%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW271+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n028.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 12:25:51 EDT 2023

% Result   : Theorem 140.44s 136.03s
% Output   : Proof 140.44s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWW271+1 : TPTP v8.1.2. Released v5.2.0.
% 0.03/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n028.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Thu May 18 23:02:03 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 140.44/136.03  
% 140.44/136.03  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 140.44/136.03  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 140.44/136.03  %-----------------------------------------------------
% 140.44/136.03  ncf(matrix, plain, [(12644 ^ _113251) ^ [] : [v_thesis____], (798 ^ _113251) ^ [_123835, _123837, _123839, _123841, _123843, _123845] : [-(c_Polynomial_Oorder(_123845, _123841, _123837) = c_Polynomial_Oorder(_123843, _123839, _123835)), _123845 = _123843, _123841 = _123839, _123837 = _123835], (812 ^ _113251) ^ [_124056, _124058, _124060, _124062, _124064, _124066] : [-(c_Power_Opower_Opower(_124066, _124062, _124058) = c_Power_Opower_Opower(_124064, _124060, _124056)), _124066 = _124064, _124062 = _124060, _124058 = _124056], (826 ^ _113251) ^ [_124277, _124279, _124281, _124283] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_124283, _124279) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_124281, _124277)), _124283 = _124281, _124279 = _124277], (836 ^ _113251) ^ [_124426, _124428, _124430, _124432, _124434, _124436, _124438, _124440] : [-(c_If(_124440, _124436, _124432, _124428) = c_If(_124438, _124434, _124430, _124426)), _124440 = _124438, _124436 = _124434, _124432 = _124430, _124428 = _124426], (854 ^ _113251) ^ [_124727, _124729, _124731, _124733, _124735, _124737, _124739, _124741, _124743, _124745] : [-(c_Polynomial_Opoly__rec(_124745, _124741, _124737, _124733, _124729) = c_Polynomial_Opoly__rec(_124743, _124739, _124735, _124731, _124727)), _124745 = _124743, _124741 = _124739, _124737 = _124735, _124733 = _124731, _124729 = _124727], (876 ^ _113251) ^ [_125116, _125118, _125120, _125122, _125124, _125126] : [-(c_Polynomial_Opcompose(_125126, _125122, _125118) = c_Polynomial_Opcompose(_125124, _125120, _125116)), _125126 = _125124, _125122 = _125120, _125118 = _125116], (890 ^ _113251) ^ [_125337, _125339, _125341, _125343, _125345, _125347] : [-(c_Polynomial_Opoly__gcd(_125347, _125343, _125339) = c_Polynomial_Opoly__gcd(_125345, _125341, _125337)), _125347 = _125345, _125343 = _125341, _125339 = _125337], (904 ^ _113251) ^ [_125558, _125560, _125562, _125564] : [-(c_Polynomial_Opoly(_125564, _125560) = c_Polynomial_Opoly(_125562, _125558)), _125564 = _125562, _125560 = _125558], (914 ^ _113251) ^ [_125707, _125709, _125711, _125713, _125715, _125717] : [-(c_Polynomial_Omonom(_125717, _125713, _125709) = c_Polynomial_Omonom(_125715, _125711, _125707)), _125717 = _125715, _125713 = _125711, _125709 = _125707], (928 ^ _113251) ^ [_125928, _125930, _125932, _125934] : [-(c_Polynomial_Ocoeff(_125934, _125930) = c_Polynomial_Ocoeff(_125932, _125928)), _125934 = _125932, _125930 = _125928], (938 ^ _113251) ^ [_126077, _126079, _126081, _126083, _126085, _126087] : [-(c_Polynomial_Osynthetic__div(_126087, _126083, _126079) = c_Polynomial_Osynthetic__div(_126085, _126081, _126077)), _126087 = _126085, _126083 = _126081, _126079 = _126077], (952 ^ _113251) ^ [_126298, _126300] : [_126300 = _126298, -(c_Power_Opower__class_Opower(_126300) = c_Power_Opower__class_Opower(_126298))], (958 ^ _113251) ^ [_126383, _126385] : [_126385 = _126383, -(c_Rings_Odvd__class_Odvd(_126385) = c_Rings_Odvd__class_Odvd(_126383))], (964 ^ _113251) ^ [_126468, _126470, _126472, _126474] : [-(c_SMT_Oz3div(_126474, _126470) = c_SMT_Oz3div(_126472, _126468)), _126474 = _126472, _126470 = _126468], (974 ^ _113251) ^ [_126617, _126619, _126621, _126623] : [-(c_Polynomial_Odegree(_126623, _126619) = c_Polynomial_Odegree(_126621, _126617)), _126623 = _126621, _126619 = _126617], (984 ^ _113251) ^ [_126766, _126768] : [_126768 = _126766, -(c_Nat_OSuc(_126768) = c_Nat_OSuc(_126766))], (990 ^ _113251) ^ [_126851, _126853, _126855, _126857] : [-(c_Nat__Transfer_Otsub(_126857, _126853) = c_Nat__Transfer_Otsub(_126855, _126851)), _126857 = _126855, _126853 = _126851], (1000 ^ _113251) ^ [_127000, _127002, _127004, _127006] : [-(c_Groups_Osgn__class_Osgn(_127006, _127002) = c_Groups_Osgn__class_Osgn(_127004, _127000)), _127006 = _127004, _127002 = _127000], (1010 ^ _113251) ^ [_127149, _127151, _127153, _127155, _127157, _127159] : [-(c_Groups_Ominus__class_Ominus(_127159, _127155, _127151) = c_Groups_Ominus__class_Ominus(_127157, _127153, _127149)), _127159 = _127157, _127155 = _127153, _127151 = _127149], (1024 ^ _113251) ^ [_127370, _127372, _127374, _127376, _127378, _127380] : [-(c_Groups_Oplus__class_Oplus(_127380, _127376, _127372) = c_Groups_Oplus__class_Oplus(_127378, _127374, _127370)), _127380 = _127378, _127376 = _127374, _127372 = _127370], (1038 ^ _113251) ^ [_127591, _127593, _127595, _127597, _127599, _127601] : [-(c_Divides_Odiv__class_Odiv(_127601, _127597, _127593) = c_Divides_Odiv__class_Odiv(_127599, _127595, _127591)), _127601 = _127599, _127597 = _127595, _127593 = _127591], (1052 ^ _113251) ^ [_127812, _127814, _127816, _127818, _127820, _127822] : [-(c_Divides_Odiv__class_Omod(_127822, _127818, _127814) = c_Divides_Odiv__class_Omod(_127820, _127816, _127812)), _127822 = _127820, _127818 = _127816, _127814 = _127812], (1066 ^ _113251) ^ [_128033, _128035, _128037, _128039] : [-(tc_fun(_128039, _128035) = tc_fun(_128037, _128033)), _128039 = _128037, _128035 = _128033], (1076 ^ _113251) ^ [_128182, _128184, _128186, _128188] : [-(c_fequal(_128188, _128184) = c_fequal(_128186, _128182)), _128188 = _128186, _128184 = _128182], (1086 ^ _113251) ^ [_128331, _128333, _128335, _128337] : [-(hAPP(_128337, _128333) = hAPP(_128335, _128331)), _128337 = _128335, _128333 = _128331], (1096 ^ _113251) ^ [_128480, _128482] : [_128482 = _128480, -(c_Groups_Otimes__class_Otimes(_128482) = c_Groups_Otimes__class_Otimes(_128480))], (1102 ^ _113251) ^ [_128565, _128567, _128569, _128571] : [-(c_Groups_Ouminus__class_Ouminus(_128571, _128567) = c_Groups_Ouminus__class_Ouminus(_128569, _128565)), _128571 = _128569, _128567 = _128565], (1112 ^ _113251) ^ [_128714, _128716, _128718, _128720, _128722, _128724] : [-(c_Polynomial_OpCons(_128724, _128720, _128716) = c_Polynomial_OpCons(_128722, _128718, _128714)), _128724 = _128722, _128720 = _128718, _128716 = _128714], (1126 ^ _113251) ^ [_128935, _128937] : [_128937 = _128935, -(c_Groups_Oone__class_Oone(_128937) = c_Groups_Oone__class_Oone(_128935))], (1132 ^ _113251) ^ [_129020, _129022] : [_129022 = _129020, -(c_Groups_Ozero__class_Ozero(_129022) = c_Groups_Ozero__class_Ozero(_129020))], (1138 ^ _113251) ^ [_129101, _129103] : [_129103 = _129101, -(tc_Polynomial_Opoly(_129103) = tc_Polynomial_Opoly(_129101))], (2 ^ _113251) ^ [_113281] : [-(_113281 = _113281)], (4 ^ _113251) ^ [_113304, _113306] : [_113306 = _113304, -(_113304 = _113306)], (10 ^ _113251) ^ [_113377, _113379, _113381] : [-(_113381 = _113377), _113381 = _113379, _113379 = _113377], (20 ^ _113251) ^ [_113514, _113516] : [-(class_Lattices_Oab__semigroup__idem__mult(_113514)), _113516 = _113514, class_Lattices_Oab__semigroup__idem__mult(_113516)], (30 ^ _113251) ^ [_113639, _113641, _113643, _113645, _113647, _113649, _113651, _113653] : [-(c_Orderings_Oorder_Omono(_113651, _113647, _113643, _113639)), c_Orderings_Oorder_Omono(_113653, _113649, _113645, _113641), _113653 = _113651, _113649 = _113647, _113645 = _113643, _113641 = _113639], (52 ^ _113251) ^ [_113992, _113994, _113996, _113998] : [-(c_Polynomial_Opos__poly(_113996, _113992)), c_Polynomial_Opos__poly(_113998, _113994), _113998 = _113996, _113994 = _113992], (66 ^ _113251) ^ [_114185, _114187, _114189, _114191, _114193, _114195, _114197, _114199, _114201, _114203] : [-(c_Polynomial_Opdivmod__rel(_114201, _114197, _114193, _114189, _114185)), c_Polynomial_Opdivmod__rel(_114203, _114199, _114195, _114191, _114187), _114203 = _114201, _114199 = _114197, _114195 = _114193, _114191 = _114189, _114187 = _114185], (92 ^ _113251) ^ [_114630, _114632, _114634, _114636, _114638, _114640] : [-(c_Orderings_Oord__class_Oless(_114638, _114634, _114630)), c_Orderings_Oord__class_Oless(_114640, _114636, _114632), _114640 = _114638, _114636 = _114634, _114632 = _114630], (110 ^ _113251) ^ [_114899, _114901, _114903, _114905, _114907, _114909] : [-(c_Orderings_Oord__class_Oless__eq(_114907, _114903, _114899)), c_Orderings_Oord__class_Oless__eq(_114909, _114905, _114901), _114909 = _114907, _114905 = _114903, _114901 = _114899], (128 ^ _113251) ^ [_115168, _115170] : [-(class_Lattices_Oboolean__algebra(_115168)), _115170 = _115168, class_Lattices_Oboolean__algebra(_115170)], (138 ^ _113251) ^ [_115293, _115295] : [-(class_RealVector_Oreal__normed__div__algebra(_115293)), _115295 = _115293, class_RealVector_Oreal__normed__div__algebra(_115295)], (148 ^ _113251) ^ [_115418, _115420] : [-(class_RealVector_Oreal__normed__algebra__1(_115418)), _115420 = _115418, class_RealVector_Oreal__normed__algebra__1(_115420)], (158 ^ _113251) ^ [_115543, _115545] : [-(class_RealVector_Oreal__normed__algebra(_115543)), _115545 = _115543, class_RealVector_Oreal__normed__algebra(_115545)], (168 ^ _113251) ^ [_115668, _115670] : [-(class_RealVector_Oreal__normed__vector(_115668)), _115670 = _115668, class_RealVector_Oreal__normed__vector(_115670)], (178 ^ _113251) ^ [_115793, _115795] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_115793)), _115795 = _115793, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_115795)], (188 ^ _113251) ^ [_115918, _115920] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_115918)), _115920 = _115918, class_Groups_Oordered__cancel__ab__semigroup__add(_115920)], (198 ^ _113251) ^ [_116043, _116045] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_116043)), _116045 = _116043, class_Groups_Oordered__ab__semigroup__add__imp__le(_116045)], (208 ^ _113251) ^ [_116168, _116170] : [-(class_Rings_Olinordered__comm__semiring__strict(_116168)), _116170 = _116168, class_Rings_Olinordered__comm__semiring__strict(_116170)], (218 ^ _113251) ^ [_116293, _116295] : [-(class_Rings_Olinordered__semiring__1__strict(_116293)), _116295 = _116293, class_Rings_Olinordered__semiring__1__strict(_116295)], (228 ^ _113251) ^ [_116418, _116420] : [-(class_Rings_Olinordered__semiring__strict(_116418)), _116420 = _116418, class_Rings_Olinordered__semiring__strict(_116420)], (238 ^ _113251) ^ [_116543, _116545] : [-(class_Groups_Oordered__ab__semigroup__add(_116543)), _116545 = _116543, class_Groups_Oordered__ab__semigroup__add(_116545)], (248 ^ _113251) ^ [_116668, _116670] : [-(class_Groups_Oordered__comm__monoid__add(_116668)), _116670 = _116668, class_Groups_Oordered__comm__monoid__add(_116670)], (258 ^ _113251) ^ [_116793, _116795] : [-(class_Groups_Olinordered__ab__group__add(_116793)), _116795 = _116793, class_Groups_Olinordered__ab__group__add(_116795)], (268 ^ _113251) ^ [_116918, _116920] : [-(class_Groups_Ocancel__ab__semigroup__add(_116918)), _116920 = _116918, class_Groups_Ocancel__ab__semigroup__add(_116920)], (278 ^ _113251) ^ [_117043, _117045] : [-(class_Rings_Oring__1__no__zero__divisors(_117043)), _117045 = _117043, class_Rings_Oring__1__no__zero__divisors(_117045)], (288 ^ _113251) ^ [_117168, _117170] : [-(class_Rings_Oordered__cancel__semiring(_117168)), _117170 = _117168, class_Rings_Oordered__cancel__semiring(_117170)], (298 ^ _113251) ^ [_117293, _117295] : [-(class_Rings_Olinordered__ring__strict(_117293)), _117295 = _117293, class_Rings_Olinordered__ring__strict(_117295)], (308 ^ _113251) ^ [_117418, _117420] : [-(class_Rings_Oring__no__zero__divisors(_117418)), _117420 = _117418, class_Rings_Oring__no__zero__divisors(_117420)], (318 ^ _113251) ^ [_117543, _117545] : [-(class_Rings_Oordered__comm__semiring(_117543)), _117545 = _117543, class_Rings_Oordered__comm__semiring(_117545)], (328 ^ _113251) ^ [_117668, _117670] : [-(class_Rings_Olinordered__semiring__1(_117668)), _117670 = _117668, class_Rings_Olinordered__semiring__1(_117670)], (338 ^ _113251) ^ [_117793, _117795] : [-(class_Groups_Oordered__ab__group__add(_117793)), _117795 = _117793, class_Groups_Oordered__ab__group__add(_117795)], (348 ^ _113251) ^ [_117918, _117920] : [-(class_Groups_Ocancel__comm__monoid__add(_117918)), _117920 = _117918, class_Groups_Ocancel__comm__monoid__add(_117920)], (358 ^ _113251) ^ [_118043, _118045] : [-(class_Groups_Ocancel__semigroup__add(_118043)), _118045 = _118043, class_Groups_Ocancel__semigroup__add(_118045)], (368 ^ _113251) ^ [_118168, _118170] : [-(class_Rings_Olinordered__semiring(_118168)), _118170 = _118168, class_Rings_Olinordered__semiring(_118170)], (378 ^ _113251) ^ [_118293, _118295] : [-(class_Rings_Olinordered__semidom(_118293)), _118295 = _118293, class_Rings_Olinordered__semidom(_118295)], (388 ^ _113251) ^ [_118418, _118420] : [-(class_Groups_Oab__semigroup__mult(_118418)), _118420 = _118418, class_Groups_Oab__semigroup__mult(_118420)], (398 ^ _113251) ^ [_118543, _118545] : [-(class_Groups_Ocomm__monoid__mult(_118543)), _118545 = _118543, class_Groups_Ocomm__monoid__mult(_118545)], (408 ^ _113251) ^ [_118668, _118670] : [-(class_Groups_Oab__semigroup__add(_118668)), _118670 = _118668, class_Groups_Oab__semigroup__add(_118670)], (418 ^ _113251) ^ [_118793, _118795] : [-(class_Rings_Oordered__semiring(_118793)), _118795 = _118793, class_Rings_Oordered__semiring(_118795)], (428 ^ _113251) ^ [_118918, _118920] : [-(class_Rings_Ono__zero__divisors(_118918)), _118920 = _118918, class_Rings_Ono__zero__divisors(_118920)], (438 ^ _113251) ^ [_119043, _119045] : [-(class_Rings_Olinordered__ring(_119043)), _119045 = _119043, class_Rings_Olinordered__ring(_119045)], (448 ^ _113251) ^ [_119168, _119170] : [-(class_Divides_Osemiring__div(_119168)), _119170 = _119168, class_Divides_Osemiring__div(_119170)], (458 ^ _113251) ^ [_119293, _119295] : [-(class_Rings_Ocomm__semiring(_119293)), _119295 = _119293, class_Rings_Ocomm__semiring(_119295)], (468 ^ _113251) ^ [_119418, _119420] : [-(class_Rings_Ozero__neq__one(_119418)), _119420 = _119418, class_Rings_Ozero__neq__one(_119420)], (478 ^ _113251) ^ [_119543, _119545] : [-(class_Rings_Oordered__ring(_119543)), _119545 = _119543, class_Rings_Oordered__ring(_119545)], (488 ^ _113251) ^ [_119668, _119670] : [-(class_Orderings_Opreorder(_119668)), _119670 = _119668, class_Orderings_Opreorder(_119670)], (498 ^ _113251) ^ [_119793, _119795] : [-(class_Orderings_Olinorder(_119793)), _119795 = _119793, class_Orderings_Olinorder(_119795)], (508 ^ _113251) ^ [_119918, _119920] : [-(class_Groups_Omonoid__mult(_119918)), _119920 = _119918, class_Groups_Omonoid__mult(_119920)], (518 ^ _113251) ^ [_120043, _120045] : [-(class_Groups_Ocomm__monoid__add(_120043)), _120045 = _120043, class_Groups_Ocomm__monoid__add(_120045)], (528 ^ _113251) ^ [_120168, _120170] : [-(class_Groups_Omonoid__add(_120168)), _120170 = _120168, class_Groups_Omonoid__add(_120170)], (538 ^ _113251) ^ [_120293, _120295] : [-(class_Rings_Osemiring__0(_120293)), _120295 = _120293, class_Rings_Osemiring__0(_120295)], (548 ^ _113251) ^ [_120418, _120420] : [-(class_Groups_Ogroup__add(_120418)), _120420 = _120418, class_Groups_Ogroup__add(_120420)], (558 ^ _113251) ^ [_120543, _120545] : [-(class_Fields_Ofield(_120543)), _120545 = _120543, class_Fields_Ofield(_120545)], (568 ^ _113251) ^ [_120668, _120670] : [-(class_Divides_Oring__div(_120668)), _120670 = _120668, class_Divides_Oring__div(_120670)], (578 ^ _113251) ^ [_120793, _120795] : [-(class_Rings_Omult__zero(_120793)), _120795 = _120793, class_Rings_Omult__zero(_120795)], (588 ^ _113251) ^ [_120918, _120920] : [-(class_Orderings_Oorder(_120918)), _120920 = _120918, class_Orderings_Oorder(_120920)], (598 ^ _113251) ^ [_121043, _121045] : [-(class_Int_Oring__char__0(_121043)), _121045 = _121043, class_Int_Oring__char__0(_121045)], (608 ^ _113251) ^ [_121168, _121170] : [-(class_Rings_Ocomm__semiring__0(_121168)), _121170 = _121168, class_Rings_Ocomm__semiring__0(_121170)], (618 ^ _113251) ^ [_121293, _121295] : [-(class_Rings_Osemiring(_121293)), _121295 = _121293, class_Rings_Osemiring(_121295)], (628 ^ _113251) ^ [_121418, _121420] : [-(class_Orderings_Oord(_121418)), _121420 = _121418, class_Orderings_Oord(_121420)], (638 ^ _113251) ^ [_121543, _121545] : [-(class_Groups_Ouminus(_121543)), _121545 = _121543, class_Groups_Ouminus(_121545)], (648 ^ _113251) ^ [_121668, _121670] : [-(class_Rings_Olinordered__idom(_121668)), _121670 = _121668, class_Rings_Olinordered__idom(_121670)], (658 ^ _113251) ^ [_121793, _121795] : [-(class_Groups_Osgn__if(_121793)), _121795 = _121793, class_Groups_Osgn__if(_121795)], (668 ^ _113251) ^ [_121918, _121920] : [-(class_Rings_Ocomm__ring__1(_121918)), _121920 = _121918, class_Rings_Ocomm__ring__1(_121920)], (678 ^ _113251) ^ [_122043, _122045] : [-(class_Rings_Oring__1(_122043)), _122045 = _122043, class_Rings_Oring__1(_122045)], (688 ^ _113251) ^ [_122168, _122170] : [-(class_Groups_Oab__group__add(_122168)), _122170 = _122168, class_Groups_Oab__group__add(_122170)], (698 ^ _113251) ^ [_122293, _122295] : [-(class_Groups_Ominus(_122293)), _122295 = _122293, class_Groups_Ominus(_122295)], (708 ^ _113251) ^ [_122418, _122420] : [-(class_Power_Opower(_122418)), _122420 = _122418, class_Power_Opower(_122420)], (718 ^ _113251) ^ [_122543, _122545] : [-(class_Groups_Ozero(_122543)), _122545 = _122543, class_Groups_Ozero(_122545)], (728 ^ _113251) ^ [_122668, _122670] : [-(class_Rings_Ocomm__ring(_122668)), _122670 = _122668, class_Rings_Ocomm__ring(_122670)], (738 ^ _113251) ^ [_122793, _122795] : [-(class_Rings_Oring(_122793)), _122795 = _122793, class_Rings_Oring(_122795)], (748 ^ _113251) ^ [_122918, _122920] : [-(class_Rings_Oidom(_122918)), _122920 = _122918, class_Rings_Oidom(_122920)], (758 ^ _113251) ^ [_123043, _123045] : [-(class_Groups_Oone(_123043)), _123045 = _123043, class_Groups_Oone(_123045)], (768 ^ _113251) ^ [_123168, _123170] : [-(class_Rings_Ocomm__semiring__1(_123168)), _123170 = _123168, class_Rings_Ocomm__semiring__1(_123170)], (778 ^ _113251) ^ [_123293, _123295] : [-(class_Rings_Odvd(_123293)), _123295 = _123293, class_Rings_Odvd(_123295)], (788 ^ _113251) ^ [_123414, _123416] : [-(hBOOL(_123414)), _123416 = _123414, hBOOL(_123416)], (1144 ^ _113251) ^ [_129276, _129278] : [hAPP(_129276, 1145 ^ [_129276, _129278]) = hAPP(_129278, 1145 ^ [_129276, _129278]), -(_129276 = _129278)], (1151 ^ _113251) ^ [] : [v_qa____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))], (1153 ^ _113251) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), v_qa____)))], (1155 ^ _113251) ^ [_129444] : [class_Rings_Ocomm__semiring__1(_129444), -(c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_129444)) = c_Polynomial_OpCons(_129444, c_Groups_Oone__class_Oone(_129444), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_129444))))], (1161 ^ _113251) ^ [_129545] : [class_Groups_Ozero(_129545), -(c_Polynomial_OpCons(_129545, c_Groups_Ozero__class_Ozero(_129545), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_129545))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_129545)))], (1167 ^ _113251) ^ [_129646, _129648, _129650] : [class_Groups_Ozero(_129646), 1170 ^ _113251 : [(1171 ^ _113251) ^ [] : [c_Polynomial_OpCons(_129646, _129648, _129650) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_129646)), 1174 ^ _113251 : [(1175 ^ _113251) ^ [] : [-(_129648 = c_Groups_Ozero__class_Ozero(_129646))], (1177 ^ _113251) ^ [] : [-(_129650 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_129646)))]]], (1179 ^ _113251) ^ [] : [-(c_Polynomial_OpCons(_129646, _129648, _129650) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_129646))), _129648 = c_Groups_Ozero__class_Ozero(_129646), _129650 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_129646))]]], (1189 ^ _113251) ^ [_129973, _129975] : [class_Rings_Ocomm__ring__1(_129973), -(c_Groups_Ouminus__class_Ouminus(_129973, _129975) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_129973), c_Groups_Ouminus__class_Ouminus(_129973, c_Groups_Oone__class_Oone(_129973))), _129975))], (1195 ^ _113251) ^ [_130080, _130082] : [class_Rings_Oring__1__no__zero__divisors(_130080), 1198 ^ _113251 : [(1209 ^ _113251) ^ [] : [1210 ^ _113251 : [(1211 ^ _113251) ^ [] : [_130082 = c_Groups_Oone__class_Oone(_130080)], (1213 ^ _113251) ^ [] : [_130082 = c_Groups_Ouminus__class_Ouminus(_130080, c_Groups_Oone__class_Oone(_130080))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_130080), _130082), _130082) = c_Groups_Oone__class_Oone(_130080))], (1199 ^ _113251) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_130080), _130082), _130082) = c_Groups_Oone__class_Oone(_130080), -(_130082 = c_Groups_Oone__class_Oone(_130080)), -(_130082 = c_Groups_Ouminus__class_Ouminus(_130080, c_Groups_Oone__class_Oone(_130080)))]]], (1217 ^ _113251) ^ [_130381, _130383] : [class_Rings_Ocomm__semiring__0(_130381), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_130381)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_130381))), _130383) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_130381)))], (1223 ^ _113251) ^ [_130492, _130494] : [class_Rings_Ocomm__semiring__0(_130492), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_130492)), _130494), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_130492))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_130492)))], (1229 ^ _113251) ^ [_130603, _130605, _130607] : [class_Groups_Oab__group__add(_130603), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_130603), c_Polynomial_OpCons(_130603, _130605, _130607)) = c_Polynomial_OpCons(_130603, c_Groups_Ouminus__class_Ouminus(_130603, _130605), c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_130603), _130607)))], (1235 ^ _113251) ^ [_130722, _130724, _130726] : [class_Groups_Oab__group__add(_130722), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_130722), c_Polynomial_OpCons(_130722, _130724, _130726)) = c_Polynomial_OpCons(_130722, c_Groups_Ouminus__class_Ouminus(_130722, _130724), c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_130722), _130726)))], (1241 ^ _113251) ^ [] : [v_pa____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))], (1243 ^ _113251) ^ [_130865, _130867, _130869] : [class_Rings_Oring(_130865), -(c_Groups_Ouminus__class_Ouminus(_130865, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_130865), _130867), _130869)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_130865), _130867), c_Groups_Ouminus__class_Ouminus(_130865, _130869)))], (1249 ^ _113251) ^ [_130986, _130988, _130990] : [class_Rings_Oring(_130986), -(c_Groups_Ouminus__class_Ouminus(_130986, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_130986), _130988), _130990)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_130986), c_Groups_Ouminus__class_Ouminus(_130986, _130988)), _130990))], (1255 ^ _113251) ^ [] : [v_na____ = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (1257 ^ _113251) ^ [] : [c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (1259 ^ _113251) ^ [_131155, _131157] : [class_Rings_Ocomm__semiring__1(_131155), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_131155), _131157), c_Groups_Ozero__class_Ozero(_131155))))], (1265 ^ _113251) ^ [] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____), v_a____) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))], (1267 ^ _113251) ^ [_131266] : [hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_pa____), _131266) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), -(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_qa____), _131266) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))], (1273 ^ _113251) ^ [_131353, _131355] : [class_Rings_Ocomm__semiring__1(_131353), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_131353), _131355), _131355)))], (1279 ^ _113251) ^ [_131442, _131444, _131446, _131448] : [class_Rings_Ocomm__semiring__1(_131442), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_131442), _131444), _131446)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_131442), _131446), _131448)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_131442), _131444), _131448)))], (1293 ^ _113251) ^ [_131675, _131677] : [class_Rings_Ocomm__semiring__1(_131675), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_131675), c_Groups_Ozero__class_Ozero(_131675)), _131677)), -(_131677 = c_Groups_Ozero__class_Ozero(_131675))], (1303 ^ _113251) ^ [_131824, _131826, _131828, _131830] : [class_Rings_Ocomm__semiring__1(_131824), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_131824), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_131824), _131826), _131828)), _131830)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_131824), _131828), _131830)))], (1313 ^ _113251) ^ [_132003, _132005, _132007, _132009] : [class_Rings_Ocomm__semiring__1(_132003), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_132003), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_132003), _132005), _132007)), _132009)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_132003), _132005), _132009)))], (1323 ^ _113251) ^ [_132182, _132184, _132186, _132188] : [class_Rings_Odvd(_132182), _132184 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_132182), _132186), _132188), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_132182), _132186), _132184)))], (1333 ^ _113251) ^ [_132347, _132349, _132351, _132353, _132355] : [class_Rings_Ocomm__semiring__1(_132347), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_132347), _132349), _132351)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_132347), _132353), _132355)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_132347), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_132347), _132349), _132353)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_132347), _132351), _132355))))], (1347 ^ _113251) ^ [_132618, _132620, _132622, _132624] : [class_Rings_Ocomm__semiring__1(_132618), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_132618), _132620), _132622)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_132618), _132620), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_132618), _132624), _132622))))], (1357 ^ _113251) ^ [_132797, _132799, _132801, _132803] : [class_Rings_Ocomm__semiring__1(_132797), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_132797), _132799), _132801)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_132797), _132799), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_132797), _132801), _132803))))], (1367 ^ _113251) ^ [_132976, _132978, _132980] : [class_Rings_Ocomm__semiring__1(_132976), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_132976), _132978), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_132976), _132980), _132978))))], (1373 ^ _113251) ^ [_133083, _133085, _133087] : [class_Rings_Ocomm__semiring__1(_133083), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_133083), _133085), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_133083), _133085), _133087))))], (1379 ^ _113251) ^ [_133190, _133192] : [class_Rings_Ocomm__semiring__1(_133190), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_133190), c_Groups_Oone__class_Oone(_133190)), _133192)))], (1385 ^ _113251) ^ [_133283, _133285, _133287] : [class_Rings_Ocomm__ring__1(_133283), 1388 ^ _113251 : [(1389 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_133283), c_Groups_Ouminus__class_Ouminus(_133283, _133285)), _133287)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_133283), _133285), _133287)))], (1395 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_133283), _133285), _133287)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_133283), c_Groups_Ouminus__class_Ouminus(_133283, _133285)), _133287)))]]], (1401 ^ _113251) ^ [_133545, _133547, _133549] : [class_Rings_Ocomm__ring__1(_133545), 1404 ^ _113251 : [(1405 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_133545), _133547), c_Groups_Ouminus__class_Ouminus(_133545, _133549))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_133545), _133547), _133549)))], (1411 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_133545), _133547), _133549)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_133545), _133547), c_Groups_Ouminus__class_Ouminus(_133545, _133549))))]]], (1417 ^ _113251) ^ [_133807] : [class_Groups_Oab__group__add(_133807), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_133807), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_133807))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_133807)))], (1423 ^ _113251) ^ [_133906, _133908, _133910, _133912] : [class_Rings_Oidom(_133906), 1426 ^ _113251 : [(1437 ^ _113251) ^ [] : [1438 ^ _113251 : [(1439 ^ _113251) ^ [] : [_133908 = c_Groups_Ozero__class_Ozero(_133906)], (1441 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_133906), _133910), _133912))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_133906), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_133906), _133908), _133910)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_133906), _133908), _133912))))], (1427 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_133906), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_133906), _133908), _133910)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_133906), _133908), _133912))), -(_133908 = c_Groups_Ozero__class_Ozero(_133906)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_133906), _133910), _133912)))]]], (1445 ^ _113251) ^ [_134264, _134266, _134268, _134270] : [class_Rings_Oidom(_134264), 1448 ^ _113251 : [(1459 ^ _113251) ^ [] : [1460 ^ _113251 : [(1461 ^ _113251) ^ [] : [_134268 = c_Groups_Ozero__class_Ozero(_134264)], (1463 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_134264), _134266), _134270))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_134264), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_134264), _134266), _134268)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_134264), _134270), _134268))))], (1449 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_134264), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_134264), _134266), _134268)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_134264), _134270), _134268))), -(_134268 = c_Groups_Ozero__class_Ozero(_134264)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_134264), _134266), _134270)))]]], (1467 ^ _113251) ^ [_134622, _134624, _134626, _134628, _134630] : [class_Rings_Ocomm__semiring__1(_134622), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_134622), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_134622), _134624), _134626)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_134622), _134628), _134630)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_134622), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_134622), _134624), _134628)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_134622), _134626), _134630)))], (1473 ^ _113251) ^ [_134799, _134801, _134803, _134805, _134807] : [class_Rings_Ocomm__semiring__1(_134799), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_134799), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_134799), _134801), _134803)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_134799), _134805), _134807)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_134799), _134805), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_134799), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_134799), _134801), _134803)), _134807)))], (1479 ^ _113251) ^ [_134976, _134978, _134980, _134982, _134984] : [class_Rings_Ocomm__semiring__1(_134976), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_134976), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_134976), _134978), _134980)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_134976), _134982), _134984)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_134976), _134978), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_134976), _134980), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_134976), _134982), _134984))))], (1485 ^ _113251) ^ [_135153, _135155, _135157, _135159] : [class_Rings_Ocomm__semiring__1(_135153), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_135153), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_135153), _135155), _135157)), _135159) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_135153), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_135153), _135155), _135159)), _135157))], (1491 ^ _113251) ^ [_135296, _135298, _135300, _135302] : [class_Rings_Ocomm__semiring__1(_135296), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_135296), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_135296), _135298), _135300)), _135302) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_135296), _135298), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_135296), _135300), _135302)))], (1497 ^ _113251) ^ [_135439, _135441, _135443, _135445] : [class_Rings_Ocomm__semiring__1(_135439), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_135439), _135441), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_135439), _135443), _135445)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_135439), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_135439), _135441), _135443)), _135445))], (1503 ^ _113251) ^ [_135582, _135584, _135586, _135588] : [class_Rings_Ocomm__semiring__1(_135582), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_135582), _135584), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_135582), _135586), _135588)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_135582), _135586), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_135582), _135584), _135588)))], (1509 ^ _113251) ^ [_135725, _135727, _135729] : [class_Rings_Ocomm__semiring__1(_135725), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_135725), _135727), _135729) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_135725), _135729), _135727))], (1515 ^ _113251) ^ [_135834, _135836, _135838, _135840, _135842] : [class_Groups_Ozero(_135834), 1518 ^ _113251 : [(1519 ^ _113251) ^ [] : [c_Polynomial_OpCons(_135834, _135836, _135838) = c_Polynomial_OpCons(_135834, _135840, _135842), 1522 ^ _113251 : [(1523 ^ _113251) ^ [] : [-(_135836 = _135840)], (1525 ^ _113251) ^ [] : [-(_135838 = _135842)]]], (1527 ^ _113251) ^ [] : [-(c_Polynomial_OpCons(_135834, _135836, _135838) = c_Polynomial_OpCons(_135834, _135840, _135842)), _135836 = _135840, _135838 = _135842]]], (1537 ^ _113251) ^ [_136159, _136161, _136163] : [class_Rings_Ono__zero__divisors(_136159), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_136159), _136161), _136163) = c_Groups_Ozero__class_Ozero(_136159), -(_136161 = c_Groups_Ozero__class_Ozero(_136159)), -(_136163 = c_Groups_Ozero__class_Ozero(_136159))], (1551 ^ _113251) ^ [_136331, _136333, _136335] : [class_Rings_Ono__zero__divisors(_136331), -(_136333 = c_Groups_Ozero__class_Ozero(_136331)), -(_136335 = c_Groups_Ozero__class_Ozero(_136331)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_136331), _136333), _136335) = c_Groups_Ozero__class_Ozero(_136331)], (1565 ^ _113251) ^ [_136551, _136553, _136555] : [class_Rings_Oring__no__zero__divisors(_136551), 1568 ^ _113251 : [(1579 ^ _113251) ^ [] : [1580 ^ _113251 : [(1581 ^ _113251) ^ [] : [_136553 = c_Groups_Ozero__class_Ozero(_136551)], (1583 ^ _113251) ^ [] : [_136555 = c_Groups_Ozero__class_Ozero(_136551)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_136551), _136553), _136555) = c_Groups_Ozero__class_Ozero(_136551))], (1569 ^ _113251) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_136551), _136553), _136555) = c_Groups_Ozero__class_Ozero(_136551), -(_136553 = c_Groups_Ozero__class_Ozero(_136551)), -(_136555 = c_Groups_Ozero__class_Ozero(_136551))]]], (1587 ^ _113251) ^ [_136849, _136851] : [class_Rings_Ocomm__semiring__1(_136849), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_136849), _136851), c_Groups_Ozero__class_Ozero(_136849)) = c_Groups_Ozero__class_Ozero(_136849))], (1593 ^ _113251) ^ [_136948, _136950] : [class_Rings_Omult__zero(_136948), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_136948), _136950), c_Groups_Ozero__class_Ozero(_136948)) = c_Groups_Ozero__class_Ozero(_136948))], (1599 ^ _113251) ^ [_137047, _137049] : [class_Rings_Ocomm__semiring__1(_137047), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_137047), c_Groups_Ozero__class_Ozero(_137047)), _137049) = c_Groups_Ozero__class_Ozero(_137047))], (1605 ^ _113251) ^ [_137146, _137148] : [class_Rings_Omult__zero(_137146), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_137146), c_Groups_Ozero__class_Ozero(_137146)), _137148) = c_Groups_Ozero__class_Ozero(_137146))], (1611 ^ _113251) ^ [_137245] : [class_Rings_Ozero__neq__one(_137245), c_Groups_Ozero__class_Ozero(_137245) = c_Groups_Oone__class_Oone(_137245)], (1617 ^ _113251) ^ [_137327] : [class_Rings_Ozero__neq__one(_137327), c_Groups_Oone__class_Oone(_137327) = c_Groups_Ozero__class_Ozero(_137327)], (1623 ^ _113251) ^ [_137409, _137411] : [class_Rings_Ocomm__semiring__1(_137409), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_137409), _137411), c_Groups_Oone__class_Oone(_137409)) = _137411)], (1629 ^ _113251) ^ [_137504, _137506] : [class_Rings_Ocomm__semiring__1(_137504), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_137504), c_Groups_Oone__class_Oone(_137504)), _137506) = _137506)], (1635 ^ _113251) ^ [_137599, _137601, _137603] : [class_Rings_Oidom(_137599), 1638 ^ _113251 : [(1649 ^ _113251) ^ [] : [1650 ^ _113251 : [(1651 ^ _113251) ^ [] : [_137601 = _137603], (1653 ^ _113251) ^ [] : [_137601 = c_Groups_Ouminus__class_Ouminus(_137599, _137603)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_137599), _137601), _137601) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_137599), _137603), _137603))], (1639 ^ _113251) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_137599), _137601), _137601) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_137599), _137603), _137603), -(_137601 = _137603), -(_137601 = c_Groups_Ouminus__class_Ouminus(_137599, _137603))]]], (1657 ^ _113251) ^ [_137912, _137914, _137916] : [class_Rings_Oring(_137912), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_137912), c_Groups_Ouminus__class_Ouminus(_137912, _137914)), c_Groups_Ouminus__class_Ouminus(_137912, _137916)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_137912), _137914), _137916))], (1663 ^ _113251) ^ [_138033, _138035, _138037] : [class_Rings_Oring(_138033), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_138033), c_Groups_Ouminus__class_Ouminus(_138033, _138035)), _138037) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_138033), _138035), c_Groups_Ouminus__class_Ouminus(_138033, _138037)))], (1669 ^ _113251) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____))), v_pa____)))], (1671 ^ _113251) ^ [] : [v_qa____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_pa____), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), v_qa____), v_na____))))], (1677 ^ _113251) ^ [_138231, _138233, _138235] : [class_RealVector_Oreal__normed__algebra(_138231), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_138231), c_Groups_Ouminus__class_Ouminus(_138231, _138233)), _138235) = c_Groups_Ouminus__class_Ouminus(_138231, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_138231), _138233), _138235)))], (1683 ^ _113251) ^ [_138352, _138354, _138356] : [class_RealVector_Oreal__normed__algebra(_138352), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_138352), c_Groups_Ouminus__class_Ouminus(_138352, _138354)), _138356) = c_Groups_Ouminus__class_Ouminus(_138352, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_138352), _138354), _138356)))], (1689 ^ _113251) ^ [_138473, _138475, _138477] : [class_RealVector_Oreal__normed__algebra(_138473), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_138473), _138475), c_Groups_Ouminus__class_Ouminus(_138473, _138477)) = c_Groups_Ouminus__class_Ouminus(_138473, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_138473), _138475), _138477)))], (1695 ^ _113251) ^ [_138594, _138596, _138598] : [class_RealVector_Oreal__normed__algebra(_138594), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_138594), _138596), c_Groups_Ouminus__class_Ouminus(_138594, _138598)) = c_Groups_Ouminus__class_Ouminus(_138594, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_138594), _138596), _138598)))], (1701 ^ _113251) ^ [_138715, _138717] : [class_Groups_Ocomm__monoid__mult(_138715), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_138715), _138717), c_Groups_Oone__class_Oone(_138715)) = _138717)], (1707 ^ _113251) ^ [_138810, _138812] : [class_Groups_Omonoid__mult(_138810), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_138810), _138812), c_Groups_Oone__class_Oone(_138810)) = _138812)], (1713 ^ _113251) ^ [_138905, _138907] : [class_Groups_Ocomm__monoid__mult(_138905), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_138905), c_Groups_Oone__class_Oone(_138905)), _138907) = _138907)], (1719 ^ _113251) ^ [_139000, _139002] : [class_Groups_Omonoid__mult(_139000), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_139000), c_Groups_Oone__class_Oone(_139000)), _139002) = _139002)], (1725 ^ _113251) ^ [_139095, _139097] : [class_Groups_Olinordered__ab__group__add(_139095), 1728 ^ _113251 : [(1729 ^ _113251) ^ [] : [c_Groups_Ouminus__class_Ouminus(_139095, _139097) = _139097, -(_139097 = c_Groups_Ozero__class_Ozero(_139095))], (1735 ^ _113251) ^ [] : [_139097 = c_Groups_Ozero__class_Ozero(_139095), -(c_Groups_Ouminus__class_Ouminus(_139095, _139097) = _139097)]]], (1741 ^ _113251) ^ [_139315, _139317] : [class_Groups_Ogroup__add(_139315), 1744 ^ _113251 : [(1745 ^ _113251) ^ [] : [c_Groups_Ouminus__class_Ouminus(_139315, _139317) = c_Groups_Ozero__class_Ozero(_139315), -(_139317 = c_Groups_Ozero__class_Ozero(_139315))], (1751 ^ _113251) ^ [] : [_139317 = c_Groups_Ozero__class_Ozero(_139315), -(c_Groups_Ouminus__class_Ouminus(_139315, _139317) = c_Groups_Ozero__class_Ozero(_139315))]]], (1757 ^ _113251) ^ [] : [v_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (1759 ^ _113251) ^ [_139565] : [hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_p), _139565) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex), -(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, v_q), _139565) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))], (1765 ^ _113251) ^ [] : [-(c_Polynomial_Odegree(tc_Complex_Ocomplex, v_pa____) = v_na____)], (1767 ^ _113251) ^ [_139670, _139672] : [class_Rings_Ocomm__semiring__1(_139670), -(hAPP(hAPP(c_Power_Opower__class_Opower(_139670), _139672), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _139672)], (1773 ^ _113251) ^ [_139761, _139763, _139765] : [class_Int_Oring__char__0(_139761), class_Rings_Oidom(_139761), 1780 ^ _113251 : [(1781 ^ _113251) ^ [] : [c_Polynomial_Opoly(_139761, _139763) = c_Polynomial_Opoly(_139761, _139765), -(_139763 = _139765)], (1787 ^ _113251) ^ [] : [_139763 = _139765, -(c_Polynomial_Opoly(_139761, _139763) = c_Polynomial_Opoly(_139761, _139765))]]], (1793 ^ _113251) ^ [_140044, _140046, _140048, _140050] : [class_Rings_Ocomm__semiring__1(_140044), -(hAPP(hAPP(c_Power_Opower__class_Opower(_140044), hAPP(hAPP(c_Power_Opower__class_Opower(_140044), _140046), _140048)), _140050) = hAPP(hAPP(c_Power_Opower__class_Opower(_140044), _140046), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _140048), _140050)))], (1799 ^ _113251) ^ [_140183, _140185, _140187, _140189] : [class_Rings_Ocomm__semiring__1(_140183), -(hAPP(c_Polynomial_Opoly(_140183, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_140183)), _140185), _140187)), _140189) = hAPP(hAPP(c_Power_Opower__class_Opower(_140183), hAPP(c_Polynomial_Opoly(_140183, _140185), _140189)), _140187))], (1805 ^ _113251) ^ [_140322, _140324, _140326, _140328] : [class_Rings_Ocomm__semiring__1(_140322), -(hAPP(hAPP(c_Power_Opower__class_Opower(_140322), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_140322), _140324), _140326)), _140328) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_140322), hAPP(hAPP(c_Power_Opower__class_Opower(_140322), _140324), _140328)), hAPP(hAPP(c_Power_Opower__class_Opower(_140322), _140326), _140328)))], (1811 ^ _113251) ^ [_140481, _140483] : [class_Rings_Ocomm__semiring__1(_140481), -(hAPP(hAPP(c_Power_Opower__class_Opower(_140481), _140483), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_140481))], (1817 ^ _113251) ^ [_140576, _140578] : [class_Int_Oring__char__0(_140576), class_Rings_Oidom(_140576), 1824 ^ _113251 : [(1825 ^ _113251) ^ [] : [c_Polynomial_Opoly(_140576, _140578) = c_Polynomial_Opoly(_140576, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_140576))), -(_140578 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_140576)))], (1831 ^ _113251) ^ [] : [_140578 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_140576)), -(c_Polynomial_Opoly(_140576, _140578) = c_Polynomial_Opoly(_140576, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_140576))))]]], (1837 ^ _113251) ^ [_140875, _140877, _140879] : [class_Rings_Oidom(_140875), 1840 ^ _113251 : [(1851 ^ _113251) ^ [] : [1852 ^ _113251 : [(1853 ^ _113251) ^ [] : [_140877 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_140875))], (1855 ^ _113251) ^ [] : [-(c_Polynomial_Oorder(_140875, _140879, _140877) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], -(hAPP(c_Polynomial_Opoly(_140875, _140877), _140879) = c_Groups_Ozero__class_Ozero(_140875))], (1841 ^ _113251) ^ [] : [hAPP(c_Polynomial_Opoly(_140875, _140877), _140879) = c_Groups_Ozero__class_Ozero(_140875), -(_140877 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_140875))), c_Polynomial_Oorder(_140875, _140879, _140877) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (1859 ^ _113251) ^ [_141219, _141221] : [class_Rings_Ocomm__semiring__0(_141219), -(hAPP(c_Polynomial_Opoly(_141219, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_141219))), _141221) = c_Groups_Ozero__class_Ozero(_141219))], (1865 ^ _113251) ^ [_141318, _141320, _141322, _141324] : [class_Rings_Ocomm__semiring__0(_141318), -(hAPP(c_Polynomial_Opoly(_141318, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_141318)), _141320), _141322)), _141324) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_141318), hAPP(c_Polynomial_Opoly(_141318, _141320), _141324)), hAPP(c_Polynomial_Opoly(_141318, _141322), _141324)))], (1871 ^ _113251) ^ [_141469, _141471, _141473] : [class_Rings_Ocomm__ring(_141469), -(hAPP(c_Polynomial_Opoly(_141469, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_141469), _141471)), _141473) = c_Groups_Ouminus__class_Ouminus(_141469, hAPP(c_Polynomial_Opoly(_141469, _141471), _141473)))], (1877 ^ _113251) ^ [_141586, _141588] : [class_Rings_Ocomm__semiring__1(_141586), -(hAPP(c_Polynomial_Opoly(_141586, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_141586))), _141588) = c_Groups_Oone__class_Oone(_141586))], (1883 ^ _113251) ^ [_141685, _141687] : [class_Groups_Ozero(_141685), 1886 ^ _113251 : [(1887 ^ _113251) ^ [] : [c_Groups_Ozero__class_Ozero(_141685) = _141687, -(_141687 = c_Groups_Ozero__class_Ozero(_141685))], (1893 ^ _113251) ^ [] : [_141687 = c_Groups_Ozero__class_Ozero(_141685), -(c_Groups_Ozero__class_Ozero(_141685) = _141687)]]], (1899 ^ _113251) ^ [_141902, _141904, _141906, _141908] : [class_Groups_Oab__semigroup__mult(_141902), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_141902), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_141902), _141904), _141906)), _141908) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_141902), _141904), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_141902), _141906), _141908)))], (1905 ^ _113251) ^ [_142045, _142047] : [class_Groups_Oone(_142045), 1908 ^ _113251 : [(1909 ^ _113251) ^ [] : [c_Groups_Oone__class_Oone(_142045) = _142047, -(_142047 = c_Groups_Oone__class_Oone(_142045))], (1915 ^ _113251) ^ [] : [_142047 = c_Groups_Oone__class_Oone(_142045), -(c_Groups_Oone__class_Oone(_142045) = _142047)]]], (1921 ^ _113251) ^ [_142262, _142264] : [class_Groups_Ogroup__add(_142262), -(c_Groups_Ouminus__class_Ouminus(_142262, c_Groups_Ouminus__class_Ouminus(_142262, _142264)) = _142264)], (1927 ^ _113251) ^ [_142349, _142351, _142353] : [class_Groups_Ogroup__add(_142349), 1930 ^ _113251 : [(1931 ^ _113251) ^ [] : [_142351 = c_Groups_Ouminus__class_Ouminus(_142349, _142353), -(_142353 = c_Groups_Ouminus__class_Ouminus(_142349, _142351))], (1937 ^ _113251) ^ [] : [_142353 = c_Groups_Ouminus__class_Ouminus(_142349, _142351), -(_142351 = c_Groups_Ouminus__class_Ouminus(_142349, _142353))]]], (1943 ^ _113251) ^ [_142578, _142580, _142582] : [class_Groups_Ogroup__add(_142578), 1946 ^ _113251 : [(1947 ^ _113251) ^ [] : [c_Groups_Ouminus__class_Ouminus(_142578, _142580) = _142582, -(c_Groups_Ouminus__class_Ouminus(_142578, _142582) = _142580)], (1953 ^ _113251) ^ [] : [c_Groups_Ouminus__class_Ouminus(_142578, _142582) = _142580, -(c_Groups_Ouminus__class_Ouminus(_142578, _142580) = _142582)]]], (1959 ^ _113251) ^ [_142807, _142809, _142811] : [class_Groups_Ogroup__add(_142807), 1962 ^ _113251 : [(1963 ^ _113251) ^ [] : [c_Groups_Ouminus__class_Ouminus(_142807, _142809) = c_Groups_Ouminus__class_Ouminus(_142807, _142811), -(_142809 = _142811)], (1969 ^ _113251) ^ [] : [_142809 = _142811, -(c_Groups_Ouminus__class_Ouminus(_142807, _142809) = c_Groups_Ouminus__class_Ouminus(_142807, _142811))]]], (1975 ^ _113251) ^ [_143036, _143038, _143040] : [class_Rings_Oidom(_143036), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_143036)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_143036)), c_Polynomial_OpCons(_143036, c_Groups_Ouminus__class_Ouminus(_143036, _143038), c_Polynomial_OpCons(_143036, c_Groups_Oone__class_Oone(_143036), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_143036))))), c_Polynomial_Oorder(_143036, _143038, _143040))), _143040)))], (1981 ^ _113251) ^ [_143193, _143195] : [class_RealVector_Oreal__normed__algebra(_143193), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_143193), c_Groups_Ozero__class_Ozero(_143193)), _143195) = c_Groups_Ozero__class_Ozero(_143193))], (1987 ^ _113251) ^ [_143292, _143294] : [class_RealVector_Oreal__normed__algebra(_143292), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_143292), c_Groups_Ozero__class_Ozero(_143292)), _143294) = c_Groups_Ozero__class_Ozero(_143292))], (1993 ^ _113251) ^ [_143391, _143393] : [class_RealVector_Oreal__normed__algebra(_143391), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_143391), _143393), c_Groups_Ozero__class_Ozero(_143391)) = c_Groups_Ozero__class_Ozero(_143391))], (1999 ^ _113251) ^ [_143490, _143492] : [class_RealVector_Oreal__normed__algebra(_143490), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_143490), _143492), c_Groups_Ozero__class_Ozero(_143490)) = c_Groups_Ozero__class_Ozero(_143490))], (2005 ^ _113251) ^ [_143589, _143591, _143593] : [class_Rings_Oidom(_143589), 2008 ^ _113251 : [(2009 ^ _113251) ^ [] : [hAPP(c_Polynomial_Opoly(_143589, _143591), _143593) = c_Groups_Ozero__class_Ozero(_143589), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_143589)), c_Polynomial_OpCons(_143589, c_Groups_Ouminus__class_Ouminus(_143589, _143593), c_Polynomial_OpCons(_143589, c_Groups_Oone__class_Oone(_143589), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_143589))))), _143591)))], (2015 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_143589)), c_Polynomial_OpCons(_143589, c_Groups_Ouminus__class_Ouminus(_143589, _143593), c_Polynomial_OpCons(_143589, c_Groups_Oone__class_Oone(_143589), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_143589))))), _143591)), -(hAPP(c_Polynomial_Opoly(_143589, _143591), _143593) = c_Groups_Ozero__class_Ozero(_143589))]]], (2021 ^ _113251) ^ [_143902, _143904, _143906] : [class_Rings_Oidom(_143902), 2024 ^ _113251 : [(2025 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_143902)), c_Polynomial_OpCons(_143902, _143904, c_Polynomial_OpCons(_143902, c_Groups_Oone__class_Oone(_143902), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_143902))))), _143906)), -(hAPP(c_Polynomial_Opoly(_143902, _143906), c_Groups_Ouminus__class_Ouminus(_143902, _143904)) = c_Groups_Ozero__class_Ozero(_143902))], (2031 ^ _113251) ^ [] : [hAPP(c_Polynomial_Opoly(_143902, _143906), c_Groups_Ouminus__class_Ouminus(_143902, _143904)) = c_Groups_Ozero__class_Ozero(_143902), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_143902)), c_Polynomial_OpCons(_143902, _143904, c_Polynomial_OpCons(_143902, c_Groups_Oone__class_Oone(_143902), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_143902))))), _143906)))]]], (2037 ^ _113251) ^ [_144215] : [class_Groups_Ogroup__add(_144215), -(c_Groups_Ouminus__class_Ouminus(_144215, c_Groups_Ozero__class_Ozero(_144215)) = c_Groups_Ozero__class_Ozero(_144215))], (2043 ^ _113251) ^ [_144302, _144304] : [class_Groups_Ogroup__add(_144302), 2046 ^ _113251 : [(2047 ^ _113251) ^ [] : [c_Groups_Ozero__class_Ozero(_144302) = c_Groups_Ouminus__class_Ouminus(_144302, _144304), -(c_Groups_Ozero__class_Ozero(_144302) = _144304)], (2053 ^ _113251) ^ [] : [c_Groups_Ozero__class_Ozero(_144302) = _144304, -(c_Groups_Ozero__class_Ozero(_144302) = c_Groups_Ouminus__class_Ouminus(_144302, _144304))]]], (2059 ^ _113251) ^ [_144528, _144530] : [class_Groups_Olinordered__ab__group__add(_144528), 2062 ^ _113251 : [(2063 ^ _113251) ^ [] : [_144530 = c_Groups_Ouminus__class_Ouminus(_144528, _144530), -(_144530 = c_Groups_Ozero__class_Ozero(_144528))], (2069 ^ _113251) ^ [] : [_144530 = c_Groups_Ozero__class_Ozero(_144528), -(_144530 = c_Groups_Ouminus__class_Ouminus(_144528, _144530))]]], (2075 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), c_Nat_OSuc(c_Polynomial_Oorder(tc_Complex_Ocomplex, v_a____, v_pa____)))), v_pa____))], (2077 ^ _113251) ^ [_144772] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Oorder(tc_Complex_Ocomplex, _144772, v_pa____), v_na____))], (2079 ^ _113251) ^ [_144800, _144802, _144804] : [class_Rings_Oring__1(_144800), -(hAPP(hAPP(c_Power_Opower__class_Opower(_144800), c_Groups_Ouminus__class_Ouminus(_144800, _144802)), _144804) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_144800), hAPP(hAPP(c_Power_Opower__class_Opower(_144800), c_Groups_Ouminus__class_Ouminus(_144800, c_Groups_Oone__class_Oone(_144800))), _144804)), hAPP(hAPP(c_Power_Opower__class_Opower(_144800), _144802), _144804)))], (2085 ^ _113251) ^ [_144957, _144959] : [class_Power_Opower(_144957), class_Rings_Osemiring__0(_144957), 2092 ^ _113251 : [(2093 ^ _113251) ^ [] : [_144959 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_144957), c_Groups_Ozero__class_Ozero(_144957)), _144959) = c_Groups_Oone__class_Oone(_144957))], (2099 ^ _113251) ^ [] : [-(_144959 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_144957), c_Groups_Ozero__class_Ozero(_144957)), _144959) = c_Groups_Ozero__class_Ozero(_144957))]]], (2105 ^ _113251) ^ [_145231, _145233] : [class_Power_Opower(_145231), -(hAPP(hAPP(c_Power_Opower__class_Opower(_145231), _145233), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_145231))], (2111 ^ _113251) ^ [_145326, _145328, _145330] : [class_Power_Opower(_145326), class_Rings_Omult__zero(_145326), class_Rings_Ono__zero__divisors(_145326), class_Rings_Ozero__neq__one(_145326), 2126 ^ _113251 : [(2127 ^ _113251) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_145326), _145328), _145330) = c_Groups_Ozero__class_Ozero(_145326), 2130 ^ _113251 : [(2131 ^ _113251) ^ [] : [-(_145328 = c_Groups_Ozero__class_Ozero(_145326))], (2133 ^ _113251) ^ [] : [_145330 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (2135 ^ _113251) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_145326), _145328), _145330) = c_Groups_Ozero__class_Ozero(_145326)), _145328 = c_Groups_Ozero__class_Ozero(_145326), -(_145330 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (2145 ^ _113251) ^ [_145818, _145820, _145822] : [class_Rings_Oidom(_145818), -(_145820 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_145818))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_145818)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_145818)), c_Polynomial_OpCons(_145818, c_Groups_Ouminus__class_Ouminus(_145818, _145822), c_Polynomial_OpCons(_145818, c_Groups_Oone__class_Oone(_145818), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_145818))))), c_Nat_OSuc(c_Polynomial_Oorder(_145818, _145822, _145820)))), _145820))], (2155 ^ _113251) ^ [_146045, _146047, _146049] : [class_Rings_Oidom(_146045), -(_146047 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_146045))), 2162 ^ _113251 : [(2163 ^ _113251) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_146045)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_146045)), c_Polynomial_OpCons(_146045, c_Groups_Ouminus__class_Ouminus(_146045, _146049), c_Polynomial_OpCons(_146045, c_Groups_Oone__class_Oone(_146045), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_146045))))), c_Polynomial_Oorder(_146045, _146049, _146047))), _146047)))], (2165 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_146045)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_146045)), c_Polynomial_OpCons(_146045, c_Groups_Ouminus__class_Ouminus(_146045, _146049), c_Polynomial_OpCons(_146045, c_Groups_Oone__class_Oone(_146045), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_146045))))), c_Nat_OSuc(c_Polynomial_Oorder(_146045, _146049, _146047)))), _146047))]]], (2167 ^ _113251) ^ [_146385, _146387, _146389, _146391] : [class_Rings_Ocomm__semiring__1(_146385), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_146385), _146387), _146389)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_146385), hAPP(hAPP(c_Power_Opower__class_Opower(_146385), _146387), _146391)), hAPP(hAPP(c_Power_Opower__class_Opower(_146385), _146389), _146391))))], (2177 ^ _113251) ^ [_146580, _146582] : [class_Groups_Omonoid__mult(_146580), -(hAPP(hAPP(c_Power_Opower__class_Opower(_146580), c_Groups_Oone__class_Oone(_146580)), _146582) = c_Groups_Oone__class_Oone(_146580))], (2183 ^ _113251) ^ [] : [-(c_Polynomial_Odegree(tc_Complex_Ocomplex, v_p) = v_n)], (2185 ^ _113251) ^ [_146697] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _146697) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (2197 ^ _113251) ^ [_146836, _146838] : [2198 ^ _113251 : [(2199 ^ _113251) ^ [] : [_146838 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (2201 ^ _113251) ^ [] : [_146836 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _146836), _146838) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (2187 ^ _113251) ^ [_146738, _146740] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _146738), _146740) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_146740 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_146738 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (2205 ^ _113251) ^ [_146965, _146967] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _146965), -(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), _146965), _146967)))], (2211 ^ _113251) ^ [_147058, _147060, _147062] : [class_Groups_Ozero(_147058), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_147058, c_Polynomial_OpCons(_147058, _147060, _147062)), c_Nat_OSuc(c_Polynomial_Odegree(_147058, _147062))))], (2217 ^ _113251) ^ [_147161, _147163, _147165] : [class_Rings_Ocomm__semiring__1(_147161), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_147161, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_147161)), _147163), _147165)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Polynomial_Odegree(_147161, _147163)), _147165)))], (2223 ^ _113251) ^ [_147284, _147286, _147288, _147290] : [class_Rings_Olinordered__semidom(_147284), hAPP(hAPP(c_Power_Opower__class_Opower(_147284), _147286), c_Nat_OSuc(_147288)) = hAPP(hAPP(c_Power_Opower__class_Opower(_147284), _147290), c_Nat_OSuc(_147288)), c_Orderings_Oord__class_Oless__eq(_147284, c_Groups_Ozero__class_Ozero(_147284), _147286), c_Orderings_Oord__class_Oless__eq(_147284, c_Groups_Ozero__class_Ozero(_147284), _147290), -(_147286 = _147290)], (2241 ^ _113251) ^ [_147583, _147585, _147587, _147589] : [class_Rings_Olinordered__semidom(_147583), c_Orderings_Oord__class_Oless__eq(_147583, hAPP(hAPP(c_Power_Opower__class_Opower(_147583), _147585), c_Nat_OSuc(_147587)), hAPP(hAPP(c_Power_Opower__class_Opower(_147583), _147589), c_Nat_OSuc(_147587))), c_Orderings_Oord__class_Oless__eq(_147583, c_Groups_Ozero__class_Ozero(_147583), _147589), -(c_Orderings_Oord__class_Oless__eq(_147583, _147585, _147589))], (2255 ^ _113251) ^ [_147824, _147826, _147828, _147830] : [class_Rings_Olinordered__semidom(_147824), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _147826, _147828), c_Orderings_Oord__class_Oless__eq(_147824, c_Groups_Oone__class_Oone(_147824), _147830), -(c_Orderings_Oord__class_Oless__eq(_147824, hAPP(hAPP(c_Power_Opower__class_Opower(_147824), _147830), _147826), hAPP(hAPP(c_Power_Opower__class_Opower(_147824), _147830), _147828)))], (2269 ^ _113251) ^ [_148057, _148059, _148061] : [class_Groups_Ozero(_148057), -(_148059 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_148057))), -(c_Polynomial_Odegree(_148057, c_Polynomial_OpCons(_148057, _148061, _148059)) = c_Nat_OSuc(c_Polynomial_Odegree(_148057, _148059)))], (2279 ^ _113251) ^ [_148181, _148183, _148185] : [class_Rings_Oidom(_148181), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_148181)), _148183), _148185)), -(_148185 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_148181))), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_148181, _148183), c_Polynomial_Odegree(_148181, _148185)))], (2293 ^ _113251) ^ [_148367, _148369, _148371, _148373] : [class_Rings_Olinordered__semidom(_148367), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _148369, _148371), c_Orderings_Oord__class_Oless__eq(_148367, c_Groups_Ozero__class_Ozero(_148367), _148373), c_Orderings_Oord__class_Oless__eq(_148367, _148373, c_Groups_Oone__class_Oone(_148367)), -(c_Orderings_Oord__class_Oless__eq(_148367, hAPP(hAPP(c_Power_Opower__class_Opower(_148367), _148373), _148371), hAPP(hAPP(c_Power_Opower__class_Opower(_148367), _148373), _148369)))], (2311 ^ _113251) ^ [_148662, _148664, _148666] : [class_Rings_Oidom(_148662), -(_148664 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_148662))), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Oorder(_148662, _148666, _148664), c_Polynomial_Odegree(_148662, _148664)))], (2321 ^ _113251) ^ [_148778, _148780, _148782] : [class_Groups_Oordered__ab__group__add(_148778), c_Orderings_Oord__class_Oless__eq(_148778, _148780, _148782), -(c_Orderings_Oord__class_Oless__eq(_148778, c_Groups_Ouminus__class_Ouminus(_148778, _148782), c_Groups_Ouminus__class_Ouminus(_148778, _148780)))], (2331 ^ _113251) ^ [_148925, _148927, _148929] : [class_Groups_Oordered__ab__group__add(_148925), 2334 ^ _113251 : [(2335 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_148925, c_Groups_Ouminus__class_Ouminus(_148925, _148927), c_Groups_Ouminus__class_Ouminus(_148925, _148929)), -(c_Orderings_Oord__class_Oless__eq(_148925, _148929, _148927))], (2341 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_148925, _148929, _148927), -(c_Orderings_Oord__class_Oless__eq(_148925, c_Groups_Ouminus__class_Ouminus(_148925, _148927), c_Groups_Ouminus__class_Ouminus(_148925, _148929)))]]], (2347 ^ _113251) ^ [_149160, _149162, _149164] : [class_Groups_Oordered__ab__group__add(_149160), 2350 ^ _113251 : [(2351 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_149160, c_Groups_Ouminus__class_Ouminus(_149160, _149162), _149164), -(c_Orderings_Oord__class_Oless__eq(_149160, c_Groups_Ouminus__class_Ouminus(_149160, _149164), _149162))], (2357 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_149160, c_Groups_Ouminus__class_Ouminus(_149160, _149164), _149162), -(c_Orderings_Oord__class_Oless__eq(_149160, c_Groups_Ouminus__class_Ouminus(_149160, _149162), _149164))]]], (2363 ^ _113251) ^ [_149395, _149397, _149399] : [class_Groups_Oordered__ab__group__add(_149395), 2366 ^ _113251 : [(2367 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_149395, _149397, c_Groups_Ouminus__class_Ouminus(_149395, _149399)), -(c_Orderings_Oord__class_Oless__eq(_149395, _149399, c_Groups_Ouminus__class_Ouminus(_149395, _149397)))], (2373 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_149395, _149399, c_Groups_Ouminus__class_Ouminus(_149395, _149397)), -(c_Orderings_Oord__class_Oless__eq(_149395, _149397, c_Groups_Ouminus__class_Ouminus(_149395, _149399)))]]], (2379 ^ _113251) ^ [_149630, _149632] : [class_Groups_Oab__group__add(_149630), -(c_Polynomial_Odegree(_149630, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_149630), _149632)) = c_Polynomial_Odegree(_149630, _149632))], (2385 ^ _113251) ^ [_149727, _149729] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_149727), c_Groups_Ozero__class_Ozero(_149727)), c_Nat_OSuc(_149729)) = c_Groups_Ozero__class_Ozero(_149727)), class_Power_Opower(_149727), class_Rings_Osemiring__0(_149727)], (2395 ^ _113251) ^ [_149880, _149882, _149884] : [class_Groups_Omonoid__mult(_149880), -(hAPP(hAPP(c_Power_Opower__class_Opower(_149880), _149882), c_Nat_OSuc(_149884)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_149880), hAPP(hAPP(c_Power_Opower__class_Opower(_149880), _149882), _149884)), _149882))], (2401 ^ _113251) ^ [_150009, _150011, _150013] : [class_Power_Opower(_150009), -(hAPP(hAPP(c_Power_Opower__class_Opower(_150009), _150011), c_Nat_OSuc(_150013)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_150009), _150011), hAPP(hAPP(c_Power_Opower__class_Opower(_150009), _150011), _150013)))], (2407 ^ _113251) ^ [_150138, _150140, _150142, _150144] : [class_Rings_Olinordered__semidom(_150138), c_Orderings_Oord__class_Oless__eq(_150138, _150140, _150142), c_Orderings_Oord__class_Oless__eq(_150138, c_Groups_Ozero__class_Ozero(_150138), _150140), -(c_Orderings_Oord__class_Oless__eq(_150138, hAPP(hAPP(c_Power_Opower__class_Opower(_150138), _150140), _150144), hAPP(hAPP(c_Power_Opower__class_Opower(_150138), _150142), _150144)))], (2421 ^ _113251) ^ [_150371, _150373, _150375] : [class_Rings_Olinordered__semidom(_150371), c_Orderings_Oord__class_Oless__eq(_150371, c_Groups_Ozero__class_Ozero(_150371), _150373), -(c_Orderings_Oord__class_Oless__eq(_150371, c_Groups_Ozero__class_Ozero(_150371), hAPP(hAPP(c_Power_Opower__class_Opower(_150371), _150373), _150375)))], (2431 ^ _113251) ^ [_150530, _150532, _150534] : [class_Rings_Olinordered__semidom(_150530), c_Orderings_Oord__class_Oless__eq(_150530, c_Groups_Oone__class_Oone(_150530), _150532), -(c_Orderings_Oord__class_Oless__eq(_150530, c_Groups_Oone__class_Oone(_150530), hAPP(hAPP(c_Power_Opower__class_Opower(_150530), _150532), _150534)))], (2441 ^ _113251) ^ [_150689, _150691, _150693, _150695, _150697] : [class_Rings_Ocomm__semiring__1(_150689), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_150689), hAPP(hAPP(c_Power_Opower__class_Opower(_150689), _150691), _150693)), _150695)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _150697, _150693), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_150689), hAPP(hAPP(c_Power_Opower__class_Opower(_150689), _150691), _150697)), _150695)))], (2455 ^ _113251) ^ [_150948, _150950, _150952, _150954, _150956] : [class_Rings_Ocomm__semiring__1(_150948), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_150948), _150950), _150952)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _150954, _150956), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_150948), hAPP(hAPP(c_Power_Opower__class_Opower(_150948), _150950), _150954)), hAPP(hAPP(c_Power_Opower__class_Opower(_150948), _150952), _150956))))], (2469 ^ _113251) ^ [_151207, _151209, _151211, _151213] : [class_Rings_Ocomm__semiring__1(_151207), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _151209, _151211), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_151207), hAPP(hAPP(c_Power_Opower__class_Opower(_151207), _151213), _151209)), hAPP(hAPP(c_Power_Opower__class_Opower(_151207), _151213), _151211))))], (2479 ^ _113251) ^ [_151390, _151392, _151394] : [class_Groups_Ozero(_151390), 2482 ^ _113251 : [(2483 ^ _113251) ^ [] : [_151392 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_151390)), -(c_Polynomial_Odegree(_151390, c_Polynomial_OpCons(_151390, _151394, _151392)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2489 ^ _113251) ^ [] : [-(_151392 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_151390))), -(c_Polynomial_Odegree(_151390, c_Polynomial_OpCons(_151390, _151394, _151392)) = c_Nat_OSuc(c_Polynomial_Odegree(_151390, _151392)))]]], (2495 ^ _113251) ^ [_151622] : [class_Groups_Ozero(_151622), -(c_Polynomial_Odegree(_151622, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_151622))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2501 ^ _113251) ^ [_151709, _151711, _151713] : [class_Rings_Oordered__cancel__semiring(_151709), -(c_Orderings_Oord__class_Oless__eq(_151709, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_151709), _151711), _151713), c_Groups_Ozero__class_Ozero(_151709))), 2506 ^ _113251 : [(2507 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_151709, c_Groups_Ozero__class_Ozero(_151709), _151711), c_Orderings_Oord__class_Oless__eq(_151709, _151713, c_Groups_Ozero__class_Ozero(_151709))], (2513 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_151709, _151711, c_Groups_Ozero__class_Ozero(_151709)), c_Orderings_Oord__class_Oless__eq(_151709, c_Groups_Ozero__class_Ozero(_151709), _151713)]]], (2521 ^ _113251) ^ [_152025, _152027, _152029] : [class_Rings_Oordered__ring(_152025), -(c_Orderings_Oord__class_Oless__eq(_152025, c_Groups_Ozero__class_Ozero(_152025), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_152025), _152027), _152029))), 2526 ^ _113251 : [(2527 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_152025, c_Groups_Ozero__class_Ozero(_152025), _152027), c_Orderings_Oord__class_Oless__eq(_152025, c_Groups_Ozero__class_Ozero(_152025), _152029)], (2533 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_152025, _152027, c_Groups_Ozero__class_Ozero(_152025)), c_Orderings_Oord__class_Oless__eq(_152025, _152029, c_Groups_Ozero__class_Ozero(_152025))]]], (2541 ^ _113251) ^ [_152341, _152343, _152345, _152347, _152349] : [class_Rings_Oordered__semiring(_152341), c_Orderings_Oord__class_Oless__eq(_152341, _152343, _152345), c_Orderings_Oord__class_Oless__eq(_152341, _152347, _152349), c_Orderings_Oord__class_Oless__eq(_152341, c_Groups_Ozero__class_Ozero(_152341), _152345), c_Orderings_Oord__class_Oless__eq(_152341, c_Groups_Ozero__class_Ozero(_152341), _152347), -(c_Orderings_Oord__class_Oless__eq(_152341, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_152341), _152343), _152347), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_152341), _152345), _152349)))], (2563 ^ _113251) ^ [_152704, _152706, _152708, _152710, _152712] : [class_Rings_Oordered__semiring(_152704), c_Orderings_Oord__class_Oless__eq(_152704, _152706, _152708), c_Orderings_Oord__class_Oless__eq(_152704, _152710, _152712), c_Orderings_Oord__class_Oless__eq(_152704, c_Groups_Ozero__class_Ozero(_152704), _152706), c_Orderings_Oord__class_Oless__eq(_152704, c_Groups_Ozero__class_Ozero(_152704), _152710), -(c_Orderings_Oord__class_Oless__eq(_152704, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_152704), _152706), _152710), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_152704), _152708), _152712)))], (2585 ^ _113251) ^ [_153067, _153069, _153071, _153073] : [class_Rings_Oordered__ring(_153067), c_Orderings_Oord__class_Oless__eq(_153067, _153069, _153071), c_Orderings_Oord__class_Oless__eq(_153067, _153073, c_Groups_Ozero__class_Ozero(_153067)), -(c_Orderings_Oord__class_Oless__eq(_153067, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_153067), _153073), _153071), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_153067), _153073), _153069)))], (2599 ^ _113251) ^ [_153300, _153302, _153304, _153306] : [class_Rings_Oordered__ring(_153300), c_Orderings_Oord__class_Oless__eq(_153300, _153302, _153304), c_Orderings_Oord__class_Oless__eq(_153300, _153306, c_Groups_Ozero__class_Ozero(_153300)), -(c_Orderings_Oord__class_Oless__eq(_153300, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_153300), _153304), _153306), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_153300), _153302), _153306)))], (2613 ^ _113251) ^ [_153533, _153535, _153537, _153539] : [class_Rings_Oordered__comm__semiring(_153533), c_Orderings_Oord__class_Oless__eq(_153533, _153535, _153537), c_Orderings_Oord__class_Oless__eq(_153533, c_Groups_Ozero__class_Ozero(_153533), _153539), -(c_Orderings_Oord__class_Oless__eq(_153533, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_153533), _153539), _153535), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_153533), _153539), _153537)))], (2627 ^ _113251) ^ [_153766, _153768, _153770, _153772] : [class_Rings_Oordered__semiring(_153766), c_Orderings_Oord__class_Oless__eq(_153766, _153768, _153770), c_Orderings_Oord__class_Oless__eq(_153766, c_Groups_Ozero__class_Ozero(_153766), _153772), -(c_Orderings_Oord__class_Oless__eq(_153766, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_153766), _153772), _153768), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_153766), _153772), _153770)))], (2641 ^ _113251) ^ [_153999, _154001, _154003, _154005] : [class_Rings_Oordered__semiring(_153999), c_Orderings_Oord__class_Oless__eq(_153999, _154001, _154003), c_Orderings_Oord__class_Oless__eq(_153999, c_Groups_Ozero__class_Ozero(_153999), _154005), -(c_Orderings_Oord__class_Oless__eq(_153999, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_153999), _154001), _154005), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_153999), _154003), _154005)))], (2655 ^ _113251) ^ [_154232, _154234, _154236] : [class_Rings_Oordered__ring(_154232), c_Orderings_Oord__class_Oless__eq(_154232, _154234, c_Groups_Ozero__class_Ozero(_154232)), c_Orderings_Oord__class_Oless__eq(_154232, _154236, c_Groups_Ozero__class_Ozero(_154232)), -(c_Orderings_Oord__class_Oless__eq(_154232, c_Groups_Ozero__class_Ozero(_154232), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_154232), _154234), _154236)))], (2669 ^ _113251) ^ [_154451, _154453, _154455] : [class_Rings_Oordered__cancel__semiring(_154451), c_Orderings_Oord__class_Oless__eq(_154451, _154453, c_Groups_Ozero__class_Ozero(_154451)), c_Orderings_Oord__class_Oless__eq(_154451, c_Groups_Ozero__class_Ozero(_154451), _154455), -(c_Orderings_Oord__class_Oless__eq(_154451, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_154451), _154453), _154455), c_Groups_Ozero__class_Ozero(_154451)))], (2683 ^ _113251) ^ [_154670, _154672, _154674] : [class_Rings_Oordered__cancel__semiring(_154670), c_Orderings_Oord__class_Oless__eq(_154670, c_Groups_Ozero__class_Ozero(_154670), _154672), c_Orderings_Oord__class_Oless__eq(_154670, _154674, c_Groups_Ozero__class_Ozero(_154670)), -(c_Orderings_Oord__class_Oless__eq(_154670, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_154670), _154674), _154672), c_Groups_Ozero__class_Ozero(_154670)))], (2697 ^ _113251) ^ [_154889, _154891, _154893] : [class_Rings_Oordered__cancel__semiring(_154889), c_Orderings_Oord__class_Oless__eq(_154889, c_Groups_Ozero__class_Ozero(_154889), _154891), c_Orderings_Oord__class_Oless__eq(_154889, _154893, c_Groups_Ozero__class_Ozero(_154889)), -(c_Orderings_Oord__class_Oless__eq(_154889, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_154889), _154891), _154893), c_Groups_Ozero__class_Ozero(_154889)))], (2711 ^ _113251) ^ [_155108, _155110, _155112] : [class_Rings_Oordered__cancel__semiring(_155108), c_Orderings_Oord__class_Oless__eq(_155108, c_Groups_Ozero__class_Ozero(_155108), _155110), c_Orderings_Oord__class_Oless__eq(_155108, c_Groups_Ozero__class_Ozero(_155108), _155112), -(c_Orderings_Oord__class_Oless__eq(_155108, c_Groups_Ozero__class_Ozero(_155108), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_155108), _155110), _155112)))], (2725 ^ _113251) ^ [_155327, _155329, _155331] : [class_Rings_Olinordered__ring__strict(_155327), 2728 ^ _113251 : [(2729 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_155327, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_155327), _155329), _155331), c_Groups_Ozero__class_Ozero(_155327)), 2734 ^ _113251 : [(2735 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_155327, c_Groups_Ozero__class_Ozero(_155327), _155329))], (2737 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_155327, _155331, c_Groups_Ozero__class_Ozero(_155327)))]], 2738 ^ _113251 : [(2739 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_155327, _155329, c_Groups_Ozero__class_Ozero(_155327)))], (2741 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_155327, c_Groups_Ozero__class_Ozero(_155327), _155331))]]], (2743 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_155327, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_155327), _155329), _155331), c_Groups_Ozero__class_Ozero(_155327))), 2744 ^ _113251 : [(2745 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_155327, c_Groups_Ozero__class_Ozero(_155327), _155329), c_Orderings_Oord__class_Oless__eq(_155327, _155331, c_Groups_Ozero__class_Ozero(_155327))], (2751 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_155327, _155329, c_Groups_Ozero__class_Ozero(_155327)), c_Orderings_Oord__class_Oless__eq(_155327, c_Groups_Ozero__class_Ozero(_155327), _155331)]]]]], (2759 ^ _113251) ^ [_155827, _155829, _155831] : [class_Rings_Olinordered__ring__strict(_155827), 2762 ^ _113251 : [(2763 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_155827, c_Groups_Ozero__class_Ozero(_155827), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_155827), _155829), _155831)), 2768 ^ _113251 : [(2769 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_155827, c_Groups_Ozero__class_Ozero(_155827), _155829))], (2771 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_155827, c_Groups_Ozero__class_Ozero(_155827), _155831))]], 2772 ^ _113251 : [(2773 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_155827, _155829, c_Groups_Ozero__class_Ozero(_155827)))], (2775 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_155827, _155831, c_Groups_Ozero__class_Ozero(_155827)))]]], (2777 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_155827, c_Groups_Ozero__class_Ozero(_155827), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_155827), _155829), _155831))), 2778 ^ _113251 : [(2779 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_155827, c_Groups_Ozero__class_Ozero(_155827), _155829), c_Orderings_Oord__class_Oless__eq(_155827, c_Groups_Ozero__class_Ozero(_155827), _155831)], (2785 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_155827, _155829, c_Groups_Ozero__class_Ozero(_155827)), c_Orderings_Oord__class_Oless__eq(_155827, _155831, c_Groups_Ozero__class_Ozero(_155827))]]]]], (2793 ^ _113251) ^ [_156327, _156329] : [class_Rings_Olinordered__ring(_156327), -(c_Orderings_Oord__class_Oless__eq(_156327, c_Groups_Ozero__class_Ozero(_156327), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_156327), _156329), _156329)))], (2799 ^ _113251) ^ [_156424] : [class_Rings_Olinordered__semidom(_156424), -(c_Orderings_Oord__class_Oless__eq(_156424, c_Groups_Ozero__class_Ozero(_156424), c_Groups_Oone__class_Oone(_156424)))], (2805 ^ _113251) ^ [_156507] : [class_Rings_Olinordered__semidom(_156507), c_Orderings_Oord__class_Oless__eq(_156507, c_Groups_Oone__class_Oone(_156507), c_Groups_Ozero__class_Ozero(_156507))], (2811 ^ _113251) ^ [_156591, _156593, _156595] : [class_Rings_Ocomm__semiring__1(_156591), -(hAPP(hAPP(c_Power_Opower__class_Opower(_156591), _156593), c_Nat_OSuc(_156595)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_156591), _156593), hAPP(hAPP(c_Power_Opower__class_Opower(_156591), _156593), _156595)))], (2817 ^ _113251) ^ [_156720, _156722, _156724] : [class_Rings_Ocomm__semiring__1(_156720), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_156720), _156722), hAPP(hAPP(c_Power_Opower__class_Opower(_156720), _156722), _156724)) = hAPP(hAPP(c_Power_Opower__class_Opower(_156720), _156722), c_Nat_OSuc(_156724)))], (2823 ^ _113251) ^ [_156849, _156851, _156853] : [class_Rings_Ocomm__semiring__1(_156849), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_156849), hAPP(hAPP(c_Power_Opower__class_Opower(_156849), _156851), _156853)), _156851) = hAPP(hAPP(c_Power_Opower__class_Opower(_156849), _156851), c_Nat_OSuc(_156853)))], (2829 ^ _113251) ^ [_156978, _156980] : [class_Groups_Olinordered__ab__group__add(_156978), 2832 ^ _113251 : [(2833 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_156978, c_Groups_Ouminus__class_Ouminus(_156978, _156980), _156980), -(c_Orderings_Oord__class_Oless__eq(_156978, c_Groups_Ozero__class_Ozero(_156978), _156980))], (2839 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_156978, c_Groups_Ozero__class_Ozero(_156978), _156980), -(c_Orderings_Oord__class_Oless__eq(_156978, c_Groups_Ouminus__class_Ouminus(_156978, _156980), _156980))]]], (2845 ^ _113251) ^ [_157204, _157206] : [class_Groups_Oordered__ab__group__add(_157204), 2848 ^ _113251 : [(2849 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_157204, c_Groups_Ouminus__class_Ouminus(_157204, _157206), c_Groups_Ozero__class_Ozero(_157204)), -(c_Orderings_Oord__class_Oless__eq(_157204, c_Groups_Ozero__class_Ozero(_157204), _157206))], (2855 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_157204, c_Groups_Ozero__class_Ozero(_157204), _157206), -(c_Orderings_Oord__class_Oless__eq(_157204, c_Groups_Ouminus__class_Ouminus(_157204, _157206), c_Groups_Ozero__class_Ozero(_157204)))]]], (2861 ^ _113251) ^ [_157436, _157438] : [class_Groups_Olinordered__ab__group__add(_157436), 2864 ^ _113251 : [(2865 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_157436, _157438, c_Groups_Ouminus__class_Ouminus(_157436, _157438)), -(c_Orderings_Oord__class_Oless__eq(_157436, _157438, c_Groups_Ozero__class_Ozero(_157436)))], (2871 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_157436, _157438, c_Groups_Ozero__class_Ozero(_157436)), -(c_Orderings_Oord__class_Oless__eq(_157436, _157438, c_Groups_Ouminus__class_Ouminus(_157436, _157438)))]]], (2877 ^ _113251) ^ [_157662, _157664] : [class_Groups_Oordered__ab__group__add(_157662), 2880 ^ _113251 : [(2881 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_157662, c_Groups_Ozero__class_Ozero(_157662), c_Groups_Ouminus__class_Ouminus(_157662, _157664)), -(c_Orderings_Oord__class_Oless__eq(_157662, _157664, c_Groups_Ozero__class_Ozero(_157662)))], (2887 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_157662, _157664, c_Groups_Ozero__class_Ozero(_157662)), -(c_Orderings_Oord__class_Oless__eq(_157662, c_Groups_Ozero__class_Ozero(_157662), c_Groups_Ouminus__class_Ouminus(_157662, _157664)))]]], (2893 ^ _113251) ^ [_157894] : [class_Rings_Ocomm__semiring__1(_157894), -(c_Polynomial_Odegree(_157894, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_157894))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2899 ^ _113251) ^ [_157981, _157983] : [class_Groups_Ozero(_157981), -(c_Polynomial_Odegree(_157981, c_Polynomial_OpCons(_157981, _157983, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_157981)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2905 ^ _113251) ^ [_158078, _158080, _158082] : [class_Rings_Olinordered__idom(_158078), c_Orderings_Oord__class_Oless__eq(_158078, c_Groups_Ozero__class_Ozero(_158078), _158080), c_Orderings_Oord__class_Oless__eq(_158078, c_Groups_Ozero__class_Ozero(_158078), _158082), c_Orderings_Oord__class_Oless__eq(_158078, _158082, c_Groups_Oone__class_Oone(_158078)), -(c_Orderings_Oord__class_Oless__eq(_158078, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_158078), _158082), _158080), _158080))], (2923 ^ _113251) ^ [_158353, _158355, _158357] : [class_Rings_Olinordered__idom(_158353), c_Orderings_Oord__class_Oless__eq(_158353, c_Groups_Ozero__class_Ozero(_158353), _158355), c_Orderings_Oord__class_Oless__eq(_158353, c_Groups_Ozero__class_Ozero(_158353), _158357), c_Orderings_Oord__class_Oless__eq(_158353, _158357, c_Groups_Oone__class_Oone(_158353)), -(c_Orderings_Oord__class_Oless__eq(_158353, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_158353), _158355), _158357), _158355))], (2941 ^ _113251) ^ [_158628, _158630, _158632, _158634] : [class_Groups_Omonoid__mult(_158628), -(hAPP(hAPP(c_Power_Opower__class_Opower(_158628), _158630), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _158632), _158634)) = hAPP(hAPP(c_Power_Opower__class_Opower(_158628), hAPP(hAPP(c_Power_Opower__class_Opower(_158628), _158630), _158632)), _158634))], (2947 ^ _113251) ^ [_158767, _158769] : [class_Groups_Omonoid__mult(_158767), -(hAPP(hAPP(c_Power_Opower__class_Opower(_158767), _158769), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _158769)], (2953 ^ _113251) ^ [_158858, _158860, _158862] : [class_Rings_Ocomm__semiring__1(_158858), -(c_Polynomial_Odegree(_158858, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_158858)), c_Polynomial_OpCons(_158858, _158860, c_Polynomial_OpCons(_158858, c_Groups_Oone__class_Oone(_158858), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_158858))))), _158862)) = _158862)], (2959 ^ _113251) ^ [_158989, _158991, _158993] : [class_Rings_Oring__1__no__zero__divisors(_158989), -(_158991 = c_Groups_Ozero__class_Ozero(_158989)), hAPP(hAPP(c_Power_Opower__class_Opower(_158989), _158991), _158993) = c_Groups_Ozero__class_Ozero(_158989)], (2969 ^ _113251) ^ [_159148, _159150, _159152, _159154] : [class_Groups_Ocomm__monoid__mult(_159148), -(hAPP(hAPP(c_Power_Opower__class_Opower(_159148), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_159148), _159150), _159152)), _159154) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_159148), hAPP(hAPP(c_Power_Opower__class_Opower(_159148), _159150), _159154)), hAPP(hAPP(c_Power_Opower__class_Opower(_159148), _159152), _159154)))], (2975 ^ _113251) ^ [_159307, _159309, _159311] : [class_Groups_Omonoid__mult(_159307), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_159307), hAPP(hAPP(c_Power_Opower__class_Opower(_159307), _159309), _159311)), _159309) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_159307), _159309), hAPP(hAPP(c_Power_Opower__class_Opower(_159307), _159309), _159311)))], (2981 ^ _113251) ^ [_159448] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _159448))], (2983 ^ _113251) ^ [_159472] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _159472)))], (2985 ^ _113251) ^ [_159497, _159499, _159501] : [class_Rings_Olinordered__semidom(_159497), c_Orderings_Oord__class_Oless__eq(_159497, c_Groups_Ozero__class_Ozero(_159497), _159499), c_Orderings_Oord__class_Oless__eq(_159497, _159499, c_Groups_Oone__class_Oone(_159497)), -(c_Orderings_Oord__class_Oless__eq(_159497, hAPP(hAPP(c_Power_Opower__class_Opower(_159497), _159499), c_Nat_OSuc(_159501)), _159499))], (2999 ^ _113251) ^ [_159716] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _159716, v_na____), 3002 ^ _113251 : [(3003 ^ _113251) ^ [_159835, _159837] : [3005 ^ _113251 : [(3006 ^ _113251) ^ [] : [-(hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, _159837), 3004 ^ [_159716, _159835, _159837]) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))], (3008 ^ _113251) ^ [] : [hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, _159835), 3004 ^ [_159716, _159835, _159837]) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)]], c_Polynomial_Odegree(tc_Complex_Ocomplex, _159837) = _159716, -(_159716 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), _159837), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), _159835), _159716))))]]], (3020 ^ _113251) ^ [_160129, _160131] : [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), _160129), _160131)), 3023 ^ _113251 : [(3024 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _160129))], (3026 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _160131))]]], (3028 ^ _113251) ^ [_160246, _160248] : [-(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), _160246), _160248))), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _160246), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _160248)], (3038 ^ _113251) ^ [_160395, _160397, _160399] : [class_Rings_Oidom(_160395), 3041 ^ _113251 : [(3052 ^ _113251) ^ [] : [3053 ^ _113251 : [(3054 ^ _113251) ^ [] : [_160397 = _160399], (3056 ^ _113251) ^ [] : [_160397 = c_Groups_Ouminus__class_Ouminus(_160395, _160399)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_160395), _160397), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(_160395), _160399), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (3042 ^ _113251) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_160395), _160397), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(_160395), _160399), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_160397 = _160399), -(_160397 = c_Groups_Ouminus__class_Ouminus(_160395, _160399))]]], (3060 ^ _113251) ^ [_160708, _160710] : [_160708 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _160708), _160710), -(_160710 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_160708 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3070 ^ _113251) ^ [_160828, _160830, _160832] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_160828)), _160830), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_160828)), _160832)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _160830, _160832))], (3076 ^ _113251) ^ [_160939, _160941, _160943] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _160941, _160943), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_160939)), _160941), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_160939)), _160943)))], (3082 ^ _113251) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (3084 ^ _113251) ^ [_161074] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _161074), _161074)))], (3086 ^ _113251) ^ [_161111] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _161111, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3088 ^ _113251) ^ [_161135, _161137] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _161135, _161137), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_161135), c_Nat_OSuc(_161137)))], (3094 ^ _113251) ^ [_161224] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _161224, c_Nat_OSuc(_161224)))], (3096 ^ _113251) ^ [_161250] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(_161250)))], (3098 ^ _113251) ^ [_161291, _161293] : [_161291 = _161293, 3101 ^ _113251 : [(3102 ^ _113251) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _161291), _161293)))], (3104 ^ _113251) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _161293), _161291)))]]], (3106 ^ _113251) ^ [_161410, _161412] : [-(_161410 = _161412), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _161410), _161412)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _161412), _161410))], (3116 ^ _113251) ^ [_161576, _161578] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _161576), _161578)), 3121 ^ _113251 : [(3122 ^ _113251) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _161576), _161578)))], (3124 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _161578), _161576))]], -(_161576 = _161578)], (3128 ^ _113251) ^ [_161766, _161768] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _161766), _161768))), 3129 ^ _113251 : [(3136 ^ _113251) ^ [] : [_161766 = _161768], (3130 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _161766), _161768)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _161768), _161766)))]]], (3140 ^ _113251) ^ [_161976, _161978] : [3147 ^ _113251 : [(3148 ^ _113251) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _161976), _161978)))], (3150 ^ _113251) ^ [] : [_161976 = _161978]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _161976), _161978)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _161978), _161976)))], (3152 ^ _113251) ^ [_162168, _162170] : [3159 ^ _113251 : [(3160 ^ _113251) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _162168), _162170)))], (3162 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _162170), _162168))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _162168), _162170)), -(_162168 = _162170)], (3164 ^ _113251) ^ [_162365, _162367] : [-(_162365 = _162367), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _162365), _162367)), 3171 ^ _113251 : [(3172 ^ _113251) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _162365), _162367)))], (3174 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _162367), _162365))]]], (3176 ^ _113251) ^ [_162556, _162558] : [_162556 = _162558, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _162556), _162558)))], (3182 ^ _113251) ^ [_162643, _162645] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _162643), _162645)), 3185 ^ _113251 : [(3186 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _162645), _162643)), -(_162645 = _162643)], (3192 ^ _113251) ^ [] : [_162645 = _162643, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _162645), _162643)))]]], (3198 ^ _113251) ^ [_162875, _162877] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _162875), _162877)), 3203 ^ _113251 : [(3204 ^ _113251) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _162875), _162877)))], (3206 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _162877), _162875))]], -(_162875 = _162877)], (3210 ^ _113251) ^ [_163069, _163071] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _163069), _163071)), -(_163069 = _163071), 3217 ^ _113251 : [(3218 ^ _113251) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _163069), _163071)))], (3220 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _163071), _163069))]]], (3222 ^ _113251) ^ [_163265, _163267, _163269] : [_163265 = _163267, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _163267), _163269)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _163265), _163269)))], (3232 ^ _113251) ^ [_163418, _163420, _163422] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _163418), _163420)), _163420 = _163422, -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _163418), _163422)))], (3242 ^ _113251) ^ [_163571, _163573] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _163571), _163573)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _163573), _163571)), -(_163571 = _163573)], (3252 ^ _113251) ^ [_163720, _163722] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _163720), _163722)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _163722), _163720)), -(_163720 = _163722)], (3262 ^ _113251) ^ [_163869, _163871, _163873] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _163869), _163871)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _163871), _163873)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _163869), _163873)))], (3272 ^ _113251) ^ [_164032, _164034, _164036] : [_164032 = _164034, 3283 ^ _113251 : [(3284 ^ _113251) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _164032), _164036)))], (3286 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _164036), _164032))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _164034), _164036)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _164036), _164034)))], (3288 ^ _113251) ^ [_164296, _164298, _164300] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _164296), _164298)), 3299 ^ _113251 : [(3300 ^ _113251) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _164296), _164300)))], (3302 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _164300), _164296))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _164298), _164300)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _164300), _164298)))], (3304 ^ _113251) ^ [_164570, _164572] : [_164570 = _164572, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _164570), _164572)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _164572), _164570)))], (3314 ^ _113251) ^ [_164723, _164725] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _164723), _164725)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _164725), _164723))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _164725), _164723)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _164723), _164725)))], (3328 ^ _113251) ^ [_164953, _164955] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _164953), _164955))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _164953), _164955)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _164955), _164953)))], (3338 ^ _113251) ^ [_165115, _165117] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _165115), _165117)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _165117), _165115))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _165117), _165115)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _165115), _165117)))], (3352 ^ _113251) ^ [_165345, _165347] : [_165345 = _165347, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _165345), _165347)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _165347), _165345)))], (3362 ^ _113251) ^ [_165498, _165500] : [_165500 = _165498, hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _165498), _165500)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _165500), _165498)))], (3372 ^ _113251) ^ [_165651, _165653, _165655] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _165651), _165653)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _165653), _165651))), _165653 = _165655, 3383 ^ _113251 : [(3384 ^ _113251) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _165651), _165655)))], (3386 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _165655), _165651))]]], (3388 ^ _113251) ^ [_165917, _165919, _165921] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _165917), _165919)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _165919), _165917))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _165919), _165921)), 3399 ^ _113251 : [(3400 ^ _113251) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _165917), _165921)))], (3402 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _165921), _165917))]]], (3404 ^ _113251) ^ [_166193, _166195] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _166193), _166195)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _166195), _166193))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _166195), _166193)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _166193), _166195)))], (3418 ^ _113251) ^ [_166423, _166425, _166427] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _166423), _166425)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _166425), _166423))), 3433 ^ _113251 : [(3434 ^ _113251) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _166423), _166427)))], (3436 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _166427), _166423))]], hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _166425), _166427)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _166427), _166425)))], (3438 ^ _113251) ^ [_166766, _166768] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _166766), _166768)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _166768), _166766))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _166768), _166766)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _166766), _166768)))], (3452 ^ _113251) ^ [_166996, _166998, _167000] : [class_Rings_Olinordered__idom(_166996), -(_166998 = _167000), -(c_Orderings_Oord__class_Oless(_166996, _166998, _167000)), -(c_Orderings_Oord__class_Oless(_166996, _167000, _166998))], (3466 ^ _113251) ^ [_167107, _167109, _167111] : [3467 ^ _113251 : [(3468 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _167107, _167109))], (3470 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(_167111, _167109), _167107))]], 3473 ^ _113251 : [(3474 ^ _113251) ^ [] : [-(_167107 = _167109)], (3476 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(_167111, _167109), _167107))]], 3479 ^ _113251 : [(3480 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _167109, _167107))], (3482 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(_167111, _167109), _167107))]], -(hBOOL(hAPP(hAPP(_167111, _167109), _167107)))], (3486 ^ _113251) ^ [_167437, _167439] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _167437, _167439), _167437 = _167439], (3492 ^ _113251) ^ [_167517, _167519] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _167517, _167519), _167519 = _167517], (3498 ^ _113251) ^ [_167606] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _167606, _167606)], (3500 ^ _113251) ^ [_167626, _167628] : [-(_167626 = _167628), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _167626, _167628)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _167628, _167626))], (3520 ^ _113251) ^ [_167721, _167723] : [3521 ^ _113251 : [(3522 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _167721, _167723)], (3524 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _167723, _167721)]], _167721 = _167723], (3510 ^ _113251) ^ [_167680, _167682] : [-(_167680 = _167682), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _167680, _167682)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _167682, _167680))], (3528 ^ _113251) ^ [_167852] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _167852, _167852)], (3530 ^ _113251) ^ [_167885] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _167885, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3532 ^ _113251) ^ [_167915] : [-(_167915 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _167915))], (3538 ^ _113251) ^ [_167946] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _167946), _167946 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3544 ^ _113251) ^ [_168035] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _168035, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3546 ^ _113251) ^ [_168059, _168061] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _168059), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _168059, _168061), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _168061), _168059))], (3556 ^ _113251) ^ [_168203, _168205] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _168203, _168205), _168205 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3562 ^ _113251) ^ [_168279] : [-(_168279 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _168279))], (3568 ^ _113251) ^ [_168314, _168316] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_168314), c_Nat_OSuc(_168316)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _168314, _168316))], (3574 ^ _113251) ^ [_168403, _168405] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_168403), _168405), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _168403, _168405))], (3580 ^ _113251) ^ [_168488, _168490] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _168488, c_Nat_OSuc(_168490)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _168488, _168490)), -(_168488 = _168490)], (3590 ^ _113251) ^ [_168588, _168590, _168592] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _168588, _168590), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _168590, _168592), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_168588), _168592))], (3600 ^ _113251) ^ [_168731, _168733] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _168731, _168733), -(c_Nat_OSuc(_168731) = _168733), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_168731), _168733))], (3610 ^ _113251) ^ [_168835, _168837] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _168835, _168837), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _168835, c_Nat_OSuc(_168837)))], (3616 ^ _113251) ^ [_168919, _168921] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _168919, _168921)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _168919, c_Nat_OSuc(_168921)), -(_168921 = _168919)], (3626 ^ _113251) ^ [_169052, _169054] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _169052, _169054)), 3629 ^ _113251 : [(3630 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _169052, c_Nat_OSuc(_169054)), -(_169052 = _169054)], (3636 ^ _113251) ^ [] : [_169052 = _169054, -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _169052, c_Nat_OSuc(_169054)))]]], (3642 ^ _113251) ^ [_169282, _169284] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_169282), c_Nat_OSuc(_169284)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _169282, _169284))], (3648 ^ _113251) ^ [_169367, _169369] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _169367, _169369), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_169367), c_Nat_OSuc(_169369)))], (3664 ^ _113251) ^ [_169567, _169569] : [3665 ^ _113251 : [(3666 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _169567, _169569)], (3668 ^ _113251) ^ [] : [_169567 = _169569]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _169567, c_Nat_OSuc(_169569)))], (3654 ^ _113251) ^ [_169473, _169475] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _169473, c_Nat_OSuc(_169475)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _169473, _169475)), -(_169473 = _169475)], (3672 ^ _113251) ^ [_169701, _169703] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _169701, _169703)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _169703, c_Nat_OSuc(_169701)))], (3678 ^ _113251) ^ [_169737, _169739] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _169739, c_Nat_OSuc(_169737)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _169737, _169739)], (3684 ^ _113251) ^ [_169825, _169827] : [3685 ^ _113251 : [(3686 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _169825, _169827)], (3688 ^ _113251) ^ [] : [_169825 = _169827]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _169825, _169827))], (3692 ^ _113251) ^ [_169944, _169946] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _169944, _169946), -(_169944 = _169946), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _169944, _169946))], (3702 ^ _113251) ^ [_170040, _170042] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _170040, _170042), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _170040, _170042))], (3718 ^ _113251) ^ [_170226, _170228] : [3719 ^ _113251 : [(3720 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _170226, _170228)], (3722 ^ _113251) ^ [] : [_170226 = _170228]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _170226, _170228))], (3708 ^ _113251) ^ [_170136, _170138] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _170136, _170138), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _170136, _170138)), -(_170136 = _170138)], (3726 ^ _113251) ^ [_170362, _170364] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _170362, _170364), 3729 ^ _113251 : [(3730 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _170362, _170364))], (3732 ^ _113251) ^ [] : [_170362 = _170364]]], (3734 ^ _113251) ^ [_170473, _170475] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _170473, _170475)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _170473, _170475), -(_170473 = _170475)], (3744 ^ _113251) ^ [_170611, _170613, _170615, _170617] : [class_Rings_Olinordered__semidom(_170611), c_Orderings_Oord__class_Oless(_170611, c_Groups_Oone__class_Oone(_170611), _170613), 3751 ^ _113251 : [(3752 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_170611, hAPP(hAPP(c_Power_Opower__class_Opower(_170611), _170613), _170615), hAPP(hAPP(c_Power_Opower__class_Opower(_170611), _170613), _170617)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _170615, _170617))], (3758 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _170615, _170617), -(c_Orderings_Oord__class_Oless(_170611, hAPP(hAPP(c_Power_Opower__class_Opower(_170611), _170613), _170615), hAPP(hAPP(c_Power_Opower__class_Opower(_170611), _170613), _170617)))]]], (3764 ^ _113251) ^ [_170944, _170946, _170948, _170950] : [class_Rings_Olinordered__semidom(_170944), c_Orderings_Oord__class_Oless(_170944, c_Groups_Oone__class_Oone(_170944), _170946), c_Orderings_Oord__class_Oless(_170944, hAPP(hAPP(c_Power_Opower__class_Opower(_170944), _170946), _170948), hAPP(hAPP(c_Power_Opower__class_Opower(_170944), _170946), _170950)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _170948, _170950))], (3778 ^ _113251) ^ [_171177, _171179, _171181, _171183] : [class_Rings_Olinordered__semidom(_171177), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _171179, _171181), c_Orderings_Oord__class_Oless(_171177, c_Groups_Oone__class_Oone(_171177), _171183), -(c_Orderings_Oord__class_Oless(_171177, hAPP(hAPP(c_Power_Opower__class_Opower(_171177), _171183), _171179), hAPP(hAPP(c_Power_Opower__class_Opower(_171177), _171183), _171181)))], (3792 ^ _113251) ^ [_171410, _171412, _171414] : [class_Groups_Oordered__ab__group__add(_171410), 3795 ^ _113251 : [(3796 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_171410, _171412, c_Groups_Ouminus__class_Ouminus(_171410, _171414)), -(c_Orderings_Oord__class_Oless(_171410, _171414, c_Groups_Ouminus__class_Ouminus(_171410, _171412)))], (3802 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_171410, _171414, c_Groups_Ouminus__class_Ouminus(_171410, _171412)), -(c_Orderings_Oord__class_Oless(_171410, _171412, c_Groups_Ouminus__class_Ouminus(_171410, _171414)))]]], (3808 ^ _113251) ^ [_171645, _171647, _171649] : [class_Groups_Oordered__ab__group__add(_171645), 3811 ^ _113251 : [(3812 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_171645, c_Groups_Ouminus__class_Ouminus(_171645, _171647), _171649), -(c_Orderings_Oord__class_Oless(_171645, c_Groups_Ouminus__class_Ouminus(_171645, _171649), _171647))], (3818 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_171645, c_Groups_Ouminus__class_Ouminus(_171645, _171649), _171647), -(c_Orderings_Oord__class_Oless(_171645, c_Groups_Ouminus__class_Ouminus(_171645, _171647), _171649))]]], (3824 ^ _113251) ^ [_171880, _171882, _171884] : [class_Groups_Oordered__ab__group__add(_171880), 3827 ^ _113251 : [(3828 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_171880, c_Groups_Ouminus__class_Ouminus(_171880, _171882), c_Groups_Ouminus__class_Ouminus(_171880, _171884)), -(c_Orderings_Oord__class_Oless(_171880, _171884, _171882))], (3834 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_171880, _171884, _171882), -(c_Orderings_Oord__class_Oless(_171880, c_Groups_Ouminus__class_Ouminus(_171880, _171882), c_Groups_Ouminus__class_Ouminus(_171880, _171884)))]]], (3840 ^ _113251) ^ [_172115, _172117, _172119] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _172115), c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _172115), _172117), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _172115), _172119)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _172117, _172119))], (3860 ^ _113251) ^ [_172395, _172397] : [3861 ^ _113251 : [(3862 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _172395)], (3864 ^ _113251) ^ [] : [_172397 = 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), _172395), _172397)))], (3850 ^ _113251) ^ [_172293, _172295] : [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), _172293), _172295)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _172293)), -(_172295 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3868 ^ _113251) ^ [_172543, _172545] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _172543, c_Nat_OSuc(_172545)), -(_172543 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 3876 ^ _113251 : [(3877 ^ _113251) ^ [] : [-(_172543 = c_Nat_OSuc(3875 ^ [_172543, _172545]))], (3879 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 3875 ^ [_172543, _172545], _172545))]]], (3881 ^ _113251) ^ [_172703, _172705] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _172703, c_Nat_OSuc(_172705))), 3882 ^ _113251 : [(3883 ^ _113251) ^ [] : [_172703 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3885 ^ _113251) ^ [_172781] : [_172703 = c_Nat_OSuc(_172781), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _172781, _172705)]]], (3893 ^ _113251) ^ [_172912] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _172912, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_172912 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3899 ^ _113251) ^ [_172985] : [_172985 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _172985, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (3905 ^ _113251) ^ [_173076] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _173076), -(_173076 = c_Nat_OSuc(3908 ^ [_173076]))], (3912 ^ _113251) ^ [_173163] : [3913 ^ _113251 : [(3914 ^ _113251) ^ [_173203] : [_173163 = c_Nat_OSuc(_173203)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _173163))], (3918 ^ _113251) ^ [_173259, _173261] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _173259), _173261)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _173261), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _173259, _173261))], (3928 ^ _113251) ^ [_173402, _173404] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_173402), _173404), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _173402, _173404))], (3934 ^ _113251) ^ [_173487, _173489] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _173487, _173489), 3937 ^ _113251 : [(3938 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _173489, c_Nat_OSuc(_173487)), -(_173489 = _173487)], (3944 ^ _113251) ^ [] : [_173489 = _173487, -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _173489, c_Nat_OSuc(_173487)))]]], (3950 ^ _113251) ^ [_173705, _173707] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _173705, _173707), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_173705), _173707))], (3956 ^ _113251) ^ [_173790, _173792] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _173790, _173792), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _173790, c_Nat_OSuc(_173792)))], (3962 ^ _113251) ^ [_173890, _173892] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_173890), _173892), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _173890, _173892))], (3968 ^ _113251) ^ [_173971, _173973] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _173971, _173973), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_173971), _173973))], (3974 ^ _113251) ^ [_174073, _174075] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _174073, c_Nat_OSuc(_174075)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _174073, _174075))], (3980 ^ _113251) ^ [_174154, _174156] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _174154, _174156), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _174154, c_Nat_OSuc(_174156)))], (3986 ^ _113251) ^ [_174256, _174258] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _174256, _174258), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_174256), _174258))], (3992 ^ _113251) ^ [_174337, _174339] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_174337), _174339), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _174337, _174339))], (3998 ^ _113251) ^ [_174439, _174441] : [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), _174439), _174441)), 4001 ^ _113251 : [(4002 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _174439))], (4004 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _174441))]]], (4006 ^ _113251) ^ [_174556, _174558] : [-(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), _174556), _174558))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _174556), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _174558)], (4016 ^ _113251) ^ [_174723, _174725, _174727] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _174723), _174725), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _174723), _174727)), 4019 ^ _113251 : [(4020 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _174723))], (4022 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _174725, _174727))]]], (4024 ^ _113251) ^ [_174854, _174856, _174858] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _174854), _174856), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _174854), _174858))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _174854), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _174856, _174858)], (4034 ^ _113251) ^ [_175037, _175039, _175041] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _175037), _175039), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _175041), _175039)), 4037 ^ _113251 : [(4038 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _175039))], (4040 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _175037, _175041))]]], (4042 ^ _113251) ^ [_175168, _175170, _175172] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _175168), _175170), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _175172), _175170))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _175170), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _175168, _175172)], (4052 ^ _113251) ^ [_175333, _175335, _175337] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _175333, _175335), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _175337), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _175333), _175337), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _175335), _175337)))], (4062 ^ _113251) ^ [_175496, _175498, _175500] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _175496, _175498), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _175500), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _175500), _175496), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _175500), _175498)))], (4072 ^ _113251) ^ [_175659, _175661, _175663] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _175659), _175661)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _175659), _175663))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _175659), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _175661), _175663)))], (4082 ^ _113251) ^ [_175856, _175858, _175860] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_175856)), _175858), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_175856)), _175860)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _175858, _175860))], (4088 ^ _113251) ^ [_175967, _175969, _175971] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _175969, _175971), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_175967)), _175969), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_175967)), _175971)))], (4094 ^ _113251) ^ [_176084, _176086, _176088, _176090] : [class_Rings_Olinordered__semidom(_176084), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _176086, _176088), c_Orderings_Oord__class_Oless(_176084, c_Groups_Ozero__class_Ozero(_176084), _176090), c_Orderings_Oord__class_Oless(_176084, _176090, c_Groups_Oone__class_Oone(_176084)), -(c_Orderings_Oord__class_Oless(_176084, hAPP(hAPP(c_Power_Opower__class_Opower(_176084), _176090), _176088), hAPP(hAPP(c_Power_Opower__class_Opower(_176084), _176090), _176086)))], (4112 ^ _113251) ^ [_176379, _176381, _176383] : [class_Rings_Olinordered__semidom(_176379), c_Orderings_Oord__class_Oless(_176379, c_Groups_Oone__class_Oone(_176379), _176381), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _176383), -(c_Orderings_Oord__class_Oless(_176379, c_Groups_Oone__class_Oone(_176379), hAPP(hAPP(c_Power_Opower__class_Opower(_176379), _176381), _176383)))], (4126 ^ _113251) ^ [_176594, _176596, _176598, _176600] : [class_Rings_Olinordered__semidom(_176594), c_Orderings_Oord__class_Oless(_176594, _176596, _176598), c_Orderings_Oord__class_Oless__eq(_176594, c_Groups_Ozero__class_Ozero(_176594), _176596), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _176600), -(c_Orderings_Oord__class_Oless(_176594, hAPP(hAPP(c_Power_Opower__class_Opower(_176594), _176596), _176600), hAPP(hAPP(c_Power_Opower__class_Opower(_176594), _176598), _176600)))], (4144 ^ _113251) ^ [_176885, _176887] : [class_Rings_Olinordered__ring(_176885), c_Orderings_Oord__class_Oless(_176885, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_176885), _176887), _176887), c_Groups_Ozero__class_Ozero(_176885))], (4150 ^ _113251) ^ [_176983, _176985, _176987, _176989] : [class_Rings_Olinordered__ring__strict(_176983), 4153 ^ _113251 : [(4154 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_176983, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_176983), _176985), _176987), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_176983), _176989), _176987)), 4159 ^ _113251 : [(4160 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(_176983, c_Groups_Ozero__class_Ozero(_176983), _176987))], (4162 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(_176983, _176985, _176989))]], 4163 ^ _113251 : [(4164 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(_176983, _176987, c_Groups_Ozero__class_Ozero(_176983)))], (4166 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(_176983, _176989, _176985))]]], (4168 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(_176983, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_176983), _176985), _176987), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_176983), _176989), _176987))), 4169 ^ _113251 : [(4170 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_176983, c_Groups_Ozero__class_Ozero(_176983), _176987), c_Orderings_Oord__class_Oless(_176983, _176985, _176989)], (4176 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_176983, _176987, c_Groups_Ozero__class_Ozero(_176983)), c_Orderings_Oord__class_Oless(_176983, _176989, _176985)]]]]], (4184 ^ _113251) ^ [_177499, _177501, _177503, _177505] : [class_Rings_Olinordered__ring__strict(_177499), 4187 ^ _113251 : [(4188 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_177499, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_177499), _177501), _177503), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_177499), _177501), _177505)), 4193 ^ _113251 : [(4194 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(_177499, c_Groups_Ozero__class_Ozero(_177499), _177501))], (4196 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(_177499, _177503, _177505))]], 4197 ^ _113251 : [(4198 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(_177499, _177501, c_Groups_Ozero__class_Ozero(_177499)))], (4200 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(_177499, _177505, _177503))]]], (4202 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(_177499, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_177499), _177501), _177503), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_177499), _177501), _177505))), 4203 ^ _113251 : [(4204 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_177499, c_Groups_Ozero__class_Ozero(_177499), _177501), c_Orderings_Oord__class_Oless(_177499, _177503, _177505)], (4210 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_177499, _177501, c_Groups_Ozero__class_Ozero(_177499)), c_Orderings_Oord__class_Oless(_177499, _177505, _177503)]]]]], (4218 ^ _113251) ^ [_178015, _178017, _178019, _178021] : [class_Rings_Olinordered__ring__strict(_178015), c_Orderings_Oord__class_Oless(_178015, c_Groups_Ozero__class_Ozero(_178015), _178017), 4225 ^ _113251 : [(4226 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_178015, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_178015), _178017), _178019), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_178015), _178017), _178021)), -(c_Orderings_Oord__class_Oless(_178015, _178019, _178021))], (4232 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_178015, _178019, _178021), -(c_Orderings_Oord__class_Oless(_178015, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_178015), _178017), _178019), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_178015), _178017), _178021)))]]], (4238 ^ _113251) ^ [_178348, _178350, _178352] : [class_Rings_Olinordered__semiring__strict(_178348), c_Orderings_Oord__class_Oless(_178348, c_Groups_Ozero__class_Ozero(_178348), _178350), c_Orderings_Oord__class_Oless(_178348, c_Groups_Ozero__class_Ozero(_178348), _178352), -(c_Orderings_Oord__class_Oless(_178348, c_Groups_Ozero__class_Ozero(_178348), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_178348), _178350), _178352)))], (4252 ^ _113251) ^ [_178567, _178569, _178571] : [class_Rings_Olinordered__semiring__strict(_178567), c_Orderings_Oord__class_Oless(_178567, c_Groups_Ozero__class_Ozero(_178567), _178569), c_Orderings_Oord__class_Oless(_178567, _178571, c_Groups_Ozero__class_Ozero(_178567)), -(c_Orderings_Oord__class_Oless(_178567, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_178567), _178569), _178571), c_Groups_Ozero__class_Ozero(_178567)))], (4266 ^ _113251) ^ [_178786, _178788, _178790] : [class_Rings_Olinordered__semiring__strict(_178786), c_Orderings_Oord__class_Oless(_178786, c_Groups_Ozero__class_Ozero(_178786), _178788), c_Orderings_Oord__class_Oless(_178786, _178790, c_Groups_Ozero__class_Ozero(_178786)), -(c_Orderings_Oord__class_Oless(_178786, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_178786), _178790), _178788), c_Groups_Ozero__class_Ozero(_178786)))], (4280 ^ _113251) ^ [_179005, _179007, _179009] : [class_Rings_Olinordered__semiring__strict(_179005), c_Orderings_Oord__class_Oless(_179005, c_Groups_Ozero__class_Ozero(_179005), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_179005), _179007), _179009)), c_Orderings_Oord__class_Oless(_179005, c_Groups_Ozero__class_Ozero(_179005), _179007), -(c_Orderings_Oord__class_Oless(_179005, c_Groups_Ozero__class_Ozero(_179005), _179009))], (4294 ^ _113251) ^ [_179224, _179226, _179228] : [class_Rings_Olinordered__semiring__strict(_179224), c_Orderings_Oord__class_Oless(_179224, c_Groups_Ozero__class_Ozero(_179224), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_179224), _179226), _179228)), c_Orderings_Oord__class_Oless(_179224, c_Groups_Ozero__class_Ozero(_179224), _179228), -(c_Orderings_Oord__class_Oless(_179224, c_Groups_Ozero__class_Ozero(_179224), _179226))], (4308 ^ _113251) ^ [_179443, _179445, _179447, _179449] : [class_Rings_Olinordered__ring__strict(_179443), c_Orderings_Oord__class_Oless(_179443, _179445, c_Groups_Ozero__class_Ozero(_179443)), 4315 ^ _113251 : [(4316 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_179443, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_179443), _179445), _179447), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_179443), _179445), _179449)), -(c_Orderings_Oord__class_Oless(_179443, _179449, _179447))], (4322 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_179443, _179449, _179447), -(c_Orderings_Oord__class_Oless(_179443, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_179443), _179445), _179447), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_179443), _179445), _179449)))]]], (4328 ^ _113251) ^ [_179776, _179778, _179780] : [class_Rings_Olinordered__semiring__strict(_179776), c_Orderings_Oord__class_Oless(_179776, _179778, c_Groups_Ozero__class_Ozero(_179776)), c_Orderings_Oord__class_Oless(_179776, c_Groups_Ozero__class_Ozero(_179776), _179780), -(c_Orderings_Oord__class_Oless(_179776, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_179776), _179778), _179780), c_Groups_Ozero__class_Ozero(_179776)))], (4342 ^ _113251) ^ [_179995, _179997, _179999] : [class_Rings_Olinordered__ring__strict(_179995), c_Orderings_Oord__class_Oless(_179995, _179997, c_Groups_Ozero__class_Ozero(_179995)), c_Orderings_Oord__class_Oless(_179995, _179999, c_Groups_Ozero__class_Ozero(_179995)), -(c_Orderings_Oord__class_Oless(_179995, c_Groups_Ozero__class_Ozero(_179995), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_179995), _179997), _179999)))], (4356 ^ _113251) ^ [_180214, _180216, _180218, _180220] : [class_Rings_Olinordered__semiring__strict(_180214), c_Orderings_Oord__class_Oless(_180214, _180216, _180218), c_Orderings_Oord__class_Oless(_180214, c_Groups_Ozero__class_Ozero(_180214), _180220), -(c_Orderings_Oord__class_Oless(_180214, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_180214), _180216), _180220), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_180214), _180218), _180220)))], (4370 ^ _113251) ^ [_180447, _180449, _180451, _180453] : [class_Rings_Olinordered__semiring__strict(_180447), c_Orderings_Oord__class_Oless(_180447, _180449, _180451), c_Orderings_Oord__class_Oless(_180447, c_Groups_Ozero__class_Ozero(_180447), _180453), -(c_Orderings_Oord__class_Oless(_180447, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_180447), _180453), _180449), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_180447), _180453), _180451)))], (4384 ^ _113251) ^ [_180680, _180682, _180684, _180686] : [class_Rings_Olinordered__comm__semiring__strict(_180680), c_Orderings_Oord__class_Oless(_180680, _180682, _180684), c_Orderings_Oord__class_Oless(_180680, c_Groups_Ozero__class_Ozero(_180680), _180686), -(c_Orderings_Oord__class_Oless(_180680, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_180680), _180686), _180682), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_180680), _180686), _180684)))], (4398 ^ _113251) ^ [_180913, _180915, _180917, _180919] : [class_Rings_Olinordered__ring__strict(_180913), c_Orderings_Oord__class_Oless(_180913, _180915, _180917), c_Orderings_Oord__class_Oless(_180913, _180919, c_Groups_Ozero__class_Ozero(_180913)), -(c_Orderings_Oord__class_Oless(_180913, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_180913), _180917), _180919), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_180913), _180915), _180919)))], (4412 ^ _113251) ^ [_181146, _181148, _181150, _181152] : [class_Rings_Olinordered__ring__strict(_181146), c_Orderings_Oord__class_Oless(_181146, _181148, _181150), c_Orderings_Oord__class_Oless(_181146, _181152, c_Groups_Ozero__class_Ozero(_181146)), -(c_Orderings_Oord__class_Oless(_181146, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_181146), _181152), _181150), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_181146), _181152), _181148)))], (4426 ^ _113251) ^ [_181379] : [class_Rings_Olinordered__semidom(_181379), c_Orderings_Oord__class_Oless(_181379, c_Groups_Oone__class_Oone(_181379), c_Groups_Ozero__class_Ozero(_181379))], (4432 ^ _113251) ^ [_181463] : [class_Rings_Olinordered__semidom(_181463), -(c_Orderings_Oord__class_Oless(_181463, c_Groups_Ozero__class_Ozero(_181463), c_Groups_Oone__class_Oone(_181463)))], (4438 ^ _113251) ^ [_181546, _181548] : [class_Groups_Oordered__ab__group__add(_181546), 4441 ^ _113251 : [(4442 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_181546, c_Groups_Ozero__class_Ozero(_181546), c_Groups_Ouminus__class_Ouminus(_181546, _181548)), -(c_Orderings_Oord__class_Oless(_181546, _181548, c_Groups_Ozero__class_Ozero(_181546)))], (4448 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_181546, _181548, c_Groups_Ozero__class_Ozero(_181546)), -(c_Orderings_Oord__class_Oless(_181546, c_Groups_Ozero__class_Ozero(_181546), c_Groups_Ouminus__class_Ouminus(_181546, _181548)))]]], (4454 ^ _113251) ^ [_181778, _181780] : [class_Groups_Oordered__ab__group__add(_181778), 4457 ^ _113251 : [(4458 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_181778, c_Groups_Ouminus__class_Ouminus(_181778, _181780), c_Groups_Ozero__class_Ozero(_181778)), -(c_Orderings_Oord__class_Oless(_181778, c_Groups_Ozero__class_Ozero(_181778), _181780))], (4464 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_181778, c_Groups_Ozero__class_Ozero(_181778), _181780), -(c_Orderings_Oord__class_Oless(_181778, c_Groups_Ouminus__class_Ouminus(_181778, _181780), c_Groups_Ozero__class_Ozero(_181778)))]]], (4470 ^ _113251) ^ [_182010, _182012] : [class_Groups_Olinordered__ab__group__add(_182010), 4473 ^ _113251 : [(4474 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_182010, c_Groups_Ouminus__class_Ouminus(_182010, _182012), _182012), -(c_Orderings_Oord__class_Oless(_182010, c_Groups_Ozero__class_Ozero(_182010), _182012))], (4480 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_182010, c_Groups_Ozero__class_Ozero(_182010), _182012), -(c_Orderings_Oord__class_Oless(_182010, c_Groups_Ouminus__class_Ouminus(_182010, _182012), _182012))]]], (4486 ^ _113251) ^ [_182236, _182238] : [class_Rings_Olinordered__idom(_182236), 4489 ^ _113251 : [(4490 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_182236, _182238, c_Groups_Ouminus__class_Ouminus(_182236, _182238)), -(c_Orderings_Oord__class_Oless(_182236, _182238, c_Groups_Ozero__class_Ozero(_182236)))], (4496 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_182236, _182238, c_Groups_Ozero__class_Ozero(_182236)), -(c_Orderings_Oord__class_Oless(_182236, _182238, c_Groups_Ouminus__class_Ouminus(_182236, _182238)))]]], (4502 ^ _113251) ^ [_182462, _182464, _182466] : [class_Rings_Olinordered__semidom(_182462), c_Orderings_Oord__class_Oless(_182462, c_Groups_Oone__class_Oone(_182462), _182464), c_Orderings_Oord__class_Oless(_182462, c_Groups_Oone__class_Oone(_182462), _182466), -(c_Orderings_Oord__class_Oless(_182462, c_Groups_Oone__class_Oone(_182462), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_182462), _182464), _182466)))], (4516 ^ _113251) ^ [_182681, _182683, _182685] : [class_Rings_Olinordered__semidom(_182681), c_Orderings_Oord__class_Oless(_182681, c_Groups_Ozero__class_Ozero(_182681), _182683), -(c_Orderings_Oord__class_Oless(_182681, c_Groups_Ozero__class_Ozero(_182681), hAPP(hAPP(c_Power_Opower__class_Opower(_182681), _182683), _182685)))], (4526 ^ _113251) ^ [_182840, _182842, _182844, _182846] : [class_Rings_Olinordered__semidom(_182840), c_Orderings_Oord__class_Oless(_182840, c_Groups_Oone__class_Oone(_182840), _182842), 4533 ^ _113251 : [(4534 ^ _113251) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_182840), _182842), _182844) = hAPP(hAPP(c_Power_Opower__class_Opower(_182840), _182842), _182846), -(_182844 = _182846)], (4540 ^ _113251) ^ [] : [_182844 = _182846, -(hAPP(hAPP(c_Power_Opower__class_Opower(_182840), _182842), _182844) = hAPP(hAPP(c_Power_Opower__class_Opower(_182840), _182842), _182846))]]], (4546 ^ _113251) ^ [_183167, _183169] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _183167), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _183169), -(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), _183169), _183167)))], (4556 ^ _113251) ^ [_183314, _183316] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _183314), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _183316), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _183314, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _183314), _183316)))], (4566 ^ _113251) ^ [_183461, _183463] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _183461), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _183463), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _183461, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _183463), _183461)))], (4586 ^ _113251) ^ [_183785, _183787, _183789] : [4587 ^ _113251 : [(4588 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _183787))], (4590 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _183785, _183789)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _183785), _183787), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _183789), _183787)))], (4576 ^ _113251) ^ [_183626, _183628, _183630] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _183626), _183628), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _183630), _183628)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _183628), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _183626, _183630))], (4604 ^ _113251) ^ [_184106, _184108, _184110] : [4605 ^ _113251 : [(4606 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _184106))], (4608 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _184108, _184110)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _184106), _184108), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _184106), _184110)))], (4594 ^ _113251) ^ [_183947, _183949, _183951] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _183947), _183949), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _183947), _183951)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _183947), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _183949, _183951))], (4612 ^ _113251) ^ [_184250, _184252] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _184250), 4615 ^ _113251 : [(4616 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _184250), _184252)), _184250)), -(_184252 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (4622 ^ _113251) ^ [] : [_184252 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _184250), _184252)), _184250)))]]], (4628 ^ _113251) ^ [_184492, _184494] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _184492), 4631 ^ _113251 : [(4632 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _184494), _184492)), _184492)), -(_184494 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (4638 ^ _113251) ^ [] : [_184494 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _184494), _184492)), _184492)))]]], (4644 ^ _113251) ^ [_184734, _184736, _184738] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _184734), _184736)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _184734), _184738))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _184734), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _184736, _184738))], (4654 ^ _113251) ^ [_184905, _184907, _184909, _184911] : [class_Rings_Olinordered__ring__strict(_184905), c_Orderings_Oord__class_Oless(_184905, c_Groups_Ozero__class_Ozero(_184905), _184907), 4661 ^ _113251 : [(4662 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_184905, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_184905), _184907), _184909), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_184905), _184907), _184911)), -(c_Orderings_Oord__class_Oless__eq(_184905, _184909, _184911))], (4668 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_184905, _184909, _184911), -(c_Orderings_Oord__class_Oless__eq(_184905, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_184905), _184907), _184909), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_184905), _184907), _184911)))]]], (4674 ^ _113251) ^ [_185238, _185240, _185242, _185244] : [class_Rings_Olinordered__ring__strict(_185238), c_Orderings_Oord__class_Oless(_185238, _185240, c_Groups_Ozero__class_Ozero(_185238)), 4681 ^ _113251 : [(4682 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_185238, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_185238), _185240), _185242), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_185238), _185240), _185244)), -(c_Orderings_Oord__class_Oless__eq(_185238, _185244, _185242))], (4688 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_185238, _185244, _185242), -(c_Orderings_Oord__class_Oless__eq(_185238, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_185238), _185240), _185242), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_185238), _185240), _185244)))]]], (4694 ^ _113251) ^ [_185571, _185573, _185575, _185577, _185579] : [class_Rings_Olinordered__semiring__strict(_185571), c_Orderings_Oord__class_Oless(_185571, _185573, _185575), c_Orderings_Oord__class_Oless(_185571, _185577, _185579), c_Orderings_Oord__class_Oless(_185571, c_Groups_Ozero__class_Ozero(_185571), _185575), c_Orderings_Oord__class_Oless__eq(_185571, c_Groups_Ozero__class_Ozero(_185571), _185577), -(c_Orderings_Oord__class_Oless(_185571, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_185571), _185573), _185577), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_185571), _185575), _185579)))], (4716 ^ _113251) ^ [_185934, _185936, _185938, _185940, _185942] : [class_Rings_Olinordered__semiring__strict(_185934), c_Orderings_Oord__class_Oless(_185934, _185936, _185938), c_Orderings_Oord__class_Oless(_185934, _185940, _185942), c_Orderings_Oord__class_Oless__eq(_185934, c_Groups_Ozero__class_Ozero(_185934), _185936), c_Orderings_Oord__class_Oless__eq(_185934, c_Groups_Ozero__class_Ozero(_185934), _185940), -(c_Orderings_Oord__class_Oless(_185934, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_185934), _185936), _185940), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_185934), _185938), _185942)))], (4738 ^ _113251) ^ [_186297, _186299, _186301, _186303, _186305] : [class_Rings_Olinordered__semiring__strict(_186297), c_Orderings_Oord__class_Oless(_186297, _186299, _186301), c_Orderings_Oord__class_Oless__eq(_186297, _186303, _186305), c_Orderings_Oord__class_Oless__eq(_186297, c_Groups_Ozero__class_Ozero(_186297), _186299), c_Orderings_Oord__class_Oless(_186297, c_Groups_Ozero__class_Ozero(_186297), _186303), -(c_Orderings_Oord__class_Oless(_186297, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_186297), _186299), _186303), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_186297), _186301), _186305)))], (4760 ^ _113251) ^ [_186660, _186662, _186664, _186666, _186668] : [class_Rings_Olinordered__semiring__strict(_186660), c_Orderings_Oord__class_Oless__eq(_186660, _186662, _186664), c_Orderings_Oord__class_Oless(_186660, _186666, _186668), c_Orderings_Oord__class_Oless(_186660, c_Groups_Ozero__class_Ozero(_186660), _186662), c_Orderings_Oord__class_Oless__eq(_186660, c_Groups_Ozero__class_Ozero(_186660), _186666), -(c_Orderings_Oord__class_Oless(_186660, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_186660), _186662), _186666), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_186660), _186664), _186668)))], (4782 ^ _113251) ^ [_187023, _187025, _187027, _187029] : [class_Rings_Olinordered__semiring(_187023), c_Orderings_Oord__class_Oless(_187023, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_187023), _187025), _187027), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_187023), _187029), _187027)), c_Orderings_Oord__class_Oless__eq(_187023, c_Groups_Ozero__class_Ozero(_187023), _187027), -(c_Orderings_Oord__class_Oless(_187023, _187025, _187029))], (4796 ^ _113251) ^ [_187256, _187258, _187260, _187262] : [class_Rings_Olinordered__semiring__strict(_187256), c_Orderings_Oord__class_Oless(_187256, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_187256), _187258), _187260), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_187256), _187262), _187260)), c_Orderings_Oord__class_Oless__eq(_187256, c_Groups_Ozero__class_Ozero(_187256), _187260), -(c_Orderings_Oord__class_Oless(_187256, _187258, _187262))], (4810 ^ _113251) ^ [_187489, _187491, _187493, _187495] : [class_Rings_Olinordered__semiring(_187489), c_Orderings_Oord__class_Oless(_187489, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_187489), _187491), _187493), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_187489), _187491), _187495)), c_Orderings_Oord__class_Oless__eq(_187489, c_Groups_Ozero__class_Ozero(_187489), _187491), -(c_Orderings_Oord__class_Oless(_187489, _187493, _187495))], (4824 ^ _113251) ^ [_187722, _187724, _187726, _187728] : [class_Rings_Olinordered__semiring__strict(_187722), c_Orderings_Oord__class_Oless(_187722, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_187722), _187724), _187726), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_187722), _187724), _187728)), c_Orderings_Oord__class_Oless__eq(_187722, c_Groups_Ozero__class_Ozero(_187722), _187724), -(c_Orderings_Oord__class_Oless(_187722, _187726, _187728))], (4838 ^ _113251) ^ [_187955, _187957, _187959, _187961] : [class_Rings_Olinordered__semiring__strict(_187955), c_Orderings_Oord__class_Oless__eq(_187955, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_187955), _187957), _187959), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_187955), _187961), _187959)), c_Orderings_Oord__class_Oless(_187955, c_Groups_Ozero__class_Ozero(_187955), _187959), -(c_Orderings_Oord__class_Oless__eq(_187955, _187957, _187961))], (4852 ^ _113251) ^ [_188188, _188190, _188192, _188194] : [class_Rings_Olinordered__semiring__strict(_188188), c_Orderings_Oord__class_Oless__eq(_188188, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_188188), _188190), _188192), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_188188), _188190), _188194)), c_Orderings_Oord__class_Oless(_188188, c_Groups_Ozero__class_Ozero(_188188), _188190), -(c_Orderings_Oord__class_Oless__eq(_188188, _188192, _188194))], (4866 ^ _113251) ^ [_188421, _188423, _188425, _188427] : [class_Rings_Olinordered__semidom(_188421), c_Orderings_Oord__class_Oless(_188421, hAPP(hAPP(c_Power_Opower__class_Opower(_188421), _188423), _188425), hAPP(hAPP(c_Power_Opower__class_Opower(_188421), _188427), _188425)), c_Orderings_Oord__class_Oless__eq(_188421, c_Groups_Ozero__class_Ozero(_188421), _188427), -(c_Orderings_Oord__class_Oless(_188421, _188423, _188427))], (4880 ^ _113251) ^ [_188654, _188656, _188658] : [class_Rings_Olinordered__semidom(_188654), c_Orderings_Oord__class_Oless(_188654, c_Groups_Oone__class_Oone(_188654), _188656), -(c_Orderings_Oord__class_Oless(_188654, c_Groups_Oone__class_Oone(_188654), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_188654), _188656), hAPP(hAPP(c_Power_Opower__class_Opower(_188654), _188656), _188658))))], (4890 ^ _113251) ^ [_188829, _188831, _188833] : [class_Rings_Olinordered__semidom(_188829), c_Orderings_Oord__class_Oless(_188829, c_Groups_Oone__class_Oone(_188829), _188831), -(c_Orderings_Oord__class_Oless(_188829, hAPP(hAPP(c_Power_Opower__class_Opower(_188829), _188831), _188833), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_188829), _188831), hAPP(hAPP(c_Power_Opower__class_Opower(_188829), _188831), _188833))))], (4900 ^ _113251) ^ [_189016, _189018, _189020] : [class_Rings_Olinordered__semidom(_189016), c_Orderings_Oord__class_Oless(_189016, c_Groups_Oone__class_Oone(_189016), _189018), -(c_Orderings_Oord__class_Oless(_189016, c_Groups_Oone__class_Oone(_189016), hAPP(hAPP(c_Power_Opower__class_Opower(_189016), _189018), c_Nat_OSuc(_189020))))], (4910 ^ _113251) ^ [_189179, _189181] : [c_Nat_OSuc(_189179) = c_Nat_OSuc(_189181), -(_189179 = _189181)], (4916 ^ _113251) ^ [_189279, _189281] : [c_Nat_OSuc(_189279) = c_Nat_OSuc(_189281), -(_189279 = _189281)], (4922 ^ _113251) ^ [_189360, _189362] : [_189360 = _189362, -(c_Nat_OSuc(_189360) = c_Nat_OSuc(_189362))], (4928 ^ _113251) ^ [_189456] : [c_Nat_OSuc(_189456) = _189456], (4930 ^ _113251) ^ [_189490] : [_189490 = c_Nat_OSuc(_189490)], (4932 ^ _113251) ^ [_189515, _189517] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _189515, _189517), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _189517, _189515), -(_189515 = _189517)], (4942 ^ _113251) ^ [_189648, _189650, _189652] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _189648, _189650), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _189650, _189652), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _189648, _189652))], (4952 ^ _113251) ^ [_189787, _189789] : [_189787 = _189789, -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _189787, _189789))], (4958 ^ _113251) ^ [_189862, _189864] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _189862, _189864)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _189864, _189862))], (4964 ^ _113251) ^ [_189900] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _189900, _189900))], (4966 ^ _113251) ^ [_189924, _189926] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _189924), _189926) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _189926), _189924))], (4968 ^ _113251) ^ [_189961, _189963, _189965] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _189961), _189963)), _189965) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _189961), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _189963), _189965)))], (4970 ^ _113251) ^ [_190024] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _190024), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(_190024 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (4976 ^ _113251) ^ [_190105] : [_190105 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _190105), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (4982 ^ _113251) ^ [_190192, _190194, _190196] : [class_Rings_Olinordered__semidom(_190192), c_Orderings_Oord__class_Oless(_190192, c_Groups_Ozero__class_Ozero(_190192), _190194), c_Orderings_Oord__class_Oless(_190192, _190194, c_Groups_Oone__class_Oone(_190192)), -(c_Orderings_Oord__class_Oless(_190192, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_190192), _190194), hAPP(hAPP(c_Power_Opower__class_Opower(_190192), _190194), _190196)), hAPP(hAPP(c_Power_Opower__class_Opower(_190192), _190194), _190196)))], (4996 ^ _113251) ^ [_190439, _190441, _190443] : [class_Rings_Olinordered__semidom(_190439), c_Orderings_Oord__class_Oless(_190439, c_Groups_Ozero__class_Ozero(_190439), _190441), c_Orderings_Oord__class_Oless(_190439, _190441, c_Groups_Oone__class_Oone(_190439)), -(c_Orderings_Oord__class_Oless(_190439, hAPP(hAPP(c_Power_Opower__class_Opower(_190439), _190441), c_Nat_OSuc(_190443)), c_Groups_Oone__class_Oone(_190439)))], (5010 ^ _113251) ^ [_190662, _190664, _190666, _190668] : [class_Rings_Olinordered__semidom(_190662), c_Orderings_Oord__class_Oless(_190662, c_Groups_Oone__class_Oone(_190662), _190664), c_Orderings_Oord__class_Oless__eq(_190662, hAPP(hAPP(c_Power_Opower__class_Opower(_190662), _190664), _190666), hAPP(hAPP(c_Power_Opower__class_Opower(_190662), _190664), _190668)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _190666, _190668))], (5024 ^ _113251) ^ [_190895, _190897, _190899, _190901] : [class_Rings_Olinordered__semidom(_190895), c_Orderings_Oord__class_Oless(_190895, c_Groups_Oone__class_Oone(_190895), _190897), 5031 ^ _113251 : [(5032 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_190895, hAPP(hAPP(c_Power_Opower__class_Opower(_190895), _190897), _190899), hAPP(hAPP(c_Power_Opower__class_Opower(_190895), _190897), _190901)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _190899, _190901))], (5038 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _190899, _190901), -(c_Orderings_Oord__class_Oless__eq(_190895, hAPP(hAPP(c_Power_Opower__class_Opower(_190895), _190897), _190899), hAPP(hAPP(c_Power_Opower__class_Opower(_190895), _190897), _190901)))]]], (5044 ^ _113251) ^ [_191228, _191230, _191232, _191234] : [class_Rings_Olinordered__semidom(_191228), hAPP(hAPP(c_Power_Opower__class_Opower(_191228), _191230), _191232) = hAPP(hAPP(c_Power_Opower__class_Opower(_191228), _191234), _191232), c_Orderings_Oord__class_Oless__eq(_191228, c_Groups_Ozero__class_Ozero(_191228), _191230), c_Orderings_Oord__class_Oless__eq(_191228, c_Groups_Ozero__class_Ozero(_191228), _191234), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _191232), -(_191230 = _191234)], (5066 ^ _113251) ^ [_191577, _191579, _191581] : [class_Rings_Ocomm__semiring__1(_191577), 5071 ^ _113251 : [(5072 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _191579)], (5074 ^ _113251) ^ [] : [_191581 = c_Groups_Oone__class_Oone(_191577)]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_191577), _191581), hAPP(hAPP(c_Power_Opower__class_Opower(_191577), _191581), _191579))))], (5078 ^ _113251) ^ [_191791] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_191791)], (5080 ^ _113251) ^ [_191825] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_191825)], (5082 ^ _113251) ^ [_191859] : [c_Nat_OSuc(_191859) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5084 ^ _113251) ^ [_191893] : [c_Nat_OSuc(_191893) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5086 ^ _113251) ^ [_191930] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _191930), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_191930 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (5092 ^ _113251) ^ [_192011] : [_192011 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _192011), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (5098 ^ _113251) ^ [_192107] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_192107)], (5100 ^ _113251) ^ [_192141] : [c_Nat_OSuc(_192141) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5102 ^ _113251) ^ [_192166] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _192166))], (5104 ^ _113251) ^ [_192202] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _192202, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_192202 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5110 ^ _113251) ^ [_192275] : [_192275 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _192275, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (5116 ^ _113251) ^ [_192354, _192356] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_192354), _192356), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _192354, _192356))], (5122 ^ _113251) ^ [_192439, _192441] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _192439, c_Nat_OSuc(_192441)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _192439, _192441)), -(_192439 = c_Nat_OSuc(_192441))], (5132 ^ _113251) ^ [_192543, _192545] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _192543, _192545), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _192543, c_Nat_OSuc(_192545)))], (5138 ^ _113251) ^ [_192643, _192645] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_192643), c_Nat_OSuc(_192645)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _192643, _192645))], (5144 ^ _113251) ^ [_192728, _192730] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _192728, _192730), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_192728), c_Nat_OSuc(_192730)))], (5160 ^ _113251) ^ [_192932, _192934] : [5161 ^ _113251 : [(5162 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _192932, _192934)], (5164 ^ _113251) ^ [] : [_192932 = c_Nat_OSuc(_192934)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _192932, c_Nat_OSuc(_192934)))], (5150 ^ _113251) ^ [_192834, _192836] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _192834, c_Nat_OSuc(_192836)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _192834, _192836)), -(_192834 = c_Nat_OSuc(_192836))], (5168 ^ _113251) ^ [_193070, _193072] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _193070, _193072)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_193072), _193070))], (5174 ^ _113251) ^ [_193106, _193108] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_193108), _193106), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _193106, _193108)], (5180 ^ _113251) ^ [_193203] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_193203), _193203)], (5182 ^ _113251) ^ [_193229] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _193229) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5184 ^ _113251) ^ [_193255] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _193255), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5196 ^ _113251) ^ [_193397, _193399] : [5197 ^ _113251 : [(5198 ^ _113251) ^ [] : [_193397 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5200 ^ _113251) ^ [] : [_193399 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _193397), _193399) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5186 ^ _113251) ^ [_193299, _193301] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _193299), _193301) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_193299 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_193301 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5214 ^ _113251) ^ [_193656, _193658, _193660] : [5215 ^ _113251 : [(5216 ^ _113251) ^ [] : [_193658 = _193660], (5218 ^ _113251) ^ [] : [_193656 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _193656), _193658) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _193656), _193660))], (5204 ^ _113251) ^ [_193544, _193546, _193548] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _193544), _193546) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _193544), _193548), -(_193546 = _193548), -(_193544 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5232 ^ _113251) ^ [_193929, _193931, _193933] : [5233 ^ _113251 : [(5234 ^ _113251) ^ [] : [_193929 = _193933], (5236 ^ _113251) ^ [] : [_193931 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _193929), _193931) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _193933), _193931))], (5222 ^ _113251) ^ [_193817, _193819, _193821] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _193817), _193819) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _193821), _193819), -(_193817 = _193821), -(_193819 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5240 ^ _113251) ^ [_194090, _194092, _194094] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_194090)), _194092) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_194090)), _194094), -(_194092 = _194094)], (5246 ^ _113251) ^ [_194197, _194199, _194201] : [_194199 = _194201, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_194197)), _194199) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_194197)), _194201))], (5252 ^ _113251) ^ [_194310] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _194310, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _194310), _194310)))], (5254 ^ _113251) ^ [_194340] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _194340, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _194340), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _194340), _194340))))], (5256 ^ _113251) ^ [_194376, _194378, _194380] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _194376, _194378), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _194376), _194380), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _194378), _194380)))], (5262 ^ _113251) ^ [_194483, _194485, _194487] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _194483, _194485), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _194487), _194483), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _194487), _194485)))], (5268 ^ _113251) ^ [_194590, _194592, _194594, _194596] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _194590, _194592), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _194594, _194596), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _194590), _194594), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _194592), _194596)))], (5278 ^ _113251) ^ [_194757] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _194757) = _194757)], (5280 ^ _113251) ^ [_194798, _194800] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _194798), _194800), 5283 ^ _113251 : [(5284 ^ _113251) ^ [] : [-(_194798 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (5286 ^ _113251) ^ [] : [-(_194800 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (5288 ^ _113251) ^ [_194909, _194911] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _194909), _194911)), _194909 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _194911 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (5298 ^ _113251) ^ [_195052] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _195052), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _195052)], (5300 ^ _113251) ^ [_195096, _195098] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _195096), _195098) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 5303 ^ _113251 : [(5304 ^ _113251) ^ [] : [-(_195096 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (5306 ^ _113251) ^ [] : [-(_195098 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (5308 ^ _113251) ^ [_195207, _195209] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _195207), _195209) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _195207 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _195209 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (5318 ^ _113251) ^ [_195365, _195367] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _195365), _195367) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 5321 ^ _113251 : [(5322 ^ _113251) ^ [] : [-(_195365 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (5324 ^ _113251) ^ [] : [-(_195367 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (5326 ^ _113251) ^ [_195476, _195478] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _195476), _195478) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _195476 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _195478 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5336 ^ _113251) ^ [_195619, _195621, _195623] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _195619), 5339 ^ _113251 : [(5340 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _195619), _195621), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _195619), _195623)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _195621, _195623))], (5346 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _195621, _195623), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _195619), _195621), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _195619), _195623)))]]], (5352 ^ _113251) ^ [_195876, _195878, _195880] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _195876), 5355 ^ _113251 : [(5356 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _195876), _195878)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _195876), _195880))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _195878), _195880)))], (5362 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _195878), _195880)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _195876), _195878)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _195876), _195880))))]]], (5368 ^ _113251) ^ [_196156, _196158, _196160] : [-(_196156 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 5371 ^ _113251 : [(5372 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _196158), _196156)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _196160), _196156))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _196158), _196160)))], (5378 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _196158), _196160)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _196158), _196156)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _196160), _196156))))]]], (5384 ^ _113251) ^ [_196433, _196435, _196437] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _196433), _196435)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _196437), _196435))), -(_196435 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _196433), _196437)))], (5404 ^ _113251) ^ [_196688, _196690] : [5405 ^ _113251 : [(5406 ^ _113251) ^ [] : [_196690 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5408 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _196688)]], -(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), _196688), _196690)))], (5394 ^ _113251) ^ [_196586, _196588] : [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), _196586), _196588)), -(_196588 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _196586))], (5422 ^ _113251) ^ [_196971, _196973, _196975] : [5423 ^ _113251 : [(5424 ^ _113251) ^ [] : [_196971 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5426 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _196973), _196975))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _196971), _196973)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _196971), _196975))))], (5412 ^ _113251) ^ [_196839, _196841, _196843] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _196839), _196841)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _196839), _196843))), -(_196839 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _196841), _196843)))], (5430 ^ _113251) ^ [_197134, _197136, _197138] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _197134), 5433 ^ _113251 : [(5434 ^ _113251) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _197134), _197136) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _197134), _197138), -(_197136 = _197138)], (5440 ^ _113251) ^ [] : [_197136 = _197138, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _197134), _197136) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _197134), _197138))]]], (5446 ^ _113251) ^ [_197385, _197387, _197389] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _197385), 5449 ^ _113251 : [(5450 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _197385), _197387), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _197385), _197389)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _197387, _197389))], (5456 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _197387, _197389), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _197385), _197387), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _197385), _197389)))]]], (5462 ^ _113251) ^ [_197642, _197644, _197646] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _197642), _197644)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _197646), _197644))), -(_197644 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _197642), _197646)))], (5472 ^ _113251) ^ [_197779, _197781, _197783] : [-(_197779 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 5475 ^ _113251 : [(5476 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _197781), _197779)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _197783), _197779))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _197781), _197783)))], (5482 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _197781), _197783)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _197781), _197779)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _197783), _197779))))]]], (5488 ^ _113251) ^ [_198056] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _198056), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (5500 ^ _113251) ^ [_198214, _198216, _198218] : [5501 ^ _113251 : [(5502 ^ _113251) ^ [] : [_198214 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (5504 ^ _113251) ^ [] : [_198216 = _198218]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _198214), _198216) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _198214), _198218))], (5490 ^ _113251) ^ [_198102, _198104, _198106] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _198102), _198104) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _198102), _198106), -(_198102 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_198104 = _198106)], (5508 ^ _113251) ^ [_198357] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _198357)))], (5510 ^ _113251) ^ [_198382] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _198382, c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_198382 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_198382 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (5520 ^ _113251) ^ [_198472, _198474] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _198472), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _198474), _198472)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _198474))], (5530 ^ _113251) ^ [_198615, _198617] : [class_Groups_Ozero(_198615), 5533 ^ _113251 : [(5534 ^ _113251) ^ [] : [_198617 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_198615)), -(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_198615, _198617) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5540 ^ _113251) ^ [] : [-(_198617 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_198615))), -(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_198615, _198617) = c_Nat_OSuc(c_Polynomial_Odegree(_198615, _198617)))]]], (5546 ^ _113251) ^ [_198827, _198829] : [class_Orderings_Opreorder(_198827), -(c_Orderings_Oord__class_Oless__eq(_198827, _198829, _198829))], (5552 ^ _113251) ^ [_198904] : [class_Power_Opower(_198904), -(c_Power_Opower__class_Opower(_198904) = c_Power_Opower_Opower(_198904, c_Groups_Oone__class_Oone(_198904), c_Groups_Otimes__class_Otimes(_198904)))], (5558 ^ _113251) ^ [_198997, _198999, _199001] : [class_Rings_Ocomm__semiring__0(_198997), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_198997, c_Polynomial_Opcompose(_198997, _198999, _199001)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Polynomial_Odegree(_198997, _198999)), c_Polynomial_Odegree(_198997, _199001))))], (5564 ^ _113251) ^ [_199114, _199116] : [class_Rings_Ocomm__semiring__0(_199114), -(c_Polynomial_Opcompose(_199114, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_199114)), _199116) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_199114)))], (5570 ^ _113251) ^ [_199213, _199215, _199217, _199219] : [class_Rings_Ocomm__semiring__0(_199213), -(hAPP(c_Polynomial_Opoly(_199213, c_Polynomial_Opcompose(_199213, _199215, _199217)), _199219) = hAPP(c_Polynomial_Opoly(_199213, _199215), hAPP(c_Polynomial_Opoly(_199213, _199217), _199219)))], (5576 ^ _113251) ^ [_199336, _199338, _199340, _199342] : [-(hAPP(hAPP(c_Power_Opower_Opower(_199336, _199338, _199340), _199342), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _199338)], (5578 ^ _113251) ^ [_199375, _199377, _199379, _199381, _199383] : [-(hAPP(hAPP(c_Power_Opower_Opower(_199375, _199377, _199379), _199381), c_Nat_OSuc(_199383)) = hAPP(hAPP(_199379, _199381), hAPP(hAPP(c_Power_Opower_Opower(_199375, _199377, _199379), _199381), _199383)))], (5580 ^ _113251) ^ [_199434, _199436, _199438] : [class_Orderings_Olinorder(_199434), -(c_Orderings_Oord__class_Oless__eq(_199434, _199436, _199438)), -(c_Orderings_Oord__class_Oless__eq(_199434, _199438, _199436))], (5590 ^ _113251) ^ [_199530, _199532, _199534, _199536, _199538] : [class_Orderings_Oord(_199530), c_Orderings_Oord__class_Oless__eq(tc_fun(_199532, _199530), _199534, _199536), -(c_Orderings_Oord__class_Oless__eq(_199530, hAPP(_199534, _199538), hAPP(_199536, _199538)))], (5600 ^ _113251) ^ [_199691, _199693, _199695, _199697] : [class_Orderings_Oorder(_199691), c_Orderings_Oord__class_Oless__eq(_199691, _199693, _199695), c_Orderings_Oord__class_Oless__eq(_199691, _199697, _199693), -(c_Orderings_Oord__class_Oless__eq(_199691, _199697, _199695))], (5614 ^ _113251) ^ [_199888, _199890, _199892] : [class_Orderings_Oorder(_199888), c_Orderings_Oord__class_Oless__eq(_199888, _199890, _199892), c_Orderings_Oord__class_Oless__eq(_199888, _199892, _199890), -(_199892 = _199890)], (5628 ^ _113251) ^ [_200077, _200079, _200081, _200083] : [class_Orderings_Opreorder(_200077), c_Orderings_Oord__class_Oless__eq(_200077, _200079, _200081), c_Orderings_Oord__class_Oless__eq(_200077, _200081, _200083), -(c_Orderings_Oord__class_Oless__eq(_200077, _200079, _200083))], (5642 ^ _113251) ^ [_200274, _200276, _200278] : [class_Orderings_Oorder(_200274), c_Orderings_Oord__class_Oless__eq(_200274, _200276, _200278), c_Orderings_Oord__class_Oless__eq(_200274, _200278, _200276), -(_200276 = _200278)], (5656 ^ _113251) ^ [_200463, _200465, _200467, _200469] : [class_Orderings_Oorder(_200463), c_Orderings_Oord__class_Oless__eq(_200463, _200465, _200467), _200465 = _200469, -(c_Orderings_Oord__class_Oless__eq(_200463, _200469, _200467))], (5670 ^ _113251) ^ [_200658, _200660, _200662, _200664] : [class_Orderings_Oord(_200658), c_Orderings_Oord__class_Oless__eq(_200658, _200660, _200662), _200662 = _200664, -(c_Orderings_Oord__class_Oless__eq(_200658, _200660, _200664))], (5684 ^ _113251) ^ [_200853, _200855, _200857, _200859] : [class_Orderings_Oorder(_200853), _200855 = _200857, c_Orderings_Oord__class_Oless__eq(_200853, _200859, _200857), -(c_Orderings_Oord__class_Oless__eq(_200853, _200859, _200855))], (5698 ^ _113251) ^ [_201048, _201050, _201052, _201054] : [class_Orderings_Oord(_201048), _201050 = _201052, c_Orderings_Oord__class_Oless__eq(_201048, _201052, _201054), -(c_Orderings_Oord__class_Oless__eq(_201048, _201050, _201054))], (5712 ^ _113251) ^ [_201243, _201245, _201247] : [class_Orderings_Oorder(_201243), c_Orderings_Oord__class_Oless__eq(_201243, _201245, _201247), 5719 ^ _113251 : [(5720 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_201243, _201247, _201245), -(_201247 = _201245)], (5726 ^ _113251) ^ [] : [_201247 = _201245, -(c_Orderings_Oord__class_Oless__eq(_201243, _201247, _201245))]]], (5732 ^ _113251) ^ [_201513, _201515, _201517, _201519, _201521] : [class_Orderings_Oord(_201513), c_Orderings_Oord__class_Oless__eq(tc_fun(_201515, _201513), _201517, _201519), -(c_Orderings_Oord__class_Oless__eq(_201513, hAPP(_201517, _201521), hAPP(_201519, _201521)))], (5742 ^ _113251) ^ [_201674, _201676, _201678] : [class_Orderings_Opreorder(_201674), _201676 = _201678, -(c_Orderings_Oord__class_Oless__eq(_201674, _201676, _201678))], (5752 ^ _113251) ^ [_201807, _201809, _201811] : [class_Orderings_Oorder(_201807), 5755 ^ _113251 : [(5756 ^ _113251) ^ [] : [_201809 = _201811, 5759 ^ _113251 : [(5760 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_201807, _201809, _201811))], (5762 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_201807, _201811, _201809))]]], (5764 ^ _113251) ^ [] : [-(_201809 = _201811), c_Orderings_Oord__class_Oless__eq(_201807, _201809, _201811), c_Orderings_Oord__class_Oless__eq(_201807, _201811, _201809)]]], (5774 ^ _113251) ^ [_202098, _202100, _202102] : [class_Orderings_Olinorder(_202098), -(c_Orderings_Oord__class_Oless__eq(_202098, _202100, _202102)), -(c_Orderings_Oord__class_Oless__eq(_202098, _202102, _202100))], (5784 ^ _113251) ^ [_202192, _202194, _202196, _202198] : [class_Orderings_Oord(_202192), 5787 ^ _113251 : [(5788 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_202194, _202192), _202196, _202198), 5791 ^ _113251 : [(5792 ^ _113251) ^ [_202331] : [-(c_Orderings_Oord__class_Oless__eq(_202192, hAPP(_202196, _202331), hAPP(_202198, _202331)))]]], (5794 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_202192, hAPP(_202196, 5795 ^ [_202192, _202194, _202196, _202198]), hAPP(_202198, 5795 ^ [_202192, _202194, _202196, _202198])), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_202194, _202192), _202196, _202198))]]], (5801 ^ _113251) ^ [_202496, _202498, _202500] : [class_Orderings_Olinorder(_202496), -(c_Orderings_Oord__class_Oless(_202496, _202498, _202500)), -(_202498 = _202500), -(c_Orderings_Oord__class_Oless(_202496, _202500, _202498))], (5815 ^ _113251) ^ [_202607, _202609, _202611] : [class_Orderings_Opreorder(_202607), c_Orderings_Oord__class_Oless(_202607, _202609, _202611), c_Orderings_Oord__class_Oless(_202607, _202611, _202609)], (5825 ^ _113251) ^ [_202743, _202745, _202747, _202749] : [class_Orderings_Oorder(_202743), c_Orderings_Oord__class_Oless(_202743, _202745, _202747), c_Orderings_Oord__class_Oless(_202743, _202749, _202745), -(c_Orderings_Oord__class_Oless(_202743, _202749, _202747))], (5839 ^ _113251) ^ [_202940, _202942, _202944, _202946] : [class_Orderings_Opreorder(_202940), c_Orderings_Oord__class_Oless(_202940, _202942, _202944), c_Orderings_Oord__class_Oless(_202940, _202944, _202946), -(c_Orderings_Oord__class_Oless(_202940, _202942, _202946))], (5853 ^ _113251) ^ [_203137, _203139, _203141, _203143] : [class_Orderings_Oorder(_203137), c_Orderings_Oord__class_Oless(_203137, _203139, _203141), _203139 = _203143, -(c_Orderings_Oord__class_Oless(_203137, _203143, _203141))], (5867 ^ _113251) ^ [_203332, _203334, _203336, _203338] : [class_Orderings_Oord(_203332), c_Orderings_Oord__class_Oless(_203332, _203334, _203336), _203336 = _203338, -(c_Orderings_Oord__class_Oless(_203332, _203334, _203338))], (5881 ^ _113251) ^ [_203527, _203529, _203531, _203533] : [class_Orderings_Oorder(_203527), _203529 = _203531, c_Orderings_Oord__class_Oless(_203527, _203533, _203531), -(c_Orderings_Oord__class_Oless(_203527, _203533, _203529))], (5895 ^ _113251) ^ [_203722, _203724, _203726, _203728] : [class_Orderings_Oord(_203722), _203724 = _203726, c_Orderings_Oord__class_Oless(_203722, _203726, _203728), -(c_Orderings_Oord__class_Oless(_203722, _203724, _203728))], (5909 ^ _113251) ^ [_203917, _203919, _203921] : [class_Orderings_Oorder(_203917), c_Orderings_Oord__class_Oless(_203917, _203919, _203921), c_Orderings_Oord__class_Oless(_203917, _203921, _203919)], (5919 ^ _113251) ^ [_204053, _204055, _204057] : [class_Orderings_Opreorder(_204053), c_Orderings_Oord__class_Oless(_204053, _204055, _204057), c_Orderings_Oord__class_Oless(_204053, _204057, _204055)], (5929 ^ _113251) ^ [_204189, _204191, _204193] : [class_Orderings_Oorder(_204189), c_Orderings_Oord__class_Oless(_204189, _204191, _204193), _204193 = _204191], (5939 ^ _113251) ^ [_204323, _204325, _204327] : [class_Orderings_Oorder(_204323), c_Orderings_Oord__class_Oless(_204323, _204325, _204327), _204325 = _204327], (5949 ^ _113251) ^ [_204457, _204459, _204461] : [class_Orderings_Opreorder(_204457), c_Orderings_Oord__class_Oless(_204457, _204459, _204461), c_Orderings_Oord__class_Oless(_204457, _204461, _204459)], (5959 ^ _113251) ^ [_204593, _204595, _204597] : [class_Orderings_Opreorder(_204593), c_Orderings_Oord__class_Oless(_204593, _204595, _204597), c_Orderings_Oord__class_Oless(_204593, _204597, _204595)], (5969 ^ _113251) ^ [_204729, _204731, _204733] : [class_Orderings_Oorder(_204729), c_Orderings_Oord__class_Oless(_204729, _204731, _204733), _204731 = _204733], (5979 ^ _113251) ^ [_204863, _204865, _204867] : [class_Orderings_Olinorder(_204863), -(_204865 = _204867), -(c_Orderings_Oord__class_Oless(_204863, _204865, _204867)), -(c_Orderings_Oord__class_Oless(_204863, _204867, _204865))], (5993 ^ _113251) ^ [_204974, _204976, _204978] : [class_Orderings_Olinorder(_204974), -(c_Orderings_Oord__class_Oless(_204974, _204976, _204978)), 6000 ^ _113251 : [(6001 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(_204974, _204978, _204976)), -(_204978 = _204976)], (6007 ^ _113251) ^ [] : [_204978 = _204976, c_Orderings_Oord__class_Oless(_204974, _204978, _204976)]]], (6013 ^ _113251) ^ [_205203, _205205, _205207] : [class_Orderings_Olinorder(_205203), -(c_Orderings_Oord__class_Oless(_205203, _205205, _205207)), -(_205205 = _205207), -(c_Orderings_Oord__class_Oless(_205203, _205207, _205205))], (6027 ^ _113251) ^ [_205310, _205312, _205314] : [class_Orderings_Olinorder(_205310), 6030 ^ _113251 : [(6041 ^ _113251) ^ [] : [6042 ^ _113251 : [(6043 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_205310, _205314, _205312)], (6045 ^ _113251) ^ [] : [_205312 = _205314]], c_Orderings_Oord__class_Oless(_205310, _205312, _205314)], (6031 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(_205310, _205312, _205314)), -(c_Orderings_Oord__class_Oless(_205310, _205314, _205312)), -(_205312 = _205314)]]], (6049 ^ _113251) ^ [_205528, _205530, _205532] : [class_Orderings_Olinorder(_205528), 6052 ^ _113251 : [(6063 ^ _113251) ^ [] : [6064 ^ _113251 : [(6065 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_205528, _205530, _205532)], (6067 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_205528, _205532, _205530)]], _205530 = _205532], (6053 ^ _113251) ^ [] : [-(_205530 = _205532), -(c_Orderings_Oord__class_Oless(_205528, _205530, _205532)), -(c_Orderings_Oord__class_Oless(_205528, _205532, _205530))]]], (6071 ^ _113251) ^ [_205746, _205748] : [class_Orderings_Opreorder(_205746), c_Orderings_Oord__class_Oless(_205746, _205748, _205748)], (6077 ^ _113251) ^ [_205824, _205826] : [class_Groups_Ozero(_205824), 6080 ^ _113251 : [(6081 ^ _113251) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_205824, _205826) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_205826 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_205824)))], (6087 ^ _113251) ^ [] : [_205826 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_205824)), -(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_205824, _205826) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (6093 ^ _113251) ^ [_206050, _206052, _206054] : [class_Orderings_Olinorder(_206050), 6096 ^ _113251 : [(6097 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(_206050, _206052, _206054)), -(c_Orderings_Oord__class_Oless__eq(_206050, _206054, _206052))], (6103 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_206050, _206054, _206052), c_Orderings_Oord__class_Oless(_206050, _206052, _206054)]]], (6109 ^ _113251) ^ [_206223, _206225, _206227] : [class_Orderings_Olinorder(_206223), 6112 ^ _113251 : [(6113 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_206223, _206225, _206227)), -(c_Orderings_Oord__class_Oless(_206223, _206227, _206225))], (6119 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_206223, _206227, _206225), c_Orderings_Oord__class_Oless__eq(_206223, _206225, _206227)]]], (6125 ^ _113251) ^ [_206396, _206398, _206400] : [class_Orderings_Olinorder(_206396), -(c_Orderings_Oord__class_Oless__eq(_206396, _206398, _206400)), -(c_Orderings_Oord__class_Oless(_206396, _206400, _206398))], (6135 ^ _113251) ^ [_206490, _206492, _206494] : [class_Orderings_Oorder(_206490), 6138 ^ _113251 : [(6139 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_206490, _206492, _206494), 6142 ^ _113251 : [(6143 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_206490, _206492, _206494))], (6145 ^ _113251) ^ [] : [_206492 = _206494]]], (6147 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(_206490, _206492, _206494)), c_Orderings_Oord__class_Oless__eq(_206490, _206492, _206494), -(_206492 = _206494)]]], (6157 ^ _113251) ^ [_206790, _206792, _206794] : [class_Orderings_Opreorder(_206790), 6160 ^ _113251 : [(6161 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_206790, _206792, _206794), 6164 ^ _113251 : [(6165 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_206790, _206792, _206794))], (6167 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_206790, _206794, _206792)]]], (6169 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(_206790, _206792, _206794)), c_Orderings_Oord__class_Oless__eq(_206790, _206792, _206794), -(c_Orderings_Oord__class_Oless__eq(_206790, _206794, _206792))]]], (6179 ^ _113251) ^ [_207093, _207095, _207097] : [class_Orderings_Oorder(_207093), 6182 ^ _113251 : [(6193 ^ _113251) ^ [] : [6194 ^ _113251 : [(6195 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_207093, _207095, _207097)], (6197 ^ _113251) ^ [] : [_207095 = _207097]], -(c_Orderings_Oord__class_Oless__eq(_207093, _207095, _207097))], (6183 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_207093, _207095, _207097), -(c_Orderings_Oord__class_Oless(_207093, _207095, _207097)), -(_207095 = _207097)]]], (6201 ^ _113251) ^ [_207355, _207357, _207359] : [class_Orderings_Olinorder(_207355), -(c_Orderings_Oord__class_Oless(_207355, _207357, _207359)), -(c_Orderings_Oord__class_Oless__eq(_207355, _207359, _207357))], (6211 ^ _113251) ^ [_207451, _207453, _207455] : [class_Orderings_Olinorder(_207451), -(c_Orderings_Oord__class_Oless__eq(_207451, _207453, _207455)), -(c_Orderings_Oord__class_Oless(_207451, _207455, _207453))], (6221 ^ _113251) ^ [_207547, _207549, _207551] : [class_Orderings_Olinorder(_207547), -(c_Orderings_Oord__class_Oless(_207547, _207549, _207551)), 6228 ^ _113251 : [(6229 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_207547, _207549, _207551), -(_207549 = _207551)], (6235 ^ _113251) ^ [] : [_207549 = _207551, -(c_Orderings_Oord__class_Oless__eq(_207547, _207549, _207551))]]], (6241 ^ _113251) ^ [_207820, _207822, _207824] : [class_Orderings_Oorder(_207820), -(_207822 = _207824), c_Orderings_Oord__class_Oless__eq(_207820, _207822, _207824), -(c_Orderings_Oord__class_Oless(_207820, _207822, _207824))], (6255 ^ _113251) ^ [_208012, _208014, _208016] : [class_Orderings_Oorder(_208012), -(_208014 = _208016), c_Orderings_Oord__class_Oless__eq(_208012, _208016, _208014), -(c_Orderings_Oord__class_Oless(_208012, _208016, _208014))], (6269 ^ _113251) ^ [_208204, _208206, _208208] : [class_Orderings_Olinorder(_208204), c_Orderings_Oord__class_Oless__eq(_208204, _208206, _208208), c_Orderings_Oord__class_Oless(_208204, _208208, _208206)], (6279 ^ _113251) ^ [_208340, _208342, _208344] : [class_Orderings_Opreorder(_208340), c_Orderings_Oord__class_Oless(_208340, _208342, _208344), -(c_Orderings_Oord__class_Oless__eq(_208340, _208342, _208344))], (6289 ^ _113251) ^ [_208475, _208477, _208479] : [class_Orderings_Olinorder(_208475), c_Orderings_Oord__class_Oless__eq(_208475, _208477, _208479), 6296 ^ _113251 : [(6297 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(_208475, _208477, _208479)), -(_208477 = _208479)], (6303 ^ _113251) ^ [] : [_208477 = _208479, c_Orderings_Oord__class_Oless(_208475, _208477, _208479)]]], (6309 ^ _113251) ^ [_208701, _208703, _208705] : [class_Orderings_Oorder(_208701), c_Orderings_Oord__class_Oless__eq(_208701, _208703, _208705), -(c_Orderings_Oord__class_Oless(_208701, _208703, _208705)), -(_208703 = _208705)], (6323 ^ _113251) ^ [_208849, _208851, _208853] : [class_Orderings_Oorder(_208849), c_Orderings_Oord__class_Oless__eq(_208849, _208851, _208853), -(_208851 = _208853), -(c_Orderings_Oord__class_Oless(_208849, _208851, _208853))], (6337 ^ _113251) ^ [_208999, _209001, _209003] : [class_Orderings_Oorder(_208999), c_Orderings_Oord__class_Oless__eq(_208999, _209001, _209003), -(_209003 = _209001), -(c_Orderings_Oord__class_Oless(_208999, _209001, _209003))], (6351 ^ _113251) ^ [_209149, _209151, _209153, _209155] : [class_Orderings_Opreorder(_209149), c_Orderings_Oord__class_Oless(_209149, _209151, _209153), c_Orderings_Oord__class_Oless__eq(_209149, _209153, _209155), -(c_Orderings_Oord__class_Oless(_209149, _209151, _209155))], (6365 ^ _113251) ^ [_209346, _209348, _209350, _209352] : [class_Orderings_Oorder(_209346), c_Orderings_Oord__class_Oless(_209346, _209348, _209350), c_Orderings_Oord__class_Oless__eq(_209346, _209352, _209348), -(c_Orderings_Oord__class_Oless(_209346, _209352, _209350))], (6379 ^ _113251) ^ [_209543, _209545, _209547, _209549] : [class_Orderings_Opreorder(_209543), c_Orderings_Oord__class_Oless__eq(_209543, _209545, _209547), c_Orderings_Oord__class_Oless(_209543, _209547, _209549), -(c_Orderings_Oord__class_Oless(_209543, _209545, _209549))], (6393 ^ _113251) ^ [_209740, _209742, _209744, _209746] : [class_Orderings_Oorder(_209740), c_Orderings_Oord__class_Oless__eq(_209740, _209742, _209744), c_Orderings_Oord__class_Oless(_209740, _209746, _209742), -(c_Orderings_Oord__class_Oless(_209740, _209746, _209744))], (6407 ^ _113251) ^ [_209937, _209939, _209941] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _209937), _209939)), _209941) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _209937), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _209939), _209941)))], (6409 ^ _113251) ^ [_209988, _209990] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _209988, _209990), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _209988, _209990))], (6415 ^ _113251) ^ [_210069, _210071, _210073] : [class_Rings_Olinordered__idom(_210069), 6418 ^ _113251 : [(6419 ^ _113251) ^ [] : [c_Polynomial_Opos__poly(_210069, c_Polynomial_OpCons(_210069, _210071, _210073)), -(c_Polynomial_Opos__poly(_210069, _210073)), 6426 ^ _113251 : [(6427 ^ _113251) ^ [] : [-(_210073 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_210069)))], (6429 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(_210069, c_Groups_Ozero__class_Ozero(_210069), _210071))]]], (6431 ^ _113251) ^ [] : [-(c_Polynomial_Opos__poly(_210069, c_Polynomial_OpCons(_210069, _210071, _210073))), 6432 ^ _113251 : [(6433 ^ _113251) ^ [] : [c_Polynomial_Opos__poly(_210069, _210073)], (6435 ^ _113251) ^ [] : [_210073 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_210069)), c_Orderings_Oord__class_Oless(_210069, c_Groups_Ozero__class_Ozero(_210069), _210071)]]]]], (6443 ^ _113251) ^ [_210447, _210449, _210451] : [class_Lattices_Oboolean__algebra(_210447), 6446 ^ _113251 : [(6447 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_210447, c_Groups_Ouminus__class_Ouminus(_210447, _210449), c_Groups_Ouminus__class_Ouminus(_210447, _210451)), -(c_Orderings_Oord__class_Oless__eq(_210447, _210451, _210449))], (6453 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_210447, _210451, _210449), -(c_Orderings_Oord__class_Oless__eq(_210447, c_Groups_Ouminus__class_Ouminus(_210447, _210449), c_Groups_Ouminus__class_Ouminus(_210447, _210451)))]]], (6459 ^ _113251) ^ [_210682, _210684, _210686] : [class_Lattices_Oboolean__algebra(_210682), c_Orderings_Oord__class_Oless__eq(_210682, _210684, _210686), -(c_Orderings_Oord__class_Oless__eq(_210682, c_Groups_Ouminus__class_Ouminus(_210682, _210686), c_Groups_Ouminus__class_Ouminus(_210682, _210684)))], (6469 ^ _113251) ^ [_210829, _210831, _210833, _210835] : [class_Orderings_Oord(_210829), 6472 ^ _113251 : [(6473 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(tc_fun(_210831, _210829), _210833, _210835), 6476 ^ _113251 : [(6477 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_fun(_210831, _210829), _210833, _210835))], (6479 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_210831, _210829), _210835, _210833)]]], (6481 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_fun(_210831, _210829), _210833, _210835)), c_Orderings_Oord__class_Oless__eq(tc_fun(_210831, _210829), _210833, _210835), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_210831, _210829), _210835, _210833))]]], (6491 ^ _113251) ^ [_211167] : [class_Rings_Olinordered__idom(_211167), c_Polynomial_Opos__poly(_211167, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_211167)))], (6497 ^ _113251) ^ [_211249, _211251, _211253] : [class_Rings_Olinordered__idom(_211249), c_Polynomial_Opos__poly(_211249, _211251), c_Polynomial_Opos__poly(_211249, _211253), -(c_Polynomial_Opos__poly(_211249, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_211249)), _211251), _211253)))], (6511 ^ _113251) ^ [_211454, _211456, _211458] : [class_Lattices_Oab__semigroup__idem__mult(_211454), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_211454), _211456), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_211454), _211456), _211458)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_211454), _211456), _211458))], (6517 ^ _113251) ^ [_211579, _211581] : [class_Lattices_Oab__semigroup__idem__mult(_211579), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_211579), _211581), _211581) = _211581)], (6523 ^ _113251) ^ [_211670, _211672] : [class_Lattices_Oab__semigroup__idem__mult(_211670), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_211670), _211672), _211672) = _211672)], (6529 ^ _113251) ^ [_211761, _211763, _211765] : [class_Lattices_Oboolean__algebra(_211761), 6532 ^ _113251 : [(6533 ^ _113251) ^ [] : [c_Groups_Ouminus__class_Ouminus(_211761, _211763) = c_Groups_Ouminus__class_Ouminus(_211761, _211765), -(_211763 = _211765)], (6539 ^ _113251) ^ [] : [_211763 = _211765, -(c_Groups_Ouminus__class_Ouminus(_211761, _211763) = c_Groups_Ouminus__class_Ouminus(_211761, _211765))]]], (6545 ^ _113251) ^ [_211990, _211992, _211994, _211996] : [class_Groups_Ouminus(_211990), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_211992, _211990), _211994), _211996) = c_Groups_Ouminus__class_Ouminus(_211990, hAPP(_211994, _211996)))], (6551 ^ _113251) ^ [_212099, _212101] : [class_Lattices_Oboolean__algebra(_212099), -(c_Groups_Ouminus__class_Ouminus(_212099, c_Groups_Ouminus__class_Ouminus(_212099, _212101)) = _212101)], (6557 ^ _113251) ^ [_212186, _212188] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _212186), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _212188), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _212186), _212188)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _212188), _212186)), -(_212186 = _212188)], (6575 ^ _113251) ^ [_212443, _212445, _212447] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _212443), _212445)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _212443), _212447))), -(_212443 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _212445), _212447)))], (6585 ^ _113251) ^ [_212581, _212583] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _212581), _212583)), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _212583), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _212581, _212583))], (6595 ^ _113251) ^ [_212724, _212726] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _212724), c_Orderings_Oord__class_Oless(tc_Int_Oint, _212724, _212726), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _212726), _212724))], (6605 ^ _113251) ^ [_212868, _212870] : [class_Rings_Olinordered__idom(_212868), -(_212870 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_212868))), -(c_Polynomial_Opos__poly(_212868, _212870)), -(c_Polynomial_Opos__poly(_212868, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_212868), _212870)))], (6619 ^ _113251) ^ [_212987, _212989, _212991, _212993] : [class_Rings_Ocomm__ring__1(_212987), -(hAPP(c_Polynomial_Opoly(_212987, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_212987)), c_Polynomial_Omonom(_212987, c_Groups_Oone__class_Oone(_212987), _212989)), _212991)), _212993) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_212987), hAPP(hAPP(c_Power_Opower__class_Opower(_212987), _212993), _212989)), hAPP(c_Polynomial_Opoly(_212987, _212991), _212993)))], (6625 ^ _113251) ^ [_213154, _213156, _213158, _213160, _213162, _213164] : [class_Groups_Ozero(_213154), hAPP(hAPP(hAPP(_213156, c_Groups_Ozero__class_Ozero(_213154)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_213154))), _213158) = _213158, -(c_Polynomial_Opoly__rec(_213160, _213154, _213158, _213156, c_Polynomial_OpCons(_213154, _213162, _213164)) = hAPP(hAPP(hAPP(_213156, _213162), _213164), c_Polynomial_Opoly__rec(_213160, _213154, _213158, _213156, _213164)))], (6635 ^ _113251) ^ [_213377, _213379, _213381] : [class_Rings_Ocomm__semiring__0(_213377), 6638 ^ _113251 : [(6639 ^ _113251) ^ [] : [c_Polynomial_Osynthetic__div(_213377, _213379, _213381) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_213377)), -(c_Polynomial_Odegree(_213377, _213379) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6645 ^ _113251) ^ [] : [c_Polynomial_Odegree(_213377, _213379) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Polynomial_Osynthetic__div(_213377, _213379, _213381) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_213377)))]]], (6651 ^ _113251) ^ [_213621, _213623, _213625] : [class_Groups_Ozero(_213621), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_213621, _213623), _213625), hAPP(c_Polynomial_Ocoeff(_213621, _213623), _213625) = c_Groups_Ozero__class_Ozero(_213621), -(_213623 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_213621))), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_213621, _213623), _213625))], (6669 ^ _113251) ^ [_213859] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _213859, _213859))], (6671 ^ _113251) ^ [_213879, _213881] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _213879, _213881)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _213881, _213879))], (6677 ^ _113251) ^ [_213917, _213919, _213921] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _213917, _213919), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _213919, _213921), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _213917, _213921))], (6687 ^ _113251) ^ [_214056, _214058] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _214056, _214058), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _214058, _214056), -(_214056 = _214058)], (6697 ^ _113251) ^ [] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (6699 ^ _113251) ^ [_214207] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _214207) = _214207)], (6701 ^ _113251) ^ [_214233] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _214233), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _214233)], (6703 ^ _113251) ^ [_214262, _214264] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _214262), _214264) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _214264), _214262))], (6705 ^ _113251) ^ [_214299, _214301] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _214299)), _214301) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _214299), _214301)))], (6707 ^ _113251) ^ [_214342, _214344, _214346] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _214342), _214344)), _214346) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _214342), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _214344), _214346)))], (6709 ^ _113251) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (6711 ^ _113251) ^ [_214413, _214415] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _214413, _214415)), -(_214413 = _214415), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _214415, _214413))], (6721 ^ _113251) ^ [_214473, _214475] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _214473, _214475), 6724 ^ _113251 : [(6725 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _214473, _214475))], (6727 ^ _113251) ^ [] : [_214473 = _214475]]], (6729 ^ _113251) ^ [_214584, _214586] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _214584, _214586)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _214584, _214586), -(_214584 = _214586)], (6739 ^ _113251) ^ [_214722, _214724, _214726] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _214722, _214724), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _214726), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _214726), _214722), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _214726), _214724)))], (6749 ^ _113251) ^ [_214885, _214887] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _214885), 6752 ^ _113251 : [(6753 ^ _113251) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _214885), _214887) = c_Groups_Oone__class_Oone(tc_Int_Oint), 6756 ^ _113251 : [(6757 ^ _113251) ^ [] : [-(_214885 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (6759 ^ _113251) ^ [] : [-(_214887 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (6761 ^ _113251) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _214885), _214887) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _214885 = c_Groups_Oone__class_Oone(tc_Int_Oint), _214887 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (6771 ^ _113251) ^ [_215196] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _215196), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _215196))], (6777 ^ _113251) ^ [_215271] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _215271), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _215271))], (6783 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (6785 ^ _113251) ^ [_215370, _215372, _215374, _215376] : [class_Groups_Ozero(_215370), 6788 ^ _113251 : [(6789 ^ _113251) ^ [] : [_215372 = _215374, -(hAPP(c_Polynomial_Ocoeff(_215370, c_Polynomial_Omonom(_215370, _215376, _215372)), _215374) = _215376)], (6795 ^ _113251) ^ [] : [-(_215372 = _215374), -(hAPP(c_Polynomial_Ocoeff(_215370, c_Polynomial_Omonom(_215370, _215376, _215372)), _215374) = c_Groups_Ozero__class_Ozero(_215370))]]], (6801 ^ _113251) ^ [_215596, _215598, _215600] : [class_Groups_Ozero(_215596), 6804 ^ _113251 : [(6805 ^ _113251) ^ [] : [_215598 = _215600, 6808 ^ _113251 : [(6809 ^ _113251) ^ [_215728] : [-(hAPP(c_Polynomial_Ocoeff(_215596, _215598), _215728) = hAPP(c_Polynomial_Ocoeff(_215596, _215600), _215728))]]], (6811 ^ _113251) ^ [] : [hAPP(c_Polynomial_Ocoeff(_215596, _215598), 6812 ^ [_215596, _215598, _215600]) = hAPP(c_Polynomial_Ocoeff(_215596, _215600), 6812 ^ [_215596, _215598, _215600]), -(_215598 = _215600)]]], (6818 ^ _113251) ^ [_215896, _215898, _215900] : [class_Groups_Ozero(_215896), 6821 ^ _113251 : [(6822 ^ _113251) ^ [] : [c_Polynomial_Ocoeff(_215896, _215898) = c_Polynomial_Ocoeff(_215896, _215900), -(_215898 = _215900)], (6828 ^ _113251) ^ [] : [_215898 = _215900, -(c_Polynomial_Ocoeff(_215896, _215898) = c_Polynomial_Ocoeff(_215896, _215900))]]], (6834 ^ _113251) ^ [_216125, _216127, _216129, _216131] : [class_Groups_Ozero(_216125), 6837 ^ _113251 : [(6838 ^ _113251) ^ [] : [c_Polynomial_Omonom(_216125, _216127, _216129) = c_Polynomial_Omonom(_216125, _216131, _216129), -(_216127 = _216131)], (6844 ^ _113251) ^ [] : [_216127 = _216131, -(c_Polynomial_Omonom(_216125, _216127, _216129) = c_Polynomial_Omonom(_216125, _216131, _216129))]]], (6850 ^ _113251) ^ [_216366, _216368] : [class_Groups_Ozero(_216366), -(hAPP(c_Polynomial_Ocoeff(_216366, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_216366))), _216368) = c_Groups_Ozero__class_Ozero(_216366))], (6856 ^ _113251) ^ [_216465, _216467, _216469] : [class_Groups_Ozero(_216465), -(hAPP(c_Polynomial_Ocoeff(_216465, c_Polynomial_OpCons(_216465, _216467, _216469)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _216467)], (6862 ^ _113251) ^ [_216562, _216564, _216566, _216568] : [class_Groups_Ozero(_216562), -(hAPP(c_Polynomial_Ocoeff(_216562, c_Polynomial_OpCons(_216562, _216564, _216566)), c_Nat_OSuc(_216568)) = hAPP(c_Polynomial_Ocoeff(_216562, _216566), _216568))], (6868 ^ _113251) ^ [_216677, _216679] : [class_Rings_Ocomm__semiring__0(_216677), -(c_Polynomial_Osynthetic__div(_216677, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_216677)), _216679) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_216677)))], (6874 ^ _113251) ^ [_216776, _216778, _216780] : [class_Groups_Oab__group__add(_216776), -(hAPP(c_Polynomial_Ocoeff(_216776, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_216776), _216778)), _216780) = c_Groups_Ouminus__class_Ouminus(_216776, hAPP(c_Polynomial_Ocoeff(_216776, _216778), _216780)))], (6880 ^ _113251) ^ [_216893, _216895, _216897] : [class_Rings_Oidom(_216893), hAPP(c_Polynomial_Ocoeff(_216893, _216895), c_Polynomial_Odegree(_216893, _216895)) = hAPP(c_Polynomial_Ocoeff(_216893, _216897), c_Polynomial_Odegree(_216893, _216897)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_216893)), _216895), _216897)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_216893)), _216897), _216895)), -(_216895 = _216897)], (6898 ^ _113251) ^ [_217204, _217206] : [class_Groups_Ozero(_217204), -(c_Polynomial_Omonom(_217204, c_Groups_Ozero__class_Ozero(_217204), _217206) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_217204)))], (6904 ^ _113251) ^ [_217299, _217301, _217303] : [class_Groups_Ozero(_217299), 6907 ^ _113251 : [(6908 ^ _113251) ^ [] : [c_Polynomial_Omonom(_217299, _217301, _217303) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_217299)), -(_217301 = c_Groups_Ozero__class_Ozero(_217299))], (6914 ^ _113251) ^ [] : [_217301 = c_Groups_Ozero__class_Ozero(_217299), -(c_Polynomial_Omonom(_217299, _217301, _217303) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_217299)))]]], (6920 ^ _113251) ^ [_217540, _217542, _217544] : [class_Groups_Ozero(_217540), -(_217542 = c_Groups_Ozero__class_Ozero(_217540)), -(c_Polynomial_Odegree(_217540, c_Polynomial_Omonom(_217540, _217542, _217544)) = _217544)], (6930 ^ _113251) ^ [_217650, _217652, _217654] : [class_Groups_Ozero(_217650), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_217650, c_Polynomial_Omonom(_217650, _217652, _217654)), _217654))], (6936 ^ _113251) ^ [_217743, _217745, _217747] : [class_Groups_Oab__group__add(_217743), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_217743), c_Polynomial_Omonom(_217743, _217745, _217747)) = c_Polynomial_Omonom(_217743, c_Groups_Ouminus__class_Ouminus(_217743, _217745), _217747))], (6942 ^ _113251) ^ [_217852, _217854, _217856] : [class_Groups_Ozero(_217852), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_217852, _217854), _217856), -(hAPP(c_Polynomial_Ocoeff(_217852, _217854), _217856) = c_Groups_Ozero__class_Ozero(_217852))], (6952 ^ _113251) ^ [_218007, _218009, _218011] : [class_Groups_Ozero(_218007), -(hAPP(c_Polynomial_Ocoeff(_218007, _218009), _218011) = c_Groups_Ozero__class_Ozero(_218007)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _218011, c_Polynomial_Odegree(_218007, _218009)))], (6962 ^ _113251) ^ [_218123, _218125] : [class_Groups_Ozero(_218123), 6965 ^ _113251 : [(6966 ^ _113251) ^ [] : [hAPP(c_Polynomial_Ocoeff(_218123, _218125), c_Polynomial_Odegree(_218123, _218125)) = c_Groups_Ozero__class_Ozero(_218123), -(_218125 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_218123)))], (6972 ^ _113251) ^ [] : [_218125 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_218123)), -(hAPP(c_Polynomial_Ocoeff(_218123, _218125), c_Polynomial_Odegree(_218123, _218125)) = c_Groups_Ozero__class_Ozero(_218123))]]], (6978 ^ _113251) ^ [_218373, _218375] : [class_Groups_Ozero(_218373), -(_218375 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_218373))), hAPP(c_Polynomial_Ocoeff(_218373, _218375), c_Polynomial_Odegree(_218373, _218375)) = c_Groups_Ozero__class_Ozero(_218373)], (6988 ^ _113251) ^ [_218534, _218536, _218538] : [class_Groups_Ozero(_218534), -(c_Polynomial_Omonom(_218534, _218536, c_Nat_OSuc(_218538)) = c_Polynomial_OpCons(_218534, c_Groups_Ozero__class_Ozero(_218534), c_Polynomial_Omonom(_218534, _218536, _218538)))], (6994 ^ _113251) ^ [_218643, _218645, _218647, _218649] : [class_Rings_Ocomm__semiring__1(_218643), -(hAPP(c_Polynomial_Opoly(_218643, c_Polynomial_Omonom(_218643, _218645, _218647)), _218649) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_218643), _218645), hAPP(hAPP(c_Power_Opower__class_Opower(_218643), _218649), _218647)))], (7000 ^ _113251) ^ [_218774, _218776] : [class_Groups_Ozero(_218774), -(c_Polynomial_Omonom(_218774, _218776, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(_218774, _218776, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_218774))))], (7006 ^ _113251) ^ [_218873, _218875, _218877, _218879] : [class_Rings_Ocomm__semiring__0(_218873), -(c_Polynomial_Osynthetic__div(_218873, c_Polynomial_OpCons(_218873, _218875, _218877), _218879) = c_Polynomial_OpCons(_218873, hAPP(c_Polynomial_Opoly(_218873, _218877), _218879), c_Polynomial_Osynthetic__div(_218873, _218877, _218879)))], (7012 ^ _113251) ^ [_218996, _218998, _219000, _219002] : [class_Groups_Ozero(_218996), hAPP(hAPP(hAPP(_218998, c_Groups_Ozero__class_Ozero(_218996)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_218996))), _219000) = _219000, -(c_Polynomial_Opoly__rec(_219002, _218996, _219000, _218998, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_218996))) = _219000)], (7022 ^ _113251) ^ [_219181, _219183] : [class_Rings_Ocomm__semiring__1(_219181), 7025 ^ _113251 : [(7026 ^ _113251) ^ [] : [_219183 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Polynomial_Ocoeff(_219181, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_219181))), _219183) = c_Groups_Oone__class_Oone(_219181))], (7032 ^ _113251) ^ [] : [-(_219183 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_Polynomial_Ocoeff(_219181, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_219181))), _219183) = c_Groups_Ozero__class_Ozero(_219181))]]], (7038 ^ _113251) ^ [_219403, _219405] : [class_Rings_Olinordered__idom(_219403), 7041 ^ _113251 : [(7042 ^ _113251) ^ [] : [c_Polynomial_Opos__poly(_219403, _219405), -(c_Orderings_Oord__class_Oless(_219403, c_Groups_Ozero__class_Ozero(_219403), hAPP(c_Polynomial_Ocoeff(_219403, _219405), c_Polynomial_Odegree(_219403, _219405))))], (7048 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_219403, c_Groups_Ozero__class_Ozero(_219403), hAPP(c_Polynomial_Ocoeff(_219403, _219405), c_Polynomial_Odegree(_219403, _219405))), -(c_Polynomial_Opos__poly(_219403, _219405))]]], (7054 ^ _113251) ^ [_219644, _219646, _219648] : [class_Rings_Ocomm__semiring__1(_219644), -(hAPP(c_Polynomial_Ocoeff(_219644, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_219644)), c_Polynomial_OpCons(_219644, _219646, c_Polynomial_OpCons(_219644, c_Groups_Oone__class_Oone(_219644), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_219644))))), _219648)), _219648) = c_Groups_Oone__class_Oone(_219644))], (7060 ^ _113251) ^ [_219785, _219787, _219789, _219791, _219793, _219795] : [class_Groups_Ozero(_219785), -(c_Polynomial_Opoly__rec(_219787, _219785, _219789, _219791, c_Polynomial_OpCons(_219785, _219793, _219795)) = hAPP(hAPP(hAPP(_219791, _219793), _219795), c_If(_219787, c_fequal(_219795, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_219785))), _219789, c_Polynomial_Opoly__rec(_219787, _219785, _219789, _219791, _219795))))], (7066 ^ _113251) ^ [_219942, _219944] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _219942), -(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), _219942), _219944)))], (7072 ^ _113251) ^ [_220034, _220036, _220038] : [-(_220034 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 7075 ^ _113251 : [(7076 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _220036), _220038)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _220034), _220036)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _220034), _220038))))], (7082 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _220034), _220036)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _220034), _220038))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _220036), _220038)))]]], (7088 ^ _113251) ^ [_220311, _220313] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _220311), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _220313), -(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), _220311), _220313)))], (7098 ^ _113251) ^ [_220458, _220460, _220462] : [class_Rings_Ocomm__ring__1(_220458), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_220458), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_220458)), c_Polynomial_OpCons(_220458, c_Groups_Ouminus__class_Ouminus(_220458, _220460), c_Polynomial_OpCons(_220458, c_Groups_Oone__class_Oone(_220458), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_220458))))), c_Polynomial_Osynthetic__div(_220458, _220462, _220460)), c_Polynomial_OpCons(_220458, hAPP(c_Polynomial_Opoly(_220458, _220462), _220460), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_220458)))) = _220462)], (7104 ^ _113251) ^ [_220637] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _220637)) = _220637)], (7106 ^ _113251) ^ [_220666, _220668] : [class_Groups_Olinordered__ab__group__add(_220666), 7109 ^ _113251 : [(7110 ^ _113251) ^ [] : [c_Groups_Oplus__class_Oplus(_220666, _220668, _220668) = c_Groups_Ozero__class_Ozero(_220666), -(_220668 = c_Groups_Ozero__class_Ozero(_220666))], (7116 ^ _113251) ^ [] : [_220668 = c_Groups_Ozero__class_Ozero(_220666), -(c_Groups_Oplus__class_Oplus(_220666, _220668, _220668) = c_Groups_Ozero__class_Ozero(_220666))]]], (7122 ^ _113251) ^ [_220895, _220897, _220899, _220901] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_220895), 7125 ^ _113251 : [(7126 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_220895, c_Groups_Oplus__class_Oplus(_220895, _220897, _220899), c_Groups_Oplus__class_Oplus(_220895, _220901, _220899)), -(c_Orderings_Oord__class_Oless__eq(_220895, _220897, _220901))], (7132 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_220895, _220897, _220901), -(c_Orderings_Oord__class_Oless__eq(_220895, c_Groups_Oplus__class_Oplus(_220895, _220897, _220899), c_Groups_Oplus__class_Oplus(_220895, _220901, _220899)))]]], (7138 ^ _113251) ^ [_221142, _221144, _221146, _221148] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_221142), 7141 ^ _113251 : [(7142 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_221142, c_Groups_Oplus__class_Oplus(_221142, _221144, _221146), c_Groups_Oplus__class_Oplus(_221142, _221144, _221148)), -(c_Orderings_Oord__class_Oless__eq(_221142, _221146, _221148))], (7148 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_221142, _221146, _221148), -(c_Orderings_Oord__class_Oless__eq(_221142, c_Groups_Oplus__class_Oplus(_221142, _221144, _221146), c_Groups_Oplus__class_Oplus(_221142, _221144, _221148)))]]], (7154 ^ _113251) ^ [_221389, _221391, _221393, _221395] : [class_Groups_Oordered__ab__semigroup__add(_221389), c_Orderings_Oord__class_Oless__eq(_221389, _221391, _221393), -(c_Orderings_Oord__class_Oless__eq(_221389, c_Groups_Oplus__class_Oplus(_221389, _221391, _221395), c_Groups_Oplus__class_Oplus(_221389, _221393, _221395)))], (7164 ^ _113251) ^ [_221544, _221546, _221548, _221550] : [class_Groups_Oordered__ab__semigroup__add(_221544), c_Orderings_Oord__class_Oless__eq(_221544, _221546, _221548), -(c_Orderings_Oord__class_Oless__eq(_221544, c_Groups_Oplus__class_Oplus(_221544, _221550, _221546), c_Groups_Oplus__class_Oplus(_221544, _221550, _221548)))], (7174 ^ _113251) ^ [_221699, _221701, _221703, _221705, _221707] : [class_Groups_Oordered__ab__semigroup__add(_221699), c_Orderings_Oord__class_Oless__eq(_221699, _221701, _221703), c_Orderings_Oord__class_Oless__eq(_221699, _221705, _221707), -(c_Orderings_Oord__class_Oless__eq(_221699, c_Groups_Oplus__class_Oplus(_221699, _221701, _221705), c_Groups_Oplus__class_Oplus(_221699, _221703, _221707)))], (7188 ^ _113251) ^ [_221918, _221920, _221922, _221924] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_221918), c_Orderings_Oord__class_Oless__eq(_221918, c_Groups_Oplus__class_Oplus(_221918, _221920, _221922), c_Groups_Oplus__class_Oplus(_221918, _221924, _221922)), -(c_Orderings_Oord__class_Oless__eq(_221918, _221920, _221924))], (7198 ^ _113251) ^ [_222073, _222075, _222077, _222079] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_222073), c_Orderings_Oord__class_Oless__eq(_222073, c_Groups_Oplus__class_Oplus(_222073, _222075, _222077), c_Groups_Oplus__class_Oplus(_222073, _222075, _222079)), -(c_Orderings_Oord__class_Oless__eq(_222073, _222077, _222079))], (7208 ^ _113251) ^ [_222228, _222230] : [class_Groups_Ocomm__monoid__add(_222228), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_222228), _222230, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_222228))) = _222230)], (7214 ^ _113251) ^ [_222323, _222325] : [class_Groups_Ocomm__monoid__add(_222323), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_222323), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_222323)), _222325) = _222325)], (7220 ^ _113251) ^ [_222418, _222420, _222422, _222424] : [class_Rings_Ocomm__semiring__0(_222418), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_222418)), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_222418), _222420, _222422)), _222424) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_222418), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_222418)), _222420), _222424), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_222418)), _222422), _222424)))], (7226 ^ _113251) ^ [_222581, _222583, _222585] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_222581), 7229 ^ _113251 : [(7230 ^ _113251) ^ [] : [_222583 = c_Groups_Oplus__class_Oplus(_222581, _222583, _222585), -(_222585 = c_Groups_Ozero__class_Ozero(_222581))], (7236 ^ _113251) ^ [] : [_222585 = c_Groups_Ozero__class_Ozero(_222581), -(_222583 = c_Groups_Oplus__class_Oplus(_222581, _222583, _222585))]]], (7242 ^ _113251) ^ [_222810, _222812] : [class_Rings_Ocomm__semiring__1(_222810), -(c_Groups_Oplus__class_Oplus(_222810, _222812, c_Groups_Ozero__class_Ozero(_222810)) = _222812)], (7248 ^ _113251) ^ [_222897, _222899] : [class_Rings_Ocomm__semiring__1(_222897), -(c_Groups_Oplus__class_Oplus(_222897, c_Groups_Ozero__class_Ozero(_222897), _222899) = _222899)], (7254 ^ _113251) ^ [_222984, _222986] : [class_Groups_Ocomm__monoid__add(_222984), -(c_Groups_Oplus__class_Oplus(_222984, _222986, c_Groups_Ozero__class_Ozero(_222984)) = _222986)], (7260 ^ _113251) ^ [_223071, _223073] : [class_Groups_Omonoid__add(_223071), -(c_Groups_Oplus__class_Oplus(_223071, _223073, c_Groups_Ozero__class_Ozero(_223071)) = _223073)], (7266 ^ _113251) ^ [_223158, _223160] : [class_Groups_Olinordered__ab__group__add(_223158), 7269 ^ _113251 : [(7270 ^ _113251) ^ [] : [c_Groups_Ozero__class_Ozero(_223158) = c_Groups_Oplus__class_Oplus(_223158, _223160, _223160), -(_223160 = c_Groups_Ozero__class_Ozero(_223158))], (7276 ^ _113251) ^ [] : [_223160 = c_Groups_Ozero__class_Ozero(_223158), -(c_Groups_Ozero__class_Ozero(_223158) = c_Groups_Oplus__class_Oplus(_223158, _223160, _223160))]]], (7282 ^ _113251) ^ [_223387, _223389] : [class_Groups_Ocomm__monoid__add(_223387), -(c_Groups_Oplus__class_Oplus(_223387, c_Groups_Ozero__class_Ozero(_223387), _223389) = _223389)], (7288 ^ _113251) ^ [_223474, _223476] : [class_Groups_Omonoid__add(_223474), -(c_Groups_Oplus__class_Oplus(_223474, c_Groups_Ozero__class_Ozero(_223474), _223476) = _223476)], (7294 ^ _113251) ^ [_223561, _223563, _223565, _223567] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_223561), c_Orderings_Oord__class_Oless(_223561, c_Groups_Oplus__class_Oplus(_223561, _223563, _223565), c_Groups_Oplus__class_Oplus(_223561, _223563, _223567)), -(c_Orderings_Oord__class_Oless(_223561, _223565, _223567))], (7304 ^ _113251) ^ [_223716, _223718, _223720, _223722] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_223716), c_Orderings_Oord__class_Oless(_223716, c_Groups_Oplus__class_Oplus(_223716, _223718, _223720), c_Groups_Oplus__class_Oplus(_223716, _223722, _223720)), -(c_Orderings_Oord__class_Oless(_223716, _223718, _223722))], (7314 ^ _113251) ^ [_223871, _223873, _223875, _223877, _223879] : [class_Groups_Oordered__cancel__ab__semigroup__add(_223871), c_Orderings_Oord__class_Oless(_223871, _223873, _223875), c_Orderings_Oord__class_Oless(_223871, _223877, _223879), -(c_Orderings_Oord__class_Oless(_223871, c_Groups_Oplus__class_Oplus(_223871, _223873, _223877), c_Groups_Oplus__class_Oplus(_223871, _223875, _223879)))], (7328 ^ _113251) ^ [_224090, _224092, _224094, _224096] : [class_Groups_Oordered__cancel__ab__semigroup__add(_224090), c_Orderings_Oord__class_Oless(_224090, _224092, _224094), -(c_Orderings_Oord__class_Oless(_224090, c_Groups_Oplus__class_Oplus(_224090, _224096, _224092), c_Groups_Oplus__class_Oplus(_224090, _224096, _224094)))], (7338 ^ _113251) ^ [_224245, _224247, _224249, _224251] : [class_Groups_Oordered__cancel__ab__semigroup__add(_224245), c_Orderings_Oord__class_Oless(_224245, _224247, _224249), -(c_Orderings_Oord__class_Oless(_224245, c_Groups_Oplus__class_Oplus(_224245, _224247, _224251), c_Groups_Oplus__class_Oplus(_224245, _224249, _224251)))], (7348 ^ _113251) ^ [_224400, _224402, _224404, _224406] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_224400), 7351 ^ _113251 : [(7352 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_224400, c_Groups_Oplus__class_Oplus(_224400, _224402, _224404), c_Groups_Oplus__class_Oplus(_224400, _224402, _224406)), -(c_Orderings_Oord__class_Oless(_224400, _224404, _224406))], (7358 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_224400, _224404, _224406), -(c_Orderings_Oord__class_Oless(_224400, c_Groups_Oplus__class_Oplus(_224400, _224402, _224404), c_Groups_Oplus__class_Oplus(_224400, _224402, _224406)))]]], (7364 ^ _113251) ^ [_224647, _224649, _224651, _224653] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_224647), 7367 ^ _113251 : [(7368 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_224647, c_Groups_Oplus__class_Oplus(_224647, _224649, _224651), c_Groups_Oplus__class_Oplus(_224647, _224653, _224651)), -(c_Orderings_Oord__class_Oless(_224647, _224649, _224653))], (7374 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_224647, _224649, _224653), -(c_Orderings_Oord__class_Oless(_224647, c_Groups_Oplus__class_Oplus(_224647, _224649, _224651), c_Groups_Oplus__class_Oplus(_224647, _224653, _224651)))]]], (7380 ^ _113251) ^ [_224894, _224896, _224898, _224900, _224902] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_224894), 7383 ^ _113251 : [(7394 ^ _113251) ^ [] : [7395 ^ _113251 : [(7396 ^ _113251) ^ [] : [_224896 = _224900], (7398 ^ _113251) ^ [] : [_224898 = _224902]], -(c_Groups_Oplus__class_Oplus(_224894, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_224894), _224896), _224898), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_224894), _224900), _224902)) = c_Groups_Oplus__class_Oplus(_224894, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_224894), _224896), _224902), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_224894), _224900), _224898)))], (7384 ^ _113251) ^ [] : [c_Groups_Oplus__class_Oplus(_224894, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_224894), _224896), _224898), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_224894), _224900), _224902)) = c_Groups_Oplus__class_Oplus(_224894, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_224894), _224896), _224902), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_224894), _224900), _224898)), -(_224896 = _224900), -(_224898 = _224902)]]], (7402 ^ _113251) ^ [_225282, _225284, _225286, _225288, _225290] : [class_Rings_Osemiring(_225282), -(c_Groups_Oplus__class_Oplus(_225282, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225282), _225284), _225286), c_Groups_Oplus__class_Oplus(_225282, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225282), _225288), _225286), _225290)) = c_Groups_Oplus__class_Oplus(_225282, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225282), c_Groups_Oplus__class_Oplus(_225282, _225284, _225288)), _225286), _225290))], (7408 ^ _113251) ^ [_225443, _225445, _225447, _225449] : [class_Rings_Ocomm__semiring__1(_225443), -(c_Groups_Oplus__class_Oplus(_225443, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225443), _225445), _225447), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225443), _225449), _225447)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225443), c_Groups_Oplus__class_Oplus(_225443, _225445, _225449)), _225447))], (7414 ^ _113251) ^ [_225586, _225588, _225590, _225592] : [class_Rings_Ocomm__semiring__1(_225586), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225586), c_Groups_Oplus__class_Oplus(_225586, _225588, _225590)), _225592) = c_Groups_Oplus__class_Oplus(_225586, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225586), _225588), _225592), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225586), _225590), _225592)))], (7420 ^ _113251) ^ [_225729, _225731, _225733, _225735] : [class_Rings_Ocomm__semiring(_225729), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225729), c_Groups_Oplus__class_Oplus(_225729, _225731, _225733)), _225735) = c_Groups_Oplus__class_Oplus(_225729, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225729), _225731), _225735), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225729), _225733), _225735)))], (7426 ^ _113251) ^ [_225872, _225874, _225876, _225878, _225880] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_225872), 7429 ^ _113251 : [(7440 ^ _113251) ^ [] : [-(c_Groups_Oplus__class_Oplus(_225872, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225872), _225874), _225878), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225872), _225876), _225880)) = c_Groups_Oplus__class_Oplus(_225872, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225872), _225874), _225880), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225872), _225876), _225878))), 7443 ^ _113251 : [(7444 ^ _113251) ^ [] : [_225874 = _225876], (7446 ^ _113251) ^ [] : [_225878 = _225880]]], (7430 ^ _113251) ^ [] : [c_Groups_Oplus__class_Oplus(_225872, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225872), _225874), _225878), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225872), _225876), _225880)) = c_Groups_Oplus__class_Oplus(_225872, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225872), _225874), _225880), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_225872), _225876), _225878)), -(_225874 = _225876), -(_225878 = _225880)]]], (7448 ^ _113251) ^ [_226266, _226268, _226270, _226272] : [class_Rings_Ocomm__semiring__1(_226266), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_226266), _226268), c_Groups_Oplus__class_Oplus(_226266, _226270, _226272)) = c_Groups_Oplus__class_Oplus(_226266, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_226266), _226268), _226270), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_226266), _226268), _226272)))], (7454 ^ _113251) ^ [_226409, _226411, _226413, _226415] : [class_RealVector_Oreal__normed__algebra(_226409), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_226409), c_Groups_Oplus__class_Oplus(_226409, _226411, _226413)), _226415) = c_Groups_Oplus__class_Oplus(_226409, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_226409), _226411), _226415), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_226409), _226413), _226415)))], (7460 ^ _113251) ^ [_226552, _226554, _226556, _226558] : [class_RealVector_Oreal__normed__algebra(_226552), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_226552), c_Groups_Oplus__class_Oplus(_226552, _226554, _226556)), _226558) = c_Groups_Oplus__class_Oplus(_226552, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_226552), _226554), _226558), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_226552), _226556), _226558)))], (7466 ^ _113251) ^ [_226695, _226697, _226699, _226701] : [class_RealVector_Oreal__normed__algebra(_226695), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_226695), _226697), c_Groups_Oplus__class_Oplus(_226695, _226699, _226701)) = c_Groups_Oplus__class_Oplus(_226695, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_226695), _226697), _226699), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_226695), _226697), _226701)))], (7472 ^ _113251) ^ [_226838, _226840, _226842, _226844] : [class_RealVector_Oreal__normed__algebra(_226838), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_226838), _226840), c_Groups_Oplus__class_Oplus(_226838, _226842, _226844)) = c_Groups_Oplus__class_Oplus(_226838, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_226838), _226840), _226842), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_226838), _226840), _226844)))], (7478 ^ _113251) ^ [_226981, _226983, _226985] : [class_Groups_Ogroup__add(_226981), -(c_Groups_Oplus__class_Oplus(_226981, c_Groups_Ouminus__class_Ouminus(_226981, _226983), c_Groups_Oplus__class_Oplus(_226981, _226983, _226985)) = _226985)], (7484 ^ _113251) ^ [_227080, _227082, _227084] : [class_Groups_Ogroup__add(_227080), -(c_Groups_Oplus__class_Oplus(_227080, _227082, c_Groups_Oplus__class_Oplus(_227080, c_Groups_Ouminus__class_Ouminus(_227080, _227082), _227084)) = _227084)], (7490 ^ _113251) ^ [_227179, _227181, _227183] : [class_Groups_Ogroup__add(_227179), -(c_Groups_Ouminus__class_Ouminus(_227179, c_Groups_Oplus__class_Oplus(_227179, _227181, _227183)) = c_Groups_Oplus__class_Oplus(_227179, c_Groups_Ouminus__class_Ouminus(_227179, _227183), c_Groups_Ouminus__class_Ouminus(_227179, _227181)))], (7496 ^ _113251) ^ [_227290, _227292, _227294] : [class_Groups_Oab__group__add(_227290), -(c_Groups_Ouminus__class_Ouminus(_227290, c_Groups_Oplus__class_Oplus(_227290, _227292, _227294)) = c_Groups_Oplus__class_Oplus(_227290, c_Groups_Ouminus__class_Ouminus(_227290, _227292), c_Groups_Ouminus__class_Ouminus(_227290, _227294)))], (7502 ^ _113251) ^ [_227401, _227403, _227405, _227407] : [class_Groups_Ocomm__monoid__add(_227401), -(hAPP(c_Polynomial_Ocoeff(_227401, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_227401), _227403, _227405)), _227407) = c_Groups_Oplus__class_Oplus(_227401, hAPP(c_Polynomial_Ocoeff(_227401, _227403), _227407), hAPP(c_Polynomial_Ocoeff(_227401, _227405), _227407)))], (7508 ^ _113251) ^ [_227536, _227538, _227540, _227542] : [class_Groups_Ocomm__monoid__add(_227536), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_227536), c_Polynomial_Omonom(_227536, _227538, _227540), c_Polynomial_Omonom(_227536, _227542, _227540)) = c_Polynomial_Omonom(_227536, c_Groups_Oplus__class_Oplus(_227536, _227538, _227542), _227540))], (7514 ^ _113251) ^ [_227659, _227661, _227663, _227665] : [class_Rings_Ocomm__semiring__1(_227659), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_227659), _227661), _227663)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_227659), _227661), _227665)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_227659), _227661), c_Groups_Oplus__class_Oplus(_227659, _227663, _227665))))], (7528 ^ _113251) ^ [_227900, _227902, _227904, _227906] : [class_Groups_Ocancel__semigroup__add(_227900), c_Groups_Oplus__class_Oplus(_227900, _227902, _227904) = c_Groups_Oplus__class_Oplus(_227900, _227906, _227904), -(_227902 = _227906)], (7538 ^ _113251) ^ [_228051, _228053, _228055, _228057] : [class_Groups_Ocancel__ab__semigroup__add(_228051), c_Groups_Oplus__class_Oplus(_228051, _228053, _228055) = c_Groups_Oplus__class_Oplus(_228051, _228053, _228057), -(_228055 = _228057)], (7548 ^ _113251) ^ [_228202, _228204, _228206, _228208] : [class_Groups_Ocancel__semigroup__add(_228202), c_Groups_Oplus__class_Oplus(_228202, _228204, _228206) = c_Groups_Oplus__class_Oplus(_228202, _228204, _228208), -(_228206 = _228208)], (7558 ^ _113251) ^ [_228353, _228355, _228357, _228359] : [class_Groups_Ocancel__semigroup__add(_228353), 7561 ^ _113251 : [(7562 ^ _113251) ^ [] : [c_Groups_Oplus__class_Oplus(_228353, _228355, _228357) = c_Groups_Oplus__class_Oplus(_228353, _228359, _228357), -(_228355 = _228359)], (7568 ^ _113251) ^ [] : [_228355 = _228359, -(c_Groups_Oplus__class_Oplus(_228353, _228355, _228357) = c_Groups_Oplus__class_Oplus(_228353, _228359, _228357))]]], (7574 ^ _113251) ^ [_228594, _228596, _228598, _228600] : [class_Groups_Ocancel__semigroup__add(_228594), 7577 ^ _113251 : [(7578 ^ _113251) ^ [] : [c_Groups_Oplus__class_Oplus(_228594, _228596, _228598) = c_Groups_Oplus__class_Oplus(_228594, _228596, _228600), -(_228598 = _228600)], (7584 ^ _113251) ^ [] : [_228598 = _228600, -(c_Groups_Oplus__class_Oplus(_228594, _228596, _228598) = c_Groups_Oplus__class_Oplus(_228594, _228596, _228600))]]], (7590 ^ _113251) ^ [_228835, _228837, _228839, _228841] : [class_Groups_Oab__semigroup__add(_228835), -(c_Groups_Oplus__class_Oplus(_228835, c_Groups_Oplus__class_Oplus(_228835, _228837, _228839), _228841) = c_Groups_Oplus__class_Oplus(_228835, _228837, c_Groups_Oplus__class_Oplus(_228835, _228839, _228841)))], (7596 ^ _113251) ^ [_228946, _228948, _228950, _228952, _228954] : [class_Rings_Ocomm__semiring__1(_228946), -(c_Groups_Oplus__class_Oplus(_228946, c_Groups_Oplus__class_Oplus(_228946, _228948, _228950), c_Groups_Oplus__class_Oplus(_228946, _228952, _228954)) = c_Groups_Oplus__class_Oplus(_228946, c_Groups_Oplus__class_Oplus(_228946, _228948, _228952), c_Groups_Oplus__class_Oplus(_228946, _228950, _228954)))], (7602 ^ _113251) ^ [_229075, _229077, _229079, _229081] : [class_Rings_Ocomm__semiring__1(_229075), -(c_Groups_Oplus__class_Oplus(_229075, c_Groups_Oplus__class_Oplus(_229075, _229077, _229079), _229081) = c_Groups_Oplus__class_Oplus(_229075, c_Groups_Oplus__class_Oplus(_229075, _229077, _229081), _229079))], (7608 ^ _113251) ^ [_229186, _229188, _229190, _229192] : [class_Rings_Ocomm__semiring__1(_229186), -(c_Groups_Oplus__class_Oplus(_229186, c_Groups_Oplus__class_Oplus(_229186, _229188, _229190), _229192) = c_Groups_Oplus__class_Oplus(_229186, _229188, c_Groups_Oplus__class_Oplus(_229186, _229190, _229192)))], (7614 ^ _113251) ^ [_229297, _229299, _229301, _229303] : [class_Rings_Ocomm__semiring__1(_229297), -(c_Groups_Oplus__class_Oplus(_229297, _229299, c_Groups_Oplus__class_Oplus(_229297, _229301, _229303)) = c_Groups_Oplus__class_Oplus(_229297, c_Groups_Oplus__class_Oplus(_229297, _229299, _229301), _229303))], (7620 ^ _113251) ^ [_229408, _229410, _229412, _229414] : [class_Rings_Ocomm__semiring__1(_229408), -(c_Groups_Oplus__class_Oplus(_229408, _229410, c_Groups_Oplus__class_Oplus(_229408, _229412, _229414)) = c_Groups_Oplus__class_Oplus(_229408, _229412, c_Groups_Oplus__class_Oplus(_229408, _229410, _229414)))], (7626 ^ _113251) ^ [_229519, _229521, _229523] : [class_Rings_Ocomm__semiring__1(_229519), -(c_Groups_Oplus__class_Oplus(_229519, _229521, _229523) = c_Groups_Oplus__class_Oplus(_229519, _229523, _229521))], (7632 ^ _113251) ^ [_229612, _229614, _229616, _229618] : [class_Rings_Ocomm__semiring__0(_229612), -(hAPP(c_Polynomial_Opoly(_229612, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_229612), _229614, _229616)), _229618) = c_Groups_Oplus__class_Oplus(_229612, hAPP(c_Polynomial_Opoly(_229612, _229614), _229618), hAPP(c_Polynomial_Opoly(_229612, _229616), _229618)))], (7638 ^ _113251) ^ [_229747, _229749, _229751, _229753, _229755] : [class_Groups_Ocomm__monoid__add(_229747), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_229747), c_Polynomial_OpCons(_229747, _229749, _229751), c_Polynomial_OpCons(_229747, _229753, _229755)) = c_Polynomial_OpCons(_229747, c_Groups_Oplus__class_Oplus(_229747, _229749, _229753), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_229747), _229751, _229755)))], (7644 ^ _113251) ^ [_229884, _229886, _229888] : [class_Rings_Olinordered__idom(_229884), c_Polynomial_Opos__poly(_229884, _229886), c_Polynomial_Opos__poly(_229884, _229888), -(c_Polynomial_Opos__poly(_229884, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_229884), _229886, _229888)))], (7658 ^ _113251) ^ [_230081, _230083] : [class_Groups_Olinordered__ab__group__add(_230081), 7661 ^ _113251 : [(7662 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_230081, c_Groups_Ozero__class_Ozero(_230081), c_Groups_Oplus__class_Oplus(_230081, _230083, _230083)), -(c_Orderings_Oord__class_Oless__eq(_230081, c_Groups_Ozero__class_Ozero(_230081), _230083))], (7668 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_230081, c_Groups_Ozero__class_Ozero(_230081), _230083), -(c_Orderings_Oord__class_Oless__eq(_230081, c_Groups_Ozero__class_Ozero(_230081), c_Groups_Oplus__class_Oplus(_230081, _230083, _230083)))]]], (7674 ^ _113251) ^ [_230316, _230318] : [class_Groups_Olinordered__ab__group__add(_230316), 7677 ^ _113251 : [(7678 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_230316, c_Groups_Oplus__class_Oplus(_230316, _230318, _230318), c_Groups_Ozero__class_Ozero(_230316)), -(c_Orderings_Oord__class_Oless__eq(_230316, _230318, c_Groups_Ozero__class_Ozero(_230316)))], (7684 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_230316, _230318, c_Groups_Ozero__class_Ozero(_230316)), -(c_Orderings_Oord__class_Oless__eq(_230316, c_Groups_Oplus__class_Oplus(_230316, _230318, _230318), c_Groups_Ozero__class_Ozero(_230316)))]]], (7690 ^ _113251) ^ [_230551, _230553, _230555] : [class_Groups_Oordered__comm__monoid__add(_230551), c_Orderings_Oord__class_Oless__eq(_230551, c_Groups_Ozero__class_Ozero(_230551), _230553), c_Orderings_Oord__class_Oless__eq(_230551, c_Groups_Ozero__class_Ozero(_230551), _230555), -(c_Orderings_Oord__class_Oless__eq(_230551, c_Groups_Ozero__class_Ozero(_230551), c_Groups_Oplus__class_Oplus(_230551, _230553, _230555)))], (7704 ^ _113251) ^ [_230762, _230764, _230766] : [class_Groups_Oordered__comm__monoid__add(_230762), c_Orderings_Oord__class_Oless__eq(_230762, c_Groups_Ozero__class_Ozero(_230762), _230764), c_Orderings_Oord__class_Oless__eq(_230762, c_Groups_Ozero__class_Ozero(_230762), _230766), 7715 ^ _113251 : [(7716 ^ _113251) ^ [] : [c_Groups_Oplus__class_Oplus(_230762, _230764, _230766) = c_Groups_Ozero__class_Ozero(_230762), 7719 ^ _113251 : [(7720 ^ _113251) ^ [] : [-(_230764 = c_Groups_Ozero__class_Ozero(_230762))], (7722 ^ _113251) ^ [] : [-(_230766 = c_Groups_Ozero__class_Ozero(_230762))]]], (7724 ^ _113251) ^ [] : [-(c_Groups_Oplus__class_Oplus(_230762, _230764, _230766) = c_Groups_Ozero__class_Ozero(_230762)), _230764 = c_Groups_Ozero__class_Ozero(_230762), _230766 = c_Groups_Ozero__class_Ozero(_230762)]]], (7734 ^ _113251) ^ [_231197, _231199, _231201, _231203] : [class_Groups_Oordered__comm__monoid__add(_231197), c_Orderings_Oord__class_Oless__eq(_231197, c_Groups_Ozero__class_Ozero(_231197), _231199), c_Orderings_Oord__class_Oless__eq(_231197, _231201, _231203), -(c_Orderings_Oord__class_Oless__eq(_231197, _231201, c_Groups_Oplus__class_Oplus(_231197, _231199, _231203)))], (7748 ^ _113251) ^ [_231406, _231408, _231410, _231412] : [class_Groups_Oordered__comm__monoid__add(_231406), c_Orderings_Oord__class_Oless__eq(_231406, c_Groups_Ozero__class_Ozero(_231406), _231408), c_Orderings_Oord__class_Oless__eq(_231406, _231410, _231412), -(c_Orderings_Oord__class_Oless__eq(_231406, _231410, c_Groups_Oplus__class_Oplus(_231406, _231412, _231408)))], (7762 ^ _113251) ^ [_231615, _231617, _231619] : [class_Groups_Oordered__comm__monoid__add(_231615), c_Orderings_Oord__class_Oless__eq(_231615, _231617, c_Groups_Ozero__class_Ozero(_231615)), c_Orderings_Oord__class_Oless__eq(_231615, _231619, c_Groups_Ozero__class_Ozero(_231615)), -(c_Orderings_Oord__class_Oless__eq(_231615, c_Groups_Oplus__class_Oplus(_231615, _231617, _231619), c_Groups_Ozero__class_Ozero(_231615)))], (7776 ^ _113251) ^ [_231826, _231828] : [class_Rings_Olinordered__idom(_231826), 7779 ^ _113251 : [(7780 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_231826, c_Groups_Oplus__class_Oplus(_231826, _231828, _231828), c_Groups_Ozero__class_Ozero(_231826)), -(c_Orderings_Oord__class_Oless(_231826, _231828, c_Groups_Ozero__class_Ozero(_231826)))], (7786 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_231826, _231828, c_Groups_Ozero__class_Ozero(_231826)), -(c_Orderings_Oord__class_Oless(_231826, c_Groups_Oplus__class_Oplus(_231826, _231828, _231828), c_Groups_Ozero__class_Ozero(_231826)))]]], (7792 ^ _113251) ^ [_232061, _232063] : [class_Groups_Olinordered__ab__group__add(_232061), 7795 ^ _113251 : [(7796 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_232061, c_Groups_Ozero__class_Ozero(_232061), c_Groups_Oplus__class_Oplus(_232061, _232063, _232063)), -(c_Orderings_Oord__class_Oless(_232061, c_Groups_Ozero__class_Ozero(_232061), _232063))], (7802 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_232061, c_Groups_Ozero__class_Ozero(_232061), _232063), -(c_Orderings_Oord__class_Oless(_232061, c_Groups_Ozero__class_Ozero(_232061), c_Groups_Oplus__class_Oplus(_232061, _232063, _232063)))]]], (7808 ^ _113251) ^ [_232296, _232298] : [class_Groups_Olinordered__ab__group__add(_232296), 7811 ^ _113251 : [(7812 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_232296, c_Groups_Oplus__class_Oplus(_232296, _232298, _232298), c_Groups_Ozero__class_Ozero(_232296)), -(c_Orderings_Oord__class_Oless(_232296, _232298, c_Groups_Ozero__class_Ozero(_232296)))], (7818 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_232296, _232298, c_Groups_Ozero__class_Ozero(_232296)), -(c_Orderings_Oord__class_Oless(_232296, c_Groups_Oplus__class_Oplus(_232296, _232298, _232298), c_Groups_Ozero__class_Ozero(_232296)))]]], (7824 ^ _113251) ^ [_232531, _232533, _232535] : [class_Groups_Oordered__comm__monoid__add(_232531), c_Orderings_Oord__class_Oless(_232531, c_Groups_Ozero__class_Ozero(_232531), _232533), c_Orderings_Oord__class_Oless(_232531, c_Groups_Ozero__class_Ozero(_232531), _232535), -(c_Orderings_Oord__class_Oless(_232531, c_Groups_Ozero__class_Ozero(_232531), c_Groups_Oplus__class_Oplus(_232531, _232533, _232535)))], (7838 ^ _113251) ^ [_232742, _232744, _232746] : [class_Groups_Oordered__comm__monoid__add(_232742), c_Orderings_Oord__class_Oless(_232742, _232744, c_Groups_Ozero__class_Ozero(_232742)), c_Orderings_Oord__class_Oless(_232742, _232746, c_Groups_Ozero__class_Ozero(_232742)), -(c_Orderings_Oord__class_Oless(_232742, c_Groups_Oplus__class_Oplus(_232742, _232744, _232746), c_Groups_Ozero__class_Ozero(_232742)))], (7852 ^ _113251) ^ [_232953, _232955, _232957, _232959] : [class_Rings_Olinordered__semidom(_232953), c_Orderings_Oord__class_Oless(_232953, c_Groups_Ozero__class_Ozero(_232953), _232955), c_Orderings_Oord__class_Oless(_232953, _232957, _232959), -(c_Orderings_Oord__class_Oless(_232953, _232957, c_Groups_Oplus__class_Oplus(_232953, _232955, _232959)))], (7866 ^ _113251) ^ [_233162, _233164, _233166] : [class_Rings_Odvd(_233162), class_Rings_Osemiring__0(_233162), 7873 ^ _113251 : [(7874 ^ _113251) ^ [] : [7875 ^ _113251 : [(7876 ^ _113251) ^ [_233350] : [hBOOL(hAPP(_233164, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_233162), _233166), _233350)))]], 7878 ^ _113251 : [(7879 ^ _113251) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_233162), _233166), c_Groups_Oplus__class_Oplus(_233162, 7877 ^ [_233162, _233164, _233166], c_Groups_Ozero__class_Ozero(_233162)))))], (7881 ^ _113251) ^ [] : [-(hBOOL(hAPP(_233164, 7877 ^ [_233162, _233164, _233166])))]]], (7883 ^ _113251) ^ [] : [-(hBOOL(hAPP(_233164, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_233162), _233166), 7890 ^ [_233162, _233164, _233166])))), 7884 ^ _113251 : [(7885 ^ _113251) ^ [_233483] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_233162), _233166), c_Groups_Oplus__class_Oplus(_233162, _233483, c_Groups_Ozero__class_Ozero(_233162)))), hBOOL(hAPP(_233164, _233483))]]]]], (7894 ^ _113251) ^ [_233648, _233650, _233652, _233654, _233656] : [class_Groups_Oordered__cancel__ab__semigroup__add(_233648), c_Orderings_Oord__class_Oless(_233648, _233650, _233652), c_Orderings_Oord__class_Oless__eq(_233648, _233654, _233656), -(c_Orderings_Oord__class_Oless(_233648, c_Groups_Oplus__class_Oplus(_233648, _233650, _233654), c_Groups_Oplus__class_Oplus(_233648, _233652, _233656)))], (7908 ^ _113251) ^ [_233867, _233869, _233871, _233873, _233875] : [class_Groups_Oordered__cancel__ab__semigroup__add(_233867), c_Orderings_Oord__class_Oless__eq(_233867, _233869, _233871), c_Orderings_Oord__class_Oless(_233867, _233873, _233875), -(c_Orderings_Oord__class_Oless(_233867, c_Groups_Oplus__class_Oplus(_233867, _233869, _233873), c_Groups_Oplus__class_Oplus(_233867, _233871, _233875)))], (7922 ^ _113251) ^ [_234086, _234088, _234090, _234092, _234094, _234096] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_234086), -(_234088 = c_Groups_Ozero__class_Ozero(_234086)), c_Groups_Oplus__class_Oplus(_234086, _234090, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_234086), _234088), _234094)) = c_Groups_Oplus__class_Oplus(_234086, _234092, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_234086), _234088), _234096)), _234090 = _234092, -(_234094 = _234096)], (7940 ^ _113251) ^ [_234408, _234410, _234412] : [class_Rings_Olinordered__ring__strict(_234408), 7943 ^ _113251 : [(7944 ^ _113251) ^ [] : [c_Groups_Oplus__class_Oplus(_234408, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_234408), _234410), _234410), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_234408), _234412), _234412)) = c_Groups_Ozero__class_Ozero(_234408), 7947 ^ _113251 : [(7948 ^ _113251) ^ [] : [-(_234410 = c_Groups_Ozero__class_Ozero(_234408))], (7950 ^ _113251) ^ [] : [-(_234412 = c_Groups_Ozero__class_Ozero(_234408))]]], (7952 ^ _113251) ^ [] : [-(c_Groups_Oplus__class_Oplus(_234408, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_234408), _234410), _234410), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_234408), _234412), _234412)) = c_Groups_Ozero__class_Ozero(_234408)), _234410 = c_Groups_Ozero__class_Ozero(_234408), _234412 = c_Groups_Ozero__class_Ozero(_234408)]]], (7962 ^ _113251) ^ [_234771, _234773] : [class_Rings_Olinordered__semidom(_234771), -(c_Orderings_Oord__class_Oless(_234771, _234773, c_Groups_Oplus__class_Oplus(_234771, _234773, c_Groups_Oone__class_Oone(_234771))))], (7968 ^ _113251) ^ [_234860, _234862, _234864] : [class_Groups_Ogroup__add(_234860), c_Groups_Oplus__class_Oplus(_234860, _234862, _234864) = c_Groups_Ozero__class_Ozero(_234860), -(c_Groups_Ouminus__class_Ouminus(_234860, _234862) = _234864)], (7978 ^ _113251) ^ [_235009, _235011] : [class_Groups_Oab__group__add(_235009), -(c_Groups_Oplus__class_Oplus(_235009, c_Groups_Ouminus__class_Ouminus(_235009, _235011), _235011) = c_Groups_Ozero__class_Ozero(_235009))], (7984 ^ _113251) ^ [_235102, _235104] : [class_Groups_Ogroup__add(_235102), -(c_Groups_Oplus__class_Oplus(_235102, c_Groups_Ouminus__class_Ouminus(_235102, _235104), _235104) = c_Groups_Ozero__class_Ozero(_235102))], (7990 ^ _113251) ^ [_235195, _235197, _235199] : [class_Groups_Ogroup__add(_235195), 7993 ^ _113251 : [(7994 ^ _113251) ^ [] : [_235197 = c_Groups_Ouminus__class_Ouminus(_235195, _235199), -(c_Groups_Oplus__class_Oplus(_235195, _235197, _235199) = c_Groups_Ozero__class_Ozero(_235195))], (8000 ^ _113251) ^ [] : [c_Groups_Oplus__class_Oplus(_235195, _235197, _235199) = c_Groups_Ozero__class_Ozero(_235195), -(_235197 = c_Groups_Ouminus__class_Ouminus(_235195, _235199))]]], (8006 ^ _113251) ^ [_235433, _235435] : [class_Groups_Ogroup__add(_235433), -(c_Groups_Oplus__class_Oplus(_235433, _235435, c_Groups_Ouminus__class_Ouminus(_235433, _235435)) = c_Groups_Ozero__class_Ozero(_235433))], (8012 ^ _113251) ^ [_235526, _235528, _235530] : [class_Groups_Ogroup__add(_235526), 8015 ^ _113251 : [(8016 ^ _113251) ^ [] : [c_Groups_Oplus__class_Oplus(_235526, _235528, _235530) = c_Groups_Ozero__class_Ozero(_235526), -(_235530 = c_Groups_Ouminus__class_Ouminus(_235526, _235528))], (8022 ^ _113251) ^ [] : [_235530 = c_Groups_Ouminus__class_Ouminus(_235526, _235528), -(c_Groups_Oplus__class_Oplus(_235526, _235528, _235530) = c_Groups_Ozero__class_Ozero(_235526))]]], (8028 ^ _113251) ^ [_235764, _235766, _235768] : [class_Rings_Ocomm__semiring__1(_235764), -(c_Groups_Oplus__class_Oplus(_235764, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_235764), _235766), _235768), _235768) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_235764), c_Groups_Oplus__class_Oplus(_235764, _235766, c_Groups_Oone__class_Oone(_235764))), _235768))], (8034 ^ _113251) ^ [_235893, _235895, _235897] : [class_Rings_Ocomm__semiring__1(_235893), -(c_Groups_Oplus__class_Oplus(_235893, _235895, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_235893), _235897), _235895)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_235893), c_Groups_Oplus__class_Oplus(_235893, _235897, c_Groups_Oone__class_Oone(_235893))), _235895))], (8040 ^ _113251) ^ [_236022, _236024] : [class_Rings_Ocomm__semiring__1(_236022), -(c_Groups_Oplus__class_Oplus(_236022, _236024, _236024) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_236022), c_Groups_Oplus__class_Oplus(_236022, c_Groups_Oone__class_Oone(_236022), c_Groups_Oone__class_Oone(_236022))), _236024))], (8046 ^ _113251) ^ [_236137, _236139, _236141, _236143] : [class_Groups_Ocomm__monoid__add(_236137), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_236137, _236139), _236141), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_236137, _236143), _236141), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_236137, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_236137), _236139, _236143)), _236141))], (8060 ^ _113251) ^ [_236364, _236366, _236368] : [class_Groups_Ocomm__monoid__add(_236364), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_236364, _236366), c_Polynomial_Odegree(_236364, _236368)), -(c_Polynomial_Odegree(_236364, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_236364), _236366, _236368)) = c_Polynomial_Odegree(_236364, _236368))], (8070 ^ _113251) ^ [_236533, _236535, _236537] : [class_Groups_Ocomm__monoid__add(_236533), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_236533, _236535), c_Polynomial_Odegree(_236533, _236537)), -(c_Polynomial_Odegree(_236533, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_236533), _236537, _236535)) = c_Polynomial_Odegree(_236533, _236537))], (8080 ^ _113251) ^ [_236702, _236704, _236706, _236708] : [class_Groups_Ocomm__monoid__add(_236702), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_236702, _236704), _236706), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_236702, _236708), _236706), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_236702, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_236702), _236704, _236708)), _236706))], (8094 ^ _113251) ^ [_236929, _236931, _236933] : [class_Groups_Oordered__comm__monoid__add(_236929), c_Orderings_Oord__class_Oless(_236929, c_Groups_Ozero__class_Ozero(_236929), _236931), c_Orderings_Oord__class_Oless__eq(_236929, c_Groups_Ozero__class_Ozero(_236929), _236933), -(c_Orderings_Oord__class_Oless(_236929, c_Groups_Ozero__class_Ozero(_236929), c_Groups_Oplus__class_Oplus(_236929, _236931, _236933)))], (8108 ^ _113251) ^ [_237140, _237142, _237144] : [class_Groups_Oordered__comm__monoid__add(_237140), c_Orderings_Oord__class_Oless__eq(_237140, c_Groups_Ozero__class_Ozero(_237140), _237142), c_Orderings_Oord__class_Oless(_237140, c_Groups_Ozero__class_Ozero(_237140), _237144), -(c_Orderings_Oord__class_Oless(_237140, c_Groups_Ozero__class_Ozero(_237140), c_Groups_Oplus__class_Oplus(_237140, _237142, _237144)))], (8122 ^ _113251) ^ [_237351, _237353, _237355, _237357] : [class_Groups_Oordered__comm__monoid__add(_237351), c_Orderings_Oord__class_Oless(_237351, c_Groups_Ozero__class_Ozero(_237351), _237353), c_Orderings_Oord__class_Oless__eq(_237351, _237355, _237357), -(c_Orderings_Oord__class_Oless(_237351, _237355, c_Groups_Oplus__class_Oplus(_237351, _237353, _237357)))], (8136 ^ _113251) ^ [_237560, _237562, _237564, _237566] : [class_Groups_Oordered__comm__monoid__add(_237560), c_Orderings_Oord__class_Oless__eq(_237560, c_Groups_Ozero__class_Ozero(_237560), _237562), c_Orderings_Oord__class_Oless(_237560, _237564, _237566), -(c_Orderings_Oord__class_Oless(_237560, _237564, c_Groups_Oplus__class_Oplus(_237560, _237562, _237566)))], (8150 ^ _113251) ^ [_237769, _237771, _237773] : [class_Groups_Oordered__comm__monoid__add(_237769), c_Orderings_Oord__class_Oless(_237769, _237771, c_Groups_Ozero__class_Ozero(_237769)), c_Orderings_Oord__class_Oless__eq(_237769, _237773, c_Groups_Ozero__class_Ozero(_237769)), -(c_Orderings_Oord__class_Oless(_237769, c_Groups_Oplus__class_Oplus(_237769, _237771, _237773), c_Groups_Ozero__class_Ozero(_237769)))], (8164 ^ _113251) ^ [_237980, _237982, _237984] : [class_Groups_Oordered__comm__monoid__add(_237980), c_Orderings_Oord__class_Oless__eq(_237980, _237982, c_Groups_Ozero__class_Ozero(_237980)), c_Orderings_Oord__class_Oless(_237980, _237984, c_Groups_Ozero__class_Ozero(_237980)), -(c_Orderings_Oord__class_Oless(_237980, c_Groups_Oplus__class_Oplus(_237980, _237982, _237984), c_Groups_Ozero__class_Ozero(_237980)))], (8178 ^ _113251) ^ [_238191, _238193, _238195] : [class_Rings_Olinordered__ring__strict(_238191), 8181 ^ _113251 : [(8182 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_238191, c_Groups_Oplus__class_Oplus(_238191, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_238191), _238193), _238193), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_238191), _238195), _238195)), c_Groups_Ozero__class_Ozero(_238191)), 8185 ^ _113251 : [(8186 ^ _113251) ^ [] : [-(_238193 = c_Groups_Ozero__class_Ozero(_238191))], (8188 ^ _113251) ^ [] : [-(_238195 = c_Groups_Ozero__class_Ozero(_238191))]]], (8190 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_238191, c_Groups_Oplus__class_Oplus(_238191, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_238191), _238193), _238193), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_238191), _238195), _238195)), c_Groups_Ozero__class_Ozero(_238191))), _238193 = c_Groups_Ozero__class_Ozero(_238191), _238195 = c_Groups_Ozero__class_Ozero(_238191)]]], (8200 ^ _113251) ^ [_238557, _238559, _238561] : [class_Rings_Olinordered__ring(_238557), -(c_Orderings_Oord__class_Oless__eq(_238557, c_Groups_Ozero__class_Ozero(_238557), c_Groups_Oplus__class_Oplus(_238557, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_238557), _238559), _238559), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_238557), _238561), _238561))))], (8206 ^ _113251) ^ [_238680, _238682, _238684] : [class_Rings_Olinordered__ring__strict(_238680), 8209 ^ _113251 : [(8220 ^ _113251) ^ [] : [8221 ^ _113251 : [(8222 ^ _113251) ^ [] : [-(_238682 = c_Groups_Ozero__class_Ozero(_238680))], (8224 ^ _113251) ^ [] : [-(_238684 = c_Groups_Ozero__class_Ozero(_238680))]], -(c_Orderings_Oord__class_Oless(_238680, c_Groups_Ozero__class_Ozero(_238680), c_Groups_Oplus__class_Oplus(_238680, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_238680), _238682), _238682), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_238680), _238684), _238684))))], (8210 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_238680, c_Groups_Ozero__class_Ozero(_238680), c_Groups_Oplus__class_Oplus(_238680, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_238680), _238682), _238682), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_238680), _238684), _238684))), _238682 = c_Groups_Ozero__class_Ozero(_238680), _238684 = c_Groups_Ozero__class_Ozero(_238680)]]], (8228 ^ _113251) ^ [_239025, _239027, _239029] : [class_Rings_Olinordered__ring(_239025), c_Orderings_Oord__class_Oless(_239025, c_Groups_Oplus__class_Oplus(_239025, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_239025), _239027), _239027), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_239025), _239029), _239029)), c_Groups_Ozero__class_Ozero(_239025))], (8234 ^ _113251) ^ [_239149] : [class_Rings_Olinordered__semidom(_239149), -(c_Orderings_Oord__class_Oless(_239149, c_Groups_Ozero__class_Ozero(_239149), c_Groups_Oplus__class_Oplus(_239149, c_Groups_Oone__class_Oone(_239149), c_Groups_Oone__class_Oone(_239149))))], (8240 ^ _113251) ^ [_239244, _239246, _239248, _239250] : [class_Rings_Ocomm__semiring__0(_239244), -(hAPP(c_Polynomial_Opoly(_239244, c_Polynomial_OpCons(_239244, _239246, _239248)), _239250) = c_Groups_Oplus__class_Oplus(_239244, _239246, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_239244), _239250), hAPP(c_Polynomial_Opoly(_239244, _239248), _239250))))], (8246 ^ _113251) ^ [_239394, _239396] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _239394), _239396)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _239394), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _239396))))], (8252 ^ _113251) ^ [_239493, _239495] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _239493), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _239495))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _239493), _239495)))], (8258 ^ _113251) ^ [_239613, _239615] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _239613), _239615)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _239613)), _239615)))], (8264 ^ _113251) ^ [_239712, _239714] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _239712)), _239714)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _239712), _239714)))], (8270 ^ _113251) ^ [_239817, _239819, _239821, _239823, _239825, _239827] : [class_Rings_Olinordered__semiring__1(_239817), c_Orderings_Oord__class_Oless__eq(_239817, _239819, _239821), c_Orderings_Oord__class_Oless__eq(_239817, _239823, _239821), c_Orderings_Oord__class_Oless__eq(_239817, c_Groups_Ozero__class_Ozero(_239817), _239825), c_Orderings_Oord__class_Oless__eq(_239817, c_Groups_Ozero__class_Ozero(_239817), _239827), c_Groups_Oplus__class_Oplus(_239817, _239825, _239827) = c_Groups_Oone__class_Oone(_239817), -(c_Orderings_Oord__class_Oless__eq(_239817, c_Groups_Oplus__class_Oplus(_239817, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_239817), _239825), _239819), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_239817), _239827), _239823)), _239821))], (8296 ^ _113251) ^ [_240270, _240272, _240274, _240276, _240278, _240280] : [class_Rings_Olinordered__semiring__1__strict(_240270), c_Orderings_Oord__class_Oless(_240270, _240272, _240274), c_Orderings_Oord__class_Oless(_240270, _240276, _240274), c_Orderings_Oord__class_Oless__eq(_240270, c_Groups_Ozero__class_Ozero(_240270), _240278), c_Orderings_Oord__class_Oless__eq(_240270, c_Groups_Ozero__class_Ozero(_240270), _240280), c_Groups_Oplus__class_Oplus(_240270, _240278, _240280) = c_Groups_Oone__class_Oone(_240270), -(c_Orderings_Oord__class_Oless(_240270, c_Groups_Oplus__class_Oplus(_240270, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_240270), _240278), _240272), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_240270), _240280), _240276)), _240274))], (8322 ^ _113251) ^ [_240723, _240725, _240727, _240729] : [class_Rings_Ocomm__semiring__0(_240723), -(c_Polynomial_Opcompose(_240723, c_Polynomial_OpCons(_240723, _240725, _240727), _240729) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_240723), c_Polynomial_OpCons(_240723, _240725, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_240723))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_240723)), _240729), c_Polynomial_Opcompose(_240723, _240727, _240729))))], (8328 ^ _113251) ^ [] : [-(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)))], (8330 ^ _113251) ^ [] : [-(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)))], (8332 ^ _113251) ^ [_240910, _240912, _240914, _240916, _240918] : [class_Fields_Ofield(_240910), 8335 ^ _113251 : [(8358 ^ _113251) ^ [] : [-(c_Polynomial_Opdivmod__rel(_240910, _240912, _240914, _240916, _240918)), _240912 = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_240910), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_240910)), _240916), _240914), _240918), 8365 ^ _113251 : [(8366 ^ _113251) ^ [] : [-(_240914 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_240910)))], (8368 ^ _113251) ^ [] : [_240916 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_240910))]], 8369 ^ _113251 : [(8370 ^ _113251) ^ [] : [_240914 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_240910))], (8372 ^ _113251) ^ [] : [_240918 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_240910))], (8374 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_240910, _240918), c_Polynomial_Odegree(_240910, _240914))]]], (8336 ^ _113251) ^ [] : [c_Polynomial_Opdivmod__rel(_240910, _240912, _240914, _240916, _240918), 8339 ^ _113251 : [(8340 ^ _113251) ^ [] : [-(_240912 = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_240910), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_240910)), _240916), _240914), _240918))], (8342 ^ _113251) ^ [] : [_240914 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_240910)), -(_240916 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_240910)))], (8348 ^ _113251) ^ [] : [-(_240914 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_240910))), -(_240918 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_240910))), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_240910, _240918), c_Polynomial_Odegree(_240910, _240914)))]]]]], (8378 ^ _113251) ^ [_241599, _241601, _241603] : [class_Groups_Ozero(_241599), 8384 ^ _113251 : [(8385 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _241601, 8383 ^ [_241599, _241601, _241603]))], (8387 ^ _113251) ^ [] : [hAPP(c_Polynomial_Ocoeff(_241599, _241603), 8383 ^ [_241599, _241601, _241603]) = c_Groups_Ozero__class_Ozero(_241599)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_241599, _241603), _241601))], (8391 ^ _113251) ^ [_241833, _241835, _241837] : [class_Fields_Ofield(_241833), 8394 ^ _113251 : [(8405 ^ _113251) ^ [] : [8406 ^ _113251 : [(8407 ^ _113251) ^ [] : [-(_241835 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_241833)))], (8409 ^ _113251) ^ [] : [-(_241837 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_241833)))]], -(hAPP(c_Polynomial_Ocoeff(_241833, c_Polynomial_Opoly__gcd(_241833, _241835, _241837)), c_Polynomial_Odegree(_241833, c_Polynomial_Opoly__gcd(_241833, _241835, _241837))) = c_Groups_Oone__class_Oone(_241833))], (8395 ^ _113251) ^ [] : [-(hAPP(c_Polynomial_Ocoeff(_241833, c_Polynomial_Opoly__gcd(_241833, _241835, _241837)), c_Polynomial_Odegree(_241833, c_Polynomial_Opoly__gcd(_241833, _241835, _241837))) = c_Groups_Ozero__class_Ozero(_241833)), _241835 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_241833)), _241837 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_241833))]]], (8413 ^ _113251) ^ [_242216, _242218, _242220] : [class_Groups_Ozero(_242216), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _242218, c_Polynomial_Odegree(_242216, _242220)), 8421 ^ _113251 : [(8422 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _242218, 8420 ^ [_242216, _242218, _242220]))], (8424 ^ _113251) ^ [] : [hAPP(c_Polynomial_Ocoeff(_242216, _242220), 8420 ^ [_242216, _242218, _242220]) = c_Groups_Ozero__class_Ozero(_242216)]]], (8426 ^ _113251) ^ [_242453, _242455, _242457] : [class_Fields_Ofield(_242453), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_242453)), c_Polynomial_Opoly__gcd(_242453, _242455, _242457)), _242457)))], (8432 ^ _113251) ^ [_242556, _242558, _242560] : [class_Fields_Ofield(_242556), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_242556)), c_Polynomial_Opoly__gcd(_242556, _242558, _242560)), _242558)))], (8438 ^ _113251) ^ [_242659, _242661, _242663] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _242659, _242661), _242663), 8441 ^ _113251 : [(8442 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _242659, _242663))], (8444 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _242661, _242663))]]], (8446 ^ _113251) ^ [_242782, _242784, _242786] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _242782, _242784), _242786), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _242782, _242786))], (8452 ^ _113251) ^ [_242873, _242875, _242877] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _242873, _242875), _242877), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _242875, _242877))], (8458 ^ _113251) ^ [_242964, _242966, _242968, _242970] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _242964, _242966), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _242968, _242970), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _242964, _242968), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _242966, _242970)))], (8468 ^ _113251) ^ [_243123, _243125, _243127] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _243123, _243125), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _243123, _243127), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _243125, _243127)))], (8474 ^ _113251) ^ [_243222, _243224, _243226] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _243222, _243224), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _243222, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _243226, _243224)))], (8480 ^ _113251) ^ [_243313, _243315, _243317] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _243313, _243315), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _243313, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _243315, _243317)))], (8486 ^ _113251) ^ [_243422, _243424, _243426] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _243422, _243424), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _243422, _243426)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _243424, _243426))], (8492 ^ _113251) ^ [_243517, _243519, _243521] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _243519, _243521), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _243517, _243519), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _243517, _243521)))], (8498 ^ _113251) ^ [_243633, _243635] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _243633, _243635), -(_243635 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _243633, 8501 ^ [_243633, _243635]))], (8505 ^ _113251) ^ [_243728, _243730] : [8506 ^ _113251 : [(8507 ^ _113251) ^ [_243772] : [_243730 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _243728, _243772)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _243728, _243730))], (8511 ^ _113251) ^ [_243830, _243832] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _243830, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _243830, _243832)))], (8513 ^ _113251) ^ [_243860, _243862] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _243860, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _243862, _243860)))], (8515 ^ _113251) ^ [_243890, _243892, _243894] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _243890, _243892), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _243894, _243890), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _243894, _243892)))], (8521 ^ _113251) ^ [_243989, _243991, _243993] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _243989, _243991), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _243989, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _243993, _243991)))], (8527 ^ _113251) ^ [_244080, _244082, _244084] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _244080, _244082), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _244080, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _244082, _244084)))], (8533 ^ _113251) ^ [_244171] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _244171) = _244171)], (8535 ^ _113251) ^ [_244198] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _244198, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _244198)], (8537 ^ _113251) ^ [_244225, _244227] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _244225, _244227)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _244225), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _244227)))], (8539 ^ _113251) ^ [_244267, _244269, _244271] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _244267), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _244269, _244271)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _244267), _244269), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _244267), _244271)))], (8541 ^ _113251) ^ [_244320, _244322, _244324] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _244320, _244322)), _244324) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _244320), _244324), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _244322), _244324)))], (8543 ^ _113251) ^ [_244373, _244375, _244377] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _244373, _244375), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _244373, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _244375, _244377)))], (8549 ^ _113251) ^ [_244464, _244466, _244468] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _244464, _244466), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _244464, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _244468, _244466)))], (8555 ^ _113251) ^ [_244555, _244557, _244559] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _244555, _244557), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _244555, _244559), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _244557, _244559)))], (8561 ^ _113251) ^ [_244654, _244656] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _244654, _244656) = _244654, -(_244656 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8567 ^ _113251) ^ [_244754, _244756] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _244754, _244756) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 8570 ^ _113251 : [(8571 ^ _113251) ^ [] : [-(_244754 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8573 ^ _113251) ^ [] : [-(_244756 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (8575 ^ _113251) ^ [_244861, _244863] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _244861, _244863) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _244861 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _244863 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (8585 ^ _113251) ^ [_245000] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _245000, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _245000)], (8587 ^ _113251) ^ [_245027] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _245027) = _245027)], (8589 ^ _113251) ^ [_245054, _245056, _245058, _245060] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _245054), _245056), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _245058), _245056), _245060)) = 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, _245054, _245058)), _245056), _245060))], (8591 ^ _113251) ^ [_245117, _245119, _245121] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _245117, _245119)), _245121) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _245117), _245121), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _245119), _245121)))], (8593 ^ _113251) ^ [_245170, _245172, _245174] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _245170), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _245172, _245174)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _245170), _245172), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _245170), _245174)))], (8595 ^ _113251) ^ [_245235, _245237] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _245235, _245237), _245235)], (8597 ^ _113251) ^ [_245277, _245279] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _245277, _245279), _245279)], (8599 ^ _113251) ^ [_245325, _245327, _245329] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _245325, _245327), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _245325, _245329)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _245327, _245329))], (8605 ^ _113251) ^ [_245420, _245422, _245424] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _245422, _245424), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _245420, _245422), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _245420, _245424)))], (8611 ^ _113251) ^ [_245521, _245523, _245525] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _245521, _245523), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _245521, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _245523, _245525)))], (8617 ^ _113251) ^ [_245612, _245614, _245616] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _245612, _245614), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _245612, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _245616, _245614)))], (8623 ^ _113251) ^ [_245703, _245705, _245707] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _245703, _245705), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _245703, _245707), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _245705, _245707)))], (8629 ^ _113251) ^ [_245802, _245804, _245806, _245808] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _245802, _245804), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _245806, _245808), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _245802, _245806), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _245804, _245808)))], (8639 ^ _113251) ^ [_245961, _245963, _245965, _245967] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _245961, _245963), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _245965, _245963) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _245961, _245967), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _245965, _245967))], (8649 ^ _113251) ^ [_246118, _246120, _246122] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _246118, _246120), _246122), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _246118, _246122))], (8655 ^ _113251) ^ [_246224, _246226] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _246224), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _246226, _246224))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _246224), _246226)))], (8661 ^ _113251) ^ [_246325, _246327] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _246325), _246327)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _246325), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _246327, _246325))))], (8667 ^ _113251) ^ [_246432, _246434] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Nat_OSuc(_246432), _246434) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _246432, c_Nat_OSuc(_246434)))], (8669 ^ _113251) ^ [_246469, _246471] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Nat_OSuc(_246469), _246471) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _246469, _246471)))], (8671 ^ _113251) ^ [_246506, _246508] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _246506, c_Nat_OSuc(_246508)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _246506, _246508)))], (8673 ^ _113251) ^ [_246543, _246545, _246547] : [class_Fields_Ofield(_246543), 8676 ^ _113251 : [(8677 ^ _113251) ^ [] : [c_Polynomial_Opoly__gcd(_246543, _246545, _246547) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_246543)), 8680 ^ _113251 : [(8681 ^ _113251) ^ [] : [-(_246545 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_246543)))], (8683 ^ _113251) ^ [] : [-(_246547 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_246543)))]]], (8685 ^ _113251) ^ [] : [-(c_Polynomial_Opoly__gcd(_246543, _246545, _246547) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_246543))), _246545 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_246543)), _246547 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_246543))]]], (8695 ^ _113251) ^ [_246876] : [class_Fields_Ofield(_246876), -(c_Polynomial_Opoly__gcd(_246876, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_246876)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_246876))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_246876)))], (8701 ^ _113251) ^ [_246981, _246983, _246985] : [class_Fields_Ofield(_246981), -(c_Polynomial_Opoly__gcd(_246981, _246983, _246985) = c_Polynomial_Opoly__gcd(_246981, _246985, _246983))], (8707 ^ _113251) ^ [_247074, _247076, _247078, _247080] : [class_Fields_Ofield(_247074), -(c_Polynomial_Opoly__gcd(_247074, _247076, c_Polynomial_Opoly__gcd(_247074, _247078, _247080)) = c_Polynomial_Opoly__gcd(_247074, _247078, c_Polynomial_Opoly__gcd(_247074, _247076, _247080)))], (8713 ^ _113251) ^ [_247185, _247187, _247189, _247191] : [class_Fields_Ofield(_247185), -(c_Polynomial_Opoly__gcd(_247185, c_Polynomial_Opoly__gcd(_247185, _247187, _247189), _247191) = c_Polynomial_Opoly__gcd(_247185, _247187, c_Polynomial_Opoly__gcd(_247185, _247189, _247191)))], (8719 ^ _113251) ^ [_247296, _247298, _247300, _247302, _247304, _247306, _247308] : [class_Fields_Ofield(_247296), c_Polynomial_Opdivmod__rel(_247296, _247298, _247300, _247302, _247304), c_Polynomial_Opdivmod__rel(_247296, _247298, _247300, _247306, _247308), -(_247302 = _247306)], (8733 ^ _113251) ^ [_247517, _247519, _247521, _247523, _247525, _247527, _247529] : [class_Fields_Ofield(_247517), c_Polynomial_Opdivmod__rel(_247517, _247519, _247521, _247523, _247525), c_Polynomial_Opdivmod__rel(_247517, _247519, _247521, _247527, _247529), -(_247525 = _247529)], (8747 ^ _113251) ^ [_247738, _247740, _247742, _247744, _247746, _247748, _247750] : [class_Fields_Ofield(_247738), c_Polynomial_Opdivmod__rel(_247738, _247740, _247742, _247744, _247746), c_Polynomial_Opdivmod__rel(_247738, _247740, _247742, _247748, _247750), 8758 ^ _113251 : [(8759 ^ _113251) ^ [] : [-(_247744 = _247748)], (8761 ^ _113251) ^ [] : [-(_247746 = _247750)]]], (8763 ^ _113251) ^ [_247985, _247987, _247989, _247991] : [class_Fields_Ofield(_247985), 8766 ^ _113251 : [(8767 ^ _113251) ^ [] : [c_Polynomial_Opdivmod__rel(_247985, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_247985)), _247987, _247989, _247991), 8770 ^ _113251 : [(8771 ^ _113251) ^ [] : [-(_247989 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_247985)))], (8773 ^ _113251) ^ [] : [-(_247991 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_247985)))]]], (8775 ^ _113251) ^ [] : [-(c_Polynomial_Opdivmod__rel(_247985, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_247985)), _247987, _247989, _247991)), _247989 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_247985)), _247991 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_247985))]]], (8785 ^ _113251) ^ [_248323, _248325, _248327, _248329] : [class_Fields_Ofield(_248323), 8788 ^ _113251 : [(8789 ^ _113251) ^ [] : [c_Polynomial_Opdivmod__rel(_248323, _248325, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_248323)), _248327, _248329), 8792 ^ _113251 : [(8793 ^ _113251) ^ [] : [-(_248327 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_248323)))], (8795 ^ _113251) ^ [] : [-(_248329 = _248325)]]], (8797 ^ _113251) ^ [] : [-(c_Polynomial_Opdivmod__rel(_248323, _248325, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_248323)), _248327, _248329)), _248327 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_248323)), _248329 = _248325]]], (8807 ^ _113251) ^ [_248649, _248651] : [class_Fields_Ofield(_248649), -(c_Polynomial_Opdivmod__rel(_248649, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_248649)), _248651, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_248649)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_248649))))], (8813 ^ _113251) ^ [_248754, _248756] : [class_Fields_Ofield(_248754), -(c_Polynomial_Opdivmod__rel(_248754, _248756, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_248754)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_248754)), _248756))], (8819 ^ _113251) ^ [_248851, _248853, _248855, _248857] : [class_Fields_Ofield(_248851), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_248851)), _248853), _248855)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_248851)), _248853), _248857)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_248851)), _248853), c_Polynomial_Opoly__gcd(_248851, _248855, _248857))))], (8833 ^ _113251) ^ [_249104, _249106, _249108, _249110] : [class_Fields_Ofield(_249104), 