree(_282205, _282207)))]]], (3756 ^ _152310) ^ [_282707, _282709] : [class_Groups_Ozero(_282707), 3759 ^ _152310 : [(3760 ^ _152310) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_282707, _282709) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_282709 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_282707)))], (3766 ^ _152310) ^ [] : [_282709 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_282707)), -(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_282707, _282709) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (3782 ^ _152310) ^ [_283520, _283522, _283524] : [3783 ^ _152310 : [(3784 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _283522))], (3786 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _283520, _283524)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _283520), _283522), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _283524), _283522)))], (3772 ^ _152310) ^ [_283229, _283231, _283233] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _283229), _283231), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _283233), _283231)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _283231), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _283229, _283233))], (3800 ^ _152310) ^ [_284179, _284181, _284183] : [3801 ^ _152310 : [(3802 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _284179))], (3804 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _284181, _284183)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _284179), _284181), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _284179), _284183)))], (3790 ^ _152310) ^ [_283888, _283890, _283892] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _283888), _283890), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _283888), _283892)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _283888), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _283890, _283892))], (3808 ^ _152310) ^ [_284518, _284520, _284522] : [class_Rings_Ocomm__semiring__0(_284518), -(hAPP(c_Polynomial_Ocoeff(_284518, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_284518)), _284520), _284522)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Polynomial_Odegree(_284518, _284520), c_Polynomial_Odegree(_284518, _284522))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_284518), hAPP(c_Polynomial_Ocoeff(_284518, _284520), c_Polynomial_Odegree(_284518, _284520))), hAPP(c_Polynomial_Ocoeff(_284518, _284522), c_Polynomial_Odegree(_284518, _284522))))], (3814 ^ _152310) ^ [_284850, _284852, _284854] : [class_Groups_Ozero(_284850), -(_284852 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_284850))), -(c_Polynomial_Odegree(_284850, c_Polynomial_OpCons(_284850, _284854, _284852)) = c_Nat_OSuc(c_Polynomial_Odegree(_284850, _284852)))], (3824 ^ _152310) ^ [_285220, _285222, _285224, _285226] : [class_Rings_Ocomm__semiring__1(_285220), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_285220), _285222), c_Groups_Oplus__class_Oplus(_285220, _285224, _285226)) = c_Groups_Oplus__class_Oplus(_285220, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_285220), _285222), _285224), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_285220), _285222), _285226)))], (3830 ^ _152310) ^ [_285546, _285548, _285550, _285552, _285554] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_285546), 3833 ^ _152310 : [(3844 ^ _152310) ^ [] : [-(c_Groups_Oplus__class_Oplus(_285546, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_285546), _285548), _285552), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_285546), _285550), _285554)) = c_Groups_Oplus__class_Oplus(_285546, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_285546), _285548), _285554), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_285546), _285550), _285552))), 3847 ^ _152310 : [(3848 ^ _152310) ^ [] : [_285548 = _285550], (3850 ^ _152310) ^ [] : [_285552 = _285554]]], (3834 ^ _152310) ^ [] : [c_Groups_Oplus__class_Oplus(_285546, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_285546), _285548), _285552), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_285546), _285550), _285554)) = c_Groups_Oplus__class_Oplus(_285546, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_285546), _285548), _285554), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_285546), _285550), _285552)), -(_285548 = _285550), -(_285552 = _285554)]]], (3852 ^ _152310) ^ [_286382, _286384, _286386, _286388] : [class_Rings_Ocomm__semiring__1(_286382), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_286382), c_Groups_Oplus__class_Oplus(_286382, _286384, _286386)), _286388) = c_Groups_Oplus__class_Oplus(_286382, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_286382), _286384), _286388), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_286382), _286386), _286388)))], (3858 ^ _152310) ^ [_286694, _286696, _286698, _286700] : [class_Rings_Ocomm__semiring__1(_286694), -(c_Groups_Oplus__class_Oplus(_286694, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_286694), _286696), _286698), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_286694), _286700), _286698)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_286694), c_Groups_Oplus__class_Oplus(_286694, _286696, _286700)), _286698))], (3864 ^ _152310) ^ [_287020, _287022, _287024, _287026, _287028] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_287020), 3867 ^ _152310 : [(3878 ^ _152310) ^ [] : [3879 ^ _152310 : [(3880 ^ _152310) ^ [] : [_287022 = _287026], (3882 ^ _152310) ^ [] : [_287024 = _287028]], -(c_Groups_Oplus__class_Oplus(_287020, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_287020), _287022), _287024), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_287020), _287026), _287028)) = c_Groups_Oplus__class_Oplus(_287020, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_287020), _287022), _287028), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_287020), _287026), _287024)))], (3868 ^ _152310) ^ [] : [c_Groups_Oplus__class_Oplus(_287020, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_287020), _287022), _287024), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_287020), _287026), _287028)) = c_Groups_Oplus__class_Oplus(_287020, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_287020), _287022), _287028), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_287020), _287026), _287024)), -(_287022 = _287026), -(_287024 = _287028)]]], (3886 ^ _152310) ^ [_287822, _287824] : [class_Groups_Ozero(_287822), -(c_Polynomial_Odegree(_287822, c_Polynomial_OpCons(_287822, _287824, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_287822)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3892 ^ _152310) ^ [_288052, _288054] : [class_Groups_Ozero(_288052), 3895 ^ _152310 : [(3896 ^ _152310) ^ [] : [hAPP(c_Polynomial_Ocoeff(_288052, _288054), c_Polynomial_Odegree(_288052, _288054)) = c_Groups_Ozero__class_Ozero(_288052), -(_288054 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_288052)))], (3902 ^ _152310) ^ [] : [_288054 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_288052)), -(hAPP(c_Polynomial_Ocoeff(_288052, _288054), c_Polynomial_Odegree(_288052, _288054)) = c_Groups_Ozero__class_Ozero(_288052))]]], (3908 ^ _152310) ^ [_288555, _288557] : [class_Groups_Ozero(_288555), -(_288557 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_288555))), hAPP(c_Polynomial_Ocoeff(_288555, _288557), c_Polynomial_Odegree(_288555, _288557)) = c_Groups_Ozero__class_Ozero(_288555)], (3918 ^ _152310) ^ [_288871, _288873] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _288871, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _288871, _288873))))], (3920 ^ _152310) ^ [_288972, _288974] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _288972, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _288974, _288972))))], (3922 ^ _152310) ^ [_289117, _289119] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _289117, _289119), -(_289119 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _289117, 3925 ^ [_289117, _289119])))], (3929 ^ _152310) ^ [_289356, _289358] : [3930 ^ _152310 : [(3931 ^ _152310) ^ [_289433] : [_289358 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _289356, _289433))]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _289356, _289358))], (3935 ^ _152310) ^ [_289604, _289606] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_289604), c_Nat_OSuc(_289606)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _289604, _289606))], (3941 ^ _152310) ^ [_289826, _289828] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_289826), _289828), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _289826, _289828))], (3947 ^ _152310) ^ [_290044, _290046] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _290044, c_Nat_OSuc(_290046)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _290044, _290046)), -(_290044 = _290046)], (3957 ^ _152310) ^ [_290368, _290370, _290372] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _290368, _290370), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _290370, _290372), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_290368), _290372))], (3967 ^ _152310) ^ [_290687, _290689] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _290687, _290689), -(c_Nat_OSuc(_290687) = _290689), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_290687), _290689))], (3977 ^ _152310) ^ [_291001, _291003] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _291001, _291003), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _291001, c_Nat_OSuc(_291003)))], (3983 ^ _152310) ^ [_291219, _291221] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _291219, _291221)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _291219, c_Nat_OSuc(_291221)), -(_291221 = _291219)], (3993 ^ _152310) ^ [_291529, _291531] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _291529, _291531)), 3996 ^ _152310 : [(3997 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _291529, c_Nat_OSuc(_291531)), -(_291529 = _291531)], (4003 ^ _152310) ^ [] : [_291529 = _291531, -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _291529, c_Nat_OSuc(_291531)))]]], (4009 ^ _152310) ^ [_292032, _292034] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_292032), c_Nat_OSuc(_292034)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _292032, _292034))], (4015 ^ _152310) ^ [_292206, _292208] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _292206, _292208), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_292206), c_Nat_OSuc(_292208)))], (4031 ^ _152310) ^ [_292719, _292721] : [4032 ^ _152310 : [(4033 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _292719, _292721)], (4035 ^ _152310) ^ [] : [_292719 = _292721]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _292719, c_Nat_OSuc(_292721)))], (4021 ^ _152310) ^ [_292459, _292461] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _292459, c_Nat_OSuc(_292461)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _292459, _292461)), -(_292459 = _292461)], (4039 ^ _152310) ^ [_293042, _293044] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _293042, _293044)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _293044, c_Nat_OSuc(_293042)))], (4045 ^ _152310) ^ [_293215, _293217] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _293217, c_Nat_OSuc(_293215)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _293215, _293217)], (4051 ^ _152310) ^ [_293450, _293452, _293454] : [class_Groups_Ozero(_293450), -(c_Polynomial_Omonom(_293450, _293452, c_Nat_OSuc(_293454)) = c_Polynomial_OpCons(_293450, c_Groups_Ozero__class_Ozero(_293450), c_Polynomial_Omonom(_293450, _293452, _293454)))], (4057 ^ _152310) ^ [_293710, _293712, _293714] : [class_Rings_Oidom(_293710), 4060 ^ _152310 : [(4061 ^ _152310) ^ [] : [_293712 = c_Groups_Ozero__class_Ozero(_293710), -(c_Polynomial_Odegree(_293710, c_Polynomial_Osmult(_293710, _293712, _293714)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4067 ^ _152310) ^ [] : [-(_293712 = c_Groups_Ozero__class_Ozero(_293710)), -(c_Polynomial_Odegree(_293710, c_Polynomial_Osmult(_293710, _293712, _293714)) = c_Polynomial_Odegree(_293710, _293714))]]], (4073 ^ _152310) ^ [_294232, _294234] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_294232), _294234), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _294232, _294234))], (4079 ^ _152310) ^ [_294450, _294452] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _294450, c_Nat_OSuc(_294452)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _294450, _294452)), -(_294450 = c_Nat_OSuc(_294452))], (4089 ^ _152310) ^ [_294764, _294766] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _294764, _294766), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _294764, c_Nat_OSuc(_294766)))], (4095 ^ _152310) ^ [_295011, _295013] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_295011), c_Nat_OSuc(_295013)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _295011, _295013))], (4101 ^ _152310) ^ [_295185, _295187] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _295185, _295187), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_295185), c_Nat_OSuc(_295187)))], (4117 ^ _152310) ^ [_295702, _295704] : [4118 ^ _152310 : [(4119 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _295702, _295704)], (4121 ^ _152310) ^ [] : [_295702 = c_Nat_OSuc(_295704)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _295702, c_Nat_OSuc(_295704)))], (4107 ^ _152310) ^ [_295438, _295440] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _295438, c_Nat_OSuc(_295440)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _295438, _295440)), -(_295438 = c_Nat_OSuc(_295440))], (4125 ^ _152310) ^ [_296029, _296031] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _296029, _296031)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_296031), _296029))], (4131 ^ _152310) ^ [_296202, _296204] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_296204), _296202), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _296202, _296204)], (4137 ^ _152310) ^ [_296393] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_296393), _296393)], (4139 ^ _152310) ^ [_296531, _296533, _296535, _296537] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _296531, _296533), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _296535, _296537), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _296531), _296535), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _296533), _296537)))], (4149 ^ _152310) ^ [_296894, _296896, _296898] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _296894, _296896), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _296898), _296894), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _296898), _296896)))], (4155 ^ _152310) ^ [_297152, _297154, _297156] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _297152, _297154), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _297152), _297156), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _297154), _297156)))], (4161 ^ _152310) ^ [_297367] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _297367, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _297367), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _297367), _297367))))], (4163 ^ _152310) ^ [_297458] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _297458, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _297458), _297458)))], (4165 ^ _152310) ^ [_297572, _297574] : [class_Groups_Omonoid__add(_297572), -(c_Groups_Oplus__class_Oplus(_297572, c_Groups_Ozero__class_Ozero(_297572), _297574) = _297574)], (4171 ^ _152310) ^ [_297792, _297794] : [class_Rings_Ocomm__semiring__1(_297792), -(c_Groups_Oplus__class_Oplus(_297792, c_Groups_Ozero__class_Ozero(_297792), _297794) = _297794)], (4177 ^ _152310) ^ [_298012, _298014] : [class_Groups_Ocomm__monoid__add(_298012), -(c_Groups_Oplus__class_Oplus(_298012, c_Groups_Ozero__class_Ozero(_298012), _298014) = _298014)], (4183 ^ _152310) ^ [_298232, _298234] : [class_Groups_Olinordered__ab__group__add(_298232), 4186 ^ _152310 : [(4187 ^ _152310) ^ [] : [c_Groups_Ozero__class_Ozero(_298232) = c_Groups_Oplus__class_Oplus(_298232, _298234, _298234), -(_298234 = c_Groups_Ozero__class_Ozero(_298232))], (4193 ^ _152310) ^ [] : [_298234 = c_Groups_Ozero__class_Ozero(_298232), -(c_Groups_Ozero__class_Ozero(_298232) = c_Groups_Oplus__class_Oplus(_298232, _298234, _298234))]]], (4199 ^ _152310) ^ [_298714, _298716] : [class_Groups_Omonoid__add(_298714), -(c_Groups_Oplus__class_Oplus(_298714, _298716, c_Groups_Ozero__class_Ozero(_298714)) = _298716)], (4205 ^ _152310) ^ [_298934, _298936] : [class_Rings_Ocomm__semiring__1(_298934), -(c_Groups_Oplus__class_Oplus(_298934, _298936, c_Groups_Ozero__class_Ozero(_298934)) = _298936)], (4211 ^ _152310) ^ [_299154, _299156] : [class_Groups_Ocomm__monoid__add(_299154), -(c_Groups_Oplus__class_Oplus(_299154, _299156, c_Groups_Ozero__class_Ozero(_299154)) = _299156)], (4217 ^ _152310) ^ [_299388, _299390, _299392] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_299388), 4220 ^ _152310 : [(4221 ^ _152310) ^ [] : [_299390 = c_Groups_Oplus__class_Oplus(_299388, _299390, _299392), -(_299392 = c_Groups_Ozero__class_Ozero(_299388))], (4227 ^ _152310) ^ [] : [_299392 = c_Groups_Ozero__class_Ozero(_299388), -(_299390 = c_Groups_Oplus__class_Oplus(_299388, _299390, _299392))]]], (4233 ^ _152310) ^ [_299880, _299882] : [class_Groups_Ozero(_299880), -(c_Polynomial_Omonom(_299880, _299882, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(_299880, _299882, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_299880))))], (4249 ^ _152310) ^ [_300407, _300409] : [4250 ^ _152310 : [(4251 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _300407)], (4253 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _300409)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _300407, _300409)))], (4239 ^ _152310) ^ [_300141, _300143] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _300141, _300143)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _300141)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _300143))], (4257 ^ _152310) ^ [_300693] : [-(_300693 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _300693))], (4263 ^ _152310) ^ [_300902, _300904] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _300902, _300904), _300904 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (4269 ^ _152310) ^ [_301085] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _301085, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4271 ^ _152310) ^ [_301208] : [-(_301208 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _301208))], (4277 ^ _152310) ^ [_301369] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _301369), _301369 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (4283 ^ _152310) ^ [_301548] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _301548, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4285 ^ _152310) ^ [_301671] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _301671, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_301671 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4291 ^ _152310) ^ [_301829] : [_301829 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _301829, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (4297 ^ _152310) ^ [_302008] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _302008))], (4299 ^ _152310) ^ [_302144, _302146, _302148, _302150] : [class_Rings_Ocomm__semiring__0(_302144), -(c_Polynomial_Osmult(_302144, _302146, c_Polynomial_Osmult(_302144, _302148, _302150)) = c_Polynomial_Osmult(_302144, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_302144), _302146), _302148), _302150))], (4305 ^ _152310) ^ [_302432, _302434, _302436, _302438] : [class_Rings_Ocomm__semiring__0(_302432), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_302432)), _302434), c_Polynomial_Osmult(_302432, _302436, _302438)) = c_Polynomial_Osmult(_302432, _302436, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_302432)), _302434), _302438)))], (4311 ^ _152310) ^ [_302736, _302738, _302740, _302742] : [class_Rings_Ocomm__semiring__0(_302736), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_302736)), c_Polynomial_Osmult(_302736, _302738, _302740)), _302742) = c_Polynomial_Osmult(_302736, _302738, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_302736)), _302740), _302742)))], (4317 ^ _152310) ^ [_303026, _303028, _303030] : [class_Rings_Ocomm__semiring__0(_303026), 4320 ^ _152310 : [(4321 ^ _152310) ^ [] : [c_Polynomial_Osynthetic__div(_303026, _303028, _303030) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_303026)), -(c_Polynomial_Odegree(_303026, _303028) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4327 ^ _152310) ^ [] : [c_Polynomial_Odegree(_303026, _303028) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Polynomial_Osynthetic__div(_303026, _303028, _303030) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_303026)))]]], (4333 ^ _152310) ^ [_303561, _303563, _303565, _303567] : [class_Rings_Ocomm__semiring__0(_303561), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_303561)), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_303561), _303563, _303565)), _303567) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_303561), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_303561)), _303563), _303567), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_303561)), _303565), _303567)))], (4339 ^ _152310) ^ [_303865, _303867] : [class_Rings_Ocomm__semiring__0(_303865), -(c_Polynomial_Osmult(_303865, _303867, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_303865))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_303865)))], (4345 ^ _152310) ^ [_304097, _304099] : [class_Int_Oring__char__0(_304097), class_Rings_Oidom(_304097), 4352 ^ _152310 : [(4353 ^ _152310) ^ [] : [c_Polynomial_Opoly(_304097, _304099) = c_Polynomial_Opoly(_304097, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_304097))), -(_304099 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_304097)))], (4359 ^ _152310) ^ [] : [_304099 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_304097)), -(c_Polynomial_Opoly(_304097, _304099) = c_Polynomial_Opoly(_304097, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_304097))))]]], (4365 ^ _152310) ^ [_304686, _304688] : [class_Groups_Ocomm__monoid__add(_304686), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_304686), _304688, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_304686))) = _304688)], (4371 ^ _152310) ^ [_304914, _304916] : [class_Groups_Ocomm__monoid__add(_304914), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_304914), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_304914)), _304916) = _304916)], (4377 ^ _152310) ^ [_305156, _305158, _305160] : [class_Rings_Olinordered__idom(_305156), c_Polynomial_Opos__poly(_305156, _305158), c_Polynomial_Opos__poly(_305156, _305160), -(c_Polynomial_Opos__poly(_305156, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_305156)), _305158), _305160)))], (4391 ^ _152310) ^ [_305562] : [class_Rings_Olinordered__idom(_305562), c_Polynomial_Opos__poly(_305562, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_305562)))], (4397 ^ _152310) ^ [_305773, _305775] : [class_Rings_Ocomm__semiring__0(_305773), -(c_Polynomial_Osynthetic__div(_305773, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_305773)), _305775) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_305773)))], (4403 ^ _152310) ^ [_306019, _306021, _306023] : [class_Rings_Ocomm__semiring__0(_306019), 4406 ^ _152310 : [(4407 ^ _152310) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_306019, _306021, _306023) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_306019)), -(_306021 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_306019)))], (4413 ^ _152310) ^ [] : [_306021 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_306019)), -(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_306019, _306021, _306023) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_306019)))]]], (4419 ^ _152310) ^ [_306529, _306531] : [class_Rings_Ocomm__semiring__0(_306529), -(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_306529, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_306529)), _306531) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_306529)))], (4425 ^ _152310) ^ [_306789, _306791, _306793, _306795] : [class_Rings_Ocomm__semiring__0(_306789), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_306789)), _306791), c_Polynomial_OpCons(_306789, _306793, _306795)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_306789), c_Polynomial_Osmult(_306789, _306793, _306791), c_Polynomial_OpCons(_306789, c_Groups_Ozero__class_Ozero(_306789), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_306789)), _306791), _306795))))], (4431 ^ _152310) ^ [_307117, _307119, _307121, _307123] : [class_Rings_Ocomm__semiring__0(_307117), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_307117)), c_Polynomial_OpCons(_307117, _307119, _307121)), _307123) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_307117), c_Polynomial_Osmult(_307117, _307119, _307123), c_Polynomial_OpCons(_307117, c_Groups_Ozero__class_Ozero(_307117), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_307117)), _307121), _307123))))], (4437 ^ _152310) ^ [_307431, _307433, _307435] : [class_Rings_Olinordered__idom(_307431), 4440 ^ _152310 : [(4441 ^ _152310) ^ [] : [c_Polynomial_Opos__poly(_307431, c_Polynomial_OpCons(_307431, _307433, _307435)), -(c_Polynomial_Opos__poly(_307431, _307435)), 4448 ^ _152310 : [(4449 ^ _152310) ^ [] : [-(_307435 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_307431)))], (4451 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(_307431, c_Groups_Ozero__class_Ozero(_307431), _307433))]]], (4453 ^ _152310) ^ [] : [-(c_Polynomial_Opos__poly(_307431, c_Polynomial_OpCons(_307431, _307433, _307435))), 4454 ^ _152310 : [(4455 ^ _152310) ^ [] : [c_Polynomial_Opos__poly(_307431, _307435)], (4457 ^ _152310) ^ [] : [_307435 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_307431)), c_Orderings_Oord__class_Oless(_307431, c_Groups_Ozero__class_Ozero(_307431), _307433)]]]]], (4465 ^ _152310) ^ [_308266, _308268] : [class_Rings_Ocomm__semiring__0(_308266), -(c_Polynomial_Opcompose(_308266, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_308266)), _308268) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_308266)))], (4471 ^ _152310) ^ [_308526, _308528, _308530, _308532] : [class_Rings_Ocomm__semiring__0(_308526), -(c_Polynomial_Opcompose(_308526, c_Polynomial_OpCons(_308526, _308528, _308530), _308532) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_308526), c_Polynomial_OpCons(_308526, _308528, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_308526))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_308526)), _308532), c_Polynomial_Opcompose(_308526, _308530, _308532))))], (4477 ^ _152310) ^ [_308818, _308820] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_308818), _308820), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _308818, _308820))], (4483 ^ _152310) ^ [_309036, _309038] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _309036, _309038), 4486 ^ _152310 : [(4487 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _309038, c_Nat_OSuc(_309036)), -(_309038 = _309036)], (4493 ^ _152310) ^ [] : [_309038 = _309036, -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _309038, c_Nat_OSuc(_309036)))]]], (4499 ^ _152310) ^ [_309507, _309509] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _309507, _309509), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_309507), _309509))], (4505 ^ _152310) ^ [_309725, _309727] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _309725, _309727), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _309725, c_Nat_OSuc(_309727)))], (4511 ^ _152310) ^ [_309972, _309974] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_309972), _309974), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _309972, _309974))], (4517 ^ _152310) ^ [_310142, _310144] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _310142, _310144), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_310142), _310144))], (4523 ^ _152310) ^ [_310391, _310393] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _310391, c_Nat_OSuc(_310393)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _310391, _310393))], (4529 ^ _152310) ^ [_310561, _310563] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _310561, _310563), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _310561, c_Nat_OSuc(_310563)))], (4535 ^ _152310) ^ [_310810, _310812] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _310810, _310812), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_310810), _310812))], (4541 ^ _152310) ^ [_310980, _310982] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_310980), _310982), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _310980, _310982))], (4547 ^ _152310) ^ [_311214, _311216, _311218] : [class_Groups_Oordered__comm__monoid__add(_311214), c_Orderings_Oord__class_Oless__eq(_311214, _311216, c_Groups_Ozero__class_Ozero(_311214)), c_Orderings_Oord__class_Oless__eq(_311214, _311218, c_Groups_Ozero__class_Ozero(_311214)), -(c_Orderings_Oord__class_Oless__eq(_311214, c_Groups_Oplus__class_Oplus(_311214, _311216, _311218), c_Groups_Ozero__class_Ozero(_311214)))], (4561 ^ _152310) ^ [_311668, _311670, _311672, _311674] : [class_Groups_Oordered__comm__monoid__add(_311668), c_Orderings_Oord__class_Oless__eq(_311668, c_Groups_Ozero__class_Ozero(_311668), _311670), c_Orderings_Oord__class_Oless__eq(_311668, _311672, _311674), -(c_Orderings_Oord__class_Oless__eq(_311668, _311672, c_Groups_Oplus__class_Oplus(_311668, _311674, _311670)))], (4575 ^ _152310) ^ [_312128, _312130, _312132, _312134] : [class_Groups_Oordered__comm__monoid__add(_312128), c_Orderings_Oord__class_Oless__eq(_312128, c_Groups_Ozero__class_Ozero(_312128), _312130), c_Orderings_Oord__class_Oless__eq(_312128, _312132, _312134), -(c_Orderings_Oord__class_Oless__eq(_312128, _312132, c_Groups_Oplus__class_Oplus(_312128, _312130, _312134)))], (4589 ^ _152310) ^ [_312574, _312576, _312578] : [class_Groups_Oordered__comm__monoid__add(_312574), c_Orderings_Oord__class_Oless__eq(_312574, c_Groups_Ozero__class_Ozero(_312574), _312576), c_Orderings_Oord__class_Oless__eq(_312574, c_Groups_Ozero__class_Ozero(_312574), _312578), 4600 ^ _152310 : [(4601 ^ _152310) ^ [] : [c_Groups_Oplus__class_Oplus(_312574, _312576, _312578) = c_Groups_Ozero__class_Ozero(_312574), 4604 ^ _152310 : [(4605 ^ _152310) ^ [] : [-(_312576 = c_Groups_Ozero__class_Ozero(_312574))], (4607 ^ _152310) ^ [] : [-(_312578 = c_Groups_Ozero__class_Ozero(_312574))]]], (4609 ^ _152310) ^ [] : [-(c_Groups_Oplus__class_Oplus(_312574, _312576, _312578) = c_Groups_Ozero__class_Ozero(_312574)), _312576 = c_Groups_Ozero__class_Ozero(_312574), _312578 = c_Groups_Ozero__class_Ozero(_312574)]]], (4619 ^ _152310) ^ [_313454, _313456, _313458] : [class_Groups_Oordered__comm__monoid__add(_313454), c_Orderings_Oord__class_Oless__eq(_313454, c_Groups_Ozero__class_Ozero(_313454), _313456), c_Orderings_Oord__class_Oless__eq(_313454, c_Groups_Ozero__class_Ozero(_313454), _313458), -(c_Orderings_Oord__class_Oless__eq(_313454, c_Groups_Ozero__class_Ozero(_313454), c_Groups_Oplus__class_Oplus(_313454, _313456, _313458)))], (4633 ^ _152310) ^ [_313880, _313882] : [class_Groups_Olinordered__ab__group__add(_313880), 4636 ^ _152310 : [(4637 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_313880, c_Groups_Oplus__class_Oplus(_313880, _313882, _313882), c_Groups_Ozero__class_Ozero(_313880)), -(c_Orderings_Oord__class_Oless__eq(_313880, _313882, c_Groups_Ozero__class_Ozero(_313880)))], (4643 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_313880, _313882, c_Groups_Ozero__class_Ozero(_313880)), -(c_Orderings_Oord__class_Oless__eq(_313880, c_Groups_Oplus__class_Oplus(_313880, _313882, _313882), c_Groups_Ozero__class_Ozero(_313880)))]]], (4649 ^ _152310) ^ [_314368, _314370] : [class_Groups_Olinordered__ab__group__add(_314368), 4652 ^ _152310 : [(4653 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_314368, c_Groups_Ozero__class_Ozero(_314368), c_Groups_Oplus__class_Oplus(_314368, _314370, _314370)), -(c_Orderings_Oord__class_Oless__eq(_314368, c_Groups_Ozero__class_Ozero(_314368), _314370))], (4659 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_314368, c_Groups_Ozero__class_Ozero(_314368), _314370), -(c_Orderings_Oord__class_Oless__eq(_314368, c_Groups_Ozero__class_Ozero(_314368), c_Groups_Oplus__class_Oplus(_314368, _314370, _314370)))]]], (4665 ^ _152310) ^ [_314870, _314872, _314874] : [class_Groups_Oordered__comm__monoid__add(_314870), c_Orderings_Oord__class_Oless(_314870, _314872, c_Groups_Ozero__class_Ozero(_314870)), c_Orderings_Oord__class_Oless(_314870, _314874, c_Groups_Ozero__class_Ozero(_314870)), -(c_Orderings_Oord__class_Oless(_314870, c_Groups_Oplus__class_Oplus(_314870, _314872, _314874), c_Groups_Ozero__class_Ozero(_314870)))], (4679 ^ _152310) ^ [_315310, _315312, _315314] : [class_Groups_Oordered__comm__monoid__add(_315310), c_Orderings_Oord__class_Oless(_315310, c_Groups_Ozero__class_Ozero(_315310), _315312), c_Orderings_Oord__class_Oless(_315310, c_Groups_Ozero__class_Ozero(_315310), _315314), -(c_Orderings_Oord__class_Oless(_315310, c_Groups_Ozero__class_Ozero(_315310), c_Groups_Oplus__class_Oplus(_315310, _315312, _315314)))], (4693 ^ _152310) ^ [_315736, _315738] : [class_Groups_Olinordered__ab__group__add(_315736), 4696 ^ _152310 : [(4697 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_315736, c_Groups_Oplus__class_Oplus(_315736, _315738, _315738), c_Groups_Ozero__class_Ozero(_315736)), -(c_Orderings_Oord__class_Oless(_315736, _315738, c_Groups_Ozero__class_Ozero(_315736)))], (4703 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_315736, _315738, c_Groups_Ozero__class_Ozero(_315736)), -(c_Orderings_Oord__class_Oless(_315736, c_Groups_Oplus__class_Oplus(_315736, _315738, _315738), c_Groups_Ozero__class_Ozero(_315736)))]]], (4709 ^ _152310) ^ [_316224, _316226] : [class_Groups_Olinordered__ab__group__add(_316224), 4712 ^ _152310 : [(4713 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_316224, c_Groups_Ozero__class_Ozero(_316224), c_Groups_Oplus__class_Oplus(_316224, _316226, _316226)), -(c_Orderings_Oord__class_Oless(_316224, c_Groups_Ozero__class_Ozero(_316224), _316226))], (4719 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_316224, c_Groups_Ozero__class_Ozero(_316224), _316226), -(c_Orderings_Oord__class_Oless(_316224, c_Groups_Ozero__class_Ozero(_316224), c_Groups_Oplus__class_Oplus(_316224, _316226, _316226)))]]], (4725 ^ _152310) ^ [_316726, _316728, _316730] : [class_Groups_Ozero(_316726), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_316726, _316728), _316730), hAPP(c_Polynomial_Ocoeff(_316726, _316728), _316730) = c_Groups_Ozero__class_Ozero(_316726), -(_316728 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_316726))), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_316726, _316728), _316730))], (4743 ^ _152310) ^ [_317274, _317276, _317278] : [class_Rings_Ocomm__semiring__0(_317274), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_317274, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_317274)), _317276), _317278)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Polynomial_Odegree(_317274, _317276), c_Polynomial_Odegree(_317274, _317278))))], (4749 ^ _152310) ^ [_317564, _317566, _317568, _317570] : [class_Groups_Ozero(_317564), -(hAPP(c_Polynomial_Ocoeff(_317564, c_Polynomial_OpCons(_317564, _317566, _317568)), c_Nat_OSuc(_317570)) = hAPP(c_Polynomial_Ocoeff(_317564, _317568), _317570))], (4755 ^ _152310) ^ [_317848, _317850, _317852, _317854] : [class_Rings_Ocomm__semiring__0(_317848), -(c_Polynomial_Osmult(_317848, _317850, c_Polynomial_OpCons(_317848, _317852, _317854)) = c_Polynomial_OpCons(_317848, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_317848), _317850), _317852), c_Polynomial_Osmult(_317848, _317850, _317854)))], (4761 ^ _152310) ^ [_318144, _318146, _318148, _318150] : [class_Rings_Ocomm__semiring__0(_318144), -(hAPP(c_Polynomial_Ocoeff(_318144, c_Polynomial_Osmult(_318144, _318146, _318148)), _318150) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_318144), _318146), hAPP(c_Polynomial_Ocoeff(_318144, _318148), _318150)))], (4767 ^ _152310) ^ [_318440, _318442, _318444, _318446] : [class_Rings_Ocomm__semiring__0(_318440), -(hAPP(c_Polynomial_Opoly(_318440, c_Polynomial_Osmult(_318440, _318442, _318444)), _318446) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_318440), _318442), hAPP(c_Polynomial_Opoly(_318440, _318444), _318446)))], (4773 ^ _152310) ^ [_318736, _318738, _318740, _318742] : [class_Rings_Ocomm__semiring__0(_318736), -(c_Polynomial_Osmult(_318736, _318738, c_Polynomial_Omonom(_318736, _318740, _318742)) = c_Polynomial_Omonom(_318736, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_318736), _318738), _318740), _318742))], (4779 ^ _152310) ^ [_319024, _319026, _319028, _319030] : [class_Rings_Ocomm__semiring__0(_319024), c_Polynomial_Osmult(_319024, _319026, _319028) = c_Polynomial_OpCons(_319024, _319030, _319028), -(_319028 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_319024)))], (4789 ^ _152310) ^ [_319379, _319381, _319383] : [class_Groups_Ozero(_319379), -(hAPP(c_Polynomial_Ocoeff(_319379, c_Polynomial_OpCons(_319379, _319381, _319383)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _319381)], (4795 ^ _152310) ^ [_319627, _319629, _319631] : [class_Groups_Ozero(_319627), -(_319629 = c_Groups_Ozero__class_Ozero(_319627)), -(c_Polynomial_Odegree(_319627, c_Polynomial_Omonom(_319627, _319629, _319631)) = _319631)], (4805 ^ _152310) ^ [_319983, _319985, _319987, _319989] : [class_Groups_Ozero(_319983), 4808 ^ _152310 : [(4809 ^ _152310) ^ [] : [_319985 = _319987, -(hAPP(c_Polynomial_Ocoeff(_319983, c_Polynomial_Omonom(_319983, _319989, _319985)), _319987) = _319989)], (4815 ^ _152310) ^ [] : [-(_319985 = _319987), -(hAPP(c_Polynomial_Ocoeff(_319983, c_Polynomial_Omonom(_319983, _319989, _319985)), _319987) = c_Groups_Ozero__class_Ozero(_319983))]]], (4821 ^ _152310) ^ [_320537, _320539, _320541] : [class_Rings_Ocomm__semiring__0(_320537), -(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_320537, c_Polynomial_OpCons(_320537, _320539, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_320537))), _320541) = c_Polynomial_OpCons(_320537, _320539, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_320537))))], (4827 ^ _152310) ^ [_320805, _320807, _320809] : [class_Groups_Oordered__comm__monoid__add(_320805), c_Orderings_Oord__class_Oless(_320805, c_Groups_Ozero__class_Ozero(_320805), _320807), c_Orderings_Oord__class_Oless__eq(_320805, c_Groups_Ozero__class_Ozero(_320805), _320809), -(c_Orderings_Oord__class_Oless(_320805, c_Groups_Ozero__class_Ozero(_320805), c_Groups_Oplus__class_Oplus(_320805, _320807, _320809)))], (4841 ^ _152310) ^ [_321245, _321247, _321249] : [class_Groups_Oordered__comm__monoid__add(_321245), c_Orderings_Oord__class_Oless__eq(_321245, c_Groups_Ozero__class_Ozero(_321245), _321247), c_Orderings_Oord__class_Oless(_321245, c_Groups_Ozero__class_Ozero(_321245), _321249), -(c_Orderings_Oord__class_Oless(_321245, c_Groups_Ozero__class_Ozero(_321245), c_Groups_Oplus__class_Oplus(_321245, _321247, _321249)))], (4855 ^ _152310) ^ [_321699, _321701, _321703, _321705] : [class_Groups_Oordered__comm__monoid__add(_321699), c_Orderings_Oord__class_Oless(_321699, c_Groups_Ozero__class_Ozero(_321699), _321701), c_Orderings_Oord__class_Oless__eq(_321699, _321703, _321705), -(c_Orderings_Oord__class_Oless(_321699, _321703, c_Groups_Oplus__class_Oplus(_321699, _321701, _321705)))], (4869 ^ _152310) ^ [_322159, _322161, _322163, _322165] : [class_Groups_Oordered__comm__monoid__add(_322159), c_Orderings_Oord__class_Oless__eq(_322159, c_Groups_Ozero__class_Ozero(_322159), _322161), c_Orderings_Oord__class_Oless(_322159, _322163, _322165), -(c_Orderings_Oord__class_Oless(_322159, _322163, c_Groups_Oplus__class_Oplus(_322159, _322161, _322165)))], (4883 ^ _152310) ^ [_322605, _322607, _322609] : [class_Groups_Oordered__comm__monoid__add(_322605), c_Orderings_Oord__class_Oless(_322605, _322607, c_Groups_Ozero__class_Ozero(_322605)), c_Orderings_Oord__class_Oless__eq(_322605, _322609, c_Groups_Ozero__class_Ozero(_322605)), -(c_Orderings_Oord__class_Oless(_322605, c_Groups_Oplus__class_Oplus(_322605, _322607, _322609), c_Groups_Ozero__class_Ozero(_322605)))], (4897 ^ _152310) ^ [_323045, _323047, _323049] : [class_Groups_Oordered__comm__monoid__add(_323045), c_Orderings_Oord__class_Oless__eq(_323045, _323047, c_Groups_Ozero__class_Ozero(_323045)), c_Orderings_Oord__class_Oless(_323045, _323049, c_Groups_Ozero__class_Ozero(_323045)), -(c_Orderings_Oord__class_Oless(_323045, c_Groups_Oplus__class_Oplus(_323045, _323047, _323049), c_Groups_Ozero__class_Ozero(_323045)))], (4911 ^ _152310) ^ [_323485, _323487, _323489] : [class_Rings_Olinordered__ring(_323485), c_Orderings_Oord__class_Oless(_323485, c_Groups_Oplus__class_Oplus(_323485, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_323485), _323487), _323487), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_323485), _323489), _323489)), c_Groups_Ozero__class_Ozero(_323485))], (4917 ^ _152310) ^ [_323760, _323762, _323764] : [class_Rings_Olinordered__ring__strict(_323760), 4920 ^ _152310 : [(4931 ^ _152310) ^ [] : [4932 ^ _152310 : [(4933 ^ _152310) ^ [] : [-(_323762 = c_Groups_Ozero__class_Ozero(_323760))], (4935 ^ _152310) ^ [] : [-(_323764 = c_Groups_Ozero__class_Ozero(_323760))]], -(c_Orderings_Oord__class_Oless(_323760, c_Groups_Ozero__class_Ozero(_323760), c_Groups_Oplus__class_Oplus(_323760, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_323760), _323762), _323762), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_323760), _323764), _323764))))], (4921 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_323760, c_Groups_Ozero__class_Ozero(_323760), c_Groups_Oplus__class_Oplus(_323760, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_323760), _323762), _323762), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_323760), _323764), _323764))), _323762 = c_Groups_Ozero__class_Ozero(_323760), _323764 = c_Groups_Ozero__class_Ozero(_323760)]]], (4939 ^ _152310) ^ [_324497, _324499, _324501] : [class_Rings_Olinordered__ring(_324497), -(c_Orderings_Oord__class_Oless__eq(_324497, c_Groups_Ozero__class_Ozero(_324497), c_Groups_Oplus__class_Oplus(_324497, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_324497), _324499), _324499), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_324497), _324501), _324501))))], (4945 ^ _152310) ^ [_324771, _324773, _324775] : [class_Rings_Olinordered__ring__strict(_324771), 4948 ^ _152310 : [(4949 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_324771, c_Groups_Oplus__class_Oplus(_324771, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_324771), _324773), _324773), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_324771), _324775), _324775)), c_Groups_Ozero__class_Ozero(_324771)), 4952 ^ _152310 : [(4953 ^ _152310) ^ [] : [-(_324773 = c_Groups_Ozero__class_Ozero(_324771))], (4955 ^ _152310) ^ [] : [-(_324775 = c_Groups_Ozero__class_Ozero(_324771))]]], (4957 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_324771, c_Groups_Oplus__class_Oplus(_324771, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_324771), _324773), _324773), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_324771), _324775), _324775)), c_Groups_Ozero__class_Ozero(_324771))), _324773 = c_Groups_Ozero__class_Ozero(_324771), _324775 = c_Groups_Ozero__class_Ozero(_324771)]]], (4967 ^ _152310) ^ [_325518, _325520, _325522, _325524] : [class_Rings_Olinordered__semiring__strict(_325518), c_Orderings_Oord__class_Oless__eq(_325518, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_325518), _325520), _325522), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_325518), _325520), _325524)), c_Orderings_Oord__class_Oless(_325518, c_Groups_Ozero__class_Ozero(_325518), _325520), -(c_Orderings_Oord__class_Oless__eq(_325518, _325522, _325524))], (4981 ^ _152310) ^ [_326002, _326004, _326006, _326008] : [class_Rings_Olinordered__semiring__strict(_326002), c_Orderings_Oord__class_Oless__eq(_326002, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_326002), _326004), _326006), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_326002), _326008), _326006)), c_Orderings_Oord__class_Oless(_326002, c_Groups_Ozero__class_Ozero(_326002), _326006), -(c_Orderings_Oord__class_Oless__eq(_326002, _326004, _326008))], (4995 ^ _152310) ^ [_326486, _326488, _326490, _326492] : [class_Rings_Olinordered__semiring__strict(_326486), c_Orderings_Oord__class_Oless(_326486, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_326486), _326488), _326490), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_326486), _326488), _326492)), c_Orderings_Oord__class_Oless__eq(_326486, c_Groups_Ozero__class_Ozero(_326486), _326488), -(c_Orderings_Oord__class_Oless(_326486, _326490, _326492))], (5009 ^ _152310) ^ [_326970, _326972, _326974, _326976] : [class_Rings_Olinordered__semiring(_326970), c_Orderings_Oord__class_Oless(_326970, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_326970), _326972), _326974), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_326970), _326972), _326976)), c_Orderings_Oord__class_Oless__eq(_326970, c_Groups_Ozero__class_Ozero(_326970), _326972), -(c_Orderings_Oord__class_Oless(_326970, _326974, _326976))], (5023 ^ _152310) ^ [_327440, _327442, _327444] : [class_Rings_Olinordered__idom(_327440), -(_327442 = _327444), -(c_Orderings_Oord__class_Oless(_327440, _327442, _327444)), -(c_Orderings_Oord__class_Oless(_327440, _327444, _327442))], (5037 ^ _152310) ^ [_327850, _327852] : [class_Rings_Omult__zero(_327850), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_327850), c_Groups_Ozero__class_Ozero(_327850)), _327852) = c_Groups_Ozero__class_Ozero(_327850))], (5043 ^ _152310) ^ [_328082, _328084] : [class_Rings_Omult__zero(_328082), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_328082), _328084), c_Groups_Ozero__class_Ozero(_328082)) = c_Groups_Ozero__class_Ozero(_328082))], (5049 ^ _152310) ^ [_328328, _328330, _328332] : [class_Rings_Oring__no__zero__divisors(_328328), 5052 ^ _152310 : [(5063 ^ _152310) ^ [] : [5064 ^ _152310 : [(5065 ^ _152310) ^ [] : [_328330 = c_Groups_Ozero__class_Ozero(_328328)], (5067 ^ _152310) ^ [] : [_328332 = c_Groups_Ozero__class_Ozero(_328328)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_328328), _328330), _328332) = c_Groups_Ozero__class_Ozero(_328328))], (5053 ^ _152310) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_328328), _328330), _328332) = c_Groups_Ozero__class_Ozero(_328328), -(_328330 = c_Groups_Ozero__class_Ozero(_328328)), -(_328332 = c_Groups_Ozero__class_Ozero(_328328))]]], (5071 ^ _152310) ^ [_329022, _329024, _329026] : [class_Rings_Ono__zero__divisors(_329022), -(_329024 = c_Groups_Ozero__class_Ozero(_329022)), -(_329026 = c_Groups_Ozero__class_Ozero(_329022)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_329022), _329024), _329026) = c_Groups_Ozero__class_Ozero(_329022)], (5085 ^ _152310) ^ [_329471, _329473, _329475] : [class_Rings_Ono__zero__divisors(_329471), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_329471), _329473), _329475) = c_Groups_Ozero__class_Ozero(_329471), -(_329473 = c_Groups_Ozero__class_Ozero(_329471)), -(_329475 = c_Groups_Ozero__class_Ozero(_329471))], (5099 ^ _152310) ^ [_329942, _329944, _329946, _329948, _329950] : [class_Rings_Osemiring(_329942), -(c_Groups_Oplus__class_Oplus(_329942, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_329942), _329944), _329946), c_Groups_Oplus__class_Oplus(_329942, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_329942), _329948), _329946), _329950)) = c_Groups_Oplus__class_Oplus(_329942, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_329942), c_Groups_Oplus__class_Oplus(_329942, _329944, _329948)), _329946), _329950))], (5105 ^ _152310) ^ [_330276, _330278, _330280, _330282] : [class_Rings_Ocomm__semiring(_330276), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_330276), c_Groups_Oplus__class_Oplus(_330276, _330278, _330280)), _330282) = c_Groups_Oplus__class_Oplus(_330276, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_330276), _330278), _330282), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_330276), _330280), _330282)))], (5111 ^ _152310) ^ [_330560, _330562] : [class_Rings_Olinordered__ring(_330560), -(c_Orderings_Oord__class_Oless__eq(_330560, c_Groups_Ozero__class_Ozero(_330560), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_330560), _330562), _330562)))], (5117 ^ _152310) ^ [_330804, _330806, _330808] : [class_Rings_Olinordered__ring__strict(_330804), 5120 ^ _152310 : [(5121 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_330804, c_Groups_Ozero__class_Ozero(_330804), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_330804), _330806), _330808)), 5126 ^ _152310 : [(5127 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_330804, c_Groups_Ozero__class_Ozero(_330804), _330806))], (5129 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_330804, c_Groups_Ozero__class_Ozero(_330804), _330808))]], 5130 ^ _152310 : [(5131 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_330804, _330806, c_Groups_Ozero__class_Ozero(_330804)))], (5133 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_330804, _330808, c_Groups_Ozero__class_Ozero(_330804)))]]], (5135 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_330804, c_Groups_Ozero__class_Ozero(_330804), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_330804), _330806), _330808))), 5136 ^ _152310 : [(5137 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_330804, c_Groups_Ozero__class_Ozero(_330804), _330806), c_Orderings_Oord__class_Oless__eq(_330804, c_Groups_Ozero__class_Ozero(_330804), _330808)], (5143 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_330804, _330806, c_Groups_Ozero__class_Ozero(_330804)), c_Orderings_Oord__class_Oless__eq(_330804, _330808, c_Groups_Ozero__class_Ozero(_330804))]]]]], (5151 ^ _152310) ^ [_331853, _331855, _331857] : [class_Rings_Olinordered__ring__strict(_331853), 5154 ^ _152310 : [(5155 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_331853, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_331853), _331855), _331857), c_Groups_Ozero__class_Ozero(_331853)), 5160 ^ _152310 : [(5161 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_331853, c_Groups_Ozero__class_Ozero(_331853), _331855))], (5163 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_331853, _331857, c_Groups_Ozero__class_Ozero(_331853)))]], 5164 ^ _152310 : [(5165 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_331853, _331855, c_Groups_Ozero__class_Ozero(_331853)))], (5167 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_331853, c_Groups_Ozero__class_Ozero(_331853), _331857))]]], (5169 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_331853, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_331853), _331855), _331857), c_Groups_Ozero__class_Ozero(_331853))), 5170 ^ _152310 : [(5171 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_331853, c_Groups_Ozero__class_Ozero(_331853), _331855), c_Orderings_Oord__class_Oless__eq(_331853, _331857, c_Groups_Ozero__class_Ozero(_331853))], (5177 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_331853, _331855, c_Groups_Ozero__class_Ozero(_331853)), c_Orderings_Oord__class_Oless__eq(_331853, c_Groups_Ozero__class_Ozero(_331853), _331857)]]]]], (5185 ^ _152310) ^ [_332902, _332904, _332906] : [class_Rings_Oordered__cancel__semiring(_332902), c_Orderings_Oord__class_Oless__eq(_332902, c_Groups_Ozero__class_Ozero(_332902), _332904), c_Orderings_Oord__class_Oless__eq(_332902, c_Groups_Ozero__class_Ozero(_332902), _332906), -(c_Orderings_Oord__class_Oless__eq(_332902, c_Groups_Ozero__class_Ozero(_332902), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_332902), _332904), _332906)))], (5199 ^ _152310) ^ [_333350, _333352, _333354] : [class_Rings_Oordered__cancel__semiring(_333350), c_Orderings_Oord__class_Oless__eq(_333350, c_Groups_Ozero__class_Ozero(_333350), _333352), c_Orderings_Oord__class_Oless__eq(_333350, _333354, c_Groups_Ozero__class_Ozero(_333350)), -(c_Orderings_Oord__class_Oless__eq(_333350, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_333350), _333352), _333354), c_Groups_Ozero__class_Ozero(_333350)))], (5213 ^ _152310) ^ [_333798, _333800, _333802] : [class_Rings_Oordered__cancel__semiring(_333798), c_Orderings_Oord__class_Oless__eq(_333798, c_Groups_Ozero__class_Ozero(_333798), _333800), c_Orderings_Oord__class_Oless__eq(_333798, _333802, c_Groups_Ozero__class_Ozero(_333798)), -(c_Orderings_Oord__class_Oless__eq(_333798, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_333798), _333802), _333800), c_Groups_Ozero__class_Ozero(_333798)))], (5227 ^ _152310) ^ [_334246, _334248, _334250] : [class_Rings_Oordered__cancel__semiring(_334246), c_Orderings_Oord__class_Oless__eq(_334246, _334248, c_Groups_Ozero__class_Ozero(_334246)), c_Orderings_Oord__class_Oless__eq(_334246, c_Groups_Ozero__class_Ozero(_334246), _334250), -(c_Orderings_Oord__class_Oless__eq(_334246, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_334246), _334248), _334250), c_Groups_Ozero__class_Ozero(_334246)))], (5241 ^ _152310) ^ [_334694, _334696, _334698] : [class_Rings_Oordered__ring(_334694), c_Orderings_Oord__class_Oless__eq(_334694, _334696, c_Groups_Ozero__class_Ozero(_334694)), c_Orderings_Oord__class_Oless__eq(_334694, _334698, c_Groups_Ozero__class_Ozero(_334694)), -(c_Orderings_Oord__class_Oless__eq(_334694, c_Groups_Ozero__class_Ozero(_334694), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_334694), _334696), _334698)))], (5255 ^ _152310) ^ [_335156, _335158, _335160, _335162] : [class_Rings_Oordered__semiring(_335156), c_Orderings_Oord__class_Oless__eq(_335156, _335158, _335160), c_Orderings_Oord__class_Oless__eq(_335156, c_Groups_Ozero__class_Ozero(_335156), _335162), -(c_Orderings_Oord__class_Oless__eq(_335156, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_335156), _335158), _335162), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_335156), _335160), _335162)))], (5269 ^ _152310) ^ [_335640, _335642, _335644, _335646] : [class_Rings_Oordered__semiring(_335640), c_Orderings_Oord__class_Oless__eq(_335640, _335642, _335644), c_Orderings_Oord__class_Oless__eq(_335640, c_Groups_Ozero__class_Ozero(_335640), _335646), -(c_Orderings_Oord__class_Oless__eq(_335640, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_335640), _335646), _335642), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_335640), _335646), _335644)))], (5283 ^ _152310) ^ [_336124, _336126, _336128, _336130] : [class_Rings_Oordered__comm__semiring(_336124), c_Orderings_Oord__class_Oless__eq(_336124, _336126, _336128), c_Orderings_Oord__class_Oless__eq(_336124, c_Groups_Ozero__class_Ozero(_336124), _336130), -(c_Orderings_Oord__class_Oless__eq(_336124, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_336124), _336130), _336126), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_336124), _336130), _336128)))], (5297 ^ _152310) ^ [_336608, _336610, _336612, _336614] : [class_Rings_Oordered__ring(_336608), c_Orderings_Oord__class_Oless__eq(_336608, _336610, _336612), c_Orderings_Oord__class_Oless__eq(_336608, _336614, c_Groups_Ozero__class_Ozero(_336608)), -(c_Orderings_Oord__class_Oless__eq(_336608, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_336608), _336612), _336614), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_336608), _336610), _336614)))], (5311 ^ _152310) ^ [_337092, _337094, _337096, _337098] : [class_Rings_Oordered__ring(_337092), c_Orderings_Oord__class_Oless__eq(_337092, _337094, _337096), c_Orderings_Oord__class_Oless__eq(_337092, _337098, c_Groups_Ozero__class_Ozero(_337092)), -(c_Orderings_Oord__class_Oless__eq(_337092, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_337092), _337098), _337096), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_337092), _337098), _337094)))], (5325 ^ _152310) ^ [_337590, _337592, _337594, _337596, _337598] : [class_Rings_Oordered__semiring(_337590), c_Orderings_Oord__class_Oless__eq(_337590, _337592, _337594), c_Orderings_Oord__class_Oless__eq(_337590, _337596, _337598), c_Orderings_Oord__class_Oless__eq(_337590, c_Groups_Ozero__class_Ozero(_337590), _337592), c_Orderings_Oord__class_Oless__eq(_337590, c_Groups_Ozero__class_Ozero(_337590), _337596), -(c_Orderings_Oord__class_Oless__eq(_337590, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_337590), _337592), _337596), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_337590), _337594), _337598)))], (5347 ^ _152310) ^ [_338312, _338314, _338316, _338318, _338320] : [class_Rings_Oordered__semiring(_338312), c_Orderings_Oord__class_Oless__eq(_338312, _338314, _338316), c_Orderings_Oord__class_Oless__eq(_338312, _338318, _338320), c_Orderings_Oord__class_Oless__eq(_338312, c_Groups_Ozero__class_Ozero(_338312), _338316), c_Orderings_Oord__class_Oless__eq(_338312, c_Groups_Ozero__class_Ozero(_338312), _338318), -(c_Orderings_Oord__class_Oless__eq(_338312, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_338312), _338314), _338318), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_338312), _338316), _338320)))], (5369 ^ _152310) ^ [_339006, _339008, _339010] : [class_Rings_Oordered__ring(_339006), -(c_Orderings_Oord__class_Oless__eq(_339006, c_Groups_Ozero__class_Ozero(_339006), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339006), _339008), _339010))), 5374 ^ _152310 : [(5375 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_339006, c_Groups_Ozero__class_Ozero(_339006), _339008), c_Orderings_Oord__class_Oless__eq(_339006, c_Groups_Ozero__class_Ozero(_339006), _339010)], (5381 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_339006, _339008, c_Groups_Ozero__class_Ozero(_339006)), c_Orderings_Oord__class_Oless__eq(_339006, _339010, c_Groups_Ozero__class_Ozero(_339006))]]], (5389 ^ _152310) ^ [_339635, _339637, _339639] : [class_Rings_Oordered__cancel__semiring(_339635), -(c_Orderings_Oord__class_Oless__eq(_339635, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339635), _339637), _339639), c_Groups_Ozero__class_Ozero(_339635))), 5394 ^ _152310 : [(5395 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_339635, c_Groups_Ozero__class_Ozero(_339635), _339637), c_Orderings_Oord__class_Oless__eq(_339635, _339639, c_Groups_Ozero__class_Ozero(_339635))], (5401 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_339635, _339637, c_Groups_Ozero__class_Ozero(_339635)), c_Orderings_Oord__class_Oless__eq(_339635, c_Groups_Ozero__class_Ozero(_339635), _339639)]]], (5409 ^ _152310) ^ [_340250, _340252] : [class_Rings_Olinordered__ring(_340250), c_Orderings_Oord__class_Oless(_340250, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_340250), _340252), _340252), c_Groups_Ozero__class_Ozero(_340250))], (5415 ^ _152310) ^ [_340509, _340511, _340513, _340515] : [class_Rings_Olinordered__ring__strict(_340509), 5418 ^ _152310 : [(5419 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_340509, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_340509), _340511), _340513), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_340509), _340515), _340513)), 5424 ^ _152310 : [(5425 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(_340509, c_Groups_Ozero__class_Ozero(_340509), _340513))], (5427 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(_340509, _340511, _340515))]], 5428 ^ _152310 : [(5429 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(_340509, _340513, c_Groups_Ozero__class_Ozero(_340509)))], (5431 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(_340509, _340515, _340511))]]], (5433 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(_340509, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_340509), _340511), _340513), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_340509), _340515), _340513))), 5434 ^ _152310 : [(5435 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_340509, c_Groups_Ozero__class_Ozero(_340509), _340513), c_Orderings_Oord__class_Oless(_340509, _340511, _340515)], (5441 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_340509, _340513, c_Groups_Ozero__class_Ozero(_340509)), c_Orderings_Oord__class_Oless(_340509, _340515, _340511)]]]]], (5449 ^ _152310) ^ [_341612, _341614, _341616, _341618] : [class_Rings_Olinordered__ring__strict(_341612), 5452 ^ _152310 : [(5453 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_341612, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_341612), _341614), _341616), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_341612), _341614), _341618)), 5458 ^ _152310 : [(5459 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(_341612, c_Groups_Ozero__class_Ozero(_341612), _341614))], (5461 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(_341612, _341616, _341618))]], 5462 ^ _152310 : [(5463 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(_341612, _341614, c_Groups_Ozero__class_Ozero(_341612)))], (5465 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(_341612, _341618, _341616))]]], (5467 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(_341612, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_341612), _341614), _341616), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_341612), _341614), _341618))), 5468 ^ _152310 : [(5469 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_341612, c_Groups_Ozero__class_Ozero(_341612), _341614), c_Orderings_Oord__class_Oless(_341612, _341616, _341618)], (5475 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_341612, _341614, c_Groups_Ozero__class_Ozero(_341612)), c_Orderings_Oord__class_Oless(_341612, _341618, _341616)]]]]], (5483 ^ _152310) ^ [_342715, _342717, _342719, _342721] : [class_Rings_Olinordered__ring__strict(_342715), c_Orderings_Oord__class_Oless(_342715, c_Groups_Ozero__class_Ozero(_342715), _342717), 5490 ^ _152310 : [(5491 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_342715, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_342715), _342717), _342719), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_342715), _342717), _342721)), -(c_Orderings_Oord__class_Oless(_342715, _342719, _342721))], (5497 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_342715, _342719, _342721), -(c_Orderings_Oord__class_Oless(_342715, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_342715), _342717), _342719), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_342715), _342717), _342721)))]]], (5503 ^ _152310) ^ [_343376, _343378, _343380] : [class_Rings_Olinordered__semiring__strict(_343376), c_Orderings_Oord__class_Oless(_343376, c_Groups_Ozero__class_Ozero(_343376), _343378), c_Orderings_Oord__class_Oless(_343376, c_Groups_Ozero__class_Ozero(_343376), _343380), -(c_Orderings_Oord__class_Oless(_343376, c_Groups_Ozero__class_Ozero(_343376), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_343376), _343378), _343380)))], (5517 ^ _152310) ^ [_343824, _343826, _343828] : [class_Rings_Olinordered__semiring__strict(_343824), c_Orderings_Oord__class_Oless(_343824, c_Groups_Ozero__class_Ozero(_343824), _343826), c_Orderings_Oord__class_Oless(_343824, _343828, c_Groups_Ozero__class_Ozero(_343824)), -(c_Orderings_Oord__class_Oless(_343824, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_343824), _343826), _343828), c_Groups_Ozero__class_Ozero(_343824)))], (5531 ^ _152310) ^ [_344272, _344274, _344276] : [class_Rings_Olinordered__semiring__strict(_344272), c_Orderings_Oord__class_Oless(_344272, c_Groups_Ozero__class_Ozero(_344272), _344274), c_Orderings_Oord__class_Oless(_344272, _344276, c_Groups_Ozero__class_Ozero(_344272)), -(c_Orderings_Oord__class_Oless(_344272, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_344272), _344276), _344274), c_Groups_Ozero__class_Ozero(_344272)))], (5545 ^ _152310) ^ [_344720, _344722, _344724] : [class_Rings_Olinordered__semiring__strict(_344720), c_Orderings_Oord__class_Oless(_344720, c_Groups_Ozero__class_Ozero(_344720), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_344720), _344722), _344724)), c_Orderings_Oord__class_Oless(_344720, c_Groups_Ozero__class_Ozero(_344720), _344722), -(c_Orderings_Oord__class_Oless(_344720, c_Groups_Ozero__class_Ozero(_344720), _344724))], (5559 ^ _152310) ^ [_345168, _345170, _345172] : [class_Rings_Olinordered__semiring__strict(_345168), c_Orderings_Oord__class_Oless(_345168, c_Groups_Ozero__class_Ozero(_345168), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_345168), _345170), _345172)), c_Orderings_Oord__class_Oless(_345168, c_Groups_Ozero__class_Ozero(_345168), _345172), -(c_Orderings_Oord__class_Oless(_345168, c_Groups_Ozero__class_Ozero(_345168), _345170))], (5573 ^ _152310) ^ [_345630, _345632, _345634, _345636] : [class_Rings_Olinordered__ring__strict(_345630), c_Orderings_Oord__class_Oless(_345630, _345632, c_Groups_Ozero__class_Ozero(_345630)), 5580 ^ _152310 : [(5581 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_345630, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_345630), _345632), _345634), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_345630), _345632), _345636)), -(c_Orderings_Oord__class_Oless(_345630, _345636, _345634))], (5587 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_345630, _345636, _345634), -(c_Orderings_Oord__class_Oless(_345630, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_345630), _345632), _345634), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_345630), _345632), _345636)))]]], (5593 ^ _152310) ^ [_346291, _346293, _346295] : [class_Rings_Olinordered__semiring__strict(_346291), c_Orderings_Oord__class_Oless(_346291, _346293, c_Groups_Ozero__class_Ozero(_346291)), c_Orderings_Oord__class_Oless(_346291, c_Groups_Ozero__class_Ozero(_346291), _346295), -(c_Orderings_Oord__class_Oless(_346291, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_346291), _346293), _346295), c_Groups_Ozero__class_Ozero(_346291)))], (5607 ^ _152310) ^ [_346739, _346741, _346743] : [class_Rings_Olinordered__ring__strict(_346739), c_Orderings_Oord__class_Oless(_346739, _346741, c_Groups_Ozero__class_Ozero(_346739)), c_Orderings_Oord__class_Oless(_346739, _346743, c_Groups_Ozero__class_Ozero(_346739)), -(c_Orderings_Oord__class_Oless(_346739, c_Groups_Ozero__class_Ozero(_346739), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_346739), _346741), _346743)))], (5621 ^ _152310) ^ [_347201, _347203, _347205, _347207] : [class_Rings_Olinordered__semiring__strict(_347201), c_Orderings_Oord__class_Oless(_347201, _347203, _347205), c_Orderings_Oord__class_Oless(_347201, c_Groups_Ozero__class_Ozero(_347201), _347207), -(c_Orderings_Oord__class_Oless(_347201, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_347201), _347203), _347207), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_347201), _347205), _347207)))], (5635 ^ _152310) ^ [_347685, _347687, _347689, _347691] : [class_Rings_Olinordered__semiring__strict(_347685), c_Orderings_Oord__class_Oless(_347685, _347687, _347689), c_Orderings_Oord__class_Oless(_347685, c_Groups_Ozero__class_Ozero(_347685), _347691), -(c_Orderings_Oord__class_Oless(_347685, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_347685), _347691), _347687), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_347685), _347691), _347689)))], (5649 ^ _152310) ^ [_348169, _348171, _348173, _348175] : [class_Rings_Olinordered__comm__semiring__strict(_348169), c_Orderings_Oord__class_Oless(_348169, _348171, _348173), c_Orderings_Oord__class_Oless(_348169, c_Groups_Ozero__class_Ozero(_348169), _348175), -(c_Orderings_Oord__class_Oless(_348169, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_348169), _348175), _348171), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_348169), _348175), _348173)))], (5663 ^ _152310) ^ [_348653, _348655, _348657, _348659] : [class_Rings_Olinordered__ring__strict(_348653), c_Orderings_Oord__class_Oless(_348653, _348655, _348657), c_Orderings_Oord__class_Oless(_348653, _348659, c_Groups_Ozero__class_Ozero(_348653)), -(c_Orderings_Oord__class_Oless(_348653, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_348653), _348657), _348659), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_348653), _348655), _348659)))], (5677 ^ _152310) ^ [_349137, _349139, _349141, _349143] : [class_Rings_Olinordered__ring__strict(_349137), c_Orderings_Oord__class_Oless(_349137, _349139, _349141), c_Orderings_Oord__class_Oless(_349137, _349143, c_Groups_Ozero__class_Ozero(_349137)), -(c_Orderings_Oord__class_Oless(_349137, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_349137), _349143), _349141), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_349137), _349143), _349139)))], (5691 ^ _152310) ^ [_349621, _349623, _349625, _349627] : [class_Rings_Olinordered__semidom(_349621), c_Orderings_Oord__class_Oless(_349621, c_Groups_Ozero__class_Ozero(_349621), _349623), c_Orderings_Oord__class_Oless(_349621, _349625, _349627), -(c_Orderings_Oord__class_Oless(_349621, _349625, c_Groups_Oplus__class_Oplus(_349621, _349623, _349627)))], (5705 ^ _152310) ^ [_350067, _350069, _350071] : [class_Rings_Olinordered__ring__strict(_350067), 5708 ^ _152310 : [(5709 ^ _152310) ^ [] : [c_Groups_Oplus__class_Oplus(_350067, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_350067), _350069), _350069), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_350067), _350071), _350071)) = c_Groups_Ozero__class_Ozero(_350067), 5712 ^ _152310 : [(5713 ^ _152310) ^ [] : [-(_350069 = c_Groups_Ozero__class_Ozero(_350067))], (5715 ^ _152310) ^ [] : [-(_350071 = c_Groups_Ozero__class_Ozero(_350067))]]], (5717 ^ _152310) ^ [] : [-(c_Groups_Oplus__class_Oplus(_350067, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_350067), _350069), _350069), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_350067), _350071), _350071)) = c_Groups_Ozero__class_Ozero(_350067)), _350069 = c_Groups_Ozero__class_Ozero(_350067), _350071 = c_Groups_Ozero__class_Ozero(_350067)]]], (5727 ^ _152310) ^ [_350811, _350813, _350815, _350817] : [class_Rings_Olinordered__ring__strict(_350811), c_Orderings_Oord__class_Oless(_350811, c_Groups_Ozero__class_Ozero(_350811), _350813), 5734 ^ _152310 : [(5735 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_350811, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_350811), _350813), _350815), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_350811), _350813), _350817)), -(c_Orderings_Oord__class_Oless__eq(_350811, _350815, _350817))], (5741 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_350811, _350815, _350817), -(c_Orderings_Oord__class_Oless__eq(_350811, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_350811), _350813), _350815), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_350811), _350813), _350817)))]]], (5747 ^ _152310) ^ [_351486, _351488, _351490, _351492] : [class_Rings_Olinordered__ring__strict(_351486), c_Orderings_Oord__class_Oless(_351486, _351488, c_Groups_Ozero__class_Ozero(_351486)), 5754 ^ _152310 : [(5755 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_351486, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_351486), _351488), _351490), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_351486), _351488), _351492)), -(c_Orderings_Oord__class_Oless__eq(_351486, _351492, _351490))], (5761 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_351486, _351492, _351490), -(c_Orderings_Oord__class_Oless__eq(_351486, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_351486), _351488), _351490), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_351486), _351488), _351492)))]]], (5767 ^ _152310) ^ [_352175, _352177, _352179, _352181, _352183] : [class_Rings_Olinordered__semiring__strict(_352175), c_Orderings_Oord__class_Oless(_352175, _352177, _352179), c_Orderings_Oord__class_Oless(_352175, _352181, _352183), c_Orderings_Oord__class_Oless(_352175, c_Groups_Ozero__class_Ozero(_352175), _352179), c_Orderings_Oord__class_Oless__eq(_352175, c_Groups_Ozero__class_Ozero(_352175), _352181), -(c_Orderings_Oord__class_Oless(_352175, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_352175), _352177), _352181), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_352175), _352179), _352183)))], (5789 ^ _152310) ^ [_352897, _352899, _352901, _352903, _352905] : [class_Rings_Olinordered__semiring__strict(_352897), c_Orderings_Oord__class_Oless(_352897, _352899, _352901), c_Orderings_Oord__class_Oless(_352897, _352903, _352905), c_Orderings_Oord__class_Oless__eq(_352897, c_Groups_Ozero__class_Ozero(_352897), _352899), c_Orderings_Oord__class_Oless__eq(_352897, c_Groups_Ozero__class_Ozero(_352897), _352903), -(c_Orderings_Oord__class_Oless(_352897, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_352897), _352899), _352903), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_352897), _352901), _352905)))], (5811 ^ _152310) ^ [_353619, _353621, _353623, _353625, _353627] : [class_Rings_Olinordered__semiring__strict(_353619), c_Orderings_Oord__class_Oless(_353619, _353621, _353623), c_Orderings_Oord__class_Oless__eq(_353619, _353625, _353627), c_Orderings_Oord__class_Oless__eq(_353619, c_Groups_Ozero__class_Ozero(_353619), _353621), c_Orderings_Oord__class_Oless(_353619, c_Groups_Ozero__class_Ozero(_353619), _353625), -(c_Orderings_Oord__class_Oless(_353619, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_353619), _353621), _353625), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_353619), _353623), _353627)))], (5833 ^ _152310) ^ [_354341, _354343, _354345, _354347, _354349] : [class_Rings_Olinordered__semiring__strict(_354341), c_Orderings_Oord__class_Oless__eq(_354341, _354343, _354345), c_Orderings_Oord__class_Oless(_354341, _354347, _354349), c_Orderings_Oord__class_Oless(_354341, c_Groups_Ozero__class_Ozero(_354341), _354343), c_Orderings_Oord__class_Oless__eq(_354341, c_Groups_Ozero__class_Ozero(_354341), _354347), -(c_Orderings_Oord__class_Oless(_354341, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_354341), _354343), _354347), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_354341), _354345), _354349)))], (5855 ^ _152310) ^ [_355049, _355051, _355053, _355055] : [class_Rings_Olinordered__semiring(_355049), c_Orderings_Oord__class_Oless(_355049, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_355049), _355051), _355053), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_355049), _355055), _355053)), c_Orderings_Oord__class_Oless__eq(_355049, c_Groups_Ozero__class_Ozero(_355049), _355053), -(c_Orderings_Oord__class_Oless(_355049, _355051, _355055))], (5869 ^ _152310) ^ [_355533, _355535, _355537, _355539] : [class_Rings_Olinordered__semiring__strict(_355533), c_Orderings_Oord__class_Oless(_355533, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_355533), _355535), _355537), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_355533), _355539), _355537)), c_Orderings_Oord__class_Oless__eq(_355533, c_Groups_Ozero__class_Ozero(_355533), _355537), -(c_Orderings_Oord__class_Oless(_355533, _355535, _355539))], (5883 ^ _152310) ^ [_356003, _356005, _356007] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _356003), 5886 ^ _152310 : [(5887 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _356003), _356005), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _356003), _356007)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _356005, _356007))], (5893 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _356005, _356007), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _356003), _356005), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _356003), _356007)))]]], (5899 ^ _152310) ^ [_356537, _356539, _356541] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _356537), 5902 ^ _152310 : [(5903 ^ _152310) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _356537), _356539) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _356537), _356541), -(_356539 = _356541)], (5909 ^ _152310) ^ [] : [_356539 = _356541, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _356537), _356539) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _356537), _356541))]]], (5915 ^ _152310) ^ [_357065, _357067, _357069] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _357065), 5918 ^ _152310 : [(5919 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _357065), _357067), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _357065), _357069)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _357067, _357069))], (5925 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _357067, _357069), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _357065), _357067), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _357065), _357069)))]]], (5931 ^ _152310) ^ [_357571] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _357571, c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_357571 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_357571 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (5941 ^ _152310) ^ [_357863, _357865] : [class_Rings_Olinordered__idom(_357863), 5944 ^ _152310 : [(5945 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_357863, c_Groups_Oplus__class_Oplus(_357863, _357865, _357865), c_Groups_Ozero__class_Ozero(_357863)), -(c_Orderings_Oord__class_Oless(_357863, _357865, c_Groups_Ozero__class_Ozero(_357863)))], (5951 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_357863, _357865, c_Groups_Ozero__class_Ozero(_357863)), -(c_Orderings_Oord__class_Oless(_357863, c_Groups_Oplus__class_Oplus(_357863, _357865, _357865), c_Groups_Ozero__class_Ozero(_357863)))]]], (5957 ^ _152310) ^ [_358351, _358353] : [class_Groups_Olinordered__ab__group__add(_358351), 5960 ^ _152310 : [(5961 ^ _152310) ^ [] : [c_Groups_Oplus__class_Oplus(_358351, _358353, _358353) = c_Groups_Ozero__class_Ozero(_358351), -(_358353 = c_Groups_Ozero__class_Ozero(_358351))], (5967 ^ _152310) ^ [] : [_358353 = c_Groups_Ozero__class_Ozero(_358351), -(c_Groups_Oplus__class_Oplus(_358351, _358353, _358353) = c_Groups_Ozero__class_Ozero(_358351))]]], (5983 ^ _152310) ^ [_359162, _359164, _359166] : [5984 ^ _152310 : [(5985 ^ _152310) ^ [] : [_359162 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5987 ^ _152310) ^ [] : [_359164 = _359166]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _359162), _359164) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _359162), _359166))], (5973 ^ _152310) ^ [_358876, _358878, _358880] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _358876), _358878) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _358876), _358880), -(_358876 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_358878 = _358880)], (5991 ^ _152310) ^ [_359493, _359495, _359497, _359499] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _359493), _359495), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _359497), _359495), _359499)) = 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, _359493, _359497)), _359495), _359499))], (5993 ^ _152310) ^ [_359654, _359656, _359658] : [class_Rings_Oidom(_359654), 5996 ^ _152310 : [(6007 ^ _152310) ^ [] : [6008 ^ _152310 : [(6009 ^ _152310) ^ [] : [_359656 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_359654))], (6011 ^ _152310) ^ [] : [-(c_Polynomial_Oorder(_359654, _359658, _359656) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], -(hAPP(c_Polynomial_Opoly(_359654, _359656), _359658) = c_Groups_Ozero__class_Ozero(_359654))], (5997 ^ _152310) ^ [] : [hAPP(c_Polynomial_Opoly(_359654, _359656), _359658) = c_Groups_Ozero__class_Ozero(_359654), -(_359656 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_359654))), c_Polynomial_Oorder(_359654, _359658, _359656) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (6015 ^ _152310) ^ [_360384, _360386, _360388, _360390, _360392] : [class_Fields_Ofield(_360384), 6018 ^ _152310 : [(6041 ^ _152310) ^ [] : [-(c_Polynomial_Opdivmod__rel(_360384, _360386, _360388, _360390, _360392)), _360386 = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_360384), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_360384)), _360390), _360388), _360392), 6048 ^ _152310 : [(6049 ^ _152310) ^ [] : [-(_360388 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_360384)))], (6051 ^ _152310) ^ [] : [_360390 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_360384))]], 6052 ^ _152310 : [(6053 ^ _152310) ^ [] : [_360388 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_360384))], (6055 ^ _152310) ^ [] : [_360392 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_360384))], (6057 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_360384, _360392), c_Polynomial_Odegree(_360384, _360388))]]], (6019 ^ _152310) ^ [] : [c_Polynomial_Opdivmod__rel(_360384, _360386, _360388, _360390, _360392), 6022 ^ _152310 : [(6023 ^ _152310) ^ [] : [-(_360386 = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_360384), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_360384)), _360390), _360388), _360392))], (6025 ^ _152310) ^ [] : [_360388 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_360384)), -(_360390 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_360384)))], (6031 ^ _152310) ^ [] : [-(_360388 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_360384))), -(_360392 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_360384))), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_360384, _360392), c_Polynomial_Odegree(_360384, _360388)))]]]]], (6061 ^ _152310) ^ [_361910, _361912, _361914] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _361910), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _361912, _361914), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _361910), _361912), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _361910), _361914)))], (6071 ^ _152310) ^ [_362249, _362251] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _362249), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _362251), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _362249), _362251)))], (6081 ^ _152310) ^ [_362636, _362638, _362640, _362642, _362644, _362646, _362648] : [class_Fields_Ofield(_362636), c_Polynomial_Opdivmod__rel(_362636, _362638, _362640, _362642, _362644), c_Polynomial_Opdivmod__rel(_362636, _362638, _362640, _362646, _362648), 6092 ^ _152310 : [(6093 ^ _152310) ^ [] : [-(_362642 = _362646)], (6095 ^ _152310) ^ [] : [-(_362644 = _362648)]]], (6097 ^ _152310) ^ [_363259, _363261, _363263, _363265, _363267, _363269, _363271] : [class_Fields_Ofield(_363259), c_Polynomial_Opdivmod__rel(_363259, _363261, _363263, _363265, _363267), c_Polynomial_Opdivmod__rel(_363259, _363261, _363263, _363269, _363271), -(_363267 = _363271)], (6111 ^ _152310) ^ [_363797, _363799, _363801, _363803, _363805, _363807, _363809] : [class_Fields_Ofield(_363797), c_Polynomial_Opdivmod__rel(_363797, _363799, _363801, _363803, _363805), c_Polynomial_Opdivmod__rel(_363797, _363799, _363801, _363807, _363809), -(_363803 = _363807)], (6125 ^ _152310) ^ [_364250, _364252] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _364250), _364252) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _364252), _364250))], (6127 ^ _152310) ^ [_364370, _364372, _364374] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _364370), _364372)), _364374) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _364370), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _364372), _364374)))], (6129 ^ _152310) ^ [_364504, _364506, _364508] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _364504, _364506)), _364508) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _364504), _364508), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _364506), _364508)))], (6131 ^ _152310) ^ [_364641, _364643] : [class_Fields_Ofield(_364641), -(c_Polynomial_Opdivmod__rel(_364641, _364643, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_364641)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_364641)), _364643))], (6137 ^ _152310) ^ [_364871, _364873] : [class_Fields_Ofield(_364871), -(c_Polynomial_Opdivmod__rel(_364871, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_364871)), _364873, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_364871)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_364871))))], (6143 ^ _152310) ^ [_365137, _365139, _365141, _365143] : [class_Fields_Ofield(_365137), 6146 ^ _152310 : [(6147 ^ _152310) ^ [] : [c_Polynomial_Opdivmod__rel(_365137, _365139, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_365137)), _365141, _365143), 6150 ^ _152310 : [(6151 ^ _152310) ^ [] : [-(_365141 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_365137)))], (6153 ^ _152310) ^ [] : [-(_365143 = _365139)]]], (6155 ^ _152310) ^ [] : [-(c_Polynomial_Opdivmod__rel(_365137, _365139, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_365137)), _365141, _365143)), _365141 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_365137)), _365143 = _365139]]], (6165 ^ _152310) ^ [_365858, _365860, _365862, _365864] : [class_Fields_Ofield(_365858), 6168 ^ _152310 : [(6169 ^ _152310) ^ [] : [c_Polynomial_Opdivmod__rel(_365858, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_365858)), _365860, _365862, _365864), 6172 ^ _152310 : [(6173 ^ _152310) ^ [] : [-(_365862 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_365858)))], (6175 ^ _152310) ^ [] : [-(_365864 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_365858)))]]], (6177 ^ _152310) ^ [] : [-(c_Polynomial_Opdivmod__rel(_365858, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_365858)), _365860, _365862, _365864)), _365862 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_365858)), _365864 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_365858))]]], (6187 ^ _152310) ^ [_366619, _366621, _366623, _366625, _366627, _366629] : [class_Fields_Ofield(_366619), c_Polynomial_Opdivmod__rel(_366619, _366621, _366623, _366625, _366627), -(c_Polynomial_Opdivmod__rel(_366619, c_Polynomial_Osmult(_366619, _366629, _366621), _366623, c_Polynomial_Osmult(_366619, _366629, _366625), c_Polynomial_Osmult(_366619, _366629, _366627)))], (6197 ^ _152310) ^ [_367076, _367078, _367080, _367082, _367084, _367086, _367088, _367090] : [class_Fields_Ofield(_367076), c_Polynomial_Opdivmod__rel(_367076, _367078, _367080, _367082, _367084), c_Polynomial_Opdivmod__rel(_367076, _367082, _367086, _367088, _367090), -(c_Polynomial_Opdivmod__rel(_367076, _367078, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_367076)), _367080), _367086), _367088, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_367076), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_367076)), _367080), _367090), _367084)))], (6211 ^ _152310) ^ [_367630, _367632, _367634] : [-(_367630 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 6214 ^ _152310 : [(6215 ^ _152310) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _367632), _367630) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _367634), _367630), -(_367632 = _367634)], (6221 ^ _152310) ^ [] : [_367632 = _367634, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _367632), _367630) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _367634), _367630))]]], (6227 ^ _152310) ^ [_368159, _368161, _368163] : [-(_368159 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 6230 ^ _152310 : [(6231 ^ _152310) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _368159), _368161) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _368159), _368163), -(_368161 = _368163)], (6237 ^ _152310) ^ [] : [_368161 = _368163, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _368159), _368161) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _368159), _368163))]]], (6243 ^ _152310) ^ [_368703, _368705] : [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _368703), _368703), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _368705), _368705)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 6246 ^ _152310 : [(6247 ^ _152310) ^ [] : [-(_368703 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (6249 ^ _152310) ^ [] : [-(_368705 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (6251 ^ _152310) ^ [_368972, _368974] : [-(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _368972), _368972), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _368974), _368974)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _368972 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _368974 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)], (6261 ^ _152310) ^ [_369334, _369336] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _369334, _369336), 6264 ^ _152310 : [(6265 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _369334, _369336))], (6267 ^ _152310) ^ [] : [_369334 = _369336]]], (6269 ^ _152310) ^ [_369576, _369578] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _369576, _369578)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _369576, _369578), -(_369576 = _369578)], (6289 ^ _152310) ^ [_370169, _370171] : [6290 ^ _152310 : [(6291 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _370169, _370171)], (6293 ^ _152310) ^ [] : [_370169 = _370171]], -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _370169, _370171))], (6279 ^ _152310) ^ [_369913, _369915] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _369913, _369915), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _369913, _369915)), -(_369913 = _369915)], (6297 ^ _152310) ^ [_370473, _370475, _370477] : [class_Rings_Oidom(_370473), -(_370475 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_370473))), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Oorder(_370473, _370477, _370475), c_Polynomial_Odegree(_370473, _370475)))], (6307 ^ _152310) ^ [_370821, _370823, _370825] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _370821), 6310 ^ _152310 : [(6311 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _370823), _370821), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _370825), _370821)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _370823, _370825))], (6317 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _370823, _370825), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _370823), _370821), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _370825), _370821)))]]], (6323 ^ _152310) ^ [_371355, _371357, _371359] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _371355), 6326 ^ _152310 : [(6327 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _371357), _371355), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _371359), _371355)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _371357, _371359))], (6333 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _371357, _371359), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _371357), _371355), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _371359), _371355)))]]], (6339 ^ _152310) ^ [_371889, _371891, _371893] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _371889), 6342 ^ _152310 : [(6343 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _371889), _371891), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _371889), _371893)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _371891, _371893))], (6349 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _371891, _371893), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _371889), _371891), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _371889), _371893)))]]], (6355 ^ _152310) ^ [_372424] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _372424), _372424))), -(_372424 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (6361 ^ _152310) ^ [_372597] : [_372597 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _372597), _372597))], (6367 ^ _152310) ^ [_372846, _372848, _372850, _372852] : [class_RealVector_Oreal__normed__algebra(_372846), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_372846), c_Groups_Oplus__class_Oplus(_372846, _372848, _372850)), _372852) = c_Groups_Oplus__class_Oplus(_372846, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_372846), _372848), _372852), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_372846), _372850), _372852)))], (6373 ^ _152310) ^ [_373158, _373160, _373162, _373164] : [class_RealVector_Oreal__normed__algebra(_373158), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_373158), c_Groups_Oplus__class_Oplus(_373158, _373160, _373162)), _373164) = c_Groups_Oplus__class_Oplus(_373158, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_373158), _373160), _373164), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_373158), _373162), _373164)))], (6379 ^ _152310) ^ [_373470, _373472, _373474, _373476] : [class_RealVector_Oreal__normed__algebra(_373470), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_373470), _373472), c_Groups_Oplus__class_Oplus(_373470, _373474, _373476)) = c_Groups_Oplus__class_Oplus(_373470, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_373470), _373472), _373474), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_373470), _373472), _373476)))], (6385 ^ _152310) ^ [_373768, _373770, _373772] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _373768, _373770), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _373772, _373768), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _373772, _373770)))], (6391 ^ _152310) ^ [_374004, _374006] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _374004, _374006), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _374006, _374004), -(_374004 = _374006)], (6401 ^ _152310) ^ [_374321, _374323, _374325] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _374321, _374323), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _374323, _374325), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _374321, _374325))], (6411 ^ _152310) ^ [_374636, _374638] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _374636, _374638)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _374638, _374636))], (6417 ^ _152310) ^ [_374822] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _374822, _374822))], (6419 ^ _152310) ^ [_374930, _374932] : [class_RealVector_Oreal__normed__algebra(_374930), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_374930), _374932), c_Groups_Ozero__class_Ozero(_374930)) = c_Groups_Ozero__class_Ozero(_374930))], (6425 ^ _152310) ^ [_375162, _375164] : [class_RealVector_Oreal__normed__algebra(_375162), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_375162), _375164), c_Groups_Ozero__class_Ozero(_375162)) = c_Groups_Ozero__class_Ozero(_375162))], (6431 ^ _152310) ^ [_375394, _375396] : [class_RealVector_Oreal__normed__algebra(_375394), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_375394), c_Groups_Ozero__class_Ozero(_375394)), _375396) = c_Groups_Ozero__class_Ozero(_375394))], (6437 ^ _152310) ^ [_375626, _375628] : [class_RealVector_Oreal__normed__algebra(_375626), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_375626), c_Groups_Ozero__class_Ozero(_375626)), _375628) = c_Groups_Ozero__class_Ozero(_375626))], (6443 ^ _152310) ^ [_375886, _375888, _375890, _375892] : [class_RealVector_Oreal__normed__algebra(_375886), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_375886), _375888), c_Groups_Oplus__class_Oplus(_375886, _375890, _375892)) = c_Groups_Oplus__class_Oplus(_375886, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_375886), _375888), _375890), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_375886), _375888), _375892)))], (6449 ^ _152310) ^ [_376184, _376186, _376188] : [class_Groups_Ozero(_376184), 6455 ^ _152310 : [(6456 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _376186, 6454 ^ [_376184, _376186, _376188]))], (6458 ^ _152310) ^ [] : [hAPP(c_Polynomial_Ocoeff(_376184, _376188), 6454 ^ [_376184, _376186, _376188]) = c_Groups_Ozero__class_Ozero(_376184)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_376184, _376188), _376186))], (6462 ^ _152310) ^ [_376737, _376739, _376741, _376743, _376745, _376747] : [class_Groups_Ozero(_376737), hAPP(hAPP(hAPP(_376739, c_Groups_Ozero__class_Ozero(_376737)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_376737))), _376741) = _376741, -(c_Polynomial_Opoly__rec(_376743, _376737, _376741, _376739, c_Polynomial_OpCons(_376737, _376745, _376747)) = hAPP(hAPP(hAPP(_376739, _376745), _376747), c_Polynomial_Opoly__rec(_376743, _376737, _376741, _376739, _376747)))], (6472 ^ _152310) ^ [_377168, _377170, _377172] : [class_Groups_Ozero(_377168), -(c_Polynomial_OpCons(_377168, _377170, _377172) = c_Polynomial_OAbs__poly(_377168, c_Nat_Onat_Onat__case(_377168, _377170, c_Polynomial_Ocoeff(_377168, _377172))))], (6478 ^ _152310) ^ [_377424, _377426, _377428] : [class_Groups_Ozero(_377424), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _377426, c_Polynomial_Odegree(_377424, _377428)), 6486 ^ _152310 : [(6487 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _377426, 6485 ^ [_377424, _377426, _377428]))], (6489 ^ _152310) ^ [] : [hAPP(c_Polynomial_Ocoeff(_377424, _377428), 6485 ^ [_377424, _377426, _377428]) = c_Groups_Ozero__class_Ozero(_377424)]]], (6491 ^ _152310) ^ [_377924, _377926] : [class_Groups_Ozero(_377924), -(c_Polynomial_OAbs__poly(_377924, c_Polynomial_Ocoeff(_377924, _377926)) = _377926)], (6497 ^ _152310) ^ [_378172, _378174, _378176, _378178] : [class_Groups_Ozero(_378172), hAPP(hAPP(hAPP(_378174, c_Groups_Ozero__class_Ozero(_378172)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_378172))), _378176) = _378176, -(c_Polynomial_Opoly__rec(_378178, _378172, _378176, _378174, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_378172))) = _378176)], (6507 ^ _152310) ^ [_378595, _378597, _378599, _378601, _378603, _378605] : [class_Groups_Ozero(_378595), -(c_Polynomial_Opoly__rec(_378597, _378595, _378599, _378601, c_Polynomial_OpCons(_378595, _378603, _378605)) = hAPP(hAPP(hAPP(_378601, _378603), _378605), c_If(_378597, c_fequal(_378605, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_378595))), _378599, c_Polynomial_Opoly__rec(_378597, _378595, _378599, _378601, _378605))))], (6513 ^ _152310) ^ [_378957, _378959, _378961, _378963, _378965, _378967] : [class_Rings_Olinordered__semiring__1__strict(_378957), c_Orderings_Oord__class_Oless(_378957, _378959, _378961), c_Orderings_Oord__class_Oless(_378957, _378963, _378961), c_Orderings_Oord__class_Oless__eq(_378957, c_Groups_Ozero__class_Ozero(_378957), _378965), c_Orderings_Oord__class_Oless__eq(_378957, c_Groups_Ozero__class_Ozero(_378957), _378967), c_Groups_Oplus__class_Oplus(_378957, _378965, _378967) = c_Groups_Oone__class_Oone(_378957), -(c_Orderings_Oord__class_Oless(_378957, c_Groups_Oplus__class_Oplus(_378957, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_378957), _378965), _378959), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_378957), _378967), _378963)), _378961))], (6539 ^ _152310) ^ [_379798, _379800, _379802] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _379798), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _379800), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _379802), -(c_NthRoot_Oroot(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _379798), _379800), _379802) = c_NthRoot_Oroot(_379798, c_NthRoot_Oroot(_379800, _379802)))], (6553 ^ _152310) ^ [_380250, _380252, _380254] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _380250), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _380252), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _380254), -(c_NthRoot_Oroot(_380250, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _380252), _380254)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_NthRoot_Oroot(_380250, _380252)), c_NthRoot_Oroot(_380250, _380254)))], (6567 ^ _152310) ^ [_380700, _380702] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _380700), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _380702), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_NthRoot_Oroot(_380700, _380702)))], (6577 ^ _152310) ^ [_381011, _381013] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _381011), 6580 ^ _152310 : [(6581 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_NthRoot_Oroot(_381011, _381013)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _381013))], (6587 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _381013), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_NthRoot_Oroot(_381011, _381013)))]]], (6593 ^ _152310) ^ [_381488, _381490] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _381488), 6596 ^ _152310 : [(6597 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Oroot(_381488, _381490), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _381490, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (6603 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _381490, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Oroot(_381488, _381490), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))]]], (6609 ^ _152310) ^ [_381979, _381981, _381983] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _381979), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _381979, _381981), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _381983), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Oroot(_381981, _381983), c_NthRoot_Oroot(_381979, _381983)))], (6623 ^ _152310) ^ [_382401, _382403] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _382401), 6626 ^ _152310 : [(6627 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_NthRoot_Oroot(_382401, _382403)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _382403))], (6633 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _382403), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_NthRoot_Oroot(_382401, _382403)))]]], (6639 ^ _152310) ^ [_382878, _382880] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _382878), 6642 ^ _152310 : [(6643 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_382878, _382880), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _382880, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (6649 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _382880, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_382878, _382880), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))]]], (6655 ^ _152310) ^ [_383369, _383371, _383373] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _383369), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _383369, _383371), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _383373), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_383371, _383373), c_NthRoot_Oroot(_383369, _383373)))], (6669 ^ _152310) ^ [_383791, _383793] : [class_Groups_Omonoid__mult(_383791), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_383791), c_Groups_Oone__class_Oone(_383791)), _383793) = _383793)], (6675 ^ _152310) ^ [_384019, _384021] : [class_Rings_Ocomm__semiring__1(_384019), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_384019), c_Groups_Oone__class_Oone(_384019)), _384021) = _384021)], (6681 ^ _152310) ^ [_384247, _384249] : [class_Groups_Ocomm__monoid__mult(_384247), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_384247), c_Groups_Oone__class_Oone(_384247)), _384249) = _384249)], (6687 ^ _152310) ^ [_384475, _384477] : [class_Groups_Omonoid__mult(_384475), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_384475), _384477), c_Groups_Oone__class_Oone(_384475)) = _384477)], (6693 ^ _152310) ^ [_384703, _384705] : [class_Rings_Ocomm__semiring__1(_384703), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_384703), _384705), c_Groups_Oone__class_Oone(_384703)) = _384705)], (6699 ^ _152310) ^ [_384931, _384933] : [class_Groups_Ocomm__monoid__mult(_384931), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_384931), _384933), c_Groups_Oone__class_Oone(_384931)) = _384933)], (6705 ^ _152310) ^ [_385130] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _385130) = _385130)], (6707 ^ _152310) ^ [_385269, _385271] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _385269), _385271), 6710 ^ _152310 : [(6711 ^ _152310) ^ [] : [-(_385269 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (6713 ^ _152310) ^ [] : [-(_385271 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (6715 ^ _152310) ^ [_385518, _385520] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _385518), _385520)), _385518 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _385520 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (6725 ^ _152310) ^ [_385802] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _385802), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _385802)], (6727 ^ _152310) ^ [_385944, _385946] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _385944), _385946) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 6730 ^ _152310 : [(6731 ^ _152310) ^ [] : [-(_385944 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (6733 ^ _152310) ^ [] : [-(_385946 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (6735 ^ _152310) ^ [_386193, _386195] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _386193), _386195) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _386193 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _386195 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (6745 ^ _152310) ^ [] : [c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)], (6747 ^ _152310) ^ [_386529] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _386529) = _386529)], (6749 ^ _152310) ^ [_386625] : [class_Rings_Ozero__neq__one(_386625), c_Groups_Ozero__class_Ozero(_386625) = c_Groups_Oone__class_Oone(_386625)], (6755 ^ _152310) ^ [_386822] : [class_Rings_Ozero__neq__one(_386822), c_Groups_Oone__class_Oone(_386822) = c_Groups_Ozero__class_Ozero(_386822)], (6761 ^ _152310) ^ [_387019] : [class_Rings_Ocomm__semiring__1(_387019), -(c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_387019)) = c_Polynomial_OpCons(_387019, c_Groups_Oone__class_Oone(_387019), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_387019))))], (6767 ^ _152310) ^ [_387249, _387251] : [class_Groups_Oone(_387249), 6770 ^ _152310 : [(6771 ^ _152310) ^ [] : [c_Groups_Oone__class_Oone(_387249) = _387251, -(_387251 = c_Groups_Oone__class_Oone(_387249))], (6777 ^ _152310) ^ [] : [_387251 = c_Groups_Oone__class_Oone(_387249), -(c_Groups_Oone__class_Oone(_387249) = _387251)]]], (6783 ^ _152310) ^ [_387719, _387721] : [class_Rings_Ocomm__semiring__1(_387719), -(hAPP(c_Polynomial_Opoly(_387719, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_387719))), _387721) = c_Groups_Oone__class_Oone(_387719))], (6789 ^ _152310) ^ [_387951, _387953] : [class_Rings_Ocomm__semiring__1(_387951), -(c_Polynomial_Osmult(_387951, c_Groups_Oone__class_Oone(_387951), _387953) = _387953)], (6795 ^ _152310) ^ [_388142] : [-(c_NthRoot_Oroot(_388142, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (6797 ^ _152310) ^ [_388238] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _388238), -(c_NthRoot_Oroot(_388238, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (6803 ^ _152310) ^ [_388450, _388452] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _388450), 6806 ^ _152310 : [(6807 ^ _152310) ^ [] : [c_NthRoot_Oroot(_388450, _388452) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal), -(_388452 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (6813 ^ _152310) ^ [] : [_388452 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal), -(c_NthRoot_Oroot(_388450, _388452) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))]]], (6819 ^ _152310) ^ [_388921, _388923] : [class_Rings_Ocomm__semiring__1(_388921), 6822 ^ _152310 : [(6823 ^ _152310) ^ [] : [_388923 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Polynomial_Ocoeff(_388921, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_388921))), _388923) = c_Groups_Oone__class_Oone(_388921))], (6829 ^ _152310) ^ [] : [-(_388923 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_Polynomial_Ocoeff(_388921, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_388921))), _388923) = c_Groups_Ozero__class_Ozero(_388921))]]], (6835 ^ _152310) ^ [_389447, _389449, _389451] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _389447), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _389447, _389449), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _389451), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _389451, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Oroot(_389447, _389451), c_NthRoot_Oroot(_389449, _389451)))], (6853 ^ _152310) ^ [_389978, _389980, _389982] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _389978), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _389978, _389980), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _389982), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _389982, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_389978, _389982), c_NthRoot_Oroot(_389980, _389982)))], (6871 ^ _152310) ^ [_390466] : [-(c_NthRoot_Oroot(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _390466) = _390466)], (6873 ^ _152310) ^ [_390590, _390592, _390594] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _390590), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _390592), -(c_NthRoot_Oroot(_390590, c_NthRoot_Oroot(_390592, _390594)) = c_NthRoot_Oroot(_390592, c_NthRoot_Oroot(_390590, _390594)))], (6883 ^ _152310) ^ [_390941, _390943, _390945] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _390941), 6886 ^ _152310 : [(6887 ^ _152310) ^ [] : [c_NthRoot_Oroot(_390941, _390943) = c_NthRoot_Oroot(_390941, _390945), -(_390943 = _390945)], (6893 ^ _152310) ^ [] : [_390943 = _390945, -(c_NthRoot_Oroot(_390941, _390943) = c_NthRoot_Oroot(_390941, _390945))]]], (6899 ^ _152310) ^ [_391423] : [class_Rings_Olinordered__semidom(_391423), -(c_Orderings_Oord__class_Oless__eq(_391423, c_Groups_Ozero__class_Ozero(_391423), c_Groups_Oone__class_Oone(_391423)))], (6905 ^ _152310) ^ [_391621] : [class_Rings_Olinordered__semidom(_391621), c_Orderings_Oord__class_Oless__eq(_391621, c_Groups_Oone__class_Oone(_391621), c_Groups_Ozero__class_Ozero(_391621))], (6911 ^ _152310) ^ [_391820] : [class_Rings_Olinordered__semidom(_391820), -(c_Orderings_Oord__class_Oless(_391820, c_Groups_Ozero__class_Ozero(_391820), c_Groups_Oone__class_Oone(_391820)))], (6917 ^ _152310) ^ [_392018] : [class_Rings_Olinordered__semidom(_392018), c_Orderings_Oord__class_Oless(_392018, c_Groups_Oone__class_Oone(_392018), c_Groups_Ozero__class_Ozero(_392018))], (6923 ^ _152310) ^ [_392245, _392247, _392249] : [class_Rings_Olinordered__semidom(_392245), c_Orderings_Oord__class_Oless(_392245, c_Groups_Oone__class_Oone(_392245), _392247), c_Orderings_Oord__class_Oless(_392245, c_Groups_Oone__class_Oone(_392245), _392249), -(c_Orderings_Oord__class_Oless(_392245, c_Groups_Oone__class_Oone(_392245), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_392245), _392247), _392249)))], (6937 ^ _152310) ^ [_392679, _392681] : [class_Rings_Olinordered__semidom(_392679), -(c_Orderings_Oord__class_Oless(_392679, _392681, c_Groups_Oplus__class_Oplus(_392679, _392681, c_Groups_Oone__class_Oone(_392679))))], (6943 ^ _152310) ^ [_392915, _392917, _392919] : [class_Rings_Ocomm__semiring__1(_392915), -(c_Groups_Oplus__class_Oplus(_392915, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_392915), _392917), _392919), _392919) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_392915), c_Groups_Oplus__class_Oplus(_392915, _392917, c_Groups_Oone__class_Oone(_392915))), _392919))], (6949 ^ _152310) ^ [_393195, _393197, _393199] : [class_Rings_Ocomm__semiring__1(_393195), -(c_Groups_Oplus__class_Oplus(_393195, _393197, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_393195), _393199), _393197)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_393195), c_Groups_Oplus__class_Oplus(_393195, _393199, c_Groups_Oone__class_Oone(_393195))), _393197))], (6955 ^ _152310) ^ [_393461, _393463] : [class_Rings_Ocomm__semiring__1(_393461), -(c_Groups_Oplus__class_Oplus(_393461, _393463, _393463) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_393461), c_Groups_Oplus__class_Oplus(_393461, c_Groups_Oone__class_Oone(_393461), c_Groups_Oone__class_Oone(_393461))), _393463))], (6961 ^ _152310) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (6963 ^ _152310) ^ [_393733] : [-(c_Nat_OSuc(_393733) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _393733))], (6965 ^ _152310) ^ [_393817] : [-(c_Nat_OSuc(_393817) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _393817, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (6967 ^ _152310) ^ [_393930, _393932] : [_393930 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _393930), _393932), -(_393932 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_393930 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6977 ^ _152310) ^ [_394228] : [class_Rings_Ocomm__semiring__1(_394228), -(c_Polynomial_Odegree(_394228, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_394228))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6983 ^ _152310) ^ [_394458, _394460, _394462] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _394458), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _394460, _394462), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Oroot(_394458, _394460), c_NthRoot_Oroot(_394458, _394462)))], (6993 ^ _152310) ^ [_394799, _394801, _394803] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _394799), 6996 ^ _152310 : [(6997 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Oroot(_394799, _394801), c_NthRoot_Oroot(_394799, _394803)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _394801, _394803))], (7003 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _394801, _394803), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Oroot(_394799, _394801), c_NthRoot_Oroot(_394799, _394803)))]]], (7009 ^ _152310) ^ [_395301, _395303] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _395301), 7012 ^ _152310 : [(7013 ^ _152310) ^ [] : [c_NthRoot_Oroot(_395301, _395303) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_395303 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (7019 ^ _152310) ^ [] : [_395303 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(c_NthRoot_Oroot(_395301, _395303) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (7025 ^ _152310) ^ [_395786, _395788, _395790] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _395786), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _395788, _395790), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_395786, _395788), c_NthRoot_Oroot(_395786, _395790)))], (7035 ^ _152310) ^ [_396127, _396129, _396131] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _396127), 7038 ^ _152310 : [(7039 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_396127, _396129), c_NthRoot_Oroot(_396127, _396131)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _396129, _396131))], (7045 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _396129, _396131), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_396127, _396129), c_NthRoot_Oroot(_396127, _396131)))]]], (7051 ^ _152310) ^ [_396643, _396645, _396647] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _396643), -(c_NthRoot_Oroot(_396643, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _396645), _396647)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_NthRoot_Oroot(_396643, _396645)), c_NthRoot_Oroot(_396643, _396647)))], (7057 ^ _152310) ^ [_396917, _396919, _396921] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _396917), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _396919), -(c_NthRoot_Oroot(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _396917), _396919), _396921) = c_NthRoot_Oroot(_396917, c_NthRoot_Oroot(_396919, _396921)))], (7067 ^ _152310) ^ [_397274, _397276, _397278] : [class_Rings_Olinordered__idom(_397274), c_Orderings_Oord__class_Oless__eq(_397274, c_Groups_Ozero__class_Ozero(_397274), _397276), c_Orderings_Oord__class_Oless__eq(_397274, c_Groups_Ozero__class_Ozero(_397274), _397278), c_Orderings_Oord__class_Oless__eq(_397274, _397278, c_Groups_Oone__class_Oone(_397274)), -(c_Orderings_Oord__class_Oless__eq(_397274, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_397274), _397278), _397276), _397276))], (7085 ^ _152310) ^ [_397817, _397819, _397821] : [class_Rings_Olinordered__idom(_397817), c_Orderings_Oord__class_Oless__eq(_397817, c_Groups_Ozero__class_Ozero(_397817), _397819), c_Orderings_Oord__class_Oless__eq(_397817, c_Groups_Ozero__class_Ozero(_397817), _397821), c_Orderings_Oord__class_Oless__eq(_397817, _397821, c_Groups_Oone__class_Oone(_397817)), -(c_Orderings_Oord__class_Oless__eq(_397817, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_397817), _397819), _397821), _397819))], (7103 ^ _152310) ^ [_398332] : [class_Rings_Olinordered__semidom(_398332), -(c_Orderings_Oord__class_Oless(_398332, c_Groups_Ozero__class_Ozero(_398332), c_Groups_Oplus__class_Oplus(_398332, c_Groups_Oone__class_Oone(_398332), c_Groups_Oone__class_Oone(_398332))))], (7109 ^ _152310) ^ [_398556, _398558] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _398556), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _398558), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_NthRoot_Oroot(_398556, _398558)))], (7119 ^ _152310) ^ [_398867, _398869] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _398867), 7122 ^ _152310 : [(7123 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Oroot(_398867, _398869), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _398869, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (7129 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _398869, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_NthRoot_Oroot(_398867, _398869), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))]]], (7135 ^ _152310) ^ [_399344, _399346] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _399344), 7138 ^ _152310 : [(7139 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_NthRoot_Oroot(_399344, _399346)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _399346))], (7145 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _399346), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_NthRoot_Oroot(_399344, _399346)))]]], (7151 ^ _152310) ^ [_399821, _399823] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _399821), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _399823), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_NthRoot_Oroot(_399821, _399823)))], (7161 ^ _152310) ^ [_400132, _400134] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _400132), 7164 ^ _152310 : [(7165 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_400132, _400134), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _400134, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (7171 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _400134, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_400132, _400134), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))]]], (7177 ^ _152310) ^ [_400609, _400611] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _400609), 7180 ^ _152310 : [(7181 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_NthRoot_Oroot(_400609, _400611)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _400611))], (7187 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _400611), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_NthRoot_Oroot(_400609, _400611)))]]], (7193 ^ _152310) ^ [_401142, _401144, _401146, _401148, _401150, _401152] : [class_Rings_Olinordered__semiring__1(_401142), c_Orderings_Oord__class_Oless__eq(_401142, _401144, _401146), c_Orderings_Oord__class_Oless__eq(_401142, _401148, _401146), c_Orderings_Oord__class_Oless__eq(_401142, c_Groups_Ozero__class_Ozero(_401142), _401150), c_Orderings_Oord__class_Oless__eq(_401142, c_Groups_Ozero__class_Ozero(_401142), _401152), c_Groups_Oplus__class_Oplus(_401142, _401150, _401152) = c_Groups_Oone__class_Oone(_401142), -(c_Orderings_Oord__class_Oless__eq(_401142, c_Groups_Oplus__class_Oplus(_401142, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_401142), _401150), _401144), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_401142), _401152), _401148)), _401146))], (7219 ^ _152310) ^ [_401983, _401985, _401987] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _401983), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _401985), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _401985, _401987), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_NthRoot_Oroot(_401983, _401985), c_NthRoot_Oroot(_401983, _401987)))], (7233 ^ _152310) ^ [_402419, _402421, _402423] : [class_Rings_Ocomm__ring__1(_402419), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_402419), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_402419)), c_Polynomial_OpCons(_402419, c_Groups_Ouminus__class_Ouminus(_402419, _402421), c_Polynomial_OpCons(_402419, c_Groups_Oone__class_Oone(_402419), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_402419))))), c_Polynomial_Osynthetic__div(_402419, _402423, _402421)), c_Polynomial_OpCons(_402419, hAPP(c_Polynomial_Opoly(_402419, _402423), _402421), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_402419)))) = _402423)], (7239 ^ _152310) ^ [_402749, _402751, _402753] : [class_Fields_Ofield(_402749), 7242 ^ _152310 : [(7253 ^ _152310) ^ [] : [7254 ^ _152310 : [(7255 ^ _152310) ^ [] : [-(_402751 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_402749)))], (7257 ^ _152310) ^ [] : [-(_402753 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_402749)))]], -(hAPP(c_Polynomial_Ocoeff(_402749, c_Polynomial_Opoly__gcd(_402749, _402751, _402753)), c_Polynomial_Odegree(_402749, c_Polynomial_Opoly__gcd(_402749, _402751, _402753))) = c_Groups_Oone__class_Oone(_402749))], (7243 ^ _152310) ^ [] : [-(hAPP(c_Polynomial_Ocoeff(_402749, c_Polynomial_Opoly__gcd(_402749, _402751, _402753)), c_Polynomial_Odegree(_402749, c_Polynomial_Opoly__gcd(_402749, _402751, _402753))) = c_Groups_Ozero__class_Ozero(_402749)), _402751 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_402749)), _402753 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_402749))]]], (7261 ^ _152310) ^ [_403507, _403509] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _403507), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _403509), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_NthRoot_Oroot(_403507, _403509)), _403507) = _403509)], (7271 ^ _152310) ^ [_403842, _403844, _403846] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _403842), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _403844), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _403844), _403842) = _403846, -(c_NthRoot_Oroot(_403842, _403846) = _403844)], (7285 ^ _152310) ^ [_404266, _404268] : [class_Fields_Ofield(_404266), -(c_Polynomial_Opoly__gcd(_404266, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_404266)), _404268) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_404266)))], (7291 ^ _152310) ^ [_404498, _404500] : [class_Fields_Ofield(_404498), -(c_Polynomial_Opoly__gcd(_404498, _404500, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_404498))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_404498)))], (7297 ^ _152310) ^ [_404730, _404732] : [class_Rings_Ocomm__semiring__1(_404730), -(hAPP(hAPP(c_Power_Opower__class_Opower(_404730), _404732), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _404732)], (7303 ^ _152310) ^ [_404968, _404970, _404972] : [class_RealVector_Oreal__normed__algebra(_404968), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_404968), _404970), c_Groups_Ouminus__class_Ouminus(_404968, _404972)) = c_Groups_Ouminus__class_Ouminus(_404968, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_404968), _404970), _404972)))], (7309 ^ _152310) ^ [_405240, _405242, _405244] : [class_RealVector_Oreal__normed__algebra(_405240), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_405240), _405242), c_Groups_Ouminus__class_Ouminus(_405240, _405244)) = c_Groups_Ouminus__class_Ouminus(_405240, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_405240), _405242), _405244)))], (7315 ^ _152310) ^ [_405512, _405514, _405516] : [class_RealVector_Oreal__normed__algebra(_405512), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_405512), c_Groups_Ouminus__class_Ouminus(_405512, _405514)), _405516) = c_Groups_Ouminus__class_Ouminus(_405512, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_405512), _405514), _405516)))], (7321 ^ _152310) ^ [_405784, _405786, _405788] : [class_RealVector_Oreal__normed__algebra(_405784), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_405784), c_Groups_Ouminus__class_Ouminus(_405784, _405786)), _405788) = c_Groups_Ouminus__class_Ouminus(_405784, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_405784), _405786), _405788)))], (7327 ^ _152310) ^ [_406056, _406058, _406060] : [class_Groups_Oordered__ab__group__add(_406056), c_Orderings_Oord__class_Oless__eq(_406056, _406058, _406060), -(c_Orderings_Oord__class_Oless__eq(_406056, c_Groups_Ouminus__class_Ouminus(_406056, _406060), c_Groups_Ouminus__class_Ouminus(_406056, _406058)))], (7337 ^ _152310) ^ [_406393, _406395, _406397] : [class_Groups_Oordered__ab__group__add(_406393), 7340 ^ _152310 : [(7341 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_406393, c_Groups_Ouminus__class_Ouminus(_406393, _406395), c_Groups_Ouminus__class_Ouminus(_406393, _406397)), -(c_Orderings_Oord__class_Oless__eq(_406393, _406397, _406395))], (7347 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_406393, _406397, _406395), -(c_Orderings_Oord__class_Oless__eq(_406393, c_Groups_Ouminus__class_Ouminus(_406393, _406395), c_Groups_Ouminus__class_Ouminus(_406393, _406397)))]]], (7353 ^ _152310) ^ [_406905, _406907, _406909] : [class_Groups_Oordered__ab__group__add(_406905), 7356 ^ _152310 : [(7357 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_406905, c_Groups_Ouminus__class_Ouminus(_406905, _406907), _406909), -(c_Orderings_Oord__class_Oless__eq(_406905, c_Groups_Ouminus__class_Ouminus(_406905, _406909), _406907))], (7363 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_406905, c_Groups_Ouminus__class_Ouminus(_406905, _406909), _406907), -(c_Orderings_Oord__class_Oless__eq(_406905, c_Groups_Ouminus__class_Ouminus(_406905, _406907), _406909))]]], (7369 ^ _152310) ^ [_407417, _407419, _407421] : [class_Groups_Oordered__ab__group__add(_407417), 7372 ^ _152310 : [(7373 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_407417, _407419, c_Groups_Ouminus__class_Ouminus(_407417, _407421)), -(c_Orderings_Oord__class_Oless__eq(_407417, _407421, c_Groups_Ouminus__class_Ouminus(_407417, _407419)))], (7379 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_407417, _407421, c_Groups_Ouminus__class_Ouminus(_407417, _407419)), -(c_Orderings_Oord__class_Oless__eq(_407417, _407419, c_Groups_Ouminus__class_Ouminus(_407417, _407421)))]]], (7385 ^ _152310) ^ [_407929, _407931, _407933] : [class_Groups_Ogroup__add(_407929), -(c_Groups_Oplus__class_Oplus(_407929, c_Groups_Ouminus__class_Ouminus(_407929, _407931), c_Groups_Oplus__class_Oplus(_407929, _407931, _407933)) = _407933)], (7391 ^ _152310) ^ [_408179, _408181, _408183] : [class_Groups_Ogroup__add(_408179), -(c_Groups_Oplus__class_Oplus(_408179, _408181, c_Groups_Oplus__class_Oplus(_408179, c_Groups_Ouminus__class_Ouminus(_408179, _408181), _408183)) = _408183)], (7397 ^ _152310) ^ [_408429, _408431, _408433] : [class_Groups_Ogroup__add(_408429), -(c_Groups_Ouminus__class_Ouminus(_408429, c_Groups_Oplus__class_Oplus(_408429, _408431, _408433)) = c_Groups_Oplus__class_Oplus(_408429, c_Groups_Ouminus__class_Ouminus(_408429, _408433), c_Groups_Ouminus__class_Ouminus(_408429, _408431)))], (7403 ^ _152310) ^ [_408691, _408693, _408695] : [class_Groups_Oab__group__add(_408691), -(c_Groups_Ouminus__class_Ouminus(_408691, c_Groups_Oplus__class_Oplus(_408691, _408693, _408695)) = c_Groups_Oplus__class_Oplus(_408691, c_Groups_Ouminus__class_Ouminus(_408691, _408693), c_Groups_Ouminus__class_Ouminus(_408691, _408695)))], (7409 ^ _152310) ^ [_408925] : [class_Groups_Oab__group__add(_408925), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_408925), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_408925))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_408925)))], (7415 ^ _152310) ^ [_409153, _409155] : [class_Groups_Oab__group__add(_409153), -(c_Polynomial_Odegree(_409153, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_409153), _409155)) = c_Polynomial_Odegree(_409153, _409155))], (7421 ^ _152310) ^ [_409397, _409399, _409401] : [class_Rings_Ocomm__ring(_409397), -(c_Polynomial_Osmult(_409397, _409399, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_409397), _409401)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_409397), c_Polynomial_Osmult(_409397, _409399, _409401)))], (7427 ^ _152310) ^ [_409661, _409663, _409665] : [class_Groups_Oab__group__add(_409661), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_409661), c_Polynomial_OpCons(_409661, _409663, _409665)) = c_Polynomial_OpCons(_409661, c_Groups_Ouminus__class_Ouminus(_409661, _409663), c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_409661), _409665)))], (7433 ^ _152310) ^ [_409931, _409933, _409935] : [class_Groups_Oab__group__add(_409931), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_409931), c_Polynomial_OpCons(_409931, _409933, _409935)) = c_Polynomial_OpCons(_409931, c_Groups_Ouminus__class_Ouminus(_409931, _409933), c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_409931), _409935)))], (7439 ^ _152310) ^ [_410201, _410203, _410205] : [class_Groups_Oab__group__add(_410201), -(hAPP(c_Polynomial_Ocoeff(_410201, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_410201), _410203)), _410205) = c_Groups_Ouminus__class_Ouminus(_410201, hAPP(c_Polynomial_Ocoeff(_410201, _410203), _410205)))], (7445 ^ _152310) ^ [_410469, _410471, _410473] : [class_Rings_Ocomm__ring(_410469), -(c_Polynomial_Osmult(_410469, c_Groups_Ouminus__class_Ouminus(_410469, _410471), _410473) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_410469), c_Polynomial_Osmult(_410469, _410471, _410473)))], (7451 ^ _152310) ^ [_410729, _410731, _410733] : [class_Rings_Ocomm__ring(_410729), -(hAPP(c_Polynomial_Opoly(_410729, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_410729), _410731)), _410733) = c_Groups_Ouminus__class_Ouminus(_410729, hAPP(c_Polynomial_Opoly(_410729, _410731), _410733)))], (7457 ^ _152310) ^ [_411011, _411013, _411015, _411017] : [class_Rings_Ocomm__semiring__1(_411011), -(hAPP(c_Polynomial_Opoly(_411011, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_411011)), _411013), _411015)), _411017) = hAPP(hAPP(c_Power_Opower__class_Opower(_411011), hAPP(c_Polynomial_Opoly(_411011, _411013), _411017)), _411015))], (7463 ^ _152310) ^ [_411305, _411307, _411309] : [class_Groups_Oab__group__add(_411305), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_411305), c_Polynomial_Omonom(_411305, _411307, _411309)) = c_Polynomial_Omonom(_411305, c_Groups_Ouminus__class_Ouminus(_411305, _411307), _411309))], (7469 ^ _152310) ^ [_411579, _411581, _411583, _411585] : [class_Fields_Ofield(_411579), -(c_Polynomial_Opoly__gcd(_411579, c_Polynomial_Opoly__gcd(_411579, _411581, _411583), _411585) = c_Polynomial_Opoly__gcd(_411579, _411581, c_Polynomial_Opoly__gcd(_411579, _411583, _411585)))], (7475 ^ _152310) ^ [_411845, _411847, _411849] : [class_Groups_Ogroup__add(_411845), 7478 ^ _152310 : [(7479 ^ _152310) ^ [] : [c_Groups_Ouminus__class_Ouminus(_411845, _411847) = c_Groups_Ouminus__class_Ouminus(_411845, _411849), -(_411847 = _411849)], (7485 ^ _152310) ^ [] : [_411847 = _411849, -(c_Groups_Ouminus__class_Ouminus(_411845, _411847) = c_Groups_Ouminus__class_Ouminus(_411845, _411849))]]], (7491 ^ _152310) ^ [_412351, _412353, _412355] : [class_Groups_Ogroup__add(_412351), 7494 ^ _152310 : [(7495 ^ _152310) ^ [] : [c_Groups_Ouminus__class_Ouminus(_412351, _412353) = _412355, -(c_Groups_Ouminus__class_Ouminus(_412351, _412355) = _412353)], (7501 ^ _152310) ^ [] : [c_Groups_Ouminus__class_Ouminus(_412351, _412355) = _412353, -(c_Groups_Ouminus__class_Ouminus(_412351, _412353) = _412355)]]], (7507 ^ _152310) ^ [_412857, _412859, _412861] : [class_Fields_Ofield(_412857), -(c_Polynomial_Opoly__gcd(_412857, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_412857), _412859), _412861) = c_Polynomial_Opoly__gcd(_412857, _412859, _412861))], (7513 ^ _152310) ^ [_413125, _413127, _413129, _413131] : [class_Fields_Ofield(_413125), -(c_Polynomial_Opoly__gcd(_413125, _413127, c_Polynomial_Opoly__gcd(_413125, _413129, _413131)) = c_Polynomial_Opoly__gcd(_413125, _413129, c_Polynomial_Opoly__gcd(_413125, _413127, _413131)))], (7519 ^ _152310) ^ [_413391, _413393, _413395] : [class_Groups_Ogroup__add(_413391), 7522 ^ _152310 : [(7523 ^ _152310) ^ [] : [_413393 = c_Groups_Ouminus__class_Ouminus(_413391, _413395), -(_413395 = c_Groups_Ouminus__class_Ouminus(_413391, _413393))], (7529 ^ _152310) ^ [] : [_413395 = c_Groups_Ouminus__class_Ouminus(_413391, _413393), -(_413393 = c_Groups_Ouminus__class_Ouminus(_413391, _413395))]]], (7535 ^ _152310) ^ [_413897, _413899, _413901] : [class_Fields_Ofield(_413897), -(c_Polynomial_Opoly__gcd(_413897, _413899, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_413897), _413901)) = c_Polynomial_Opoly__gcd(_413897, _413899, _413901))], (7541 ^ _152310) ^ [_414151, _414153, _414155] : [class_Fields_Ofield(_414151), -(c_Polynomial_Opoly__gcd(_414151, _414153, _414155) = c_Polynomial_Opoly__gcd(_414151, _414155, _414153))], (7547 ^ _152310) ^ [_414381, _414383] : [class_Groups_Ogroup__add(_414381), -(c_Groups_Ouminus__class_Ouminus(_414381, c_Groups_Ouminus__class_Ouminus(_414381, _414383)) = _414383)], (7553 ^ _152310) ^ [_414615, _414617, _414619] : [class_Groups_Oordered__ab__group__add(_414615), 7556 ^ _152310 : [(7557 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_414615, _414617, c_Groups_Ouminus__class_Ouminus(_414615, _414619)), -(c_Orderings_Oord__class_Oless(_414615, _414619, c_Groups_Ouminus__class_Ouminus(_414615, _414617)))], (7563 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_414615, _414619, c_Groups_Ouminus__class_Ouminus(_414615, _414617)), -(c_Orderings_Oord__class_Oless(_414615, _414617, c_Groups_Ouminus__class_Ouminus(_414615, _414619)))]]], (7569 ^ _152310) ^ [_415127, _415129, _415131] : [class_Groups_Oordered__ab__group__add(_415127), 7572 ^ _152310 : [(7573 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_415127, c_Groups_Ouminus__class_Ouminus(_415127, _415129), _415131), -(c_Orderings_Oord__class_Oless(_415127, c_Groups_Ouminus__class_Ouminus(_415127, _415131), _415129))], (7579 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_415127, c_Groups_Ouminus__class_Ouminus(_415127, _415131), _415129), -(c_Orderings_Oord__class_Oless(_415127, c_Groups_Ouminus__class_Ouminus(_415127, _415129), _415131))]]], (7585 ^ _152310) ^ [_415639, _415641, _415643] : [class_Groups_Oordered__ab__group__add(_415639), 7588 ^ _152310 : [(7589 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_415639, c_Groups_Ouminus__class_Ouminus(_415639, _415641), c_Groups_Ouminus__class_Ouminus(_415639, _415643)), -(c_Orderings_Oord__class_Oless(_415639, _415643, _415641))], (7595 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_415639, _415643, _415641), -(c_Orderings_Oord__class_Oless(_415639, c_Groups_Ouminus__class_Ouminus(_415639, _415641), c_Groups_Ouminus__class_Ouminus(_415639, _415643)))]]], (7601 ^ _152310) ^ [_416123] : [class_Groups_Ogroup__add(_416123), -(c_Groups_Ouminus__class_Ouminus(_416123, c_Groups_Ozero__class_Ozero(_416123)) = c_Groups_Ozero__class_Ozero(_416123))], (7607 ^ _152310) ^ [_416339, _416341] : [class_Groups_Ogroup__add(_416339), 7610 ^ _152310 : [(7611 ^ _152310) ^ [] : [c_Groups_Ozero__class_Ozero(_416339) = c_Groups_Ouminus__class_Ouminus(_416339, _416341), -(c_Groups_Ozero__class_Ozero(_416339) = _416341)], (7617 ^ _152310) ^ [] : [c_Groups_Ozero__class_Ozero(_416339) = _416341, -(c_Groups_Ozero__class_Ozero(_416339) = c_Groups_Ouminus__class_Ouminus(_416339, _416341))]]], (7623 ^ _152310) ^ [_416818, _416820] : [class_Groups_Olinordered__ab__group__add(_416818), 7626 ^ _152310 : [(7627 ^ _152310) ^ [] : [_416820 = c_Groups_Ouminus__class_Ouminus(_416818, _416820), -(_416820 = c_Groups_Ozero__class_Ozero(_416818))], (7633 ^ _152310) ^ [] : [_416820 = c_Groups_Ozero__class_Ozero(_416818), -(_416820 = c_Groups_Ouminus__class_Ouminus(_416818, _416820))]]], (7639 ^ _152310) ^ [_417291, _417293] : [class_Groups_Ogroup__add(_417291), 7642 ^ _152310 : [(7643 ^ _152310) ^ [] : [c_Groups_Ouminus__class_Ouminus(_417291, _417293) = c_Groups_Ozero__class_Ozero(_417291), -(_417293 = c_Groups_Ozero__class_Ozero(_417291))], (7649 ^ _152310) ^ [] : [_417293 = c_Groups_Ozero__class_Ozero(_417291), -(c_Groups_Ouminus__class_Ouminus(_417291, _417293) = c_Groups_Ozero__class_Ozero(_417291))]]], (7655 ^ _152310) ^ [_417770, _417772] : [class_Groups_Olinordered__ab__group__add(_417770), 7658 ^ _152310 : [(7659 ^ _152310) ^ [] : [c_Groups_Ouminus__class_Ouminus(_417770, _417772) = _417772, -(_417772 = c_Groups_Ozero__class_Ozero(_417770))], (7665 ^ _152310) ^ [] : [_417772 = c_Groups_Ozero__class_Ozero(_417770), -(c_Groups_Ouminus__class_Ouminus(_417770, _417772) = _417772)]]], (7671 ^ _152310) ^ [_418257, _418259, _418261] : [class_Rings_Oidom(_418257), 7674 ^ _152310 : [(7685 ^ _152310) ^ [] : [7686 ^ _152310 : [(7687 ^ _152310) ^ [] : [_418259 = _418261], (7689 ^ _152310) ^ [] : [_418259 = c_Groups_Ouminus__class_Ouminus(_418257, _418261)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_418257), _418259), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(_418257), _418261), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (7675 ^ _152310) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_418257), _418259), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(_418257), _418261), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_418259 = _418261), -(_418259 = c_Groups_Ouminus__class_Ouminus(_418257, _418261))]]], (7693 ^ _152310) ^ [_418966, _418968, _418970] : [class_Rings_Oidom(_418966), 7696 ^ _152310 : [(7707 ^ _152310) ^ [] : [7708 ^ _152310 : [(7709 ^ _152310) ^ [] : [_418968 = _418970], (7711 ^ _152310) ^ [] : [_418968 = c_Groups_Ouminus__class_Ouminus(_418966, _418970)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_418966), _418968), _418968) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_418966), _418970), _418970))], (7697 ^ _152310) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_418966), _418968), _418968) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_418966), _418970), _418970), -(_418968 = _418970), -(_418968 = c_Groups_Ouminus__class_Ouminus(_418966, _418970))]]], (7715 ^ _152310) ^ [_419675, _419677, _419679] : [class_Rings_Oring(_419675), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_419675), c_Groups_Ouminus__class_Ouminus(_419675, _419677)), c_Groups_Ouminus__class_Ouminus(_419675, _419679)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_419675), _419677), _419679))], (7721 ^ _152310) ^ [_419947, _419949, _419951] : [class_Rings_Oring(_419947), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_419947), c_Groups_Ouminus__class_Ouminus(_419947, _419949)), _419951) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_419947), _419949), c_Groups_Ouminus__class_Ouminus(_419947, _419951)))], (7727 ^ _152310) ^ [_420219, _420221, _420223] : [class_Rings_Oring(_420219), -(c_Groups_Ouminus__class_Ouminus(_420219, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_420219), _420221), _420223)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_420219), c_Groups_Ouminus__class_Ouminus(_420219, _420221)), _420223))], (7733 ^ _152310) ^ [_420491, _420493, _420495] : [class_Rings_Oring(_420491), -(c_Groups_Ouminus__class_Ouminus(_420491, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_420491), _420493), _420495)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_420491), _420493), c_Groups_Ouminus__class_Ouminus(_420491, _420495)))], (7739 ^ _152310) ^ [_420777, _420779, _420781, _420783] : [class_Rings_Ocomm__semiring__1(_420777), -(hAPP(hAPP(c_Power_Opower__class_Opower(_420777), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_420777), _420779), _420781)), _420783) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_420777), hAPP(hAPP(c_Power_Opower__class_Opower(_420777), _420779), _420783)), hAPP(hAPP(c_Power_Opower__class_Opower(_420777), _420781), _420783)))], (7745 ^ _152310) ^ [_421105, _421107, _421109, _421111] : [class_Rings_Ocomm__semiring__1(_421105), -(hAPP(hAPP(c_Power_Opower__class_Opower(_421105), hAPP(hAPP(c_Power_Opower__class_Opower(_421105), _421107), _421109)), _421111) = hAPP(hAPP(c_Power_Opower__class_Opower(_421105), _421107), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _421109), _421111)))], (7751 ^ _152310) ^ [_421399, _421401, _421403] : [class_Fields_Ofield(_421399), 7754 ^ _152310 : [(7755 ^ _152310) ^ [] : [c_Polynomial_Opoly__gcd(_421399, _421401, _421403) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_421399)), 7758 ^ _152310 : [(7759 ^ _152310) ^ [] : [-(_421401 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_421399)))], (7761 ^ _152310) ^ [] : [-(_421403 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_421399)))]]], (7763 ^ _152310) ^ [] : [-(c_Polynomial_Opoly__gcd(_421399, _421401, _421403) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_421399))), _421401 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_421399)), _421403 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_421399))]]], (7773 ^ _152310) ^ [_422071] : [class_Fields_Ofield(_422071), -(c_Polynomial_Opoly__gcd(_422071, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_422071)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_422071))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_422071)))], (7779 ^ _152310) ^ [_422305, _422307] : [class_Groups_Oordered__ab__group__add(_422305), 7782 ^ _152310 : [(7783 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_422305, c_Groups_Ozero__class_Ozero(_422305), c_Groups_Ouminus__class_Ouminus(_422305, _422307)), -(c_Orderings_Oord__class_Oless__eq(_422305, _422307, c_Groups_Ozero__class_Ozero(_422305)))], (7789 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_422305, _422307, c_Groups_Ozero__class_Ozero(_422305)), -(c_Orderings_Oord__class_Oless__eq(_422305, c_Groups_Ozero__class_Ozero(_422305), c_Groups_Ouminus__class_Ouminus(_422305, _422307)))]]], (7795 ^ _152310) ^ [_422790, _422792] : [class_Groups_Olinordered__ab__group__add(_422790), 7798 ^ _152310 : [(7799 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_422790, _422792, c_Groups_Ouminus__class_Ouminus(_422790, _422792)), -(c_Orderings_Oord__class_Oless__eq(_422790, _422792, c_Groups_Ozero__class_Ozero(_422790)))], (7805 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_422790, _422792, c_Groups_Ozero__class_Ozero(_422790)), -(c_Orderings_Oord__class_Oless__eq(_422790, _422792, c_Groups_Ouminus__class_Ouminus(_422790, _422792)))]]], (7811 ^ _152310) ^ [_423269, _423271] : [class_Groups_Oordered__ab__group__add(_423269), 7814 ^ _152310 : [(7815 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_423269, c_Groups_Ouminus__class_Ouminus(_423269, _423271), c_Groups_Ozero__class_Ozero(_423269)), -(c_Orderings_Oord__class_Oless__eq(_423269, c_Groups_Ozero__class_Ozero(_423269), _423271))], (7821 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_423269, c_Groups_Ozero__class_Ozero(_423269), _423271), -(c_Orderings_Oord__class_Oless__eq(_423269, c_Groups_Ouminus__class_Ouminus(_423269, _423271), c_Groups_Ozero__class_Ozero(_423269)))]]], (7827 ^ _152310) ^ [_423754, _423756] : [class_Groups_Olinordered__ab__group__add(_423754), 7830 ^ _152310 : [(7831 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_423754, c_Groups_Ouminus__class_Ouminus(_423754, _423756), _423756), -(c_Orderings_Oord__class_Oless__eq(_423754, c_Groups_Ozero__class_Ozero(_423754), _423756))], (7837 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_423754, c_Groups_Ozero__class_Ozero(_423754), _423756), -(c_Orderings_Oord__class_Oless__eq(_423754, c_Groups_Ouminus__class_Ouminus(_423754, _423756), _423756))]]], (7843 ^ _152310) ^ [_424233, _424235] : [class_Rings_Olinordered__idom(_424233), 7846 ^ _152310 : [(7847 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_424233, _424235, c_Groups_Ouminus__class_Ouminus(_424233, _424235)), -(c_Orderings_Oord__class_Oless(_424233, _424235, c_Groups_Ozero__class_Ozero(_424233)))], (7853 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_424233, _424235, c_Groups_Ozero__class_Ozero(_424233)), -(c_Orderings_Oord__class_Oless(_424233, _424235, c_Groups_Ouminus__class_Ouminus(_424233, _424235)))]]], (7859 ^ _152310) ^ [_424712, _424714] : [class_Groups_Olinordered__ab__group__add(_424712), 7862 ^ _152310 : [(7863 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_424712, c_Groups_Ouminus__class_Ouminus(_424712, _424714), _424714), -(c_Orderings_Oord__class_Oless(_424712, c_Groups_Ozero__class_Ozero(_424712), _424714))], (7869 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_424712, c_Groups_Ozero__class_Ozero(_424712), _424714), -(c_Orderings_Oord__class_Oless(_424712, c_Groups_Ouminus__class_Ouminus(_424712, _424714), _424714))]]], (7875 ^ _152310) ^ [_425191, _425193] : [class_Groups_Oordered__ab__group__add(_425191), 7878 ^ _152310 : [(7879 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_425191, c_Groups_Ouminus__class_Ouminus(_425191, _425193), c_Groups_Ozero__class_Ozero(_425191)), -(c_Orderings_Oord__class_Oless(_425191, c_Groups_Ozero__class_Ozero(_425191), _425193))], (7885 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_425191, c_Groups_Ozero__class_Ozero(_425191), _425193), -(c_Orderings_Oord__class_Oless(_425191, c_Groups_Ouminus__class_Ouminus(_425191, _425193), c_Groups_Ozero__class_Ozero(_425191)))]]], (7891 ^ _152310) ^ [_425676, _425678] : [class_Groups_Oordered__ab__group__add(_425676), 7894 ^ _152310 : [(7895 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_425676, c_Groups_Ozero__class_Ozero(_425676), c_Groups_Ouminus__class_Ouminus(_425676, _425678)), -(c_Orderings_Oord__class_Oless(_425676, _425678, c_Groups_Ozero__class_Ozero(_425676)))], (7901 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_425676, _425678, c_Groups_Ozero__class_Ozero(_425676)), -(c_Orderings_Oord__class_Oless(_425676, c_Groups_Ozero__class_Ozero(_425676), c_Groups_Ouminus__class_Ouminus(_425676, _425678)))]]], (7907 ^ _152310) ^ [_426175, _426177, _426179] : [class_Groups_Ogroup__add(_426175), 7910 ^ _152310 : [(7911 ^ _152310) ^ [] : [c_Groups_Oplus__class_Oplus(_426175, _426177, _426179) = c_Groups_Ozero__class_Ozero(_426175), -(_426179 = c_Groups_Ouminus__class_Ouminus(_426175, _426177))], (7917 ^ _152310) ^ [] : [_426179 = c_Groups_Ouminus__class_Ouminus(_426175, _426177), -(c_Groups_Oplus__class_Oplus(_426175, _426177, _426179) = c_Groups_Ozero__class_Ozero(_426175))]]], (7923 ^ _152310) ^ [_426676, _426678] : [class_Groups_Ogroup__add(_426676), -(c_Groups_Oplus__class_Oplus(_426676, _426678, c_Groups_Ouminus__class_Ouminus(_426676, _426678)) = c_Groups_Ozero__class_Ozero(_426676))], (7929 ^ _152310) ^ [_426916, _426918, _426920] : [class_Groups_Ogroup__add(_426916), 7932 ^ _152310 : [(7933 ^ _152310) ^ [] : [_426918 = c_Groups_Ouminus__class_Ouminus(_426916, _426920), -(c_Groups_Oplus__class_Oplus(_426916, _426918, _426920) = c_Groups_Ozero__class_Ozero(_426916))], (7939 ^ _152310) ^ [] : [c_Groups_Oplus__class_Oplus(_426916, _426918, _426920) = c_Groups_Ozero__class_Ozero(_426916), -(_426918 = c_Groups_Ouminus__class_Ouminus(_426916, _426920))]]], (7945 ^ _152310) ^ [_427417, _427419] : [class_Groups_Ogroup__add(_427417), -(c_Groups_Oplus__class_Oplus(_427417, c_Groups_Ouminus__class_Ouminus(_427417, _427419), _427419) = c_Groups_Ozero__class_Ozero(_427417))], (7951 ^ _152310) ^ [_427643, _427645] : [class_Groups_Oab__group__add(_427643), -(c_Groups_Oplus__class_Oplus(_427643, c_Groups_Ouminus__class_Ouminus(_427643, _427645), _427645) = c_Groups_Ozero__class_Ozero(_427643))], (7957 ^ _152310) ^ [_427883, _427885, _427887] : [class_Groups_Ogroup__add(_427883), c_Groups_Oplus__class_Oplus(_427883, _427885, _427887) = c_Groups_Ozero__class_Ozero(_427883), -(c_Groups_Ouminus__class_Ouminus(_427883, _427885) = _427887)], (7967 ^ _152310) ^ [_428208, _428210] : [class_Rings_Ocomm__ring__1(_428208), -(c_Groups_Ouminus__class_Ouminus(_428208, _428210) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_428208), c_Groups_Ouminus__class_Ouminus(_428208, c_Groups_Oone__class_Oone(_428208))), _428210))], (7973 ^ _152310) ^ [_428448, _428450] : [class_Rings_Oring__1__no__zero__divisors(_428448), 7976 ^ _152310 : [(7987 ^ _152310) ^ [] : [7988 ^ _152310 : [(7989 ^ _152310) ^ [] : [_428450 = c_Groups_Oone__class_Oone(_428448)], (7991 ^ _152310) ^ [] : [_428450 = c_Groups_Ouminus__class_Ouminus(_428448, c_Groups_Oone__class_Oone(_428448))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_428448), _428450), _428450) = c_Groups_Oone__class_Oone(_428448))], (7977 ^ _152310) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_428448), _428450), _428450) = c_Groups_Oone__class_Oone(_428448), -(_428450 = c_Groups_Oone__class_Oone(_428448)), -(_428450 = c_Groups_Ouminus__class_Ouminus(_428448, c_Groups_Oone__class_Oone(_428448)))]]], (7995 ^ _152310) ^ [_429129, _429131, _429133] : [class_Rings_Ocomm__semiring__1(_429129), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_429129), hAPP(hAPP(c_Power_Opower__class_Opower(_429129), _429131), _429133)), _429131) = hAPP(hAPP(c_Power_Opower__class_Opower(_429129), _429131), c_Nat_OSuc(_429133)))], (8001 ^ _152310) ^ [_429409, _429411, _429413] : [class_Rings_Ocomm__semiring__1(_429409), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_429409), _429411), hAPP(hAPP(c_Power_Opower__class_Opower(_429409), _429411), _429413)) = hAPP(hAPP(c_Power_Opower__class_Opower(_429409), _429411), c_Nat_OSuc(_429413)))], (8007 ^ _152310) ^ [_429689, _429691, _429693] : [class_Rings_Ocomm__semiring__1(_429689), -(hAPP(hAPP(c_Power_Opower__class_Opower(_429689), _429691), c_Nat_OSuc(_429693)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_429689), _429691), hAPP(hAPP(c_Power_Opower__class_Opower(_429689), _429691), _429693)))], (8013 ^ _152310) ^ [_429955, _429957] : [class_Rings_Ocomm__semiring__1(_429955), -(hAPP(hAPP(c_Power_Opower__class_Opower(_429955), _429957), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_429955))], (8019 ^ _152310) ^ [_430211, _430213, _430215, _430217] : [class_Rings_Ocomm__semiring__1(_430211), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_430211), hAPP(hAPP(c_Power_Opower__class_Opower(_430211), _430213), _430215)), hAPP(hAPP(c_Power_Opower__class_Opower(_430211), _430213), _430217)) = hAPP(hAPP(c_Power_Opower__class_Opower(_430211), _430213), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _430215, _430217)))], (8025 ^ _152310) ^ [_430488, _430490] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _430488), _430488)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _430490), _430490)))], (8027 ^ _152310) ^ [_430642, _430644] : [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _430642, _430644) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_430644 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _430642))], (8033 ^ _152310) ^ [_430818, _430820] : [_430820 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _430818), -(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _430818, _430820) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (8039 ^ _152310) ^ [_431073, _431075] : [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _431073, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _431075)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_431073 = _431075)], (8045 ^ _152310) ^ [_431249, _431251] : [_431249 = _431251, -(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _431249, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _431251)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (8051 ^ _152310) ^ [_431475, _431477] : [class_Rings_Olinordered__idom(_431475), -(_431477 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_431475))), -(c_Polynomial_Opos__poly(_431475, _431477)), -(c_Polynomial_Opos__poly(_431475, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_431475), _431477)))], (8065 ^ _152310) ^ [_431910, _431912] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _431910, _431912)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _431910), _431912))], (8071 ^ _152310) ^ [_432090, _432092] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _432090), _432092), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _432090, _432092)))], (8077 ^ _152310) ^ [_432349, _432351] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _432349, _432351), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _432351, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _432349)))], (8083 ^ _152310) ^ [_432529, _432531] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _432531, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _432529)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _432529, _432531), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (8089 ^ _152310) ^ [_432788, _432790] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _432788, _432790), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _432790, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _432788)))], (8095 ^ _152310) ^ [_432968, _432970] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _432970, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _432968)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _432968, _432970), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (8101 ^ _152310) ^ [_433227, _433229] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _433227, _433229)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _433227), _433229))], (8107 ^ _152310) ^ [_433407, _433409] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _433407), _433409), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _433407, _433409)))], (8113 ^ _152310) ^ [_433637, _433639] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _433637), -(c_NthRoot_Oroot(_433637, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _433639)) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, c_NthRoot_Oroot(_433637, _433639)))], (8119 ^ _152310) ^ [_433887, _433889, _433891] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _433887), -(c_NthRoot_Oroot(_433887, hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _433889), _433891)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_NthRoot_Oroot(_433887, _433889)), _433891))], (8125 ^ _152310) ^ [_434169, _434171, _434173, _434175] : [class_Rings_Ocomm__semiring__1(_434169), -(hAPP(c_Polynomial_Opoly(_434169, c_Polynomial_Omonom(_434169, _434171, _434173)), _434175) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_434169), _434171), hAPP(hAPP(c_Power_Opower__class_Opower(_434169), _434175), _434173)))], (8131 ^ _152310) ^ [_434455, _434457, _434459] : [class_Rings_Olinordered__semidom(_434455), c_Orderings_Oord__class_Oless__eq(_434455, c_Groups_Ozero__class_Ozero(_434455), _434457), c_Orderings_Oord__class_Oless__eq(_434455, _434457, c_Groups_Oone__class_Oone(_434455)), -(c_Orderings_Oord__class_Oless__eq(_434455, hAPP(hAPP(c_Power_Opower__class_Opower(_434455), _434457), c_Nat_OSuc(_434459)), _434457))], (8145 ^ _152310) ^ [_434889, _434891] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _434889), -(c_NthRoot_Oroot(c_Nat_OSuc(_434891), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _434889), c_Nat_OSuc(_434891))) = _434889)], (8151 ^ _152310) ^ [_435127, _435129] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _435127), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _435129), -(c_NthRoot_Oroot(_435127, hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _435129), _435127)) = _435129)], (8161 ^ _152310) ^ [_435448, _435450] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _435448), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _435450), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_NthRoot_Oroot(_435448, _435450)), _435448) = _435450)], (8171 ^ _152310) ^ [_435797, _435799, _435801, _435803] : [class_Rings_Olinordered__semidom(_435797), c_Orderings_Oord__class_Oless(_435797, _435799, _435801), c_Orderings_Oord__class_Oless__eq(_435797, c_Groups_Ozero__class_Ozero(_435797), _435799), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _435803), -(c_Orderings_Oord__class_Oless(_435797, hAPP(hAPP(c_Power_Opower__class_Opower(_435797), _435799), _435803), hAPP(hAPP(c_Power_Opower__class_Opower(_435797), _435801), _435803)))], (8189 ^ _152310) ^ [_436366, _436368, _436370] : [class_Rings_Olinordered__semidom(_436366), c_Orderings_Oord__class_Oless(_436366, c_Groups_Oone__class_Oone(_436366), _436368), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _436370), -(c_Orderings_Oord__class_Oless(_436366, c_Groups_Oone__class_Oone(_436366), hAPP(hAPP(c_Power_Opower__class_Opower(_436366), _436368), _436370)))], (8203 ^ _152310) ^ [_436824, _436826, _436828, _436830] : [class_Rings_Olinordered__semidom(_436824), c_Orderings_Oord__class_Oless(_436824, c_Groups_Oone__class_Oone(_436824), _436826), 8210 ^ _152310 : [(8211 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_436824, hAPP(hAPP(c_Power_Opower__class_Opower(_436824), _436826), _436828), hAPP(hAPP(c_Power_Opower__class_Opower(_436824), _436826), _436830)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _436828, _436830))], (8217 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _436828, _436830), -(c_Orderings_Oord__class_Oless__eq(_436824, hAPP(hAPP(c_Power_Opower__class_Opower(_436824), _436826), _436828), hAPP(hAPP(c_Power_Opower__class_Opower(_436824), _436826), _436830)))]]], (8223 ^ _152310) ^ [_437470, _437472, _437474] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _437470), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _437472, _437474)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _437470), _437472)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _437470), _437474)))], (8235 ^ _152310) ^ [_437906, _437908] : [8236 ^ _152310 : [(8237 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _437906)], (8239 ^ _152310) ^ [] : [_437908 = 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), _437906), _437908)))], (8225 ^ _152310) ^ [_437638, _437640] : [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), _437638), _437640)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _437638)), -(_437640 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8243 ^ _152310) ^ [_438222, _438224, _438226] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _438222), c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _438222), _438224), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _438222), _438226)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _438224, _438226))], (8253 ^ _152310) ^ [_438532] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _438532) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (8265 ^ _152310) ^ [_438935, _438937] : [8266 ^ _152310 : [(8267 ^ _152310) ^ [] : [_438937 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (8269 ^ _152310) ^ [] : [_438935 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _438935), _438937) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (8255 ^ _152310) ^ [_438671, _438673] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _438671), _438673) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_438673 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_438671 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (8273 ^ _152310) ^ [_439232, _439234, _439236] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _439232), _439234)), _439236) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _439232), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _439234), _439236)))], (8275 ^ _152310) ^ [_439367, _439369] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _439367), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _439367), _439369)))], (8291 ^ _152310) ^ [_439890, _439892] : [8292 ^ _152310 : [(8293 ^ _152310) ^ [] : [_439892 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (8295 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _439890)]], -(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), _439890), _439892)))], (8281 ^ _152310) ^ [_439622, _439624] : [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), _439622), _439624)), -(_439624 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _439622))], (8299 ^ _152310) ^ [_440206, _440208, _440210] : [class_Rings_Ocomm__semiring__1(_440206), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_440206, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_440206)), _440208), _440210)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Polynomial_Odegree(_440206, _440208)), _440210)))], (8305 ^ _152310) ^ [_440480, _440482, _440484] : [class_Rings_Ocomm__semiring__1(_440480), -(c_Polynomial_Odegree(_440480, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_440480)), c_Polynomial_OpCons(_440480, _440482, c_Polynomial_OpCons(_440480, c_Groups_Oone__class_Oone(_440480), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_440480))))), _440484)) = _440484)], (8311 ^ _152310) ^ [_440762, _440764, _440766] : [class_Rings_Ocomm__semiring__1(_440762), -(hAPP(c_Polynomial_Ocoeff(_440762, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_440762)), c_Polynomial_OpCons(_440762, _440764, c_Polynomial_OpCons(_440762, c_Groups_Oone__class_Oone(_440762), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_440762))))), _440766)), _440766) = c_Groups_Oone__class_Oone(_440762))], (8317 ^ _152310) ^ [_441054, _441056, _441058] : [class_Rings_Oring__1__no__zero__divisors(_441054), -(_441056 = c_Groups_Ozero__class_Ozero(_441054)), hAPP(hAPP(c_Power_Opower__class_Opower(_441054), _441056), _441058) = c_Groups_Ozero__class_Ozero(_441054)], (8327 ^ _152310) ^ [_441403, _441405, _441407] : [class_Groups_Omonoid__mult(_441403), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_441403), hAPP(hAPP(c_Power_Opower__class_Opower(_441403), _441405), _441407)), _441405) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_441403), _441405), hAPP(hAPP(c_Power_Opower__class_Opower(_441403), _441405), _441407)))], (8333 ^ _152310) ^ [_441709, _441711, _441713, _441715] : [class_Groups_Ocomm__monoid__mult(_441709), -(hAPP(hAPP(c_Power_Opower__class_Opower(_441709), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_441709), _441711), _441713)), _441715) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_441709), hAPP(hAPP(c_Power_Opower__class_Opower(_441709), _441711), _441715)), hAPP(hAPP(c_Power_Opower__class_Opower(_441709), _441713), _441715)))], (8339 ^ _152310) ^ [_442009, _442011] : [class_Groups_Omonoid__mult(_442009), -(hAPP(hAPP(c_Power_Opower__class_Opower(_442009), c_Groups_Oone__class_Oone(_442009)), _442011) = c_Groups_Oone__class_Oone(_442009))], (8345 ^ _152310) ^ [_442269, _442271, _442273, _442275] : [class_Groups_Omonoid__mult(_442269), -(hAPP(hAPP(c_Power_Opower__class_Opower(_442269), _442271), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _442273), _442275)) = hAPP(hAPP(c_Power_Opower__class_Opower(_442269), hAPP(hAPP(c_Power_Opower__class_Opower(_442269), _442271), _442273)), _442275))], (8351 ^ _152310) ^ [_442549, _442551] : [class_Groups_Omonoid__mult(_442549), -(hAPP(hAPP(c_Power_Opower__class_Opower(_442549), _442551), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _442551)], (8357 ^ _152310) ^ [_442801, _442803, _442805, _442807] : [class_Rings_Olinordered__semidom(_442801), c_Orderings_Oord__class_Oless__eq(_442801, _442803, _442805), c_Orderings_Oord__class_Oless__eq(_442801, c_Groups_Ozero__class_Ozero(_442801), _442803), -(c_Orderings_Oord__class_Oless__eq(_442801, hAPP(hAPP(c_Power_Opower__class_Opower(_442801), _442803), _442807), hAPP(hAPP(c_Power_Opower__class_Opower(_442801), _442805), _442807)))], (8371 ^ _152310) ^ [_443271, _443273, _443275] : [class_Rings_Olinordered__semidom(_443271), c_Orderings_Oord__class_Oless__eq(_443271, c_Groups_Ozero__class_Ozero(_443271), _443273), -(c_Orderings_Oord__class_Oless__eq(_443271, c_Groups_Ozero__class_Ozero(_443271), hAPP(hAPP(c_Power_Opower__class_Opower(_443271), _443273), _443275)))], (8381 ^ _152310) ^ [_443620, _443622, _443624] : [class_Rings_Olinordered__semidom(_443620), c_Orderings_Oord__class_Oless(_443620, c_Groups_Ozero__class_Ozero(_443620), _443622), -(c_Orderings_Oord__class_Oless(_443620, c_Groups_Ozero__class_Ozero(_443620), hAPP(hAPP(c_Power_Opower__class_Opower(_443620), _443622), _443624)))], (8391 ^ _152310) ^ [_443969, _443971, _443973] : [class_Rings_Olinordered__semidom(_443969), c_Orderings_Oord__class_Oless__eq(_443969, c_Groups_Oone__class_Oone(_443969), _443971), -(c_Orderings_Oord__class_Oless__eq(_443969, c_Groups_Oone__class_Oone(_443969), hAPP(hAPP(c_Power_Opower__class_Opower(_443969), _443971), _443973)))], (8401 ^ _152310) ^ [_444318, _444320, _444322] : [class_Power_Opower(_444318), class_Rings_Omult__zero(_444318), class_Rings_Ono__zero__divisors(_444318), class_Rings_Ozero__neq__one(_444318), 8416 ^ _152310 : [(8417 ^ _152310) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_444318), _444320), _444322) = c_Groups_Ozero__class_Ozero(_444318), 8420 ^ _152310 : [(8421 ^ _152310) ^ [] : [-(_444320 = c_Groups_Ozero__class_Ozero(_444318))], (8423 ^ _152310) ^ [] : [_444322 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (8425 ^ _152310) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_444318), _444320), _444322) = c_Groups_Ozero__class_Ozero(_444318)), _444320 = c_Groups_Ozero__class_Ozero(_444318), -(_444322 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (8435 ^ _152310) ^ [_445301, _445303, _445305, _445307] : [class_Rings_Olinordered__semidom(_445301), c_Orderings_Oord__class_Oless(_445301, c_Groups_Oone__class_Oone(_445301), _445303), 8442 ^ _152310 : [(8443 ^ _152310) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_445301), _445303), _445305) = hAPP(hAPP(c_Power_Opower__class_Opower(_445301), _445303), _445307), -(_445305 = _445307)], (8449 ^ _152310) ^ [] : [_445305 = _445307, -(hAPP(hAPP(c_Power_Opower__class_Opower(_445301), _445303), _445305) = hAPP(hAPP(c_Power_Opower__class_Opower(_445301), _445303), _445307))]]], (8455 ^ _152310) ^ [_445942, _445944] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_445942), c_Groups_Ozero__class_Ozero(_445942)), c_Nat_OSuc(_445944)) = c_Groups_Ozero__class_Ozero(_445942)), class_Power_Opower(_445942), class_Rings_Osemiring__0(_445942)], (8465 ^ _152310) ^ [_446279, _446281, _446283] : [class_Groups_Omonoid__mult(_446279), -(hAPP(hAPP(c_Power_Opower__class_Opower(_446279), _446281), c_Nat_OSuc(_446283)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_446279), hAPP(hAPP(c_Power_Opower__class_Opower(_446279), _446281), _446283)), _446281))], (8471 ^ _152310) ^ [_446559, _446561, _446563] : [class_Power_Opower(_446559), -(hAPP(hAPP(c_Power_Opower__class_Opower(_446559), _446561), c_Nat_OSuc(_446563)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_446559), _446561), hAPP(hAPP(c_Power_Opower__class_Opower(_446559), _446561), _446563)))], (8477 ^ _152310) ^ [_446825, _446827] : [class_Power_Opower(_446825), -(hAPP(hAPP(c_Power_Opower__class_Opower(_446825), _446827), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_446825))], (8483 ^ _152310) ^ [_447081, _447083, _447085, _447087] : [class_Groups_Omonoid__mult(_447081), -(hAPP(hAPP(c_Power_Opower__class_Opower(_447081), _447083), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _447085, _447087)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_447081), hAPP(hAPP(c_Power_Opower__class_Opower(_447081), _447083), _447085)), hAPP(hAPP(c_Power_Opower__class_Opower(_447081), _447083), _447087)))], (8489 ^ _152310) ^ [_447401, _447403, _447405, _447407] : [class_Rings_Olinordered__semidom(_447401), c_Orderings_Oord__class_Oless(_447401, hAPP(hAPP(c_Power_Opower__class_Opower(_447401), _447403), _447405), hAPP(hAPP(c_Power_Opower__class_Opower(_447401), _447407), _447405)), c_Orderings_Oord__class_Oless__eq(_447401, c_Groups_Ozero__class_Ozero(_447401), _447407), -(c_Orderings_Oord__class_Oless(_447401, _447403, _447407))], (8503 ^ _152310) ^ [_447885, _447887, _447889, _447891] : [class_Rings_Olinordered__semidom(_447885), hAPP(hAPP(c_Power_Opower__class_Opower(_447885), _447887), c_Nat_OSuc(_447889)) = hAPP(hAPP(c_Power_Opower__class_Opower(_447885), _447891), c_Nat_OSuc(_447889)), c_Orderings_Oord__class_Oless__eq(_447885, c_Groups_Ozero__class_Ozero(_447885), _447887), c_Orderings_Oord__class_Oless__eq(_447885, c_Groups_Ozero__class_Ozero(_447885), _447891), -(_447887 = _447891)], (8521 ^ _152310) ^ [_448476, _448478, _448480, _448482] : [class_Rings_Olinordered__semidom(_448476), c_Orderings_Oord__class_Oless__eq(_448476, hAPP(hAPP(c_Power_Opower__class_Opower(_448476), _448478), c_Nat_OSuc(_448480)), hAPP(hAPP(c_Power_Opower__class_Opower(_448476), _448482), c_Nat_OSuc(_448480))), c_Orderings_Oord__class_Oless__eq(_448476, c_Groups_Ozero__class_Ozero(_448476), _448482), -(c_Orderings_Oord__class_Oless__eq(_448476, _448478, _448482))], (8535 ^ _152310) ^ [_448954, _448956, _448958] : [class_Rings_Olinordered__semidom(_448954), c_Orderings_Oord__class_Oless(_448954, c_Groups_Oone__class_Oone(_448954), _448956), -(c_Orderings_Oord__class_Oless(_448954, c_Groups_Oone__class_Oone(_448954), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_448954), _448956), hAPP(hAPP(c_Power_Opower__class_Opower(_448954), _448956), _448958))))], (8545 ^ _152310) ^ [_449319, _449321, _449323] : [class_Rings_Olinordered__semidom(_449319), c_Orderings_Oord__class_Oless(_449319, c_Groups_Oone__class_Oone(_449319), _449321), -(c_Orderings_Oord__class_Oless(_449319, hAPP(hAPP(c_Power_Opower__class_Opower(_449319), _449321), _449323), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_449319), _449321), hAPP(hAPP(c_Power_Opower__class_Opower(_449319), _449321), _449323))))], (8555 ^ _152310) ^ [_449682, _449684] : [class_Power_Opower(_449682), class_Rings_Osemiring__0(_449682), 8562 ^ _152310 : [(8563 ^ _152310) ^ [] : [_449684 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_449682), c_Groups_Ozero__class_Ozero(_449682)), _449684) = c_Groups_Oone__class_Oone(_449682))], (8569 ^ _152310) ^ [] : [-(_449684 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_449682), c_Groups_Ozero__class_Ozero(_449682)), _449684) = c_Groups_Ozero__class_Ozero(_449682))]]], (8575 ^ _152310) ^ [_450297, _450299, _450301] : [class_Rings_Olinordered__semidom(_450297), c_Orderings_Oord__class_Oless(_450297, c_Groups_Oone__class_Oone(_450297), _450299), -(c_Orderings_Oord__class_Oless(_450297, c_Groups_Oone__class_Oone(_450297), hAPP(hAPP(c_Power_Opower__class_Opower(_450297), _450299), c_Nat_OSuc(_450301))))], (8585 ^ _152310) ^ [_450650, _450652, _450654] : [class_Rings_Oring__1(_450650), -(hAPP(hAPP(c_Power_Opower__class_Opower(_450650), c_Groups_Ouminus__class_Ouminus(_450650, _450652)), _450654) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_450650), hAPP(hAPP(c_Power_Opower__class_Opower(_450650), c_Groups_Ouminus__class_Ouminus(_450650, c_Groups_Oone__class_Oone(_450650))), _450654)), hAPP(hAPP(c_Power_Opower__class_Opower(_450650), _450652), _450654)))], (8591 ^ _152310) ^ [_450972, _450974, _450976, _450978] : [class_Rings_Olinordered__semidom(_450972), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _450974, _450976), c_Orderings_Oord__class_Oless(_450972, c_Groups_Oone__class_Oone(_450972), _450978), -(c_Orderings_Oord__class_Oless(_450972, hAPP(hAPP(c_Power_Opower__class_Opower(_450972), _450978), _450974), hAPP(hAPP(c_Power_Opower__class_Opower(_450972), _450978), _450976)))], (8605 ^ _152310) ^ [_451456, _451458, _451460, _451462] : [class_Rings_Olinordered__semidom(_451456), c_Orderings_Oord__class_Oless(_451456, c_Groups_Oone__class_Oone(_451456), _451458), c_Orderings_Oord__class_Oless(_451456, hAPP(hAPP(c_Power_Opower__class_Opower(_451456), _451458), _451460), hAPP(hAPP(c_Power_Opower__class_Opower(_451456), _451458), _451462)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _451460, _451462))], (8619 ^ _152310) ^ [_451940, _451942, _451944, _451946] : [class_Rings_Olinordered__semidom(_451940), c_Orderings_Oord__class_Oless(_451940, c_Groups_Oone__class_Oone(_451940), _451942), 8626 ^ _152310 : [(8627 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_451940, hAPP(hAPP(c_Power_Opower__class_Opower(_451940), _451942), _451944), hAPP(hAPP(c_Power_Opower__class_Opower(_451940), _451942), _451946)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _451944, _451946))], (8633 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _451944, _451946), -(c_Orderings_Oord__class_Oless(_451940, hAPP(hAPP(c_Power_Opower__class_Opower(_451940), _451942), _451944), hAPP(hAPP(c_Power_Opower__class_Opower(_451940), _451942), _451946)))]]], (8639 ^ _152310) ^ [_452615, _452617, _452619, _452621] : [class_Rings_Olinordered__semidom(_452615), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _452617, _452619), c_Orderings_Oord__class_Oless__eq(_452615, c_Groups_Oone__class_Oone(_452615), _452621), -(c_Orderings_Oord__class_Oless__eq(_452615, hAPP(hAPP(c_Power_Opower__class_Opower(_452615), _452621), _452617), hAPP(hAPP(c_Power_Opower__class_Opower(_452615), _452621), _452619)))], (8653 ^ _152310) ^ [_453085, _453087, _453089] : [class_Rings_Olinordered__semidom(_453085), c_Orderings_Oord__class_Oless(_453085, c_Groups_Ozero__class_Ozero(_453085), _453087), c_Orderings_Oord__class_Oless(_453085, _453087, c_Groups_Oone__class_Oone(_453085)), -(c_Orderings_Oord__class_Oless(_453085, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_453085), _453087), hAPP(hAPP(c_Power_Opower__class_Opower(_453085), _453087), _453089)), hAPP(hAPP(c_Power_Opower__class_Opower(_453085), _453087), _453089)))], (8667 ^ _152310) ^ [_453561, _453563, _453565] : [class_Rings_Olinordered__semidom(_453561), c_Orderings_Oord__class_Oless(_453561, c_Groups_Ozero__class_Ozero(_453561), _453563), c_Orderings_Oord__class_Oless(_453561, _453563, c_Groups_Oone__class_Oone(_453561)), -(c_Orderings_Oord__class_Oless(_453561, hAPP(hAPP(c_Power_Opower__class_Opower(_453561), _453563), c_Nat_OSuc(_453565)), c_Groups_Oone__class_Oone(_453561)))], (8681 ^ _152310) ^ [_454027, _454029, _454031, _454033] : [class_Rings_Olinordered__semidom(_454027), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _454029, _454031), c_Orderings_Oord__class_Oless(_454027, c_Groups_Ozero__class_Ozero(_454027), _454033), c_Orderings_Oord__class_Oless(_454027, _454033, c_Groups_Oone__class_Oone(_454027)), -(c_Orderings_Oord__class_Oless(_454027, hAPP(hAPP(c_Power_Opower__class_Opower(_454027), _454033), _454031), hAPP(hAPP(c_Power_Opower__class_Opower(_454027), _454033), _454029)))], (8699 ^ _152310) ^ [_454614, _454616, _454618, _454620] : [class_Rings_Olinordered__semidom(_454614), hAPP(hAPP(c_Power_Opower__class_Opower(_454614), _454616), _454618) = hAPP(hAPP(c_Power_Opower__class_Opower(_454614), _454620), _454618), c_Orderings_Oord__class_Oless__eq(_454614, c_Groups_Ozero__class_Ozero(_454614), _454616), c_Orderings_Oord__class_Oless__eq(_454614, c_Groups_Ozero__class_Ozero(_454614), _454620), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _454618), -(_454616 = _454620)], (8721 ^ _152310) ^ [_455296, _455298, _455300, _455302] : [class_Rings_Olinordered__semidom(_455296), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _455298, _455300), c_Orderings_Oord__class_Oless__eq(_455296, c_Groups_Ozero__class_Ozero(_455296), _455302), c_Orderings_Oord__class_Oless__eq(_455296, _455302, c_Groups_Oone__class_Oone(_455296)), -(c_Orderings_Oord__class_Oless__eq(_455296, hAPP(hAPP(c_Power_Opower__class_Opower(_455296), _455302), _455300), hAPP(hAPP(c_Power_Opower__class_Opower(_455296), _455302), _455298)))], (8739 ^ _152310) ^ [_455883, _455885, _455887, _455889] : [class_Rings_Olinordered__semidom(_455883), c_Orderings_Oord__class_Oless(_455883, c_Groups_Oone__class_Oone(_455883), _455885), c_Orderings_Oord__class_Oless__eq(_455883, hAPP(hAPP(c_Power_Opower__class_Opower(_455883), _455885), _455887), hAPP(hAPP(c_Power_Opower__class_Opower(_455883), _455885), _455889)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _455887, _455889))], (8753 ^ _152310) ^ [_456325] : [class_Power_Opower(_456325), -(c_Power_Opower__class_Opower(_456325) = c_Power_Opower_Opower(_456325, c_Groups_Oone__class_Oone(_456325), c_Groups_Otimes__class_Otimes(_456325)))], (8759 ^ _152310) ^ [_456561, _456563, _456565] : [class_Rings_Oidom(_456561), -(_456563 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_456561))), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_456561), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_456561)), c_Polynomial_OpCons(_456561, c_Groups_Ouminus__class_Ouminus(_456561, _456565), c_Polynomial_OpCons(_456561, c_Groups_Oone__class_Oone(_456561), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_456561))))), c_Nat_OSuc(c_Polynomial_Oorder(_456561, _456565, _456563))), _456563)], (8769 ^ _152310) ^ [_456966, _456968, _456970] : [class_Rings_Oidom(_456966), -(_456968 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_456966))), 8776 ^ _152310 : [(8777 ^ _152310) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_456966), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_456966)), c_Polynomial_OpCons(_456966, c_Groups_Ouminus__class_Ouminus(_456966, _456970), c_Polynomial_OpCons(_456966, c_Groups_Oone__class_Oone(_456966), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_456966))))), c_Polynomial_Oorder(_456966, _456970, _456968)), _456968))], (8779 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_456966), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_456966)), c_Polynomial_OpCons(_456966, c_Groups_Ouminus__class_Ouminus(_456966, _456970), c_Polynomial_OpCons(_456966, c_Groups_Oone__class_Oone(_456966), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_456966))))), c_Nat_OSuc(c_Polynomial_Oorder(_456966, _456970, _456968))), _456968)]]], (8781 ^ _152310) ^ [_457502, _457504] : [class_Rings_Ocomm__semiring__1(_457502), -(c_Rings_Odvd__class_Odvd(_457502, _457504, c_Groups_Ozero__class_Ozero(_457502)))], (8787 ^ _152310) ^ [_457730, _457732, _457734] : [class_Fields_Ofield(_457730), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_457730), c_Polynomial_Opoly__gcd(_457730, _457732, _457734), _457732))], (8793 ^ _152310) ^ [_457972, _457974, _457976] : [class_Fields_Ofield(_457972), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_457972), c_Polynomial_Opoly__gcd(_457972, _457974, _457976), _457976))], (8799 ^ _152310) ^ [_458228, _458230, _458232, _458234] : [class_Rings_Ocomm__semiring__1(_458228), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _458230, _458232), -(c_Rings_Odvd__class_Odvd(_458228, hAPP(hAPP(c_Power_Opower__class_Opower(_458228), _458234), _458230), hAPP(hAPP(c_Power_Opower__class_Opower(_458228), _458234), _458232)))], (8809 ^ _152310) ^ [_458623, _458625, _458627, _458629, _458631] : [class_Rings_Ocomm__semiring__1(_458623), c_Rings_Odvd__class_Odvd(_458623, _458625, _458627), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _458629, _458631), -(c_Rings_Odvd__class_Odvd(_458623, hAPP(hAPP(c_Power_Opower__class_Opower(_458623), _458625), _458629), hAPP(hAPP(c_Power_Opower__class_Opower(_458623), _458627), _458631)))], (8823 ^ _152310) ^ [_459131, _459133, _459135, _459137, _459139] : [class_Rings_Ocomm__semiring__1(_459131), c_Rings_Odvd__class_Odvd(_459131, hAPP(hAPP(c_Power_Opower__class_Opower(_459131), _459133), _459135), _459137), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _459139, _459135), -(c_Rings_Odvd__class_Odvd(_459131, hAPP(hAPP(c_Power_Opower__class_Opower(_459131), _459133), _459139), _459137))], (8837 ^ _152310) ^ [_459625, _459627, _459629, _459631] : [class_Rings_Ocomm__semiring__1(_459625), c_Rings_Odvd__class_Odvd(_459625, _459627, _459629), -(c_Rings_Odvd__class_Odvd(_459625, hAPP(hAPP(c_Power_Opower__class_Opower(_459625), _459627), _459631), hAPP(hAPP(c_Power_Opower__class_Opower(_459625), _459629), _459631)))], (8847 ^ _152310) ^ [_459992, _459994, _459996] : [class_Rings_Ocomm__ring__1(_459992), 8850 ^ _152310 : [(8851 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(_459992, c_Groups_Ouminus__class_Ouminus(_459992, _459994), _459996), -(c_Rings_Odvd__class_Odvd(_459992, _459994, _459996))], (8857 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(_459992, _459994, _459996), -(c_Rings_Odvd__class_Odvd(_459992, c_Groups_Ouminus__class_Ouminus(_459992, _459994), _459996))]]], (8863 ^ _152310) ^ [_460495, _460497, _460499] : [class_Rings_Ocomm__ring__1(_460495), 8866 ^ _152310 : [(8867 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(_460495, _460497, c_Groups_Ouminus__class_Ouminus(_460495, _460499)), -(c_Rings_Odvd__class_Odvd(_460495, _460497, _460499))], (8873 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(_460495, _460497, _460499), -(c_Rings_Odvd__class_Odvd(_460495, _460497, c_Groups_Ouminus__class_Ouminus(_460495, _460499)))]]], (8879 ^ _152310) ^ [_460969, _460971] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _460969)), _460971) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _460969), _460971)))], (8881 ^ _152310) ^ [_461124, _461126, _461128, _461130] : [class_Rings_Oidom(_461124), 8884 ^ _152310 : [(8895 ^ _152310) ^ [] : [8896 ^ _152310 : [(8897 ^ _152310) ^ [] : [_461126 = c_Groups_Ozero__class_Ozero(_461124)], (8899 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(_461124, _461128, _461130)]], -(c_Rings_Odvd__class_Odvd(_461124, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_461124), _461126), _461128), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_461124), _461126), _461130)))], (8885 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(_461124, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_461124), _461126), _461128), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_461124), _461126), _461130)), -(_461126 = c_Groups_Ozero__class_Ozero(_461124)), -(c_Rings_Odvd__class_Odvd(_461124, _461128, _461130))]]], (8903 ^ _152310) ^ [_461872, _461874, _461876, _461878] : [class_Rings_Oidom(_461872), 8906 ^ _152310 : [(8917 ^ _152310) ^ [] : [8918 ^ _152310 : [(8919 ^ _152310) ^ [] : [_461876 = c_Groups_Ozero__class_Ozero(_461872)], (8921 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(_461872, _461874, _461878)]], -(c_Rings_Odvd__class_Odvd(_461872, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_461872), _461874), _461876), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_461872), _461878), _461876)))], (8907 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(_461872, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_461872), _461874), _461876), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_461872), _461878), _461876)), -(_461876 = c_Groups_Ozero__class_Ozero(_461872)), -(c_Rings_Odvd__class_Odvd(_461872, _461874, _461878))]]], (8925 ^ _152310) ^ [_462591, _462593, _462595] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _462591), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _462593, _462595)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _462591), _462593), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _462591), _462595)))], (8927 ^ _152310) ^ [_462727, _462729, _462731] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _462727, _462729)), _462731) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _462727), _462731), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _462729), _462731)))], (8929 ^ _152310) ^ [_462892, _462894, _462896, _462898] : [class_Rings_Ocomm__semiring__1(_462892), c_Rings_Odvd__class_Odvd(_462892, _462894, _462896), c_Rings_Odvd__class_Odvd(_462892, _462894, _462898), -(c_Rings_Odvd__class_Odvd(_462892, _462894, c_Groups_Oplus__class_Oplus(_462892, _462896, _462898)))], (8943 ^ _152310) ^ [_463348, _463350, _463352, _463354] : [class_Rings_Ocomm__semiring__1(_463348), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_463348), _463350, _463352), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_463348), _463350, c_Polynomial_Osmult(_463348, _463354, _463352)))], (8953 ^ _152310) ^ [_463713, _463715, _463717, _463719] : [class_Rings_Ocomm__semiring__1(_463713), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_463713), c_Polynomial_Osmult(_463713, _463715, _463717), _463719), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_463713), _463717, _463719))], (8963 ^ _152310) ^ [_464078, _464080, _464082, _464084] : [class_Rings_Ocomm__semiring__1(_464078), c_Rings_Odvd__class_Odvd(_464078, _464080, _464082), c_Rings_Odvd__class_Odvd(_464078, _464082, _464084), -(c_Rings_Odvd__class_Odvd(_464078, _464080, _464084))], (8977 ^ _152310) ^ [_464498, _464500] : [class_Rings_Ocomm__semiring__1(_464498), -(c_Rings_Odvd__class_Odvd(_464498, _464500, _464500))], (8983 ^ _152310) ^ [_464708, _464710] : [class_Rings_Ocomm__semiring__1(_464708), c_Rings_Odvd__class_Odvd(_464708, c_Groups_Ozero__class_Ozero(_464708), _464710), -(_464710 = c_Groups_Ozero__class_Ozero(_464708))], (8993 ^ _152310) ^ [_465043, _465045, _465047, _465049] : [class_Rings_Ocomm__semiring__1(_465043), c_Rings_Odvd__class_Odvd(_465043, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_465043), _465045), _465047), _465049), -(c_Rings_Odvd__class_Odvd(_465043, _465047, _465049))], (9003 ^ _152310) ^ [_465408, _465410, _465412, _465414] : [class_Rings_Ocomm__semiring__1(_465408), c_Rings_Odvd__class_Odvd(_465408, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_465408), _465410), _465412), _465414), -(c_Rings_Odvd__class_Odvd(_465408, _465410, _465414))], (9013 ^ _152310) ^ [_465773, _465775, _465777, _465779] : [class_Rings_Odvd(_465773), _465775 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_465773), _465777), _465779), -(c_Rings_Odvd__class_Odvd(_465773, _465777, _465775))], (9023 ^ _152310) ^ [_466150, _466152, _466154, _466156, _466158] : [class_Rings_Ocomm__semiring__1(_466150), c_Rings_Odvd__class_Odvd(_466150, _466152, _466154), c_Rings_Odvd__class_Odvd(_466150, _466156, _466158), -(c_Rings_Odvd__class_Odvd(_466150, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_466150), _466152), _466156), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_466150), _466154), _466158)))], (9037 ^ _152310) ^ [_466644, _466646, _466648, _466650] : [class_Rings_Ocomm__semiring__1(_466644), c_Rings_Odvd__class_Odvd(_466644, _466646, _466648), -(c_Rings_Odvd__class_Odvd(_466644, _466646, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_466644), _466650), _466648)))], (9047 ^ _152310) ^ [_467009, _467011, _467013, _467015] : [class_Rings_Ocomm__semiring__1(_467009), c_Rings_Odvd__class_Odvd(_467009, _467011, _467013), -(c_Rings_Odvd__class_Odvd(_467009, _467011, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_467009), _467013), _467015)))], (9057 ^ _152310) ^ [_467360, _467362, _467364] : [class_Rings_Ocomm__semiring__1(_467360), -(c_Rings_Odvd__class_Odvd(_467360, _467362, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_467360), _467364), _467362)))], (9063 ^ _152310) ^ [_467606, _467608, _467610] : [class_Rings_Ocomm__semiring__1(_467606), -(c_Rings_Odvd__class_Odvd(_467606, _467608, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_467606), _467608), _467610)))], (9069 ^ _152310) ^ [_467823, _467825] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _467823), _467825) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _467825), _467823))], (9071 ^ _152310) ^ [_467943, _467945, _467947] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _467943), _467945)), _467947) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _467943), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _467945), _467947)))], (9073 ^ _152310) ^ [_468092, _468094, _468096] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _468092, _468094), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _468096), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _468096), _468092), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _468096), _468094)))], (9083 ^ _152310) ^ [_468459, _468461, _468463, _468465] : [class_Fields_Ofield(_468459), 9086 ^ _152310 : [(9087 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_468459), _468461, c_Polynomial_Opoly__gcd(_468459, _468463, _468465)), 9090 ^ _152310 : [(9091 ^ _152310) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_468459), _468461, _468463))], (9093 ^ _152310) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_468459), _468461, _468465))]]], (9095 ^ _152310) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_468459), _468461, c_Polynomial_Opoly__gcd(_468459, _468463, _468465))), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_468459), _468461, _468463), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_468459), _468461, _468465)]]], (9105 ^ _152310) ^ [_469186, _469188, _469190, _469192] : [class_Fields_Ofield(_469186), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_469186), _469188, _469190), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_469186), _469188, _469192), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_469186), _469188, c_Polynomial_Opoly__gcd(_469186, _469190, _469192)))], (9119 ^ _152310) ^ [_469626, _469628] : [class_Rings_Ocomm__semiring__1(_469626), -(c_Rings_Odvd__class_Odvd(_469626, c_Groups_Oone__class_Oone(_469626), _469628))], (9125 ^ _152310) ^ [_469811] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _469811) = _469811)], (9127 ^ _152310) ^ [_469892] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _469892), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _469892)], (9129 ^ _152310) ^ [_470005, _470007] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _470005), 9132 ^ _152310 : [(9133 ^ _152310) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _470005), _470007) = c_Groups_Oone__class_Oone(tc_Int_Oint), 9136 ^ _152310 : [(9137 ^ _152310) ^ [] : [-(_470005 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (9139 ^ _152310) ^ [] : [-(_470007 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (9141 ^ _152310) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _470005), _470007) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _470005 = c_Groups_Oone__class_Oone(tc_Int_Oint), _470007 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (9151 ^ _152310) ^ [_470671, _470673, _470675, _470677] : [class_Fields_Ofield(_470671), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_470671), _470673, c_Polynomial_Osmult(_470671, _470675, _470677)), -(_470675 = c_Groups_Ozero__class_Ozero(_470671)), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_470671), _470673, _470677))], (9165 ^ _152310) ^ [_471140, _471142, _471144, _471146] : [class_Fields_Ofield(_471140), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_471140), _471142, _471144), -(_471146 = c_Groups_Ozero__class_Ozero(_471140)), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_471140), c_Polynomial_Osmult(_471140, _471146, _471142), _471144))], (9179 ^ _152310) ^ [_471609, _471611, _471613, _471615] : [class_Fields_Ofield(_471609), -(_471611 = c_Groups_Ozero__class_Ozero(_471609)), 9186 ^ _152310 : [(9187 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_471609), _471613, c_Polynomial_Osmult(_471609, _471611, _471615)), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_471609), _471613, _471615))], (9193 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_471609), _471613, _471615), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_471609), _471613, c_Polynomial_Osmult(_471609, _471611, _471615)))]]], (9199 ^ _152310) ^ [_472247, _472249, _472251] : [class_Rings_Oidom(_472247), hAPP(c_Polynomial_Ocoeff(_472247, _472249), c_Polynomial_Odegree(_472247, _472249)) = hAPP(c_Polynomial_Ocoeff(_472247, _472251), c_Polynomial_Odegree(_472247, _472251)), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_472247), _472249, _472251), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_472247), _472251, _472249), -(_472249 = _472251)], (9217 ^ _152310) ^ [_472816, _472818, _472820, _472822] : [class_Fields_Ofield(_472816), 9220 ^ _152310 : [(9237 ^ _152310) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_472816), c_Polynomial_Osmult(_472816, _472818, _472820), _472822)), 9240 ^ _152310 : [(9241 ^ _152310) ^ [] : [-(_472818 = c_Groups_Ozero__class_Ozero(_472816))], (9243 ^ _152310) ^ [] : [_472822 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_472816))]], 9244 ^ _152310 : [(9245 ^ _152310) ^ [] : [_472818 = c_Groups_Ozero__class_Ozero(_472816)], (9247 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_472816), _472820, _472822)]]], (9221 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_472816), c_Polynomial_Osmult(_472816, _472818, _472820), _472822), 9224 ^ _152310 : [(9225 ^ _152310) ^ [] : [_472818 = c_Groups_Ozero__class_Ozero(_472816), -(_472822 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_472816)))], (9231 ^ _152310) ^ [] : [-(_472818 = c_Groups_Ozero__class_Ozero(_472816)), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_472816), _472820, _472822))]]]]], (9251 ^ _152310) ^ [_473886, _473888, _473890] : [class_Rings_Oidom(_473886), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_473886), _473888, _473890), -(_473890 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_473886))), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_473886, _473888), c_Polynomial_Odegree(_473886, _473890)))], (9265 ^ _152310) ^ [_474330, _474332, _474334, _474336] : [-(hAPP(hAPP(c_Power_Opower_Opower(_474330, _474332, _474334), _474336), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _474332)], (9267 ^ _152310) ^ [_474480, _474482, _474484, _474486, _474488] : [-(hAPP(hAPP(c_Power_Opower_Opower(_474480, _474482, _474484), _474486), c_Nat_OSuc(_474488)) = hAPP(hAPP(_474484, _474486), hAPP(hAPP(c_Power_Opower_Opower(_474480, _474482, _474484), _474486), _474488)))], (9269 ^ _152310) ^ [_474637, _474639, _474641] : [class_Rings_Ocomm__semiring__1(_474637), 9274 ^ _152310 : [(9275 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _474639)], (9277 ^ _152310) ^ [] : [_474641 = c_Groups_Oone__class_Oone(_474637)]], -(c_Rings_Odvd__class_Odvd(_474637, _474641, hAPP(hAPP(c_Power_Opower__class_Opower(_474637), _474641), _474639)))], (9281 ^ _152310) ^ [_475058, _475060, _475062] : [class_Rings_Oidom(_475058), 9284 ^ _152310 : [(9285 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_475058), c_Polynomial_OpCons(_475058, _475060, c_Polynomial_OpCons(_475058, c_Groups_Oone__class_Oone(_475058), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_475058)))), _475062), -(hAPP(c_Polynomial_Opoly(_475058, _475062), c_Groups_Ouminus__class_Ouminus(_475058, _475060)) = c_Groups_Ozero__class_Ozero(_475058))], (9291 ^ _152310) ^ [] : [hAPP(c_Polynomial_Opoly(_475058, _475062), c_Groups_Ouminus__class_Ouminus(_475058, _475060)) = c_Groups_Ozero__class_Ozero(_475058), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_475058), c_Polynomial_OpCons(_475058, _475060, c_Polynomial_OpCons(_475058, c_Groups_Oone__class_Oone(_475058), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_475058)))), _475062))]]], (9297 ^ _152310) ^ [_475630, _475632, _475634] : [class_Rings_Oidom(_475630), 9300 ^ _152310 : [(9301 ^ _152310) ^ [] : [hAPP(c_Polynomial_Opoly(_475630, _475632), _475634) = c_Groups_Ozero__class_Ozero(_475630), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_475630), c_Polynomial_OpCons(_475630, c_Groups_Ouminus__class_Ouminus(_475630, _475634), c_Polynomial_OpCons(_475630, c_Groups_Oone__class_Oone(_475630), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_475630)))), _475632))], (9307 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_475630), c_Polynomial_OpCons(_475630, c_Groups_Ouminus__class_Ouminus(_475630, _475634), c_Polynomial_OpCons(_475630, c_Groups_Oone__class_Oone(_475630), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_475630)))), _475632), -(hAPP(c_Polynomial_Opoly(_475630, _475632), _475634) = c_Groups_Ozero__class_Ozero(_475630))]]], (9313 ^ _152310) ^ [_476202, _476204, _476206] : [class_Rings_Oidom(_476202), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_476202), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_476202)), c_Polynomial_OpCons(_476202, c_Groups_Ouminus__class_Ouminus(_476202, _476204), c_Polynomial_OpCons(_476202, c_Groups_Oone__class_Oone(_476202), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_476202))))), c_Polynomial_Oorder(_476202, _476204, _476206)), _476206))], (9319 ^ _152310) ^ [_476498, _476500, _476502] : [class_Rings_Odvd(_476498), class_Rings_Osemiring__0(_476498), 9326 ^ _152310 : [(9327 ^ _152310) ^ [] : [9328 ^ _152310 : [(9329 ^ _152310) ^ [_476807] : [hBOOL(hAPP(_476500, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_476498), _476502), _476807)))]], 9331 ^ _152310 : [(9332 ^ _152310) ^ [] : [-(c_Rings_Odvd__class_Odvd(_476498, _476502, c_Groups_Oplus__class_Oplus(_476498, 9330 ^ [_476498, _476500, _476502], c_Groups_Ozero__class_Ozero(_476498))))], (9334 ^ _152310) ^ [] : [-(hBOOL(hAPP(_476500, 9330 ^ [_476498, _476500, _476502])))]]], (9336 ^ _152310) ^ [] : [-(hBOOL(hAPP(_476500, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_476498), _476502), 9343 ^ [_476498, _476500, _476502])))), 9337 ^ _152310 : [(9338 ^ _152310) ^ [_477147] : [c_Rings_Odvd__class_Odvd(_476498, _476502, c_Groups_Oplus__class_Oplus(_476498, _477147, c_Groups_Ozero__class_Ozero(_476498))), hBOOL(hAPP(_476500, _477147))]]]]], (9347 ^ _152310) ^ [_477560, _477562, _477564, _477566] : [class_Fields_Ofield(_477560), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_477560), _477562, _477564), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_477560), _477562, _477566), 9361 ^ _152310 : [(9362 ^ _152310) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_477560), 9360 ^ [_477560, _477562, _477564, _477566], _477564))], (9364 ^ _152310) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_477560), 9360 ^ [_477560, _477562, _477564, _477566], _477566))], (9366 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_477560), 9360 ^ [_477560, _477562, _477564, _477566], _477562)]], -(c_Polynomial_Opoly__gcd(_477560, _477564, _477566) = _477562), 9371 ^ _152310 : [(9372 ^ _152310) ^ [] : [-(_477564 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_477560)))], (9374 ^ _152310) ^ [] : [-(_477566 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_477560)))], (9376 ^ _152310) ^ [] : [hAPP(c_Polynomial_Ocoeff(_477560, _477562), c_Polynomial_Odegree(_477560, _477562)) = c_Groups_Ozero__class_Ozero(_477560)]], 9377 ^ _152310 : [(9384 ^ _152310) ^ [] : [hAPP(c_Polynomial_Ocoeff(_477560, _477562), c_Polynomial_Odegree(_477560, _477562)) = c_Groups_Oone__class_Oone(_477560)], (9378 ^ _152310) ^ [] : [_477564 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_477560)), _477566 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_477560))]]], (9388 ^ _152310) ^ [_478998, _479000, _479002] : [class_Lattices_Oboolean__algebra(_478998), 9391 ^ _152310 : [(9392 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_478998, c_Groups_Ouminus__class_Ouminus(_478998, _479000), c_Groups_Ouminus__class_Ouminus(_478998, _479002)), -(c_Orderings_Oord__class_Oless__eq(_478998, _479002, _479000))], (9398 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_478998, _479002, _479000), -(c_Orderings_Oord__class_Oless__eq(_478998, c_Groups_Ouminus__class_Ouminus(_478998, _479000), c_Groups_Ouminus__class_Ouminus(_478998, _479002)))]]], (9404 ^ _152310) ^ [_479467] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _479467))], (9406 ^ _152310) ^ [_479604, _479606] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _479604, _479606), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _479604, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _479606)))], (9412 ^ _152310) ^ [_479776, _479778] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _479776, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _479778)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _479776, _479778))], (9418 ^ _152310) ^ [_480027, _480029] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _480027, _480029), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _480027), _480029))], (9424 ^ _152310) ^ [_480199, _480201] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _480199), _480201), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _480199, _480201))], (9430 ^ _152310) ^ [_480464, _480466, _480468] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _480464, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _480466, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _480464), _480468))), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _480464, _480466))], (9436 ^ _152310) ^ [_480656, _480658, _480660] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _480656, _480658), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _480656, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _480658, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _480656), _480660))))], (9442 ^ _152310) ^ [_480940, _480942, _480944, _480946, _480948] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _480940, _480942), 9445 ^ _152310 : [(9446 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _480940, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _480944, _480946)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _480940, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _480944, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _480948), _480942)), _480946)))], (9452 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _480940, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _480944, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _480948), _480942)), _480946)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _480940, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _480944, _480946)))]]], (9458 ^ _152310) ^ [_481539, _481541] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _481539, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _481541, _481539)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _481539, _481541))], (9464 ^ _152310) ^ [_481713, _481715] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _481713, _481715), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _481713, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _481715, _481713)))], (9470 ^ _152310) ^ [_481937, _481939] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _481937), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _481939), c_Rings_Odvd__class_Odvd(tc_Int_Oint, _481937, _481939), c_Rings_Odvd__class_Odvd(tc_Int_Oint, _481939, _481937), -(_481937 = _481939)], (9488 ^ _152310) ^ [_482422, _482424] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _482422, _482424), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _482424), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _482422, _482424))], (9498 ^ _152310) ^ [_482727, _482729] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _482727), c_Orderings_Oord__class_Oless(tc_Int_Oint, _482727, _482729), c_Rings_Odvd__class_Odvd(tc_Int_Oint, _482729, _482727)], (9508 ^ _152310) ^ [_483047, _483049, _483051] : [-(_483047 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 9511 ^ _152310 : [(9512 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _483049, _483051), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _483047), _483049), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _483047), _483051)))], (9518 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _483047), _483049), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _483047), _483051)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _483049, _483051))]]], (9524 ^ _152310) ^ [_483582, _483584, _483586] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _483582), _483584), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _483582), _483586)), -(_483582 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _483584, _483586))], (9534 ^ _152310) ^ [_483937] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _483937, c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_483937 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (9540 ^ _152310) ^ [_484095] : [_484095 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _484095, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (9546 ^ _152310) ^ [_484318] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _484318, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_484318 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (9552 ^ _152310) ^ [_484476] : [_484476 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _484476, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (9558 ^ _152310) ^ [_484684, _484686] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _484684), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _484684, _484686), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _484686, _484684)], (9578 ^ _152310) ^ [_485323, _485325, _485327] : [9579 ^ _152310 : [(9580 ^ _152310) ^ [] : [_485323 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (9582 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _485325, _485327)]], -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _485323), _485325), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _485323), _485327)))], (9568 ^ _152310) ^ [_485033, _485035, _485037] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _485033), _485035), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _485033), _485037)), -(_485033 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _485035, _485037))], (9586 ^ _152310) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (9588 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (9590 ^ _152310) ^ [_485779, _485781] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _485779, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _485781, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _485779, _485781))], (9596 ^ _152310) ^ [_485953, _485955] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _485953, _485955), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _485953, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _485955, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (9612 ^ _152310) ^ [_486470, _486472] : [9613 ^ _152310 : [(9614 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _486470, _486472)], (9616 ^ _152310) ^ [] : [_486470 = _486472]], -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _486470, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _486472, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (9602 ^ _152310) ^ [_486206, _486208] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _486206, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _486208, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _486206, _486208)), -(_486206 = _486208)], (9620 ^ _152310) ^ [_486797, _486799] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _486797, c_Groups_Oone__class_Oone(tc_Int_Oint)), _486799), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _486797, _486799))], (9626 ^ _152310) ^ [_486971, _486973] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _486971, _486973), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _486971, c_Groups_Oone__class_Oone(tc_Int_Oint)), _486973))], (9632 ^ _152310) ^ [_487210] : [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), _487210), _487210), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _487210, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9638 ^ _152310) ^ [_487386] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _487386, 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), _487386), _487386), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9644 ^ _152310) ^ [_487598] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _487598), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _487598)))], (9650 ^ _152310) ^ [_487814, _487816] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _487814, _487816), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _487814, c_Groups_Oone__class_Oone(tc_Int_Oint)), _487816))], (9656 ^ _152310) ^ [_488051] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _488051), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _488051))], (9662 ^ _152310) ^ [_488211] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _488211), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _488211))], (9668 ^ _152310) ^ [_488391] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _488391), _488391) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (9670 ^ _152310) ^ [_488506, _488508] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _488506, _488508)), -(_488506 = _488508), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _488508, _488506))], (9680 ^ _152310) ^ [_488825, _488827, _488829] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _488825, _488827), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _488825, _488829), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _488827, _488829)))], (9686 ^ _152310) ^ [_489089, _489091, _489093, _489095] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _489089, _489091), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _489093, _489095), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _489089, _489093), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _489091, _489095)))], (9696 ^ _152310) ^ [_489459, _489461] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _489459, _489461), 9699 ^ _152310 : [(9700 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _489459, _489461))], (9702 ^ _152310) ^ [] : [_489459 = _489461]]], (9704 ^ _152310) ^ [_489701, _489703] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _489701, _489703)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _489701, _489703), -(_489701 = _489703)], (9714 ^ _152310) ^ [_489980] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _489980) = _489980)], (9716 ^ _152310) ^ [_490062] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _490062, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _490062)], (9718 ^ _152310) ^ [_490172, _490174, _490176] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _490172, _490174), _490176) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _490172, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _490174, _490176)))], (9720 ^ _152310) ^ [_490298, _490300, _490302] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _490298, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _490300, _490302)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _490300, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _490298, _490302)))], (9722 ^ _152310) ^ [_490410, _490412] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _490410, _490412) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _490412, _490410))], (9724 ^ _152310) ^ [_490541, _490543, _490545] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _490541, _490543), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _490545, _490541), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _490545, _490543)))], (9730 ^ _152310) ^ [_490748] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _490748)) = _490748)], (9732 ^ _152310) ^ [] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (9734 ^ _152310) ^ [_490885] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _490885), _490885) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (9736 ^ _152310) ^ [_490984, _490986] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _490984, _490986)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _490984), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _490986)))], (9738 ^ _152310) ^ [_491110, _491112] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _491110, _491112), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _491112), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _491110, _491112))], (9748 ^ _152310) ^ [_491429, _491431, _491433] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _491429), 9751 ^ _152310 : [(9752 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _491429), _491431), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _491429), _491433)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _491431, _491433))], (9758 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _491431, _491433), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _491429), _491431), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _491429), _491433)))]]], (9764 ^ _152310) ^ [_491963, _491965, _491967] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _491963), _491965), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _491963), _491967)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _491963), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _491965, _491967))], (9774 ^ _152310) ^ [_492316, _492318, _492320] : [class_Lattices_Oab__semigroup__idem__mult(_492316), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_492316), _492318), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_492316), _492318), _492320)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_492316), _492318), _492320))], (9780 ^ _152310) ^ [_492578, _492580] : [class_Lattices_Oab__semigroup__idem__mult(_492578), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_492578), _492580), _492580) = _492580)], (9786 ^ _152310) ^ [_492802, _492804] : [class_Lattices_Oab__semigroup__idem__mult(_492802), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_492802), _492804), _492804) = _492804)], (9792 ^ _152310) ^ [_493040, _493042, _493044] : [class_Lattices_Oboolean__algebra(_493040), 9795 ^ _152310 : [(9796 ^ _152310) ^ [] : [c_Groups_Ouminus__class_Ouminus(_493040, _493042) = c_Groups_Ouminus__class_Ouminus(_493040, _493044), -(_493042 = _493044)], (9802 ^ _152310) ^ [] : [_493042 = _493044, -(c_Groups_Ouminus__class_Ouminus(_493040, _493042) = c_Groups_Ouminus__class_Ouminus(_493040, _493044))]]], (9808 ^ _152310) ^ [_493560, _493562, _493564, _493566] : [class_Groups_Ouminus(_493560), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_493562, _493560), _493564), _493566) = c_Groups_Ouminus__class_Ouminus(_493560, hAPP(_493564, _493566)))], (9814 ^ _152310) ^ [_493810, _493812] : [class_Lattices_Oboolean__algebra(_493810), -(c_Groups_Ouminus__class_Ouminus(_493810, c_Groups_Ouminus__class_Ouminus(_493810, _493812)) = _493812)], (9820 ^ _152310) ^ [_494030, _494032] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _494030), 9823 ^ _152310 : [(9824 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _494032), _494030), _494030), -(_494032 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (9830 ^ _152310) ^ [] : [_494032 = 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), _494032), _494030), _494030))]]], (9836 ^ _152310) ^ [_494513, _494515] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _494513), 9839 ^ _152310 : [(9840 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _494513), _494515), _494513), -(_494515 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (9846 ^ _152310) ^ [] : [_494515 = 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), _494513), _494515), _494513))]]], (9852 ^ _152310) ^ [_495010, _495012, _495014] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _495010), _495012), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _495010), _495014)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _495010), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _495012, _495014))], (9862 ^ _152310) ^ [_495363, _495365, _495367] : [class_Lattices_Oboolean__algebra(_495363), c_Orderings_Oord__class_Oless__eq(_495363, _495365, _495367), -(c_Orderings_Oord__class_Oless__eq(_495363, c_Groups_Ouminus__class_Ouminus(_495363, _495367), c_Groups_Ouminus__class_Ouminus(_495363, _495365)))], (9872 ^ _152310) ^ [_495700, _495702, _495704] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _495700), _495700 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _495702, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _495700), _495704)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _495702), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _495704, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (9886 ^ _152310) ^ [_496142, _496144, _496146] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _496142), _496142 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _496144, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _496142), _496146)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _496144, _496142), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _496146))], (9900 ^ _152310) ^ [_496541] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _496541, _496541))], (9902 ^ _152310) ^ [_496649, _496651] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _496649, _496651), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _496651, _496649)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _496651, _496649), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _496649, _496651))], (9916 ^ _152310) ^ [_497068, _497070, _497072] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _497068, _497070), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _497070, _497068)), 9931 ^ _152310 : [(9932 ^ _152310) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _497068, _497072))], (9934 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _497072, _497068)]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _497070, _497072), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _497072, _497070))], (9936 ^ _152310) ^ [_497661, _497663] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _497661, _497663), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _497663, _497661)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _497663, _497661), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _497661, _497663))], (9950 ^ _152310) ^ [_498080, _498082, _498084] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _498080, _498082), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _498082, _498080)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _498082, _498084), 9961 ^ _152310 : [(9962 ^ _152310) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _498080, _498084))], (9964 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _498084, _498080)]]], (9966 ^ _152310) ^ [_498589, _498591, _498593] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _498589, _498591), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _498591, _498589)), _498591 = _498593, 9977 ^ _152310 : [(9978 ^ _152310) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _498589, _498593))], (9980 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _498593, _498589)]]], (9982 ^ _152310) ^ [_499082, _499084] : [_499084 = _499082, c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _499082, _499084), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _499084, _499082))], (9992 ^ _152310) ^ [_499389, _499391] : [_499389 = _499391, c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _499389, _499391), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _499391, _499389))], (10002 ^ _152310) ^ [_499696, _499698] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _499696, _499698), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _499698, _499696)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _499698, _499696), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _499696, _499698))], (10016 ^ _152310) ^ [_500101, _500103] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _500101, _500103)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _500101, _500103), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _500103, _500101))], (10026 ^ _152310) ^ [_500409, _500411] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _500409, _500411), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _500411, _500409)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _500411, _500409), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _500409, _500411))], (10040 ^ _152310) ^ [_500814, _500816] : [_500814 = _500816, c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _500814, _500816), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _500816, _500814))], (10050 ^ _152310) ^ [_501135, _501137, _501139] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _501135, _501137), 10061 ^ _152310 : [(10062 ^ _152310) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _501135, _501139))], (10064 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _501139, _501135)]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _501137, _501139), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _501139, _501137))], (10066 ^ _152310) ^ [_501642, _501644, _501646] : [_501642 = _501644, 10077 ^ _152310 : [(10078 ^ _152310) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _501642, _501646))], (10080 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _501646, _501642)]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _501644, _501646), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _501646, _501644))], (10082 ^ _152310) ^ [_502147, _502149, _502151] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _502147, _502149), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _502149, _502151), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _502147, _502151))], (10092 ^ _152310) ^ [_502462, _502464] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _502462, _502464), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _502464, _502462), -(_502462 = _502464)], (10102 ^ _152310) ^ [_502765, _502767] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _502765, _502767), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _502767, _502765), -(_502765 = _502767)], (10112 ^ _152310) ^ [_503082, _503084, _503086] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _503082, _503084), _503084 = _503086, -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _503082, _503086))], (10122 ^ _152310) ^ [_503409, _503411, _503413] : [_503409 = _503411, c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _503411, _503413), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _503409, _503413))], (10132 ^ _152310) ^ [_503722, _503724] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _503722, _503724), -(_503722 = _503724), 10139 ^ _152310 : [(10140 ^ _152310) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _503722, _503724))], (10142 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _503724, _503722)]]], (10144 ^ _152310) ^ [_504106, _504108] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _504106, _504108), 10149 ^ _152310 : [(10150 ^ _152310) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _504106, _504108))], (10152 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _504108, _504106)]], -(_504106 = _504108)], (10156 ^ _152310) ^ [_504488, _504490] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _504488, _504490), 10159 ^ _152310 : [(10160 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _504490, _504488), -(_504490 = _504488)], (10166 ^ _152310) ^ [] : [_504490 = _504488, -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _504490, _504488))]]], (10172 ^ _152310) ^ [_504953, _504955] : [_504953 = _504955, -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _504953, _504955))], (10178 ^ _152310) ^ [_505165, _505167] : [-(_505165 = _505167), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _505165, _505167), 10185 ^ _152310 : [(10186 ^ _152310) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _505165, _505167))], (10188 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _505167, _505165)]]], (10190 ^ _152310) ^ [_505578, _505580] : [10197 ^ _152310 : [(10198 ^ _152310) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _505578, _505580))], (10200 ^ _152310) ^ [] : [_505578 = _505580]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _505578, _505580), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _505580, _505578))], (10202 ^ _152310) ^ [_505914, _505916] : [10209 ^ _152310 : [(10210 ^ _152310) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _505914, _505916))], (10212 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _505916, _505914)]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _505914, _505916), -(_505914 = _505916)], (10214 ^ _152310) ^ [_506329, _506331] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _506329, _506331), 10219 ^ _152310 : [(10220 ^ _152310) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _506329, _506331))], (10222 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _506331, _506329)]], -(_506329 = _506331)], (10226 ^ _152310) ^ [_506663, _506665] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _506663, _506665)), 10227 ^ _152310 : [(10234 ^ _152310) ^ [] : [_506663 = _506665], (10228 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _506663, _506665), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _506665, _506663))]]], (10238 ^ _152310) ^ [_507076, _507078] : [_507076 = _507078, 10241 ^ _152310 : [(10242 ^ _152310) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _507076, _507078))], (10244 ^ _152310) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _507078, _507076))]]], (10246 ^ _152310) ^ [_507317, _507319] : [-(_507317 = _507319), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _507317, _507319), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _507319, _507317)], (10256 ^ _152310) ^ [_507622, _507624] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _507622, _507624), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _507624, _507622), -(_507622 = _507624)], (10266 ^ _152310) ^ [_507939, _507941, _507943] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _507939, _507941), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _507941, _507943), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _507939, _507943))], (10276 ^ _152310) ^ [_508254, _508256] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _508254, _508256)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _508256, _508254))], (10282 ^ _152310) ^ [_508440] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _508440, _508440))], (10284 ^ _152310) ^ [_508604, _508606, _508608, _508610, _508612, _508614] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _508604), _508606), _508608) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _508610), _508612), _508614), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _508610), _508612), _508614), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _508608, _508604), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _508614), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _508610), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _508610, _508604), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _508612, _508606))], (10310 ^ _152310) ^ [_509477, _509479, _509481, _509483, _509485] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _509477), _509479), _509481), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _509477), _509483), _509485)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _509485, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _509477, _509485), c_Orderings_Oord__class_Oless(tc_Int_Oint, _509477, _509481), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _509483, _509479))], (10328 ^ _152310) ^ [_510114, _510116, _510118, _510120, _510122, _510124] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _510114), _510116), _510118) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _510120), _510122), _510124), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _510120), _510122), _510124)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _510124, _510120), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _510118), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _510120), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _510120, _510114), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _510116, _510122))], (10354 ^ _152310) ^ [_510987, _510989, _510991, _510993, _510995] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _510987), _510989), _510991), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _510987), _510993), _510995)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _510991), c_Orderings_Oord__class_Oless(tc_Int_Oint, _510991, _510987), c_Orderings_Oord__class_Oless(tc_Int_Oint, _510995, _510987), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _510989, _510993))], (10372 ^ _152310) ^ [_511582, _511584, _511586] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _511582), _511584), _511586), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _511586), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _511582), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _511584, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (10386 ^ _152310) ^ [_512026, _512028, _512030] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _512026), _512028), _512030)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _512030, _512026), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _512026), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _512028))], (10400 ^ _152310) ^ [_512470, _512472, _512474] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _512470), _512472), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _512474), _512472)), -(_512472 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _512470, _512474))], (10410 ^ _152310) ^ [_512824, _512826, _512828] : [-(_512824 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 10413 ^ _152310 : [(10414 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _512826), _512824), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _512828), _512824)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _512826, _512828))], (10420 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _512826, _512828), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _512826), _512824), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _512828), _512824)))]]], (10426 ^ _152310) ^ [_513316] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _513316, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10428 ^ _152310) ^ [_513395] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _513395))], (10430 ^ _152310) ^ [_513503, _513505] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _513503), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _513505, _513503), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _513505))], (10440 ^ _152310) ^ [_513822, _513824, _513826] : [-(_513822 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 10443 ^ _152310 : [(10444 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _513824), _513822), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _513826), _513822)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _513824, _513826))], (10450 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _513824, _513826), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _513824), _513822), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _513826), _513822)))]]], (10456 ^ _152310) ^ [_514357, _514359, _514361] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _514357), _514359), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _514361), _514359)), -(_514359 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _514357, _514361))], (10466 ^ _152310) ^ [_514697, _514699] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _514697), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _514697), _514699)))], (10472 ^ _152310) ^ [_514923, _514925] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _514923), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _514925), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _514923), _514925)))], (10482 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (10484 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (10486 ^ _152310) ^ [_515346, _515348] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _515346), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _515348), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _515346, _515348)))], (10496 ^ _152310) ^ [_515673, _515675, _515677] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _515673), 10502 ^ _152310 : [(10503 ^ _152310) ^ [] : [-(hBOOL(hAPP(_515675, 10501 ^ [_515673, _515675, _515677])))], (10505 ^ _152310) ^ [] : [hBOOL(hAPP(_515675, c_Groups_Oplus__class_Oplus(tc_Int_Oint, 10501 ^ [_515673, _515675, _515677], _515673)))]], c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _515677), 10510 ^ _152310 : [(10511 ^ _152310) ^ [_516188] : [hBOOL(hAPP(_515675, _516188)), -(hBOOL(hAPP(_515675, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _516188, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _515677), _515673)))))]]], (10517 ^ _152310) ^ [_516458, _516460] : [-(hBOOL(hAPP(_516458, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_516458, _516460)), 10525 ^ _152310 : [(10526 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 10524 ^ [_516458, _516460], _516460))], (10534 ^ _152310) ^ [] : [-(hBOOL(hAPP(_516458, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, 10524 ^ [_516458, _516460], c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (10528 ^ _152310) ^ [_516894] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _516894, 10524 ^ [_516458, _516460]), hBOOL(hAPP(_516458, _516894))]]], (10536 ^ _152310) ^ [_517207, _517209] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _517207), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _517209), 10544 ^ _152310 : [(10545 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 10543 ^ [_517207, _517209]))], (10547 ^ _152310) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), 10543 ^ [_517207, _517209]), _517207) = _517209)], (10549 ^ _152310) ^ [_517711] : [-(_517711 = 10543 ^ [_517207, _517209]), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _517711), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _517711), _517207) = _517209]]], (10559 ^ _152310) ^ [_518065, _518067] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _518065), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _518067), 10567 ^ _152310 : [(10568 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 10566 ^ [_518065, _518067]))], (10570 ^ _152310) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), 10566 ^ [_518065, _518067]), _518065) = _518067)]]], (10572 ^ _152310) ^ [_518520] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _518520), -(c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _518520, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatceiling(_518520), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (10578 ^ _152310) ^ [_518750, _518752] : [class_Fields_Ofield(_518750), -(c_Polynomial_Opoly__gcd(_518750, _518752, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_518750))) = c_Polynomial_Osmult(_518750, c_Rings_Oinverse__class_Oinverse(_518750, hAPP(c_Polynomial_Ocoeff(_518750, _518752), c_Polynomial_Odegree(_518750, _518752))), _518752))], (10584 ^ _152310) ^ [_519006, _519008] : [class_Rings_Odivision__ring(_519006), -(_519008 = c_Groups_Ozero__class_Ozero(_519006)), -(c_Rings_Oinverse__class_Oinverse(_519006, c_Groups_Ouminus__class_Ouminus(_519006, _519008)) = c_Groups_Ouminus__class_Ouminus(_519006, c_Rings_Oinverse__class_Oinverse(_519006, _519008)))], (10594 ^ _152310) ^ [_519305] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_RComplete_Onatceiling(_519305)))], (10596 ^ _152310) ^ [_519415, _519417] : [class_Rings_Odivision__ring__inverse__zero(_519415), -(c_Rings_Oinverse__class_Oinverse(_519415, c_Groups_Ouminus__class_Ouminus(_519415, _519417)) = c_Groups_Ouminus__class_Ouminus(_519415, c_Rings_Oinverse__class_Oinverse(_519415, _519417)))], (10602 ^ _152310) ^ [_519647, _519649] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _519647, _519649), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_519647), c_RComplete_Onatceiling(_519649)))], (10608 ^ _152310) ^ [_519883, _519885, _519887] : [class_Rings_Odivision__ring__inverse__zero(_519883), -(c_Rings_Oinverse__class_Oinverse(_519883, hAPP(hAPP(c_Power_Opower__class_Opower(_519883), _519885), _519887)) = hAPP(hAPP(c_Power_Opower__class_Opower(_519883), c_Rings_Oinverse__class_Oinverse(_519883, _519885)), _519887))], (10614 ^ _152310) ^ [_520141, _520143] : [class_Rings_Odivision__ring__inverse__zero(_520141), -(c_Rings_Oinverse__class_Oinverse(_520141, c_Rings_Oinverse__class_Oinverse(_520141, _520143)) = _520143)], (10620 ^ _152310) ^ [_520375, _520377, _520379] : [class_Rings_Odivision__ring__inverse__zero(_520375), 10623 ^ _152310 : [(10624 ^ _152310) ^ [] : [c_Rings_Oinverse__class_Oinverse(_520375, _520377) = c_Rings_Oinverse__class_Oinverse(_520375, _520379), -(_520377 = _520379)], (10630 ^ _152310) ^ [] : [_520377 = _520379, -(c_Rings_Oinverse__class_Oinverse(_520375, _520377) = c_Rings_Oinverse__class_Oinverse(_520375, _520379))]]], (10636 ^ _152310) ^ [_520881, _520883, _520885] : [class_Rings_Odivision__ring__inverse__zero(_520881), c_Rings_Oinverse__class_Oinverse(_520881, _520883) = c_Rings_Oinverse__class_Oinverse(_520881, _520885), -(_520883 = _520885)], (10646 ^ _152310) ^ [] : [-(c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10648 ^ _152310) ^ [] : [-(c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (10650 ^ _152310) ^ [_521292] : [class_Rings_Odivision__ring__inverse__zero(_521292), -(c_Rings_Oinverse__class_Oinverse(_521292, c_Groups_Ozero__class_Ozero(_521292)) = c_Groups_Ozero__class_Ozero(_521292))], (10656 ^ _152310) ^ [_521508, _521510] : [class_Rings_Odivision__ring__inverse__zero(_521508), 10659 ^ _152310 : [(10660 ^ _152310) ^ [] : [c_Rings_Oinverse__class_Oinverse(_521508, _521510) = c_Groups_Ozero__class_Ozero(_521508), -(_521510 = c_Groups_Ozero__class_Ozero(_521508))], (10666 ^ _152310) ^ [] : [_521510 = c_Groups_Ozero__class_Ozero(_521508), -(c_Rings_Oinverse__class_Oinverse(_521508, _521510) = c_Groups_Ozero__class_Ozero(_521508))]]], (10672 ^ _152310) ^ [_521987, _521989] : [class_Rings_Odivision__ring(_521987), -(_521989 = c_Groups_Ozero__class_Ozero(_521987)), c_Rings_Oinverse__class_Oinverse(_521987, _521989) = c_Groups_Ozero__class_Ozero(_521987)], (10682 ^ _152310) ^ [_522302, _522304] : [class_Rings_Odivision__ring(_522302), -(_522304 = c_Groups_Ozero__class_Ozero(_522302)), -(c_Rings_Oinverse__class_Oinverse(_522302, c_Rings_Oinverse__class_Oinverse(_522302, _522304)) = _522304)], (10692 ^ _152310) ^ [_522618, _522620] : [class_Rings_Odivision__ring(_522618), c_Rings_Oinverse__class_Oinverse(_522618, _522620) = c_Groups_Ozero__class_Ozero(_522618), -(_522620 = c_Groups_Ozero__class_Ozero(_522618))], (10702 ^ _152310) ^ [_522943, _522945, _522947] : [class_Rings_Odivision__ring(_522943), c_Rings_Oinverse__class_Oinverse(_522943, _522945) = c_Rings_Oinverse__class_Oinverse(_522943, _522947), -(_522945 = c_Groups_Ozero__class_Ozero(_522943)), -(_522947 = c_Groups_Ozero__class_Ozero(_522943)), -(_522945 = _522947)], (10720 ^ _152310) ^ [] : [-(c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (10722 ^ _152310) ^ [_523501] : [class_Rings_Odivision__ring(_523501), -(c_Rings_Oinverse__class_Oinverse(_523501, c_Groups_Oone__class_Oone(_523501)) = c_Groups_Oone__class_Oone(_523501))], (10728 ^ _152310) ^ [_523731, _523733, _523735] : [class_Rings_Odivision__ring(_523731), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_523731), _523733), _523735) = c_Groups_Oone__class_Oone(_523731), -(c_Rings_Oinverse__class_Oinverse(_523731, _523733) = _523735)], (10738 ^ _152310) ^ [_524078, _524080, _524082] : [class_Rings_Odivision__ring(_524078), -(_524080 = c_Groups_Ozero__class_Ozero(_524078)), -(_524082 = c_Groups_Ozero__class_Ozero(_524078)), -(c_Rings_Oinverse__class_Oinverse(_524078, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_524078), _524080), _524082)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_524078), c_Rings_Oinverse__class_Oinverse(_524078, _524082)), c_Rings_Oinverse__class_Oinverse(_524078, _524080)))], (10752 ^ _152310) ^ [_524556, _524558, _524560] : [class_Rings_Odivision__ring(_524556), -(_524558 = c_Groups_Ozero__class_Ozero(_524556)), -(c_Rings_Oinverse__class_Oinverse(_524556, hAPP(hAPP(c_Power_Opower__class_Opower(_524556), _524558), _524560)) = hAPP(hAPP(c_Power_Opower__class_Opower(_524556), c_Rings_Oinverse__class_Oinverse(_524556, _524558)), _524560))], (10762 ^ _152310) ^ [_524914, _524916] : [class_Rings_Odivision__ring(_524914), -(_524916 = c_Groups_Ozero__class_Ozero(_524914)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_524914), c_Rings_Oinverse__class_Oinverse(_524914, _524916)), _524916) = c_Groups_Oone__class_Oone(_524914))], (10772 ^ _152310) ^ [_525244, _525246] : [class_Rings_Odivision__ring(_525244), -(_525246 = c_Groups_Ozero__class_Ozero(_525244)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_525244), _525246), c_Rings_Oinverse__class_Oinverse(_525244, _525246)) = c_Groups_Oone__class_Oone(_525244))], (10782 ^ _152310) ^ [_525588, _525590, _525592] : [class_Rings_Odivision__ring(_525588), -(_525590 = c_Groups_Ozero__class_Ozero(_525588)), -(_525592 = c_Groups_Ozero__class_Ozero(_525588)), -(c_Groups_Oplus__class_Oplus(_525588, c_Rings_Oinverse__class_Oinverse(_525588, _525590), c_Rings_Oinverse__class_Oinverse(_525588, _525592)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_525588), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_525588), c_Rings_Oinverse__class_Oinverse(_525588, _525590)), c_Groups_Oplus__class_Oplus(_525588, _525590, _525592))), c_Rings_Oinverse__class_Oinverse(_525588, _525592)))], (10796 ^ _152310) ^ [_526060] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _526060, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_RComplete_Onatceiling(_526060) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10802 ^ _152310) ^ [_526256] : [-(_526256 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, _526256)), _526256) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (10808 ^ _152310) ^ [_526481, _526483] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _526481), -(c_NthRoot_Oroot(_526481, c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, _526483)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, c_NthRoot_Oroot(_526481, _526483)))], (10814 ^ _152310) ^ [_526773, _526775, _526777, _526779, _526781, _526783] : [class_Fields_Ofield(_526773), -(_526775 = c_Groups_Ozero__class_Ozero(_526773)), c_Polynomial_Opdivmod__rel(_526773, _526777, _526779, _526781, _526783), -(c_Polynomial_Opdivmod__rel(_526773, _526777, c_Polynomial_Osmult(_526773, _526775, _526779), c_Polynomial_Osmult(_526773, c_Rings_Oinverse__class_Oinverse(_526773, _526775), _526781), _526783))], (10828 ^ _152310) ^ [_527271] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_527271), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _527271, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (10834 ^ _152310) ^ [_527435] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _527435, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_527435), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (10840 ^ _152310) ^ [_527649, _527651] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _527649), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _527651), -(c_NthRoot_Oroot(_527649, c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, _527651)) = c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, c_NthRoot_Oroot(_527649, _527651)))], (10850 ^ _152310) ^ [_527976, _527978] : [class_Fields_Olinordered__field__inverse__zero(_527976), 10853 ^ _152310 : [(10854 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_527976, c_Groups_Oone__class_Oone(_527976), c_Rings_Oinverse__class_Oinverse(_527976, _527978)), 10857 ^ _152310 : [(10858 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(_527976, c_Groups_Ozero__class_Ozero(_527976), _527978))], (10860 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_527976, _527978, c_Groups_Oone__class_Oone(_527976)))]]], (10862 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_527976, c_Groups_Oone__class_Oone(_527976), c_Rings_Oinverse__class_Oinverse(_527976, _527978))), c_Orderings_Oord__class_Oless(_527976, c_Groups_Ozero__class_Ozero(_527976), _527978), c_Orderings_Oord__class_Oless__eq(_527976, _527978, c_Groups_Oone__class_Oone(_527976))]]], (10872 ^ _152310) ^ [_528628, _528630] : [class_Fields_Olinordered__field__inverse__zero(_528628), 10875 ^ _152310 : [(10886 ^ _152310) ^ [] : [10887 ^ _152310 : [(10888 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_528628, _528630, c_Groups_Ozero__class_Ozero(_528628))], (10890 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_528628, c_Groups_Oone__class_Oone(_528628), _528630)]], -(c_Orderings_Oord__class_Oless(_528628, c_Rings_Oinverse__class_Oinverse(_528628, _528630), c_Groups_Oone__class_Oone(_528628)))], (10876 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_528628, c_Rings_Oinverse__class_Oinverse(_528628, _528630), c_Groups_Oone__class_Oone(_528628)), -(c_Orderings_Oord__class_Oless__eq(_528628, _528630, c_Groups_Ozero__class_Ozero(_528628))), -(c_Orderings_Oord__class_Oless(_528628, c_Groups_Oone__class_Oone(_528628), _528630))]]], (10894 ^ _152310) ^ [_529266] : [class_Fields_Ofield__inverse__zero(_529266), -(c_Rings_Oinverse__class_Oinverse(_529266, c_Groups_Ozero__class_Ozero(_529266)) = c_Groups_Ozero__class_Ozero(_529266))], (10900 ^ _152310) ^ [_529496, _529498, _529500] : [class_Fields_Ofield__inverse__zero(_529496), -(c_Rings_Oinverse__class_Oinverse(_529496, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_529496), _529498), _529500)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_529496), c_Rings_Oinverse__class_Oinverse(_529496, _529498)), c_Rings_Oinverse__class_Oinverse(_529496, _529500)))], (10906 ^ _152310) ^ [_529760, _529762] : [class_Fields_Ofield__inverse__zero(_529760), 10909 ^ _152310 : [(10910 ^ _152310) ^ [] : [c_Rings_Oinverse__class_Oinverse(_529760, _529762) = c_Groups_Oone__class_Oone(_529760), -(_529762 = c_Groups_Oone__class_Oone(_529760))], (10916 ^ _152310) ^ [] : [_529762 = c_Groups_Oone__class_Oone(_529760), -(c_Rings_Oinverse__class_Oinverse(_529760, _529762) = c_Groups_Oone__class_Oone(_529760))]]], (10922 ^ _152310) ^ [_530239, _530241] : [class_Fields_Olinordered__field__inverse__zero(_530239), 10925 ^ _152310 : [(10926 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_530239, c_Groups_Ozero__class_Ozero(_530239), c_Rings_Oinverse__class_Oinverse(_530239, _530241)), -(c_Orderings_Oord__class_Oless__eq(_530239, c_Groups_Ozero__class_Ozero(_530239), _530241))], (10932 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_530239, c_Groups_Ozero__class_Ozero(_530239), _530241), -(c_Orderings_Oord__class_Oless__eq(_530239, c_Groups_Ozero__class_Ozero(_530239), c_Rings_Oinverse__class_Oinverse(_530239, _530241)))]]], (10938 ^ _152310) ^ [_530724, _530726] : [class_Fields_Olinordered__field__inverse__zero(_530724), 10941 ^ _152310 : [(10942 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_530724, c_Rings_Oinverse__class_Oinverse(_530724, _530726), c_Groups_Ozero__class_Ozero(_530724)), -(c_Orderings_Oord__class_Oless__eq(_530724, _530726, c_Groups_Ozero__class_Ozero(_530724)))], (10948 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_530724, _530726, c_Groups_Ozero__class_Ozero(_530724)), -(c_Orderings_Oord__class_Oless__eq(_530724, c_Rings_Oinverse__class_Oinverse(_530724, _530726), c_Groups_Ozero__class_Ozero(_530724)))]]], (10954 ^ _152310) ^ [_531209, _531211] : [class_Fields_Olinordered__field__inverse__zero(_531209), 10957 ^ _152310 : [(10958 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_531209, c_Groups_Ozero__class_Ozero(_531209), c_Rings_Oinverse__class_Oinverse(_531209, _531211)), -(c_Orderings_Oord__class_Oless(_531209, c_Groups_Ozero__class_Ozero(_531209), _531211))], (10964 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_531209, c_Groups_Ozero__class_Ozero(_531209), _531211), -(c_Orderings_Oord__class_Oless(_531209, c_Groups_Ozero__class_Ozero(_531209), c_Rings_Oinverse__class_Oinverse(_531209, _531211)))]]], (10970 ^ _152310) ^ [_531694, _531696] : [class_Fields_Olinordered__field__inverse__zero(_531694), 10973 ^ _152310 : [(10974 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_531694, c_Rings_Oinverse__class_Oinverse(_531694, _531696), c_Groups_Ozero__class_Ozero(_531694)), -(c_Orderings_Oord__class_Oless(_531694, _531696, c_Groups_Ozero__class_Ozero(_531694)))], (10980 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_531694, _531696, c_Groups_Ozero__class_Ozero(_531694)), -(c_Orderings_Oord__class_Oless(_531694, c_Rings_Oinverse__class_Oinverse(_531694, _531696), c_Groups_Ozero__class_Ozero(_531694)))]]], (10986 ^ _152310) ^ [_532179, _532181] : [class_Fields_Olinordered__field(_532179), c_Orderings_Oord__class_Oless(_532179, c_Groups_Ozero__class_Ozero(_532179), _532181), -(c_Orderings_Oord__class_Oless(_532179, c_Groups_Ozero__class_Ozero(_532179), c_Rings_Oinverse__class_Oinverse(_532179, _532181)))], (10996 ^ _152310) ^ [_532494, _532496] : [class_Fields_Olinordered__field(_532494), c_Orderings_Oord__class_Oless(_532494, c_Groups_Ozero__class_Ozero(_532494), c_Rings_Oinverse__class_Oinverse(_532494, _532496)), -(_532496 = c_Groups_Ozero__class_Ozero(_532494)), -(c_Orderings_Oord__class_Oless(_532494, c_Groups_Ozero__class_Ozero(_532494), _532496))], (11010 ^ _152310) ^ [_532905, _532907] : [class_Fields_Olinordered__field(_532905), c_Orderings_Oord__class_Oless(_532905, _532907, c_Groups_Ozero__class_Ozero(_532905)), -(c_Orderings_Oord__class_Oless(_532905, c_Rings_Oinverse__class_Oinverse(_532905, _532907), c_Groups_Ozero__class_Ozero(_532905)))], (11020 ^ _152310) ^ [_533234, _533236, _533238] : [class_Fields_Olinordered__field(_533234), c_Orderings_Oord__class_Oless(_533234, _533236, _533238), c_Orderings_Oord__class_Oless(_533234, c_Groups_Ozero__class_Ozero(_533234), _533236), -(c_Orderings_Oord__class_Oless(_533234, c_Rings_Oinverse__class_Oinverse(_533234, _533238), c_Rings_Oinverse__class_Oinverse(_533234, _533236)))], (11034 ^ _152310) ^ [_533670, _533672, _533674] : [class_Fields_Olinordered__field(_533670), c_Orderings_Oord__class_Oless(_533670, _533672, _533674), c_Orderings_Oord__class_Oless(_533670, _533674, c_Groups_Ozero__class_Ozero(_533670)), -(c_Orderings_Oord__class_Oless(_533670, c_Rings_Oinverse__class_Oinverse(_533670, _533674), c_Rings_Oinverse__class_Oinverse(_533670, _533672)))], (11048 ^ _152310) ^ [_534092, _534094] : [class_Fields_Olinordered__field(_534092), c_Orderings_Oord__class_Oless(_534092, c_Rings_Oinverse__class_Oinverse(_534092, _534094), c_Groups_Ozero__class_Ozero(_534092)), -(_534094 = c_Groups_Ozero__class_Ozero(_534092)), -(c_Orderings_Oord__class_Oless(_534092, _534094, c_Groups_Ozero__class_Ozero(_534092)))], (11062 ^ _152310) ^ [_534517, _534519, _534521] : [class_Fields_Olinordered__field(_534517), c_Orderings_Oord__class_Oless(_534517, c_Rings_Oinverse__class_Oinverse(_534517, _534519), c_Rings_Oinverse__class_Oinverse(_534517, _534521)), c_Orderings_Oord__class_Oless(_534517, c_Groups_Ozero__class_Ozero(_534517), _534519), -(c_Orderings_Oord__class_Oless(_534517, _534521, _534519))], (11076 ^ _152310) ^ [_534953, _534955, _534957] : [class_Fields_Olinordered__field(_534953), c_Orderings_Oord__class_Oless(_534953, c_Rings_Oinverse__class_Oinverse(_534953, _534955), c_Rings_Oinverse__class_Oinverse(_534953, _534957)), c_Orderings_Oord__class_Oless(_534953, _534957, c_Groups_Ozero__class_Ozero(_534953)), -(c_Orderings_Oord__class_Oless(_534953, _534957, _534955))], (11090 ^ _152310) ^ [_535389, _535391, _535393] : [class_Fields_Olinordered__field(_535389), c_Orderings_Oord__class_Oless__eq(_535389, c_Rings_Oinverse__class_Oinverse(_535389, _535391), c_Rings_Oinverse__class_Oinverse(_535389, _535393)), c_Orderings_Oord__class_Oless(_535389, _535393, c_Groups_Ozero__class_Ozero(_535389)), -(c_Orderings_Oord__class_Oless__eq(_535389, _535393, _535391))], (11104 ^ _152310) ^ [_535825, _535827, _535829] : [class_Fields_Olinordered__field(_535825), c_Orderings_Oord__class_Oless__eq(_535825, c_Rings_Oinverse__class_Oinverse(_535825, _535827), c_Rings_Oinverse__class_Oinverse(_535825, _535829)), c_Orderings_Oord__class_Oless(_535825, c_Groups_Ozero__class_Ozero(_535825), _535827), -(c_Orderings_Oord__class_Oless__eq(_535825, _535829, _535827))], (11118 ^ _152310) ^ [_536261, _536263, _536265] : [class_Fields_Olinordered__field(_536261), c_Orderings_Oord__class_Oless__eq(_536261, _536263, _536265), c_Orderings_Oord__class_Oless(_536261, _536265, c_Groups_Ozero__class_Ozero(_536261)), -(c_Orderings_Oord__class_Oless__eq(_536261, c_Rings_Oinverse__class_Oinverse(_536261, _536265), c_Rings_Oinverse__class_Oinverse(_536261, _536263)))], (11132 ^ _152310) ^ [_536697, _536699, _536701] : [class_Fields_Olinordered__field(_536697), c_Orderings_Oord__class_Oless__eq(_536697, _536699, _536701), c_Orderings_Oord__class_Oless(_536697, c_Groups_Ozero__class_Ozero(_536697), _536699), -(c_Orderings_Oord__class_Oless__eq(_536697, c_Rings_Oinverse__class_Oinverse(_536697, _536701), c_Rings_Oinverse__class_Oinverse(_536697, _536699)))], (11146 ^ _152310) ^ [_537119, _537121] : [class_Fields_Olinordered__field__inverse__zero(_537119), 11149 ^ _152310 : [(11160 ^ _152310) ^ [] : [11161 ^ _152310 : [(11162 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_537119, _537121, c_Groups_Ozero__class_Ozero(_537119))], (11164 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_537119, c_Groups_Oone__class_Oone(_537119), _537121)]], -(c_Orderings_Oord__class_Oless__eq(_537119, c_Rings_Oinverse__class_Oinverse(_537119, _537121), c_Groups_Oone__class_Oone(_537119)))], (11150 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_537119, c_Rings_Oinverse__class_Oinverse(_537119, _537121), c_Groups_Oone__class_Oone(_537119)), -(c_Orderings_Oord__class_Oless__eq(_537119, _537121, c_Groups_Ozero__class_Ozero(_537119))), -(c_Orderings_Oord__class_Oless__eq(_537119, c_Groups_Oone__class_Oone(_537119), _537121))]]], (11168 ^ _152310) ^ [_537785, _537787, _537789] : [class_Fields_Ofield(_537785), -(_537787 = c_Groups_Ozero__class_Ozero(_537785)), -(_537789 = c_Groups_Ozero__class_Ozero(_537785)), -(c_Groups_Oplus__class_Oplus(_537785, c_Rings_Oinverse__class_Oinverse(_537785, _537787), c_Rings_Oinverse__class_Oinverse(_537785, _537789)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_537785), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_537785), c_Groups_Oplus__class_Oplus(_537785, _537787, _537789)), c_Rings_Oinverse__class_Oinverse(_537785, _537787))), c_Rings_Oinverse__class_Oinverse(_537785, _537789)))], (11182 ^ _152310) ^ [_538271, _538273] : [class_Fields_Olinordered__field__inverse__zero(_538271), 11185 ^ _152310 : [(11186 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless(_538271, c_Groups_Oone__class_Oone(_538271), c_Rings_Oinverse__class_Oinverse(_538271, _538273)), 11189 ^ _152310 : [(11190 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(_538271, c_Groups_Ozero__class_Ozero(_538271), _538273))], (11192 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(_538271, _538273, c_Groups_Oone__class_Oone(_538271)))]]], (11194 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(_538271, c_Groups_Oone__class_Oone(_538271), c_Rings_Oinverse__class_Oinverse(_538271, _538273))), c_Orderings_Oord__class_Oless(_538271, c_Groups_Ozero__class_Ozero(_538271), _538273), c_Orderings_Oord__class_Oless(_538271, _538273, c_Groups_Oone__class_Oone(_538271))]]], (11204 ^ _152310) ^ [_538923, _538925] : [class_Fields_Olinordered__field(_538923), c_Orderings_Oord__class_Oless(_538923, c_Groups_Ozero__class_Ozero(_538923), _538925), c_Orderings_Oord__class_Oless(_538923, _538925, c_Groups_Oone__class_Oone(_538923)), -(c_Orderings_Oord__class_Oless(_538923, c_Groups_Oone__class_Oone(_538923), c_Rings_Oinverse__class_Oinverse(_538923, _538925)))], (11218 ^ _152310) ^ [_539333, _539335] : [class_Fields_Ofield(_539333), -(_539335 = c_Groups_Ozero__class_Ozero(_539333)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_539333), c_Rings_Oinverse__class_Oinverse(_539333, _539335)), _539335) = c_Groups_Oone__class_Oone(_539333))], (11228 ^ _152310) ^ [_539663, _539665] : [class_Fields_Olinordered__field(_539663), c_Orderings_Oord__class_Oless(_539663, c_Groups_Ozero__class_Ozero(_539663), _539665), c_Orderings_Oord__class_Oless__eq(_539663, _539665, c_Groups_Oone__class_Oone(_539663)), -(c_Orderings_Oord__class_Oless__eq(_539663, c_Groups_Oone__class_Oone(_539663), c_Rings_Oinverse__class_Oinverse(_539663, _539665)))], (11242 ^ _152310) ^ [_540101, _540103, _540105, _540107] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _540101), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _540103), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _540103), _540105), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _540101), _540107)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, _540101)), _540105), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, _540103)), _540107)))], (11256 ^ _152310) ^ [_540613, _540615, _540617, _540619] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _540613), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _540615), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _540615), _540617), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _540613), _540619)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _540617), c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, _540613)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _540619), c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, _540615))))], (11270 ^ _152310) ^ [_541083] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _541083), -(c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _541083, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatfloor(_541083), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (11276 ^ _152310) ^ [_541313, _541315] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _541313), _541315), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _541315, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _541313), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_RComplete_Onatceiling(_541315) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _541313, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (11286 ^ _152310) ^ [_541619] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _541619)))], (11288 ^ _152310) ^ [_541730, _541732] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _541730, c_RealDef_Oreal(tc_Nat_Onat, _541732)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_541730), _541732))], (11294 ^ _152310) ^ [_541954, _541956] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatfloor(_541954), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _541956), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _541954, c_RealDef_Oreal(tc_Nat_Onat, _541956)))], (11300 ^ _152310) ^ [_542186, _542188] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _542186), _542188), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _542188, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _542186), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_RComplete_Onatfloor(_542188) = _542186)], (11310 ^ _152310) ^ [_542484] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_RComplete_Onatfloor(_542484)))], (11312 ^ _152310) ^ [_542594, _542596] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _542594), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _542594, c_RealDef_Oreal(tc_Nat_Onat, _542596)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_RComplete_Onatfloor(_542594), _542596))], (11322 ^ _152310) ^ [_542909, _542911] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _542909), -(c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _542909, c_RealDef_Oreal(tc_Nat_Onat, _542911))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatfloor(_542909), _542911))], (11328 ^ _152310) ^ [_543151, _543153] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _543151), 11331 ^ _152310 : [(11332 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _543153, c_RComplete_Onatfloor(_543151)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _543153), _543151))], (11338 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _543153), _543151), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _543153, c_RComplete_Onatfloor(_543151)))]]], (11344 ^ _152310) ^ [_543620] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _543620), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_543620)), _543620))], (11350 ^ _152310) ^ [_543809] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _543809, c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatceiling(_543809))))], (11352 ^ _152310) ^ [_543922, _543924] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _543922), _543924), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _543922, c_RComplete_Onatfloor(_543924)))], (11358 ^ _152310) ^ [_544146, _544148] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _544146, _544148), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatfloor(_544146), c_RComplete_Onatfloor(_544148)))], (11364 ^ _152310) ^ [_544368, _544370] : [_544368 = c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_544368)), -(c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _544368), _544370)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_RComplete_Onatfloor(_544368)), _544370))], (11370 ^ _152310) ^ [_544591] : [-(c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat, _544591)) = _544591)], (11372 ^ _152310) ^ [_544674] : [-(c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat, _544674)) = _544674)], (11374 ^ _152310) ^ [] : [-(c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11376 ^ _152310) ^ [_544810] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _544810, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, c_RComplete_Onatfloor(_544810)), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (11378 ^ _152310) ^ [] : [-(c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (11380 ^ _152310) ^ [] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (11382 ^ _152310) ^ [_545048] : [c_RealDef_Oreal(tc_Nat_Onat, _545048) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_545048 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11388 ^ _152310) ^ [_545210] : [_545210 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_RealDef_Oreal(tc_Nat_Onat, _545210) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (11394 ^ _152310) ^ [_545392] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _545392), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (11396 ^ _152310) ^ [_545532, _545534] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _545532), c_RealDef_Oreal(tc_Nat_Onat, _545534)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _545532, _545534))], (11402 ^ _152310) ^ [_545710, _545712] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _545710, _545712), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _545710), c_RealDef_Oreal(tc_Nat_Onat, _545712)))], (11408 ^ _152310) ^ [_545923, _545925] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _545923, _545925)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _545923), c_RealDef_Oreal(tc_Nat_Onat, _545925)))], (11410 ^ _152310) ^ [] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (11412 ^ _152310) ^ [_546087, _546089] : [-(c_RealDef_Oreal(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _546087), _546089)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _546087)), _546089))], (11414 ^ _152310) ^ [_546199, _546201] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _546199)), _546201) = c_RealDef_Oreal(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _546199), _546201)))], (11416 ^ _152310) ^ [_546355, _546357] : [c_RealDef_Oreal(tc_Nat_Onat, _546355) = c_RealDef_Oreal(tc_Nat_Onat, _546357), -(_546355 = _546357)], (11422 ^ _152310) ^ [_546529, _546531] : [_546529 = _546531, -(c_RealDef_Oreal(tc_Nat_Onat, _546529) = c_RealDef_Oreal(tc_Nat_Onat, _546531))], (11428 ^ _152310) ^ [_546738, _546740] : [-(c_RealDef_Oreal(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _546738), _546740)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _546738)), c_RealDef_Oreal(tc_Nat_Onat, _546740)))], (11430 ^ _152310) ^ [_546897, _546899] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _546897), c_RealDef_Oreal(tc_Nat_Onat, _546899)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _546897, _546899))], (11436 ^ _152310) ^ [_547075, _547077] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _547075, _547077), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _547075), c_RealDef_Oreal(tc_Nat_Onat, _547077)))], (11442 ^ _152310) ^ [_547274] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_547274)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _547274), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (11444 ^ _152310) ^ [] : [-(c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (11446 ^ _152310) ^ [_547417] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(_547417))))], (11448 ^ _152310) ^ [_547545] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _547545), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(_547545 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11454 ^ _152310) ^ [_547709] : [_547709 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _547709), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (11460 ^ _152310) ^ [_547909] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _547909, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_RComplete_Onatfloor(_547909) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11466 ^ _152310) ^ [_548134] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _548134)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _548134))], (11472 ^ _152310) ^ [_548300] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _548300), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _548300)))], (11478 ^ _152310) ^ [_548545, _548547] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _548545, _548547), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _548545), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_RealDef_Oreal(tc_Nat_Onat, _548547)))], (11484 ^ _152310) ^ [_548731, _548733] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _548731), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), c_RealDef_Oreal(tc_Nat_Onat, _548733)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _548731, _548733))], (11490 ^ _152310) ^ [_548996, _548998] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _548996, _548998), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _548996), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _548998), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))))], (11496 ^ _152310) ^ [_549182, _549184] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _549182), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, _549184), c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _549182, _549184))], (11502 ^ _152310) ^ [_549418, _549420] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _549418), 11505 ^ _152310 : [(11506 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_549418), _549420), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _549418, c_RealDef_Oreal(tc_Nat_Onat, _549420)))], (11512 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _549418, c_RealDef_Oreal(tc_Nat_Onat, _549420)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_RComplete_Onatceiling(_549418), _549420))]]], (11518 ^ _152310) ^ [_549916] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), c_RComplete_Onatfloor(_549916)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _549916))], (11524 ^ _152310) ^ [_550080] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), _550080), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), c_RComplete_Onatfloor(_550080)))], (11530 ^ _152310) ^ [_550294, _550296] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _550294), -(c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _550294, c_RealDef_Oreal(tc_Nat_Onat, _550296))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_RComplete_Onatceiling(_550294), _550296))], (11536 ^ _152310) ^ [_550536, _550538] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _550536), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _550538), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_RComplete_Onatfloor(_550536)), c_RComplete_Onatfloor(_550538)), c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _550536), _550538))))], (11546 ^ _152310) ^ [_550877, _550879] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _550877), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, _550879)), _550877), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _550877, c_Groups_Oone__class_Oone(tc_RealDef_Oreal))), _550879)))], (11552 ^ _152310) ^ [_551137, _551139] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _551137), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _551139), 11560 ^ _152310 : [(11561 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, 11559 ^ [_551137, _551139])), _551137), _551139))], (11563 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _551139, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(11559 ^ [_551137, _551139]))), _551137)))]]], (11565 ^ _152310) ^ [_551651, _551653] : [class_Orderings_Oorder(_551651), 11568 ^ _152310 : [(11579 ^ _152310) ^ [] : [11582 ^ _152310 : [(11583 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, 11580 ^ [_551651, _551653], 11581 ^ [_551651, _551653]))], (11585 ^ _152310) ^ [] : [c_Orderings_Oord__class_Oless__eq(_551651, hAPP(_551653, 11581 ^ [_551651, _551653]), hAPP(_551653, 11580 ^ [_551651, _551653]))]], -(c_SEQ_Odecseq(_551651, _551653))], (11569 ^ _152310) ^ [] : [c_SEQ_Odecseq(_551651, _551653), 11572 ^ _152310 : [(11573 ^ _152310) ^ [_551927, _551929] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _551929, _551927), -(c_Orderings_Oord__class_Oless__eq(_551651, hAPP(_551653, _551927), hAPP(_551653, _551929)))]]]]], (11589 ^ _152310) ^ [_552538] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _552538), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(11592 ^ [_552538]))), _552538))], (11596 ^ _152310) ^ [_552808] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _552808), 11600 ^ _152310 : [(11601 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealDef_Oreal(tc_Nat_Onat, 11599 ^ [_552808]), _552808))], (11603 ^ _152310) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _552808, c_RealDef_Oreal(tc_Nat_Onat, c_Nat_OSuc(11599 ^ [_552808]))))]]], (11605 ^ _152310) ^ [_553193, _553195, _553197] : [class_Fields_Ofield(_553193), 11608 ^ _152310 : [(11609 ^ _152310) ^ [] : [_553195 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_553193)), -(c_Polynomial_Opoly__gcd(_553193, _553197, _553195) = c_Polynomial_Osmult(_553193, c_Rings_Oinverse__class_Oinverse(_553193, hAPP(c_Polynomial_Ocoeff(_553193, _553197), c_Polynomial_Odegree(_553193, _553197))), _553197))], (11615 ^ _152310) ^ [] : [-(_553195 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_553193))), -(c_Polynomial_Opoly__gcd(_553193, _553197, _553195) = c_Polynomial_Opoly__gcd(_553193, _553195, c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(_553193), _553197, _553195)))]]], (11621 ^ _152310) ^ [_553771, _553773, _553775] : [class_Fields_Ofield(_553771), -(_553773 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_553771))), -(c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(_553771), _553775, _553773) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_553771))), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_553771, c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(_553771), _553775, _553773)), c_Polynomial_Odegree(_553771, _553773)))], (11635 ^ _152310) ^ [_554257, _554259, _554261, _554263] : [class_Divides_Osemiring__div(_554257), -(c_Divides_Odiv__class_Omod(_554257, c_Groups_Oplus__class_Oplus(_554257, _554259, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_554257), _554261), _554263)), _554261) = c_Divides_Odiv__class_Omod(_554257, _554259, _554261))], (11641 ^ _152310) ^ [_554545, _554547, _554549, _554551] : [class_Divides_Osemiring__div(_554545), -(c_Divides_Odiv__class_Omod(_554545, c_Groups_Oplus__class_Oplus(_554545, _554547, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_554545), _554549), _554551)), _554551) = c_Divides_Odiv__class_Omod(_554545, _554547, _554551))], (11647 ^ _152310) ^ [_554833, _554835, _554837, _554839] : [class_Divides_Osemiring__div(_554833), c_Rings_Odvd__class_Odvd(_554833, _554835, _554837), 11654 ^ _152310 : [(11655 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(_554833, _554835, c_Divides_Odiv__class_Omod(_554833, _554839, _554837)), -(c_Rings_Odvd__class_Odvd(_554833, _554835, _554839))], (11661 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(_554833, _554835, _554839), -(c_Rings_Odvd__class_Odvd(_554833, _554835, c_Divides_Odiv__class_Omod(_554833, _554839, _554837)))]]], (11667 ^ _152310) ^ [_555468, _555470, _555472, _555474] : [class_Divides_Osemiring__div(_555468), c_Rings_Odvd__class_Odvd(_555468, _555470, _555472), -(c_Divides_Odiv__class_Omod(_555468, c_Divides_Odiv__class_Omod(_555468, _555474, _555472), _555470) = c_Divides_Odiv__class_Omod(_555468, _555474, _555470))], (11677 ^ _152310) ^ [_555839, _555841, _555843, _555845] : [class_Divides_Osemiring__div(_555839), c_Rings_Odvd__class_Odvd(_555839, _555841, _555843), c_Rings_Odvd__class_Odvd(_555839, _555841, _555845), -(c_Rings_Odvd__class_Odvd(_555839, _555841, c_Divides_Odiv__class_Omod(_555839, _555843, _555845)))], (11691 ^ _152310) ^ [_556295, _556297, _556299, _556301] : [class_Divides_Osemiring__div(_556295), c_Rings_Odvd__class_Odvd(_556295, _556297, c_Divides_Odiv__class_Omod(_556295, _556299, _556301)), c_Rings_Odvd__class_Odvd(_556295, _556297, _556301), -(c_Rings_Odvd__class_Odvd(_556295, _556297, _556299))], (11705 ^ _152310) ^ [_556737, _556739, _556741] : [class_Divides_Osemiring__div(_556737), 11708 ^ _152310 : [(11709 ^ _152310) ^ [] : [c_Rings_Odvd__class_Odvd(_556737, _556739, _556741), -(c_Divides_Odiv__class_Omod(_556737, _556741, _556739) = c_Groups_Ozero__class_Ozero(_556737))], (11715 ^ _152310) ^ [] : [c_Divides_Odiv__class_Omod(_556737, _556741, _556739) = c_Groups_Ozero__class_Ozero(_556737), -(c_Rings_Odvd__class_Odvd(_556737, _556739, _556741))]]], (11721 ^ _152310) ^ [_557246, _557248, _557250] : [class_Divides_Osemiring__div(_557246), c_Rings_Odvd__class_Odvd(_557246, _557248, _557250), -(c_Divides_Odiv__class_Omod(_557246, _557250, _557248) = c_Groups_Ozero__class_Ozero(_557246))], (11731 ^ _152310) ^ [_557581, _557583, _557585] : [class_Divides_Osemiring__div(_557581), -(c_Divides_Odiv__class_Omod(_557581, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_557581), _557583), _557585), _557585) = c_Groups_Ozero__class_Ozero(_557581))], (11737 ^ _152310) ^ [_557837, _557839, _557841] : [class_Divides_Osemiring__div(_557837), -(c_Divides_Odiv__class_Omod(_557837, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_557837), _557839), _557841), _557839) = c_Groups_Ozero__class_Ozero(_557837))], (11743 ^ _152310) ^ [_558079, _558081] : [class_Divides_Osemiring__div(_558079), -(c_Divides_Odiv__class_Omod(_558079, _558081, c_Groups_Oone__class_Oone(_558079)) = c_Groups_Ozero__class_Ozero(_558079))], (11749 ^ _152310) ^ [_558303, _558305] : [class_Divides_Osemiring__div(_558303), -(c_Divides_Odiv__class_Omod(_558303, _558305, _558305) = c_Groups_Ozero__class_Ozero(_558303))], (11755 ^ _152310) ^ [_558523, _558525] : [class_Divides_Osemiring__div(_558523), -(c_Divides_Odiv__class_Omod(_558523, _558525, c_Groups_Ozero__class_Ozero(_558523)) = _558525)], (11761 ^ _152310) ^ [_558743, _558745] : [class_Divides_Osemiring__div(_558743), -(c_Divides_Odiv__class_Omod(_558743, c_Groups_Ozero__class_Ozero(_558743), _558745) = c_Groups_Ozero__class_Ozero(_558743))], (11767 ^ _152310) ^ [_558981, _558983, _558985] : [class_Divides_Osemiring__div(_558981), -(c_Divides_Odiv__class_Omod(_558981, c_Groups_Oplus__class_Oplus(_558981, _558983, _558985), _558985) = c_Divides_Odiv__class_Omod(_558981, _558983, _558985))], (11773 ^ _152310) ^ [_559233, _559235, _559237] : [class_Divides_Osemiring__div(_559233), -(c_Divides_Odiv__class_Omod(_559233, c_Groups_Oplus__class_Oplus(_559233, _559235, _559237), _559235) = c_Divides_Odiv__class_Omod(_559233, _559237, _559235))], (11779 ^ _152310) ^ [_559499, _559501, _559503, _559505] : [class_Divides_Osemiring__div(_559499), -(c_Divides_Odiv__class_Omod(_559499, c_Groups_Oplus__class_Oplus(_559499, _559501, _559503), _559505) = c_Divides_Odiv__class_Omod(_559499, c_Groups_Oplus__class_Oplus(_559499, _559501, c_Divides_Odiv__class_Omod(_559499, _559503, _559505)), _559505))], (11785 ^ _152310) ^ [_559787, _559789, _559791, _559793] : [class_Divides_Osemiring__div(_559787), -(c_Divides_Odiv__class_Omod(_559787, c_Groups_Oplus__class_Oplus(_559787, _559789, _559791), _559793) = c_Divides_Odiv__class_Omod(_559787, c_Groups_Oplus__class_Oplus(_559787, c_Divides_Odiv__class_Omod(_559787, _559789, _559793), _559791), _559793))], (11791 ^ _152310) ^ [_560075, _560077, _560079, _560081] : [class_Divides_Osemiring__div(_560075), -(c_Divides_Odiv__class_Omod(_560075, c_Groups_Oplus__class_Oplus(_560075, _560077, _560079), _560081) = c_Divides_Odiv__class_Omod(_560075, c_Groups_Oplus__class_Oplus(_560075, c_Divides_Odiv__class_Omod(_560075, _560077, _560081), c_Divides_Odiv__class_Omod(_560075, _560079, _560081)), _560081))], (11797 ^ _152310) ^ [_560371, _560373, _560375, _560377] : [class_Divides_Osemiring__div(_560371), -(c_Divides_Odiv__class_Omod(_560371, c_Groups_Oplus__class_Oplus(_560371, _560373, c_Divides_Odiv__class_Omod(_560371, _560375, _560377)), _560377) = c_Divides_Odiv__class_Omod(_560371, c_Groups_Oplus__class_Oplus(_560371, _560373, _560375), _560377))], (11803 ^ _152310) ^ [_560659, _560661, _560663, _560665] : [class_Divides_Osemiring__div(_560659), -(c_Divides_Odiv__class_Omod(_560659, c_Groups_Oplus__class_Oplus(_560659, c_Divides_Odiv__class_Omod(_560659, _560661, _560663), _560665), _560663) = c_Divides_Odiv__class_Omod(_560659, c_Groups_Oplus__class_Oplus(_560659, _560661, _560665), _560663))], (11809 ^ _152310) ^ [_560975, _560977, _560979, _560981, _560983, _560985] : [class_Divides_Osemiring__div(_560975), c_Divides_Odiv__class_Omod(_560975, _560977, _560979) = c_Divides_Odiv__class_Omod(_560975, _560981, _560979), c_Divides_Odiv__class_Omod(_560975, _560983, _560979) = c_Divides_Odiv__class_Omod(_560975, _560985, _560979), -(c_Divides_Odiv__class_Omod(_560975, c_Groups_Oplus__class_Oplus(_560975, _560977, _560983), _560979) = c_Divides_Odiv__class_Omod(_560975, c_Groups_Oplus__class_Oplus(_560975, _560981, _560985), _560979))], (11823 ^ _152310) ^ [_561495, _561497, _561499] : [class_Fields_Ofield(_561495), -(c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(_561495), _561497, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_561495), _561499)) = c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(_561495), _561497, _561499))], (11829 ^ _152310) ^ [_561757, _561759, _561761] : [class_Fields_Ofield(_561757), -(c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(_561757), c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_561757), _561759), _561761) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_561757), c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(_561757), _561759, _561761)))], (11835 ^ _152310) ^ [_562043, _562045, _562047, _562049] : [class_Divides_Oring__div(_562043), c_Divides_Odiv__class_Omod(_562043, _562045, _562047) = c_Divides_Odiv__class_Omod(_562043, _562049, _562047), -(c_Divides_Odiv__class_Omod(_562043, c_Groups_Ouminus__class_Ouminus(_562043, _562045), _562047) = c_Divides_Odiv__class_Omod(_562043, c_Groups_Ouminus__class_Ouminus(_562043, _562049), _562047))], (11845 ^ _152310) ^ [_562418, _562420, _562422] : [class_Divides_Oring__div(_562418), -(c_Divides_Odiv__class_Omod(_562418, c_Groups_Ouminus__class_Ouminus(_562418, _562420), _562422) = c_Divides_Odiv__class_Omod(_562418, c_Groups_Ouminus__class_Ouminus(_562418, c_Divides_Odiv__class_Omod(_562418, _562420, _562422)), _562422))], (11851 ^ _152310) ^ [_562682, _562684, _562686] : [class_Divides_Osemiring__div(_562682), -(c_Divides_Odiv__class_Omod(_562682, c_Divides_Odiv__class_Omod(_562682, _562684, _562686), _562686) = c_Divides_Odiv__class_Omod(_562682, _562684, _562686))], (11857 ^ _152310) ^ [_562948, _562950, _562952, _562954] : [class_Divides_Osemiring__div(_562948), -(c_Divides_Odiv__class_Omod(_562948, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_562948), _562950), _562952), _562954) = c_Divides_Odiv__class_Omod(_562948, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_562948), _562950), c_Divides_Odiv__class_Omod(_562948, _562952, _562954)), _562954))], (11863 ^ _152310) ^ [_563252, _563254, _563256, _563258] : [class_Divides_Osemiring__div(_563252), -(c_Divides_Odiv__class_Omod(_563252, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_563252), _563254), _563256), _563258) = c_Divides_Odiv__class_Omod(_563252, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_563252), c_Divides_Odiv__class_Omod(_563252, _563254, _563258)), _563256), _563258))], (11869 ^ _152310) ^ [_563556, _563558, _563560, _563562] : [class_Divides_Osemiring__div(_563556), -(c_Divides_Odiv__class_Omod(_563556, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_563556), _563558), _563560), _563562) = c_Divides_Odiv__class_Omod(_563556, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_563556), c_Divides_Odiv__class_Omod(_563556, _563558, _563562)), c_Divides_Odiv__class_Omod(_563556, _563560, _563562)), _563562))], (11875 ^ _152310) ^ [_563826] : [class_Groups_Ocancel__comm__monoid__add(_563826), -(class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(_563826)))], (11881 ^ _152310) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex))], (11883 ^ _152310) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal))], (11885 ^ _152310) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat))], (11887 ^ _152310) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint))], (11889 ^ _152310) ^ [_564242, _564244] : [class_Lattices_Oboolean__algebra(_564242), -(class_Lattices_Oboolean__algebra(tc_fun(_564244, _564242)))], (11895 ^ _152310) ^ [_564454, _564456] : [class_Orderings_Opreorder(_564454), -(class_Orderings_Opreorder(tc_fun(_564456, _564454)))], (11901 ^ _152310) ^ [_564666, _564668] : [class_Orderings_Oorder(_564666), -(class_Orderings_Oorder(tc_fun(_564668, _564666)))], (11907 ^ _152310) ^ [_564878, _564880] : [class_Orderings_Oord(_564878), -(class_Orderings_Oord(tc_fun(_564880, _564878)))], (11913 ^ _152310) ^ [_565090, _565092] : [class_Groups_Ouminus(_565090), -(class_Groups_Ouminus(tc_fun(_565092, _565090)))], (11919 ^ _152310) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (11921 ^ _152310) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (11923 ^ _152310) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (11925 ^ _152310) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (11927 ^ _152310) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (11929 ^ _152310) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (11931 ^ _152310) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (11933 ^ _152310) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (11935 ^ _152310) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (11937 ^ _152310) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (11939 ^ _152310) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (11941 ^ _152310) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (11943 ^ _152310) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (11945 ^ _152310) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (11947 ^ _152310) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (11949 ^ _152310) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (11951 ^ _152310) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (11953 ^ _152310) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (11955 ^ _152310) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (11957 ^ _152310) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (11959 ^ _152310) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (11961 ^ _152310) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (11963 ^ _152310) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (11965 ^ _152310) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (11967 ^ _152310) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (11969 ^ _152310) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], 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_152310) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (12109 ^ _152310) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (12111 ^ _152310) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (12113 ^ _152310) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (12115 ^ _152310) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (12117 ^ _152310) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal))], (12119 ^ _152310) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal))], (12121 ^ _152310) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal))], (12123 ^ _152310) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal))], (12125 ^ _152310) ^ [] : [-(class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal))], (12127 ^ _152310) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal))], (12129 ^ _152310) ^ [] : 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: [-(class_Rings_Ono__zero__divisors(tc_RealDef_Oreal))], (12177 ^ _152310) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal))], (12179 ^ _152310) ^ [] : [-(class_Rings_Olinordered__ring(tc_RealDef_Oreal))], (12181 ^ _152310) ^ [] : [-(class_Rings_Olinordered__idom(tc_RealDef_Oreal))], (12183 ^ _152310) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal))], (12185 ^ _152310) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal))], (12187 ^ _152310) ^ [] : [-(class_Rings_Odivision__ring(tc_RealDef_Oreal))], (12189 ^ _152310) ^ [] : [-(class_Rings_Ocomm__semiring(tc_RealDef_Oreal))], (12191 ^ _152310) ^ [] : [-(class_Groups_Oab__group__add(tc_RealDef_Oreal))], (12193 ^ _152310) ^ [] : [-(class_Rings_Ozero__neq__one(tc_RealDef_Oreal))], (12195 ^ _152310) ^ [] : [-(class_Rings_Oordered__ring(tc_RealDef_Oreal))], (12197 ^ _152310) ^ [] : [-(class_Orderings_Opreorder(tc_RealDef_Oreal))], (12199 ^ _152310) ^ [] : [-(class_Orderings_Olinorder(tc_RealDef_Oreal))], (12201 ^ _152310) ^ [] : [-(class_Groups_Omonoid__mult(tc_RealDef_Oreal))], (12203 ^ _152310) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_RealDef_Oreal))], (12205 ^ _152310) ^ [] : [-(class_Groups_Omonoid__add(tc_RealDef_Oreal))], (12207 ^ _152310) ^ [] : [-(class_Rings_Osemiring__0(tc_RealDef_Oreal))], (12209 ^ _152310) ^ [] : [-(class_Groups_Ogroup__add(tc_RealDef_Oreal))], (12211 ^ _152310) ^ [] : [-(class_Rings_Omult__zero(tc_RealDef_Oreal))], (12213 ^ _152310) ^ [] : [-(class_Rings_Ocomm__ring(tc_RealDef_Oreal))], (12215 ^ _152310) ^ [] : [-(class_Orderings_Oorder(tc_RealDef_Oreal))], (12217 ^ _152310) ^ [] : [-(class_Int_Oring__char__0(tc_RealDef_Oreal))], (12219 ^ _152310) ^ [] : [-(class_Rings_Osemiring(tc_RealDef_Oreal))], (12221 ^ _152310) ^ [] : [-(class_Orderings_Oord(tc_RealDef_Oreal))], (12223 ^ _152310) ^ [] : [-(class_Groups_Ouminus(tc_RealDef_Oreal))], (12225 ^ _152310) ^ [] : [-(class_Rings_Oring__1(tc_RealDef_Oreal))], (12227 ^ _152310) ^ [] : [-(class_Fields_Ofield(tc_RealDef_Oreal))], (12229 ^ _152310) ^ [] : [-(class_Power_Opower(tc_RealDef_Oreal))], (12231 ^ _152310) ^ [] : [-(class_Groups_Ozero(tc_RealDef_Oreal))], (12233 ^ _152310) ^ [] : [-(class_Rings_Oring(tc_RealDef_Oreal))], (12235 ^ _152310) ^ [] : [-(class_Rings_Oidom(tc_RealDef_Oreal))], (12237 ^ _152310) ^ [] : [-(class_Groups_Oone(tc_RealDef_Oreal))], (12239 ^ _152310) ^ [] : [-(class_Rings_Odvd(tc_RealDef_Oreal))], (12241 ^ _152310) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex))], (12243 ^ _152310) ^ [] : [-(class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex))], (12245 ^ _152310) ^ [] : [-(class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex))], (12247 ^ _152310) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex))], (12249 ^ _152310) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex))], (12251 ^ _152310) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex))], (12253 ^ _152310) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex))], (12255 ^ _152310) ^ [] : [-(class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex))], (12257 ^ _152310) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex))], (12259 ^ _152310) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex))], (12261 ^ _152310) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex))], (12263 ^ _152310) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex))], (12265 ^ _152310) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex))], (12267 ^ _152310) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex))], (12269 ^ _152310) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex))], (12271 ^ _152310) ^ [] : [-(class_Rings_Odivision__ring(tc_Complex_Ocomplex))], (12273 ^ _152310) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Complex_Ocomplex))], (12275 ^ _152310) ^ [] : [-(class_Groups_Oab__group__add(tc_Complex_Ocomplex))], (12277 ^ _152310) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Complex_Ocomplex))], (12279 ^ _152310) ^ [] : [-(class_Groups_Omonoid__mult(tc_Complex_Ocomplex))], (12281 ^ _152310) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex))], (12283 ^ _152310) ^ [] : [-(class_Groups_Omonoid__add(tc_Complex_Ocomplex))], (12285 ^ _152310) ^ [] : [-(class_Rings_Osemiring__0(tc_Complex_Ocomplex))], (12287 ^ _152310) ^ [] : [-(class_Groups_Ogroup__add(tc_Complex_Ocomplex))], (12289 ^ _152310) ^ [] : [-(class_Rings_Omult__zero(tc_Complex_Ocomplex))], (12291 ^ _152310) ^ [] : [-(class_Rings_Ocomm__ring(tc_Complex_Ocomplex))], (12293 ^ _152310) ^ [] : [-(class_Int_Oring__char__0(tc_Complex_Ocomplex))], (12295 ^ _152310) ^ [] : [-(class_Rings_Osemiring(tc_Complex_Ocomplex))], (12297 ^ _152310) ^ [] : [-(class_Groups_Ouminus(tc_Complex_Ocomplex))], (12299 ^ _152310) ^ [] : [-(class_Rings_Oring__1(tc_Complex_Ocomplex))], (12301 ^ _152310) ^ [] : [-(class_Fields_Ofield(tc_Complex_Ocomplex))], (12303 ^ _152310) ^ [] : [-(class_Power_Opower(tc_Complex_Ocomplex))], (12305 ^ _152310) ^ [] : [-(class_Groups_Ozero(tc_Complex_Ocomplex))], (12307 ^ _152310) ^ [] : [-(class_Rings_Oring(tc_Complex_Ocomplex))], (12309 ^ _152310) ^ [] : [-(class_Rings_Oidom(tc_Complex_Ocomplex))], (12311 ^ _152310) ^ [] : [-(class_Groups_Oone(tc_Complex_Ocomplex))], (12313 ^ _152310) ^ [] : [-(class_Rings_Odvd(tc_Complex_Ocomplex))], (12315 ^ _152310) ^ [_575782] : [class_Rings_Oidom(_575782), -(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(_575782)))], (12321 ^ _152310) ^ [_575972] : [class_Rings_Olinordered__idom(_575972), -(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(_575972)))], (12327 ^ _152310) ^ [_576162] : [class_Rings_Olinordered__idom(_576162), -(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(_576162)))], (12333 ^ _152310) ^ [_576352] : [class_Rings_Olinordered__idom(_576352), -(class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(_576352)))], (12339 ^ _152310) ^ [_576542] : [class_Rings_Olinordered__idom(_576542), -(class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(_576542)))], (12345 ^ _152310) ^ [_576732] : [class_Rings_Olinordered__idom(_576732), -(class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(_576732)))], (12351 ^ _152310) ^ [_576922] : [class_Rings_Olinordered__idom(_576922), -(class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(_576922)))], (12357 ^ _152310) ^ [_577112] : [class_Rings_Olinordered__idom(_577112), -(class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(_577112)))], (12363 ^ _152310) ^ [_577302] : [class_Rings_Olinordered__idom(_577302), -(class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(_577302)))], (12369 ^ _152310) ^ [_577492] : [class_Groups_Ocancel__comm__monoid__add(_577492), -(class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(_577492)))], (12375 ^ _152310) ^ [_577682] : [class_Rings_Oidom(_577682), -(class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(_577682)))], (12381 ^ _152310) ^ [_577872] : [class_Rings_Olinordered__idom(_577872), -(class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(_577872)))], (12387 ^ _152310) ^ [_578062] : [class_Rings_Olinordered__idom(_578062), -(class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(_578062)))], (12393 ^ _152310) ^ [_578252] : [class_Rings_Oidom(_578252), -(class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(_578252)))], (12399 ^ _152310) ^ [_578442] : [class_Rings_Olinordered__idom(_578442), -(class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(_578442)))], (12405 ^ _152310) ^ [_578632] : [class_Rings_Olinordered__idom(_578632), -(class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(_578632)))], (12411 ^ _152310) ^ [_578822] : [class_Rings_Olinordered__idom(_578822), -(class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(_578822)))], (12417 ^ _152310) ^ [_579012] : [class_Groups_Ocancel__comm__monoid__add(_579012), -(class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(_579012)))], (12423 ^ _152310) ^ [_579202] : [class_Rings_Olinordered__idom(_579202), -(class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(_579202)))], (12429 ^ _152310) ^ [_579392] : [class_Rings_Olinordered__idom(_579392), -(class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(_579392)))], (12435 ^ _152310) ^ [_579582] : [class_Rings_Ocomm__semiring__0(_579582), -(class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(_579582)))], (12441 ^ _152310) ^ [_579772] : [class_Rings_Ocomm__semiring__1(_579772), -(class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(_579772)))], (12447 ^ _152310) ^ [_579962] : [class_Groups_Ocomm__monoid__add(_579962), -(class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(_579962)))], (12453 ^ _152310) ^ [_580152] : [class_Rings_Olinordered__idom(_580152), -(class_Rings_Oordered__semiring(tc_Polynomial_Opoly(_580152)))], (12459 ^ _152310) ^ [_580342] : [class_Rings_Oidom(_580342), -(class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(_580342)))], (12465 ^ _152310) ^ [_580532] : [class_Groups_Ocomm__monoid__add(_580532), -(class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(_580532)))], (12471 ^ _152310) ^ [_580722] : [class_Rings_Olinordered__idom(_580722), -(class_Rings_Olinordered__ring(tc_Polynomial_Opoly(_580722)))], (12477 ^ _152310) ^ [_580912] : [class_Rings_Olinordered__idom(_580912), -(class_Rings_Olinordered__idom(tc_Polynomial_Opoly(_580912)))], (12483 ^ _152310) ^ [_581102] : [class_Rings_Ocomm__semiring__1(_581102), -(class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(_581102)))], (12489 ^ _152310) ^ [_581292] : [class_Rings_Ocomm__semiring__0(_581292), -(class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(_581292)))], (12495 ^ _152310) ^ [_581482] : [class_Fields_Ofield(_581482), -(class_Divides_Osemiring__div(tc_Polynomial_Opoly(_581482)))], (12501 ^ _152310) ^ [_581672] : [class_Rings_Ocomm__semiring__0(_581672), -(class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(_581672)))], (12507 ^ _152310) ^ [_581862] : [class_Groups_Oab__group__add(_581862), -(class_Groups_Oab__group__add(tc_Polynomial_Opoly(_581862)))], (12513 ^ _152310) ^ [_582052] : [class_Rings_Ocomm__semiring__1(_582052), -(class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(_582052)))], (12519 ^ _152310) ^ [_582242] : [class_Rings_Olinordered__idom(_582242), -(class_Rings_Oordered__ring(tc_Polynomial_Opoly(_582242)))], (12525 ^ _152310) ^ [_582432] : [class_Rings_Olinordered__idom(_582432), -(class_Orderings_Opreorder(tc_Polynomial_Opoly(_582432)))], (12531 ^ _152310) ^ [_582622] : [class_Rings_Olinordered__idom(_582622), -(class_Orderings_Olinorder(tc_Polynomial_Opoly(_582622)))], (12537 ^ _152310) ^ [_582812] : [class_Rings_Ocomm__semiring__1(_582812), -(class_Groups_Omonoid__mult(tc_Polynomial_Opoly(_582812)))], (12543 ^ _152310) ^ [_583002] : [class_Rings_Ocomm__ring__1(_583002), -(class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(_583002)))], (12549 ^ _152310) ^ [_583192] : [class_Groups_Ocomm__monoid__add(_583192), -(class_Groups_Omonoid__add(tc_Polynomial_Opoly(_583192)))], (12555 ^ _152310) ^ [_583382] : [class_Rings_Ocomm__semiring__0(_583382), -(class_Rings_Osemiring__0(tc_Polynomial_Opoly(_583382)))], (12561 ^ _152310) ^ [_583572] : [class_Groups_Oab__group__add(_583572), -(class_Groups_Ogroup__add(tc_Polynomial_Opoly(_583572)))], (12567 ^ _152310) ^ [_583762] : [class_Fields_Ofield(_583762), -(class_Divides_Oring__div(tc_Polynomial_Opoly(_583762)))], (12573 ^ _152310) ^ [_583952] : [class_Rings_Ocomm__semiring__0(_583952), -(class_Rings_Omult__zero(tc_Polynomial_Opoly(_583952)))], (12579 ^ _152310) ^ [_584142] : [class_Rings_Ocomm__ring(_584142), -(class_Rings_Ocomm__ring(tc_Polynomial_Opoly(_584142)))], (12585 ^ _152310) ^ [_584332] : [class_Rings_Olinordered__idom(_584332), -(class_Orderings_Oorder(tc_Polynomial_Opoly(_584332)))], (12591 ^ _152310) ^ [_584522] : [class_Rings_Olinordered__idom(_584522), -(class_Int_Oring__char__0(tc_Polynomial_Opoly(_584522)))], (12597 ^ _152310) ^ [_584712] : [class_Rings_Ocomm__semiring__0(_584712), -(class_Rings_Osemiring(tc_Polynomial_Opoly(_584712)))], (12603 ^ _152310) ^ [_584902] : [class_Rings_Olinordered__idom(_584902), -(class_Orderings_Oord(tc_Polynomial_Opoly(_584902)))], (12609 ^ _152310) ^ [_585092] : [class_Groups_Oab__group__add(_585092), -(class_Groups_Ouminus(tc_Polynomial_Opoly(_585092)))], (12615 ^ _152310) ^ [_585282] : [class_Rings_Ocomm__ring__1(_585282), -(class_Rings_Oring__1(tc_Polynomial_Opoly(_585282)))], (12621 ^ _152310) ^ [_585472] : [class_Rings_Ocomm__semiring__1(_585472), -(class_Power_Opower(tc_Polynomial_Opoly(_585472)))], (12627 ^ _152310) ^ [_585662] : [class_Groups_Ozero(_585662), -(class_Groups_Ozero(tc_Polynomial_Opoly(_585662)))], (12633 ^ _152310) ^ [_585852] : [class_Rings_Ocomm__ring(_585852), -(class_Rings_Oring(tc_Polynomial_Opoly(_585852)))], (12639 ^ _152310) ^ [_586042] : [class_Rings_Oidom(_586042), -(class_Rings_Oidom(tc_Polynomial_Opoly(_586042)))], (12645 ^ _152310) ^ [_586232] : [class_Rings_Ocomm__semiring__1(_586232), -(class_Groups_Oone(tc_Polynomial_Opoly(_586232)))], (12651 ^ _152310) ^ [_586422] : [class_Rings_Ocomm__semiring__1(_586422), -(class_Rings_Odvd(tc_Polynomial_Opoly(_586422)))], (12657 ^ _152310) ^ [_586626, _586628] : [hBOOL(c_fequal(_586626, _586628)), -(_586626 = _586628)], (12663 ^ _152310) ^ [_586842, _586844] : [_586842 = _586844, -(hBOOL(c_fequal(_586842, _586844)))], (12669 ^ _152310) ^ [_587024] : [c_Polynomial_Odegree(tc_Complex_Ocomplex, _587024) = c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, _587024), 12674 ^ [_587024]) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_z, 12674 ^ [_587024])), -(v_thesis____)]], input).
% 101.63/98.81 ncf('1',plain,[v_thesis____],start(12680 ^ 0)).
% 101.63/98.81 ncf('1.1',plain,[-(v_thesis____), c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex, v_p, v_z)) = c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p), hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex, v_p, v_z)), 12674 ^ [c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex, v_p, v_z)]) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_z, 12674 ^ [c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex, v_p, v_z)]))],extension(12669 ^ 1,bind([[_587024], [c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex, v_p, v_z)]]))).
% 101.63/98.81 ncf('1.1.1',plain,[-(c_Polynomial_Odegree(tc_Complex_Ocomplex, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex, v_p, v_z)) = c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p)), class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)],extension(1311 ^ 2,bind([[_196260, _196262, _196264], [tc_Complex_Ocomplex, v_p, v_z]]))).
% 101.63/98.81 ncf('1.1.1.1',plain,[-(class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex))],extension(12269 ^ 3)).
% 101.63/98.81 ncf('1.1.2',plain,[-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex, v_p, v_z)), 12674 ^ [c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex, v_p, v_z)]) = hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, v_z, 12674 ^ [c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex, v_p, v_z)]))), class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex)],extension(1211 ^ 2,bind([[_192343, _192345, _192347, _192349], [tc_Complex_Ocomplex, v_p, v_z, 12674 ^ [c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(tc_Complex_Ocomplex, v_p, v_z)]]]))).
% 101.63/98.81 ncf('1.1.2.1',plain,[-(class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex))],extension(12269 ^ 3)).
% 101.63/98.81 %-----------------------------------------------------
% 101.63/98.81 End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------