8836 ^ _113251 : [(8837 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_249104)), _249106), c_Polynomial_Opoly__gcd(_249104, _249108, _249110))), 8840 ^ _113251 : [(8841 ^ _113251) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_249104)), _249106), _249108)))], (8843 ^ _113251) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_249104)), _249106), _249110)))]]], (8845 ^ _113251) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_249104)), _249106), c_Polynomial_Opoly__gcd(_249104, _249108, _249110)))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_249104)), _249106), _249108)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_249104)), _249106), _249110))]]], (8855 ^ _113251) ^ [_249490, _249492, _249494] : [class_Fields_Ofield(_249490), -(c_Polynomial_Opoly__gcd(_249490, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_249490), _249492), _249494) = c_Polynomial_Opoly__gcd(_249490, _249492, _249494))], (8861 ^ _113251) ^ [_249593, _249595, _249597] : [class_Fields_Ofield(_249593), -(c_Polynomial_Opoly__gcd(_249593, _249595, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_249593), _249597)) = c_Polynomial_Opoly__gcd(_249593, _249595, _249597))], (8867 ^ _113251) ^ [_249696, _249698] : [class_Fields_Ofield(_249696), -(c_Polynomial_Opoly__gcd(_249696, _249698, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_249696))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_249696)))], (8873 ^ _113251) ^ [_249795, _249797] : [class_Fields_Ofield(_249795), -(c_Polynomial_Opoly__gcd(_249795, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_249795)), _249797) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_249795)))], (8879 ^ _113251) ^ [_249894, _249896, _249898, _249900] : [class_Rings_Ocomm__semiring__1(_249894), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_249894), hAPP(hAPP(c_Power_Opower__class_Opower(_249894), _249896), _249898)), hAPP(hAPP(c_Power_Opower__class_Opower(_249894), _249896), _249900)) = hAPP(hAPP(c_Power_Opower__class_Opower(_249894), _249896), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _249898, _249900)))], (8885 ^ _113251) ^ [_250045, _250047, _250049, _250051] : [class_Groups_Omonoid__mult(_250045), -(hAPP(hAPP(c_Power_Opower__class_Opower(_250045), _250047), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _250049, _250051)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_250045), hAPP(hAPP(c_Power_Opower__class_Opower(_250045), _250047), _250049)), hAPP(hAPP(c_Power_Opower__class_Opower(_250045), _250047), _250051)))], (8891 ^ _113251) ^ [_250211, _250213] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _250211, _250213) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 8896 ^ _113251 : [(8897 ^ _113251) ^ [] : [-(_250211 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (8899 ^ _113251) ^ [] : [-(_250213 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 8900 ^ _113251 : [(8901 ^ _113251) ^ [] : [-(_250211 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8903 ^ _113251) ^ [] : [-(_250213 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (8905 ^ _113251) ^ [_250391, _250393] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _250391, _250393) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 8906 ^ _113251 : [(8907 ^ _113251) ^ [] : [_250391 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _250393 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (8913 ^ _113251) ^ [] : [_250391 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _250393 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (8921 ^ _113251) ^ [_250628, _250630] : [c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _250628, _250630), 8926 ^ _113251 : [(8927 ^ _113251) ^ [] : [-(_250628 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (8929 ^ _113251) ^ [] : [-(_250630 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 8930 ^ _113251 : [(8931 ^ _113251) ^ [] : [-(_250628 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8933 ^ _113251) ^ [] : [-(_250630 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (8935 ^ _113251) ^ [_250808, _250810] : [-(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _250808, _250810)), 8936 ^ _113251 : [(8937 ^ _113251) ^ [] : [_250808 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _250810 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (8943 ^ _113251) ^ [] : [_250808 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _250810 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (8961 ^ _113251) ^ [_251145, _251147] : [8962 ^ _113251 : [(8963 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _251145)], (8965 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _251147)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _251145, _251147)))], (8951 ^ _113251) ^ [_251045, _251047] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _251045, _251047)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _251045)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _251047))], (8969 ^ _113251) ^ [_251276, _251278] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _251276), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _251278), -(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, _251276, _251278)))], (8979 ^ _113251) ^ [_251419, _251421] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _251419, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _251419, _251421))))], (8981 ^ _113251) ^ [_251451, _251453] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _251451, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _251453, _251451))))], (8983 ^ _113251) ^ [_251498, _251500] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _251498, _251500), -(_251500 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _251498, 8986 ^ [_251498, _251500])))], (8990 ^ _113251) ^ [_251597, _251599] : [8991 ^ _113251 : [(8992 ^ _113251) ^ [_251643] : [_251599 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _251597, _251643))]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _251597, _251599))], (8996 ^ _113251) ^ [_251712] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _251712), _251712) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (8998 ^ _113251) ^ [_251743, _251745, _251747, _251749] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _251743, _251745), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _251747, _251749), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _251743, _251747), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _251745, _251749)))], (9008 ^ _113251) ^ [_251902, _251904] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _251902), c_Nat_OSuc(_251904)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _251902, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _251902), _251904)))], (9010 ^ _113251) ^ [_251945, _251947] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_251945)), _251947) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _251947, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _251945), _251947)))], (9022 ^ _113251) ^ [_252101, _252103] : [9023 ^ _113251 : [(9024 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _252101, _252103)], (9026 ^ _113251) ^ [] : [_252101 = _252103]], -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _252101, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _252103, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (9012 ^ _113251) ^ [_252003, _252005] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _252003, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _252005, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _252003, _252005)), -(_252003 = _252005)], (9030 ^ _113251) ^ [_252230] : [-(c_Nat_OSuc(_252230) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _252230))], (9032 ^ _113251) ^ [_252259] : [-(c_Nat_OSuc(_252259) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _252259, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (9034 ^ _113251) ^ [_252288] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _252288), _252288) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (9036 ^ _113251) ^ [_252318, _252320, _252322, _252324, _252326] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _252318), _252320)), 9039 ^ _113251 : [(9040 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _252318), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _252322, _252324))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _252318), c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _252322, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _252326), _252320)), _252324))))], (9046 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _252318), c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _252322, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _252326), _252320)), _252324))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _252318), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _252322, _252324))))]]], (9052 ^ _113251) ^ [_252655, _252657, _252659] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _252655), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _252657, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _252655), _252659)))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _252655), _252657)))], (9058 ^ _113251) ^ [_252770, _252772, _252774] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _252770), _252772)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _252770), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _252772, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _252770), _252774)))))], (9064 ^ _113251) ^ [_252891, _252893, _252895] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _252891), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _252893, _252895)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _252891), _252893)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _252891), _252895)))], (9066 ^ _113251) ^ [_252958] : [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), _252958), _252958), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _252958, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9072 ^ _113251) ^ [_253049] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _253049, 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), _253049), _253049), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9078 ^ _113251) ^ [_253161, _253163] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _253161, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _253163, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _253161, _253163))], (9084 ^ _113251) ^ [_253246, _253248] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _253246, _253248), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _253246, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _253248, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (9090 ^ _113251) ^ [_253352, _253354] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _253352, c_Groups_Oone__class_Oone(tc_Int_Oint)), _253354), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _253352, _253354))], (9096 ^ _113251) ^ [_253437, _253439] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _253437, _253439), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _253437, c_Groups_Oone__class_Oone(tc_Int_Oint)), _253439))], (9102 ^ _113251) ^ [_253528, _253530] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _253528, _253530), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _253528, c_Groups_Oone__class_Oone(tc_Int_Oint)), _253530))], (9108 ^ _113251) ^ [_253617, _253619, _253621, _253623, _253625, _253627, _253629, _253631] : [class_Fields_Ofield(_253617), c_Polynomial_Opdivmod__rel(_253617, _253619, _253621, _253623, _253625), c_Polynomial_Opdivmod__rel(_253617, _253623, _253627, _253629, _253631), -(c_Polynomial_Opdivmod__rel(_253617, _253619, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_253617)), _253621), _253627), _253629, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_253617), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_253617)), _253621), _253631), _253625)))], (9122 ^ _113251) ^ [_253902, _253904, _253906] : [class_Rings_Ocomm__semiring__0(_253902), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_253902, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_253902)), _253904), _253906)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Polynomial_Odegree(_253902, _253904), c_Polynomial_Odegree(_253902, _253906))))], (9128 ^ _113251) ^ [_254027, _254029, _254031] : [class_Rings_Oidom(_254027), -(_254029 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_254027))), -(_254031 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_254027))), -(c_Polynomial_Odegree(_254027, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_254027)), _254029), _254031)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Polynomial_Odegree(_254027, _254029), c_Polynomial_Odegree(_254027, _254031)))], (9142 ^ _113251) ^ [_254196, _254198, _254200, _254202, _254204] : [class_Rings_Ocomm__semiring__0(_254196), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_254196)), c_Polynomial_Omonom(_254196, _254198, _254200)), c_Polynomial_Omonom(_254196, _254202, _254204)) = c_Polynomial_Omonom(_254196, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_254196), _254198), _254202), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _254200, _254204)))], (9148 ^ _113251) ^ [_254345] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _254345), -(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), _254345)))], (9154 ^ _113251) ^ [_254432, _254434, _254436] : [class_Rings_Ocomm__semiring__0(_254432), -(hAPP(c_Polynomial_Ocoeff(_254432, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_254432)), _254434), _254436)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Polynomial_Odegree(_254432, _254434), c_Polynomial_Odegree(_254432, _254436))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_254432), hAPP(c_Polynomial_Ocoeff(_254432, _254434), c_Polynomial_Odegree(_254432, _254434))), hAPP(c_Polynomial_Ocoeff(_254432, _254436), c_Polynomial_Odegree(_254432, _254436))))], (9160 ^ _113251) ^ [_254613, _254615, _254617] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _254613), _254613 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _254615, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _254613), _254617)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _254615, _254613), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _254617))], (9174 ^ _113251) ^ [_254826, _254828, _254830] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _254826), _254826 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _254828, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _254826), _254830)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _254828), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _254830, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (9188 ^ _113251) ^ [_255039, _255041, _255043, _255045, _255047, _255049] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _255039), _255041), _255043) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _255045), _255047), _255049), 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), _255045), _255047), _255049), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _255043, _255039), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _255049), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _255045), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _255045, _255039), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _255047, _255041))], (9214 ^ _113251) ^ [_255514, _255516, _255518] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _255514, _255516) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _255518, _255516), -(_255514 = _255518)], (9220 ^ _113251) ^ [_255605, _255607, _255609] : [_255605 = _255609, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _255605, _255607) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _255609, _255607))], (9226 ^ _113251) ^ [_255720, _255722, _255724] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _255720, _255722) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _255720, _255724), -(_255722 = _255724)], (9232 ^ _113251) ^ [_255811, _255813, _255815] : [_255813 = _255815, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _255811, _255813) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _255811, _255815))], (9238 ^ _113251) ^ [_255908, _255910, _255912] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _255908, _255910), _255912) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _255908, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _255910, _255912)))], (9240 ^ _113251) ^ [_255951, _255953, _255955] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _255951, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _255953, _255955)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _255953, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _255951, _255955)))], (9242 ^ _113251) ^ [_255994, _255996] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _255994, _255996) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _255996, _255994))], (9244 ^ _113251) ^ [_256027, _256029, _256031] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _256027, _256029), _256031) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _256027, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _256029, _256031)))], (9246 ^ _113251) ^ [_256070, _256072, _256074] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _256070, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _256072, _256074)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _256072, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _256070, _256074)))], (9248 ^ _113251) ^ [_256113, _256115] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _256113, _256115) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _256115, _256113))], (9250 ^ _113251) ^ [_256146, _256148, _256150] : [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), _256146), _256148), _256150)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _256150, _256146), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _256146), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _256148))], (9264 ^ _113251) ^ [_256361, _256363, _256365] : [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), _256361), _256363), _256365), 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), _256365), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _256361), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _256363, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9278 ^ _113251) ^ [_256576, _256578, _256580, _256582, _256584] : [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), _256576), _256578), _256580), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _256576), _256582), _256584)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _256580), c_Orderings_Oord__class_Oless(tc_Int_Oint, _256580, _256576), c_Orderings_Oord__class_Oless(tc_Int_Oint, _256584, _256576), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _256578, _256582))], (9296 ^ _113251) ^ [_256883, _256885, _256887, _256889, _256891, _256893] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _256883), _256885), _256887) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _256889), _256891), _256893), 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), _256889), _256891), _256893)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _256893, _256889), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _256887), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _256889), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _256889, _256883), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _256885, _256891))], (9322 ^ _113251) ^ [_257340, _257342, _257344, _257346, _257348] : [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), _257340), _257342), _257344), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _257340), _257346), _257348)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _257348, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _257340, _257348), c_Orderings_Oord__class_Oless(tc_Int_Oint, _257340, _257344), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _257346, _257342))], (9340 ^ _113251) ^ [_257647, _257649, _257651, _257653] : [class_Fields_Ofield(_257647), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_257647)), _257649), _257651)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_257647)), _257649), _257653)), 9354 ^ _113251 : [(9355 ^ _113251) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_257647)), 9353 ^ [_257647, _257649, _257651, _257653]), _257651)))], (9357 ^ _113251) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_257647)), 9353 ^ [_257647, _257649, _257651, _257653]), _257653)))], (9359 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_257647)), 9353 ^ [_257647, _257649, _257651, _257653]), _257649))]], -(c_Polynomial_Opoly__gcd(_257647, _257651, _257653) = _257649), 9364 ^ _113251 : [(9365 ^ _113251) ^ [] : [-(_257651 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_257647)))], (9367 ^ _113251) ^ [] : [-(_257653 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_257647)))], (9369 ^ _113251) ^ [] : [hAPP(c_Polynomial_Ocoeff(_257647, _257649), c_Polynomial_Odegree(_257647, _257649)) = c_Groups_Ozero__class_Ozero(_257647)]], 9370 ^ _113251 : [(9377 ^ _113251) ^ [] : [hAPP(c_Polynomial_Ocoeff(_257647, _257649), c_Polynomial_Odegree(_257647, _257649)) = c_Groups_Oone__class_Oone(_257647)], (9371 ^ _113251) ^ [] : [_257651 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_257647)), _257653 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_257647))]]], (9381 ^ _113251) ^ [_258483, _258485] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _258483, _258485), -(_258485 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _258483, 9384 ^ [_258483, _258485]))], (9388 ^ _113251) ^ [_258578, _258580] : [9389 ^ _113251 : [(9390 ^ _113251) ^ [_258622] : [_258580 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _258578, _258622)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _258578, _258580))], (9394 ^ _113251) ^ [_258680, _258682, _258684] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _258680), 9400 ^ _113251 : [(9401 ^ _113251) ^ [] : [-(hBOOL(hAPP(_258682, 9399 ^ [_258680, _258682, _258684])))], (9403 ^ _113251) ^ [] : [hBOOL(hAPP(_258682, c_Groups_Oplus__class_Oplus(tc_Int_Oint, 9399 ^ [_258680, _258682, _258684], _258680)))]], c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _258684), 9408 ^ _113251 : [(9409 ^ _113251) ^ [_258957] : [hBOOL(hAPP(_258682, _258957)), -(hBOOL(hAPP(_258682, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _258957, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _258684), _258680)))))]]], (9415 ^ _113251) ^ [_259075, _259077] : [-(hBOOL(hAPP(_259075, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_259075, _259077)), 9423 ^ _113251 : [(9424 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 9422 ^ [_259075, _259077], _259077))], (9432 ^ _113251) ^ [] : [-(hBOOL(hAPP(_259075, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, 9422 ^ [_259075, _259077], c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (9426 ^ _113251) ^ [_259293] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _259293, 9422 ^ [_259075, _259077]), hBOOL(hAPP(_259075, _259293))]]], (9434 ^ _113251) ^ [_259435, _259437, _259439] : [class_Groups_Omonoid__mult(_259435), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _259437), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_259435), hAPP(hAPP(c_Power_Opower__class_Opower(_259435), _259439), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _259437, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _259439) = hAPP(hAPP(c_Power_Opower__class_Opower(_259435), _259439), _259437))], (9444 ^ _113251) ^ [_259624, _259626, _259628, _259630] : [class_Orderings_Oorder(_259624), c_Orderings_Oorder_Omono(tc_Nat_Onat, _259624, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _259626), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _259628), _259630)), -(c_Orderings_Oord__class_Oless__eq(_259624, hAPP(_259626, _259628), hAPP(_259626, _259630)))], (9458 ^ _113251) ^ [_259843, _259845, _259847] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _259843, _259845), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _259847, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _259845, _259843)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _259847, _259843), _259845))], (9464 ^ _113251) ^ [_259974, _259976, _259978] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _259974, _259976), _259978), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _259974, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _259978, _259976)))], (9470 ^ _113251) ^ [_260069, _260071, _260073] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _260069, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _260073, _260071)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _260069, _260071), _260073))], (9476 ^ _113251) ^ [_260170, _260172, _260174] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _260170, _260172), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _260174, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _260172, _260174), _260170)))], (9482 ^ _113251) ^ [_260269, _260271] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _260269, _260271), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _260269, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _260271, _260269)) = _260271)], (9488 ^ _113251) ^ [_260364, _260366, _260368] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _260364, _260366), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _260368, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _260366, _260364)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _260368, _260366), _260364))], (9494 ^ _113251) ^ [_260477, _260479, _260481] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _260477, _260479), 9497 ^ _113251 : [(9498 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _260481, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _260479, _260477)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _260481, _260477), _260479))], (9504 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _260481, _260477), _260479), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _260481, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _260479, _260477)))]]], (9510 ^ _113251) ^ [_260722, _260724] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _260722, _260724), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _260724, _260722), _260722) = _260724)], (9516 ^ _113251) ^ [_260817, _260819, _260821] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _260817, _260819), 9519 ^ _113251 : [(9520 ^ _113251) ^ [] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _260819, _260817) = _260821, -(_260819 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _260821, _260817))], (9526 ^ _113251) ^ [] : [_260819 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _260821, _260817), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _260819, _260817) = _260821)]]], (9532 ^ _113251) ^ [_261056, _261058, _261060] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _261056, _261058), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _261060, _261058), _261056) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _261060, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _261058, _261056)))], (9538 ^ _113251) ^ [_261169, _261171, _261173] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _261169, _261171), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _261171, _261169), _261173) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _261171, _261173), _261169))], (9544 ^ _113251) ^ [_261282, _261284, _261286] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _261282, _261284), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _261284, _261286), _261282) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _261284, _261282), _261286))], (9550 ^ _113251) ^ [_261391, _261393] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _261391, _261393)), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _261393, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _261391, _261393)) = _261391)], (9556 ^ _113251) ^ [_261454, _261456, _261458] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _261454, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _261456, _261458)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _261454, _261458), _261456))], (9562 ^ _113251) ^ [_261549, _261551, _261553] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _261549, _261553), _261551), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _261549, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _261551, _261553)))], (9568 ^ _113251) ^ [_261650, _261652] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _261650, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _261650, _261652)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9570 ^ _113251) ^ [_261683, _261685, _261687] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _261683, _261685), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _261687, _261685)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _261683, _261687))], (9572 ^ _113251) ^ [_261726, _261728, _261730] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _261726, _261728), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _261726, _261730)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _261728, _261730))], (9574 ^ _113251) ^ [_261769, _261771, _261773] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _261769, _261771), _261773) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _261769, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _261771, _261773)))], (9576 ^ _113251) ^ [_261812, _261814] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _261812, _261814), _261812) = _261814)], (9578 ^ _113251) ^ [_261845, _261847] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _261845, _261847), _261847) = _261845)], (9580 ^ _113251) ^ [_261878, _261880, _261882] : [class_Groups_Ogroup__add(_261878), -(c_Groups_Ominus__class_Ominus(_261878, c_Groups_Oplus__class_Oplus(_261878, _261880, _261882), _261882) = _261880)], (9586 ^ _113251) ^ [_261971, _261973, _261975] : [class_Groups_Ogroup__add(_261971), -(c_Groups_Oplus__class_Oplus(_261971, c_Groups_Ominus__class_Ominus(_261971, _261973, _261975), _261975) = _261973)], (9592 ^ _113251) ^ [_262064, _262066, _262068, _262070, _262072] : [class_Rings_Oring(_262064), -(c_Groups_Ominus__class_Ominus(_262064, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_262064), _262066), _262068), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_262064), _262070), _262072)) = c_Groups_Oplus__class_Oplus(_262064, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_262064), _262066), c_Groups_Ominus__class_Ominus(_262064, _262068, _262072)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_262064), c_Groups_Ominus__class_Ominus(_262064, _262066, _262070)), _262072)))], (9598 ^ _113251) ^ [_262241, _262243, _262245, _262247, _262249, _262251] : [class_Rings_Oring(_262241), 9601 ^ _113251 : [(9602 ^ _113251) ^ [] : [c_Groups_Oplus__class_Oplus(_262241, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_262241), _262243), _262245), _262247) = c_Groups_Oplus__class_Oplus(_262241, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_262241), _262249), _262245), _262251), -(_262247 = c_Groups_Oplus__class_Oplus(_262241, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_262241), c_Groups_Ominus__class_Ominus(_262241, _262249, _262243)), _262245), _262251))], (9608 ^ _113251) ^ [] : [_262247 = c_Groups_Oplus__class_Oplus(_262241, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_262241), c_Groups_Ominus__class_Ominus(_262241, _262249, _262243)), _262245), _262251), -(c_Groups_Oplus__class_Oplus(_262241, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_262241), _262243), _262245), _262247) = c_Groups_Oplus__class_Oplus(_262241, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_262241), _262249), _262245), _262251))]]], (9614 ^ _113251) ^ [_262590, _262592, _262594, _262596, _262598, _262600] : [class_Rings_Oring(_262590), 9617 ^ _113251 : [(9618 ^ _113251) ^ [] : [c_Groups_Oplus__class_Oplus(_262590, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_262590), _262592), _262594), _262596) = c_Groups_Oplus__class_Oplus(_262590, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_262590), _262598), _262594), _262600), -(c_Groups_Oplus__class_Oplus(_262590, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_262590), c_Groups_Ominus__class_Ominus(_262590, _262592, _262598)), _262594), _262596) = _262600)], (9624 ^ _113251) ^ [] : [c_Groups_Oplus__class_Oplus(_262590, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_262590), c_Groups_Ominus__class_Ominus(_262590, _262592, _262598)), _262594), _262596) = _262600, -(c_Groups_Oplus__class_Oplus(_262590, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_262590), _262592), _262594), _262596) = c_Groups_Oplus__class_Oplus(_262590, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_262590), _262598), _262594), _262600))]]], (9630 ^ _113251) ^ [_262939, _262941, _262943, _262945, _262947] : [class_RealVector_Oreal__normed__algebra(_262939), -(c_Groups_Ominus__class_Ominus(_262939, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_262939), _262941), _262943), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_262939), _262945), _262947)) = c_Groups_Oplus__class_Oplus(_262939, c_Groups_Oplus__class_Oplus(_262939, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_262939), c_Groups_Ominus__class_Ominus(_262939, _262941, _262945)), c_Groups_Ominus__class_Ominus(_262939, _262943, _262947)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_262939), c_Groups_Ominus__class_Ominus(_262939, _262941, _262945)), _262947)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_262939), _262945), c_Groups_Ominus__class_Ominus(_262939, _262943, _262947))))], (9636 ^ _113251) ^ [_263156, _263158, _263160] : [class_Rings_Ocomm__ring__1(_263156), -(c_Groups_Ominus__class_Ominus(_263156, _263158, _263160) = c_Groups_Oplus__class_Oplus(_263156, _263158, c_Groups_Ouminus__class_Ouminus(_263156, _263160)))], (9642 ^ _113251) ^ [_263255, _263257, _263259] : [class_Groups_Ogroup__add(_263255), -(c_Groups_Ominus__class_Ominus(_263255, _263257, c_Groups_Ouminus__class_Ouminus(_263255, _263259)) = c_Groups_Oplus__class_Oplus(_263255, _263257, _263259))], (9648 ^ _113251) ^ [_263354, _263356, _263358] : [class_Groups_Oab__group__add(_263354), -(c_Groups_Ominus__class_Ominus(_263354, _263356, _263358) = c_Groups_Oplus__class_Oplus(_263354, _263356, c_Groups_Ouminus__class_Ouminus(_263354, _263358)))], (9654 ^ _113251) ^ [_263453, _263455, _263457] : [class_Groups_Ogroup__add(_263453), -(c_Groups_Ominus__class_Ominus(_263453, _263455, _263457) = c_Groups_Oplus__class_Oplus(_263453, _263455, c_Groups_Ouminus__class_Ouminus(_263453, _263457)))], (9660 ^ _113251) ^ [_263567, _263569] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _263567, _263569)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _263569, _263567))], (9666 ^ _113251) ^ [_263652, _263654] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _263654, _263652), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _263652, _263654)))], (9672 ^ _113251) ^ [_263743, _263745] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _263743), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _263745), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _263745, _263743), _263745))], (9682 ^ _113251) ^ [_263886, _263888] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _263886, _263888), c_Nat_OSuc(_263886)))], (9684 ^ _113251) ^ [_263933, _263935] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _263933, _263935) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _263933, _263935))], (9690 ^ _113251) ^ [_264016, _264018] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _264016, _264018), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _264016, _264018) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9696 ^ _113251) ^ [_264105, _264107] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _264105, _264107), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _264105, _264107) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9702 ^ _113251) ^ [_264192, _264194] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _264192, _264194), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_264194), _264192) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _264194, _264192)))], (9708 ^ _113251) ^ [_264295, _264297, _264299] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _264295, _264297), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _264295, _264299), 9715 ^ _113251 : [(9716 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _264297, _264295), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _264299, _264295)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _264297, _264299))], (9722 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _264297, _264299), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _264297, _264295), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _264299, _264295)))]]], (9728 ^ _113251) ^ [_264596, _264598, _264600] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _264596, _264598), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _264600, _264596), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _264596, _264600), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _264598, _264600)))], (9738 ^ _113251) ^ [_264751, _264753, _264755] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _264751), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _264753, _264755))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _264751), _264753)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _264755, _264753), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _264751), _264755)))], (9752 ^ _113251) ^ [_264978, _264980, _264982] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _264978), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _264980, _264982))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _264978), _264982)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _264982, _264980), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _264978), _264980)))], (9766 ^ _113251) ^ [_265205] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_265205), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _265205)], (9768 ^ _113251) ^ [_265234, _265236] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _265234, c_Nat_OSuc(_265236)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _265234, c_Groups_Oone__class_Oone(tc_Nat_Onat)), _265236))], (9770 ^ _113251) ^ [_265273, _265275, _265277] : [class_Groups_Oab__group__add(_265273), -(c_Groups_Ouminus__class_Ouminus(_265273, c_Groups_Ominus__class_Ominus(_265273, _265275, _265277)) = c_Groups_Ominus__class_Ominus(_265273, _265277, _265275))], (9776 ^ _113251) ^ [_265372, _265374, _265376, _265378, _265380] : [class_Groups_Ominus(_265372), -(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_265374, _265372), _265376, _265378), _265380) = c_Groups_Ominus__class_Ominus(_265372, hAPP(_265376, _265380), hAPP(_265378, _265380)))], (9782 ^ _113251) ^ [_265493, _265495] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_265493), c_Nat_OSuc(_265495)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _265493, _265495))], (9784 ^ _113251) ^ [_265530, _265532, _265534] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_265530), _265532), c_Nat_OSuc(_265534)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _265530, _265532), _265534))], (9786 ^ _113251) ^ [_265577, _265579, _265581, _265583, _265585] : [class_Groups_Oab__group__add(_265577), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_265577), c_Polynomial_OpCons(_265577, _265579, _265581), c_Polynomial_OpCons(_265577, _265583, _265585)) = c_Polynomial_OpCons(_265577, c_Groups_Ominus__class_Ominus(_265577, _265579, _265583), c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_265577), _265581, _265585)))], (9792 ^ _113251) ^ [_265714, _265716, _265718, _265720] : [class_Rings_Ocomm__ring(_265714), -(hAPP(c_Polynomial_Opoly(_265714, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_265714), _265716, _265718)), _265720) = c_Groups_Ominus__class_Ominus(_265714, hAPP(c_Polynomial_Opoly(_265714, _265716), _265720), hAPP(c_Polynomial_Opoly(_265714, _265718), _265720)))], (9798 ^ _113251) ^ [_265849, _265851, _265853, _265855, _265857] : [class_Groups_Oab__group__add(_265849), c_Groups_Ominus__class_Ominus(_265849, _265851, _265853) = c_Groups_Ominus__class_Ominus(_265849, _265855, _265857), 9805 ^ _113251 : [(9806 ^ _113251) ^ [] : [_265851 = _265853, -(_265855 = _265857)], (9812 ^ _113251) ^ [] : [_265855 = _265857, -(_265851 = _265853)]]], (9818 ^ _113251) ^ [_266146, _266148, _266150] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _266146, _266148), _266150) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _266146, _266150), _266148))], (9820 ^ _113251) ^ [_266189, _266191, _266193] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _266189), _266191)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _266189), _266193)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _266189), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _266191, _266193))))], (9830 ^ _113251) ^ [_266360, _266362, _266364, _266366] : [class_Rings_Ocomm__ring__1(_266360), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_266360), _266362), _266364)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_266360), _266362), _266366)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_266360), _266362), c_Groups_Ominus__class_Ominus(_266360, _266364, _266366))))], (9844 ^ _113251) ^ [_266601, _266603, _266605, _266607] : [class_Groups_Oab__group__add(_266601), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_266601), c_Polynomial_Omonom(_266601, _266603, _266605), c_Polynomial_Omonom(_266601, _266607, _266605)) = c_Polynomial_Omonom(_266601, c_Groups_Ominus__class_Ominus(_266601, _266603, _266607), _266605))], (9850 ^ _113251) ^ [_266724, _266726, _266728, _266730] : [class_Groups_Oab__group__add(_266724), -(hAPP(c_Polynomial_Ocoeff(_266724, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_266724), _266726, _266728)), _266730) = c_Groups_Ominus__class_Ominus(_266724, hAPP(c_Polynomial_Ocoeff(_266724, _266726), _266730), hAPP(c_Polynomial_Ocoeff(_266724, _266728), _266730)))], (9856 ^ _113251) ^ [_266859, _266861, _266863] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _266859), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _266861, _266863)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _266859), _266861), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _266859), _266863)))], (9858 ^ _113251) ^ [_266912, _266914, _266916] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _266912, _266914)), _266916) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _266912), _266916), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _266914), _266916)))], (9860 ^ _113251) ^ [_266965, _266967, _266969] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _266965, _266967), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _266965, _266969), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _266969, _266967), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _266969, _266965)))], (9870 ^ _113251) ^ [_267120, _267122, _267124] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _267120, _267122), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _267120, _267124), _267122))], (9876 ^ _113251) ^ [_267211, _267213] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _267211, _267213) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _267213, _267211) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_267211 = _267213)], (9886 ^ _113251) ^ [_267356] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _267356, _267356) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9888 ^ _113251) ^ [_267383] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _267383, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _267383)], (9890 ^ _113251) ^ [_267410] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _267410) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9892 ^ _113251) ^ [_267437, _267439, _267441, _267443] : [class_RealVector_Oreal__normed__algebra(_267437), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_267437), _267439), c_Groups_Ominus__class_Ominus(_267437, _267441, _267443)) = c_Groups_Ominus__class_Ominus(_267437, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_267437), _267439), _267441), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_267437), _267439), _267443)))], (9898 ^ _113251) ^ [_267580, _267582, _267584, _267586] : [class_RealVector_Oreal__normed__algebra(_267580), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_267580), _267582), c_Groups_Ominus__class_Ominus(_267580, _267584, _267586)) = c_Groups_Ominus__class_Ominus(_267580, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_267580), _267582), _267584), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_267580), _267582), _267586)))], (9904 ^ _113251) ^ [_267723, _267725, _267727, _267729] : [class_RealVector_Oreal__normed__algebra(_267723), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_267723), c_Groups_Ominus__class_Ominus(_267723, _267725, _267727)), _267729) = c_Groups_Ominus__class_Ominus(_267723, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_267723), _267725), _267729), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_267723), _267727), _267729)))], (9910 ^ _113251) ^ [_267866, _267868, _267870, _267872] : [class_RealVector_Oreal__normed__algebra(_267866), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_267866), c_Groups_Ominus__class_Ominus(_267866, _267868, _267870)), _267872) = c_Groups_Ominus__class_Ominus(_267866, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_267866), _267868), _267872), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_267866), _267870), _267872)))], (9916 ^ _113251) ^ [_268009, _268011, _268013, _268015, _268017] : [class_Groups_Oordered__ab__group__add(_268009), c_Groups_Ominus__class_Ominus(_268009, _268011, _268013) = c_Groups_Ominus__class_Ominus(_268009, _268015, _268017), 9923 ^ _113251 : [(9924 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_268009, _268011, _268013), -(c_Orderings_Oord__class_Oless(_268009, _268015, _268017))], (9930 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_268009, _268015, _268017), -(c_Orderings_Oord__class_Oless(_268009, _268011, _268013))]]], (9936 ^ _113251) ^ [_268312, _268314] : [class_Groups_Ogroup__add(_268312), -(c_Groups_Ominus__class_Ominus(_268312, _268314, c_Groups_Ozero__class_Ozero(_268312)) = _268314)], (9942 ^ _113251) ^ [_268399, _268401] : [class_Groups_Ogroup__add(_268399), -(c_Groups_Ominus__class_Ominus(_268399, _268401, _268401) = c_Groups_Ozero__class_Ozero(_268399))], (9948 ^ _113251) ^ [_268486, _268488, _268490] : [class_Groups_Oab__group__add(_268486), 9951 ^ _113251 : [(9952 ^ _113251) ^ [] : [_268488 = _268490, -(c_Groups_Ominus__class_Ominus(_268486, _268488, _268490) = c_Groups_Ozero__class_Ozero(_268486))], (9958 ^ _113251) ^ [] : [c_Groups_Ominus__class_Ominus(_268486, _268488, _268490) = c_Groups_Ozero__class_Ozero(_268486), -(_268488 = _268490)]]], (9964 ^ _113251) ^ [_268715, _268717, _268719] : [class_Groups_Ogroup__add(_268715), 9967 ^ _113251 : [(9968 ^ _113251) ^ [] : [c_Groups_Ominus__class_Ominus(_268715, _268717, _268719) = c_Groups_Ozero__class_Ozero(_268715), -(_268717 = _268719)], (9974 ^ _113251) ^ [] : [_268717 = _268719, -(c_Groups_Ominus__class_Ominus(_268715, _268717, _268719) = c_Groups_Ozero__class_Ozero(_268715))]]], (9980 ^ _113251) ^ [_268944, _268946, _268948, _268950, _268952] : [class_Groups_Oordered__ab__group__add(_268944), c_Groups_Ominus__class_Ominus(_268944, _268946, _268948) = c_Groups_Ominus__class_Ominus(_268944, _268950, _268952), 9987 ^ _113251 : [(9988 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_268944, _268946, _268948), -(c_Orderings_Oord__class_Oless__eq(_268944, _268950, _268952))], (9994 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_268944, _268950, _268952), -(c_Orderings_Oord__class_Oless__eq(_268944, _268946, _268948))]]], (10000 ^ _113251) ^ [_269316, _269318] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _269316, _269318), _269316))], (10002 ^ _113251) ^ [_269444, _269446, _269448] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _269444, _269446), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _269448, _269446), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _269448, _269444)))], (10008 ^ _113251) ^ [_269694, _269696, _269698] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _269694, _269696), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _269694, _269698), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _269696, _269698)))], (10014 ^ _113251) ^ [_269930, _269932] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _269930, _269932), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _269932, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _269932, _269930)) = _269930)], (10020 ^ _113251) ^ [_270172, _270174, _270176] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _270172, _270174), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _270172, _270176), 10027 ^ _113251 : [(10028 ^ _113251) ^ [] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _270174, _270172) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _270176, _270172), -(_270174 = _270176)], (10034 ^ _113251) ^ [] : [_270174 = _270176, -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _270174, _270172) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _270176, _270172))]]], (10040 ^ _113251) ^ [_270783, _270785, _270787] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _270783, _270785), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _270783, _270787), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _270785, _270783), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _270787, _270783)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _270785, _270787))], (10050 ^ _113251) ^ [_271142, _271144, _271146] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _271142, _271144), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _271142, _271146), 10057 ^ _113251 : [(10058 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _271144, _271142), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _271146, _271142)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _271144, _271146))], (10064 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _271144, _271146), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _271144, _271142), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _271146, _271142)))]]], (10070 ^ _113251) ^ [_271745, _271747] : [class_Groups_Ogroup__add(_271745), -(c_Groups_Ominus__class_Ominus(_271745, c_Groups_Ozero__class_Ozero(_271745), _271747) = c_Groups_Ouminus__class_Ouminus(_271745, _271747))], (10076 ^ _113251) ^ [_271985, _271987, _271989] : [class_Groups_Oordered__ab__group__add(_271985), 10079 ^ _113251 : [(10080 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_271985, _271987, _271989), -(c_Orderings_Oord__class_Oless(_271985, c_Groups_Ominus__class_Ominus(_271985, _271987, _271989), c_Groups_Ozero__class_Ozero(_271985)))], (10086 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_271985, c_Groups_Ominus__class_Ominus(_271985, _271987, _271989), c_Groups_Ozero__class_Ozero(_271985)), -(c_Orderings_Oord__class_Oless(_271985, _271987, _271989))]]], (10092 ^ _113251) ^ [_272497, _272499, _272501] : [class_Groups_Oordered__ab__group__add(_272497), 10095 ^ _113251 : [(10096 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_272497, _272499, _272501), -(c_Orderings_Oord__class_Oless__eq(_272497, c_Groups_Ominus__class_Ominus(_272497, _272499, _272501), c_Groups_Ozero__class_Ozero(_272497)))], (10102 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_272497, c_Groups_Ominus__class_Ominus(_272497, _272499, _272501), c_Groups_Ozero__class_Ozero(_272497)), -(c_Orderings_Oord__class_Oless__eq(_272497, _272499, _272501))]]], (10108 ^ _113251) ^ [_273051, _273053, _273055, _273057, _273059, _273061] : [class_Rings_Oordered__ring(_273051), 10111 ^ _113251 : [(10112 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_273051, c_Groups_Oplus__class_Oplus(_273051, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_273051), _273053), _273055), _273057), c_Groups_Oplus__class_Oplus(_273051, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_273051), _273059), _273055), _273061)), -(c_Orderings_Oord__class_Oless__eq(_273051, c_Groups_Oplus__class_Oplus(_273051, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_273051), c_Groups_Ominus__class_Ominus(_273051, _273053, _273059)), _273055), _273057), _273061))], (10118 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_273051, c_Groups_Oplus__class_Oplus(_273051, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_273051), c_Groups_Ominus__class_Ominus(_273051, _273053, _273059)), _273055), _273057), _273061), -(c_Orderings_Oord__class_Oless__eq(_273051, c_Groups_Oplus__class_Oplus(_273051, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_273051), _273053), _273055), _273057), c_Groups_Oplus__class_Oplus(_273051, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_273051), _273059), _273055), _273061)))]]], (10124 ^ _113251) ^ [_273755, _273757, _273759, _273761, _273763, _273765] : [class_Rings_Oordered__ring(_273755), 10127 ^ _113251 : [(10128 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_273755, c_Groups_Oplus__class_Oplus(_273755, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_273755), _273757), _273759), _273761), c_Groups_Oplus__class_Oplus(_273755, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_273755), _273763), _273759), _273765)), -(c_Orderings_Oord__class_Oless__eq(_273755, _273761, c_Groups_Oplus__class_Oplus(_273755, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_273755), c_Groups_Ominus__class_Ominus(_273755, _273763, _273757)), _273759), _273765)))], (10134 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(_273755, _273761, c_Groups_Oplus__class_Oplus(_273755, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_273755), c_Groups_Ominus__class_Ominus(_273755, _273763, _273757)), _273759), _273765)), -(c_Orderings_Oord__class_Oless__eq(_273755, c_Groups_Oplus__class_Oplus(_273755, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_273755), _273757), _273759), _273761), c_Groups_Oplus__class_Oplus(_273755, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_273755), _273763), _273759), _273765)))]]], (10140 ^ _113251) ^ [_274459, _274461, _274463, _274465, _274467, _274469] : [class_Rings_Oordered__ring(_274459), 10143 ^ _113251 : [(10144 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_274459, c_Groups_Oplus__class_Oplus(_274459, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_274459), _274461), _274463), _274465), c_Groups_Oplus__class_Oplus(_274459, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_274459), _274467), _274463), _274469)), -(c_Orderings_Oord__class_Oless(_274459, c_Groups_Oplus__class_Oplus(_274459, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_274459), c_Groups_Ominus__class_Ominus(_274459, _274461, _274467)), _274463), _274465), _274469))], (10150 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_274459, c_Groups_Oplus__class_Oplus(_274459, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_274459), c_Groups_Ominus__class_Ominus(_274459, _274461, _274467)), _274463), _274465), _274469), -(c_Orderings_Oord__class_Oless(_274459, c_Groups_Oplus__class_Oplus(_274459, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_274459), _274461), _274463), _274465), c_Groups_Oplus__class_Oplus(_274459, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_274459), _274467), _274463), _274469)))]]], (10156 ^ _113251) ^ [_275163, _275165, _275167, _275169, _275171, _275173] : [class_Rings_Oordered__ring(_275163), 10159 ^ _113251 : [(10160 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_275163, c_Groups_Oplus__class_Oplus(_275163, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_275163), _275165), _275167), _275169), c_Groups_Oplus__class_Oplus(_275163, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_275163), _275171), _275167), _275173)), -(c_Orderings_Oord__class_Oless(_275163, _275169, c_Groups_Oplus__class_Oplus(_275163, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_275163), c_Groups_Ominus__class_Ominus(_275163, _275171, _275165)), _275167), _275173)))], (10166 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_275163, _275169, c_Groups_Oplus__class_Oplus(_275163, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_275163), c_Groups_Ominus__class_Ominus(_275163, _275171, _275165)), _275167), _275173)), -(c_Orderings_Oord__class_Oless(_275163, c_Groups_Oplus__class_Oplus(_275163, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_275163), _275165), _275167), _275169), c_Groups_Oplus__class_Oplus(_275163, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_275163), _275171), _275167), _275173)))]]], (10172 ^ _113251) ^ [_275811, _275813] : [class_Rings_Oring__1(_275811), -(c_Groups_Ominus__class_Ominus(_275811, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_275811), _275813), _275813), c_Groups_Oone__class_Oone(_275811)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_275811), c_Groups_Oplus__class_Oplus(_275811, _275813, c_Groups_Oone__class_Oone(_275811))), c_Groups_Ominus__class_Ominus(_275811, _275813, c_Groups_Oone__class_Oone(_275811))))], (10178 ^ _113251) ^ [_276115, _276117, _276119, _276121] : [class_Rings_Ocomm__ring(_276115), class_Rings_Odvd(_276115), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_276115), _276117), _276119)), 10189 ^ _113251 : [(10190 ^ _113251) ^ [_276542, _276544] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_276115), _276117), c_Groups_Oplus__class_Oplus(_276115, _276544, _276121))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_276115), _276117), c_Groups_Oplus__class_Oplus(_276115, c_Groups_Ominus__class_Ominus(_276115, _276544, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_276115), _276542), _276119)), _276121))))], (10196 ^ _113251) ^ [_276804, _276806] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_276115), _276117), c_Groups_Oplus__class_Oplus(_276115, c_Groups_Ominus__class_Ominus(_276115, _276806, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_276115), _276804), _276119)), _276121))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_276115), _276117), c_Groups_Oplus__class_Oplus(_276115, _276806, _276121))))]]], (10202 ^ _113251) ^ [_277155, _277157, _277159, _277161] : [class_Rings_Ocomm__ring(_277155), class_Rings_Odvd(_277155), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_277155), _277157), _277159)), 10213 ^ _113251 : [(10214 ^ _113251) ^ [_277582, _277584] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_277155), _277157), c_Groups_Oplus__class_Oplus(_277155, _277584, _277161))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_277155), _277157), c_Groups_Oplus__class_Oplus(_277155, c_Groups_Ominus__class_Ominus(_277155, _277584, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_277155), _277582), _277159)), _277161))))], (10220 ^ _113251) ^ [_277844, _277846] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_277155), _277157), c_Groups_Oplus__class_Oplus(_277155, c_Groups_Ominus__class_Ominus(_277155, _277846, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_277155), _277844), _277159)), _277161))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_277155), _277157), c_Groups_Oplus__class_Oplus(_277155, _277846, _277161))))]]], (10226 ^ _113251) ^ [_278167, _278169] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _278167), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _278167, c_Nat_OSuc(_278169)), _278167))], (10232 ^ _113251) ^ [_278379] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _278379), -(c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _278379, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _278379)], (10254 ^ _113251) ^ [_279179, _279181, _279183] : [-(hBOOL(hAPP(_279179, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _279181, _279183)))), 10257 ^ _113251 : [(10258 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _279181, _279183))], (10260 ^ _113251) ^ [] : [hBOOL(hAPP(_279179, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 10262 ^ _113251 : [(10263 ^ _113251) ^ [] : [-(_279181 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _279183, 10261 ^ [_279179, _279181, _279183]))], (10265 ^ _113251) ^ [] : [hBOOL(hAPP(_279179, 10261 ^ [_279179, _279181, _279183]))]]], (10238 ^ _113251) ^ [_278640, _278642, _278644] : [hBOOL(hAPP(_278640, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _278642, _278644))), 10241 ^ _113251 : [(10242 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _278642, _278644), -(hBOOL(hAPP(_278640, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (10248 ^ _113251) ^ [_278978] : [_278642 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _278644, _278978), -(hBOOL(hAPP(_278640, _278978)))]]], (10285 ^ _113251) ^ [_280340, _280342, _280344] : [-(hBOOL(hAPP(_280340, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _280342, _280344)))), 10288 ^ _113251 : [(10289 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _280342, _280344))], (10291 ^ _113251) ^ [] : [hBOOL(hAPP(_280340, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 10293 ^ _113251 : [(10294 ^ _113251) ^ [] : [-(_280342 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _280344, 10292 ^ [_280340, _280342, _280344]))], (10296 ^ _113251) ^ [] : [hBOOL(hAPP(_280340, 10292 ^ [_280340, _280342, _280344]))]]], (10269 ^ _113251) ^ [_279809, _279811, _279813] : [hBOOL(hAPP(_279809, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _279811, _279813))), 10272 ^ _113251 : [(10273 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _279811, _279813), -(hBOOL(hAPP(_279809, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (10279 ^ _113251) ^ [_280141] : [_279811 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _279813, _280141), -(hBOOL(hAPP(_279809, _280141)))]]], (10300 ^ _113251) ^ [_280933, _280935, _280937] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _280933, _280935), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _280935, _280933)), _280937) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_280935), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _280933, _280937)))], (10306 ^ _113251) ^ [_281205, _281207, _281209] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _281205, _281207), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _281209, c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _281207, _281205))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _281209, _281205), c_Nat_OSuc(_281207)))], (10312 ^ _113251) ^ [_281505, _281507, _281509, _281511, _281513] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _281505, _281507), 10315 ^ _113251 : [(10316 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _281507), _281509), _281511), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _281505), _281509), _281513)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _281507, _281505)), _281509), _281511), _281513))], (10322 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _281507, _281505)), _281509), _281511), _281513), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _281507), _281509), _281511), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _281505), _281509), _281513)))]]], (10328 ^ _113251) ^ [_282165, _282167, _282169, _282171, _282173] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _282165, _282167), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _282167), _282169), _282171), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _282165), _282169), _282173)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _282167, _282165)), _282169), _282171), _282173))], (10334 ^ _113251) ^ [_282521, _282523, _282525, _282527, _282529] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _282521, _282523), 10337 ^ _113251 : [(10338 ^ _113251) ^ [] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _282523), _282525), _282527) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _282521), _282525), _282529), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _282523, _282521)), _282525), _282527) = _282529)], (10344 ^ _113251) ^ [] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _282523, _282521)), _282525), _282527) = _282529, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _282523), _282525), _282527) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _282521), _282525), _282529))]]], (10350 ^ _113251) ^ [_283175, _283177, _283179, _283181, _283183] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _283175, _283177), 10353 ^ _113251 : [(10354 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _283175), _283179), _283181), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _283177), _283179), _283183)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _283181, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _283177, _283175)), _283179), _283183)))], (10360 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _283181, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _283177, _283175)), _283179), _283183)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _283175), _283179), _283181), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _283177), _283179), _283183)))]]], (10366 ^ _113251) ^ [_283835, _283837, _283839, _283841, _283843] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _283835, _283837), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _283835), _283839), _283841), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _283837), _283839), _283843)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _283841, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _283837, _283835)), _283839), _283843)))], (10372 ^ _113251) ^ [_284191, _284193, _284195, _284197, _284199] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _284191, _284193), 10375 ^ _113251 : [(10376 ^ _113251) ^ [] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _284191), _284195), _284197) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _284193), _284195), _284199), -(_284197 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _284193, _284191)), _284195), _284199))], (10382 ^ _113251) ^ [] : [_284197 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _284193, _284191)), _284195), _284199), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _284191), _284195), _284197) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _284193), _284195), _284199))]]], (10388 ^ _113251) ^ [_284817, _284819, _284821] : [class_Rings_Ocomm__semiring__0(_284817), -(c_Polynomial_Odegree(_284817, c_Polynomial_Osynthetic__div(_284817, _284819, _284821)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Polynomial_Odegree(_284817, _284819), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (10394 ^ _113251) ^ [_285045] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _285045), -(_285045 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _285045, c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (10400 ^ _113251) ^ [_285249] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _285249), -(c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _285249, c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _285249)], (10406 ^ _113251) ^ [_285487, _285489] : [_285487 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _285487, _285489) = _285489)], (10412 ^ _113251) ^ [_285657, _285659] : [-(_285657 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _285657, _285659) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _285657, c_Groups_Oone__class_Oone(tc_Nat_Onat)), _285659)))], (10418 ^ _113251) ^ [_285942, _285944, _285946, _285948, _285950] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _285942, _285944), 10421 ^ _113251 : [(10422 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _285942), _285946), _285948), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _285944), _285946), _285950)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _285948, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _285944, _285942)), _285946), _285950)))], (10428 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _285948, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _285944, _285942)), _285946), _285950)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _285942), _285946), _285948), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _285944), _285946), _285950)))]]], (10434 ^ _113251) ^ [_286602, _286604, _286606, _286608, _286610] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _286602, _286604), 10437 ^ _113251 : [(10438 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _286604), _286606), _286608), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _286602), _286606), _286610)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _286604, _286602)), _286606), _286608), _286610))], (10444 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _286604, _286602)), _286606), _286608), _286610), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _286604), _286606), _286608), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _286602), _286606), _286610)))]]], (10450 ^ _113251) ^ [_287240, _287242] : [_287240 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _287240), _287242) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10456 ^ _113251) ^ [_287414, _287416] : [-(_287414 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _287414), _287416) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _287416, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _287414, c_Groups_Oone__class_Oone(tc_Nat_Onat))), _287416)))], (10462 ^ _113251) ^ [_287689, _287691] : [_287689 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _287691), _287689) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (10468 ^ _113251) ^ [_287863, _287865] : [-(_287863 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _287865), _287863) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _287865), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _287865), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _287863, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (10474 ^ _113251) ^ [_288136, _288138, _288140] : [class_Rings_Ocomm__ring__1(_288136), -(c_Groups_Ominus__class_Ominus(_288136, hAPP(hAPP(c_Power_Opower__class_Opower(_288136), _288138), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(hAPP(c_Power_Opower__class_Opower(_288136), _288140), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_288136), c_Groups_Ominus__class_Ominus(_288136, _288138, _288140)), c_Groups_Oplus__class_Oplus(_288136, _288138, _288140)))], (10480 ^ _113251) ^ [_288436, _288438, _288440] : [class_Power_Opower(_288436), 10483 ^ _113251 : [(10484 ^ _113251) ^ [] : [_288438 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_288436), _288440), _288438) = c_Groups_Oone__class_Oone(_288436))], (10490 ^ _113251) ^ [] : [-(_288438 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_288436), _288440), _288438) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_288436), _288440), hAPP(hAPP(c_Power_Opower__class_Opower(_288436), _288440), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _288438, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))]]], (10496 ^ _113251) ^ [_289020, _289022, _289024, _289026] : [class_Groups_Omonoid__mult(_289020), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _289022, _289024), -(hAPP(hAPP(c_Power_Opower__class_Opower(_289020), _289026), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_289024), _289022)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_289020), hAPP(hAPP(c_Power_Opower__class_Opower(_289020), _289026), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _289024, _289022))), _289026))], (10506 ^ _113251) ^ [_289392, _289394] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _289392, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _289394)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _289392, _289394))], (10508 ^ _113251) ^ [_289497, _289499] : [-(c_Groups_Ominus__class_Ominus(tc_Int_Oint, _289497, _289499) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _289497, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _289499)))], (10510 ^ _113251) ^ [_289646, _289648] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _289646, _289648), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _289646, _289648), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (10516 ^ _113251) ^ [_289820, _289822] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _289820, _289822), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _289820, _289822))], (10522 ^ _113251) ^ [_290072, _290074, _290076, _290078] : [class_Groups_Oab__group__add(_290072), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_290072, _290074), _290076), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_290072, _290078), _290076), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_290072, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_290072), _290074, _290078)), _290076))], (10536 ^ _113251) ^ [_290550, _290552, _290554, _290556] : [class_Groups_Oab__group__add(_290550), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_290550, _290552), _290554), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_290550, _290556), _290554), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_290550, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_290550), _290552, _290556)), _290554))], (10550 ^ _113251) ^ [_291000, _291002] : [class_Groups_Oab__group__add(_291000), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_291000), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_291000)), _291002) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_291000), _291002))], (10556 ^ _113251) ^ [_291252, _291254, _291256] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _291252), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _291254, _291256))), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _291252), _291256)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _291252), _291254)))], (10566 ^ _113251) ^ [_291613, _291615, _291617] : [class_Rings_Olinordered__idom(_291613), 10569 ^ _113251 : [(10580 ^ _113251) ^ [] : [10581 ^ _113251 : [(10582 ^ _113251) ^ [] : [_291615 = _291617], (10584 ^ _113251) ^ [] : [c_Polynomial_Opos__poly(_291613, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_291613), _291617, _291615))]], -(c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(_291613), _291615, _291617))], (10570 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(_291613), _291615, _291617), -(_291615 = _291617), -(c_Polynomial_Opos__poly(_291613, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_291613), _291617, _291615)))]]], (10588 ^ _113251) ^ [_292292, _292294, _292296] : [class_Rings_Olinordered__idom(_292292), 10591 ^ _113251 : [(10592 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_292292), _292294, _292296), -(c_Polynomial_Opos__poly(_292292, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_292292), _292296, _292294)))], (10598 ^ _113251) ^ [] : [c_Polynomial_Opos__poly(_292292, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_292292), _292296, _292294)), -(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_292292), _292294, _292296))]]], (10604 ^ _113251) ^ [_292793, _292795] : [class_Groups_Oab__group__add(_292793), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_292793), _292795, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_292793))) = _292795)], (10610 ^ _113251) ^ [_293020, _293022, _293024] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _293020, _293022)), _293024) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _293020), _293024), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _293022), _293024)))], (10612 ^ _113251) ^ [_293156, _293158, _293160] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _293156), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _293158, _293160)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _293156), _293158), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _293156), _293160)))], (10614 ^ _113251) ^ [_293322, _293324] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _293322, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _293324, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _293322, _293324))], (10620 ^ _113251) ^ [_293496, _293498] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _293496, _293498), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _293496, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _293498, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (10626 ^ _113251) ^ [_293734, _293736, _293738] : [class_Groups_Oab__group__add(_293734), -(c_Groups_Ominus__class_Ominus(_293734, c_Groups_Ouminus__class_Ouminus(_293734, _293736), c_Groups_Ouminus__class_Ouminus(_293734, _293738)) = c_Groups_Ouminus__class_Ouminus(_293734, c_Groups_Ominus__class_Ominus(_293734, _293736, _293738)))], (10632 ^ _113251) ^ [_293982, _293984] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _293982), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _293984), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _293984), _293982), _293984) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _293984), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _293982, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (10642 ^ _113251) ^ [_294354, _294356] : [c_Divides_Odiv__class_Odiv(tc_Int_Oint, _294354, _294356) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_294356 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 10651 ^ _113251 : [(10652 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _294354))], (10654 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _294354, _294356))]], 10655 ^ _113251 : [(10656 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _294354, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (10658 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _294356, _294354))]]], (10660 ^ _113251) ^ [_294862, _294864] : [-(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _294862, _294864) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 10661 ^ _113251 : [(10662 ^ _113251) ^ [] : [_294864 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (10664 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _294862), c_Orderings_Oord__class_Oless(tc_Int_Oint, _294862, _294864)], (10670 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _294862, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _294864, _294862)]]], (10678 ^ _113251) ^ [_295415, _295417] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _295415), 10681 ^ _113251 : [(10682 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _295417, _295415)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _295417))], (10688 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _295417), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _295417, _295415)))]]], (10694 ^ _113251) ^ [_295895, _295897] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _295895), 10697 ^ _113251 : [(10698 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _295897, _295895)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _295895, _295897))], (10704 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _295895, _295897), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _295897, _295895)))]]], (10710 ^ _113251) ^ [_296375, _296377] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _296375), 10713 ^ _113251 : [(10714 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _296375, _296377)), 10717 ^ _113251 : [(10718 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _296377, _296375))], (10720 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _296377))]]], (10722 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _296375, _296377))), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _296377, _296375), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _296377)]]], (10732 ^ _113251) ^ [_297030, _297032, _297034] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _297030), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _297032), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _297032, _297034), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _297030, _297034), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _297030, _297032)))], (10746 ^ _113251) ^ [_297456, _297458] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _297456), c_Orderings_Oord__class_Oless(tc_Int_Oint, _297458, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _297456, _297458), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (10756 ^ _113251) ^ [_297769, _297771] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _297769), c_Orderings_Oord__class_Oless(tc_Int_Oint, _297769, _297771), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _297769, _297771) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (10766 ^ _113251) ^ [_298080, _298082] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _298080, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 10769 ^ _113251 : [(10770 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _298082, _298080)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _298082, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (10776 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _298082, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _298082, _298080)))]]], (10782 ^ _113251) ^ [_298560, _298562] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _298560, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _298562), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _298560, _298562), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (10792 ^ _113251) ^ [_298887, _298889, _298891] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _298887, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _298889), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _298889, _298891), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _298887, _298889), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _298887, _298891)))], (10806 ^ _113251) ^ [_299313, _299315] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _299313, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _299315, _299313), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _299313, _299315) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (10816 ^ _113251) ^ [_299638, _299640, _299642] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _299638, _299640), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _299642), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _299638, _299642), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _299640, _299642)))], (10826 ^ _113251) ^ [_299983, _299985, _299987] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _299983, _299985), c_Orderings_Oord__class_Oless(tc_Int_Oint, _299987, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _299985, _299987), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _299983, _299987)))], (10836 ^ _113251) ^ [_300314, _300316] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _300314), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _300316), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _300314, _300316), _300314))], (10846 ^ _113251) ^ [_300641, _300643, _300645] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _300641), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _300643, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _300645), _300641)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _300643, _300645), _300641))], (10852 ^ _113251) ^ [_300923, _300925, _300927, _300929] : [class_Divides_Osemiring__div(_300923), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_300923), _300925), _300927)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_300923), _300925), _300929)), -(c_Divides_Odiv__class_Odiv(_300923, c_Groups_Oplus__class_Oplus(_300923, _300927, _300929), _300925) = c_Groups_Oplus__class_Oplus(_300923, c_Divides_Odiv__class_Odiv(_300923, _300927, _300925), c_Divides_Odiv__class_Odiv(_300923, _300929, _300925)))], (10866 ^ _113251) ^ [_301405, _301407] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _301405), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _301407), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _301405, _301407)))], (10876 ^ _113251) ^ [_301746, _301748, _301750, _301752] : [class_Divides_Osemiring__div(_301746), -(_301748 = c_Groups_Ozero__class_Ozero(_301746)), -(c_Divides_Odiv__class_Odiv(_301746, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_301746), _301748), _301750), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_301746), _301748), _301752)) = c_Divides_Odiv__class_Odiv(_301746, _301750, _301752))], (10886 ^ _113251) ^ [_302146, _302148, _302150, _302152] : [class_Divides_Osemiring__div(_302146), -(_302148 = c_Groups_Ozero__class_Ozero(_302146)), -(c_Divides_Odiv__class_Odiv(_302146, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_302146), _302150), _302148), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_302146), _302152), _302148)) = c_Divides_Odiv__class_Odiv(_302146, _302150, _302152))], (10896 ^ _113251) ^ [_302532, _302534, _302536] : [class_Divides_Osemiring__div(_302532), -(_302534 = c_Groups_Ozero__class_Ozero(_302532)), -(c_Divides_Odiv__class_Odiv(_302532, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_302532), _302534), _302536), _302534) = _302536)], (10906 ^ _113251) ^ [_302884, _302886, _302888] : [class_Divides_Osemiring__div(_302884), -(_302886 = c_Groups_Ozero__class_Ozero(_302884)), -(c_Divides_Odiv__class_Odiv(_302884, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_302884), _302888), _302886), _302886) = _302888)], (10916 ^ _113251) ^ [_303250, _303252, _303254, _303256] : [class_Divides_Osemiring__div(_303250), 10919 ^ _113251 : [(10920 ^ _113251) ^ [] : [_303252 = c_Groups_Ozero__class_Ozero(_303250), -(c_Divides_Odiv__class_Odiv(_303250, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_303250), _303252), _303254), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_303250), _303252), _303256)) = c_Groups_Ozero__class_Ozero(_303250))], (10926 ^ _113251) ^ [] : [-(_303252 = c_Groups_Ozero__class_Ozero(_303250)), -(c_Divides_Odiv__class_Odiv(_303250, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_303250), _303252), _303254), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_303250), _303252), _303256)) = c_Divides_Odiv__class_Odiv(_303250, _303254, _303256))]]], (10932 ^ _113251) ^ [_303860, _303862, _303864] : [class_Divides_Osemiring__div(_303860), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_303860), _303862), _303864)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_303860), _303862), c_Divides_Odiv__class_Odiv(_303860, _303864, _303862)) = _303864)], (10942 ^ _113251) ^ [_304233, _304235, _304237, _304239] : [class_Divides_Osemiring__div(_304233), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_304233), _304235), _304237)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_304233), _304239), c_Divides_Odiv__class_Odiv(_304233, _304237, _304235)) = c_Divides_Odiv__class_Odiv(_304233, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_304233), _304239), _304237), _304235))], (10952 ^ _113251) ^ [_304626, _304628, _304630] : [class_Divides_Osemiring__div(_304626), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_304626), _304628), _304630)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_304626), c_Divides_Odiv__class_Odiv(_304626, _304630, _304628)), _304628) = _304630)], (10962 ^ _113251) ^ [_304999, _305001, _305003, _305005] : [class_Divides_Osemiring__div(_304999), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_304999), _305001), _305003)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_304999), c_Divides_Odiv__class_Odiv(_304999, _305003, _305001)), _305005) = c_Divides_Odiv__class_Odiv(_304999, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_304999), _305003), _305005), _305001))], (10972 ^ _113251) ^ [_305420, _305422, _305424, _305426, _305428] : [class_Divides_Osemiring__div(_305420), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_305420), _305422), _305424)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_305420), _305426), _305428)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_305420), c_Divides_Odiv__class_Odiv(_305420, _305424, _305422)), c_Divides_Odiv__class_Odiv(_305420, _305428, _305426)) = c_Divides_Odiv__class_Odiv(_305420, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_305420), _305424), _305428), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_305420), _305422), _305426)))], (10986 ^ _113251) ^ [_305948, _305950] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _305948, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _305950), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _305948, _305950), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (10996 ^ _113251) ^ [_306261, _306263] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _306261, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 10999 ^ _113251 : [(11000 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _306263, _306261), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _306263))], (11006 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _306263), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _306263, _306261), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (11012 ^ _113251) ^ [_306741, _306743] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _306741), 11015 ^ _113251 : [(11016 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _306743, _306741), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _306743, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (11022 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _306743, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _306743, _306741), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (11028 ^ _113251) ^ [_307192] : [-(c_Divides_Odiv__class_Odiv(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _307192) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (11030 ^ _113251) ^ [_307303, _307305] : [class_Divides_Osemiring__div(_307303), -(c_Divides_Odiv__class_Odiv(_307303, _307305, c_Groups_Ozero__class_Ozero(_307303)) = c_Groups_Ozero__class_Ozero(_307303))], (11036 ^ _113251) ^ [_307527, _307529] : [class_Divides_Osemiring__div(_307527), -(c_Divides_Odiv__class_Odiv(_307527, c_Groups_Ozero__class_Ozero(_307527), _307529) = c_Groups_Ozero__class_Ozero(_307527))], (11042 ^ _113251) ^ [_307751, _307753] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint), _307751), _307753)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _307751), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _307753, _307751)) = _307753)], (11048 ^ _113251) ^ [_308019, _308021, _308023, _308025] : [class_Divides_Osemiring__div(_308019), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_308019), _308021), _308023)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_308019), c_Divides_Odiv__class_Odiv(_308019, _308023, _308021)), _308025) = c_Divides_Odiv__class_Odiv(_308019, hAPP(hAPP(c_Power_Opower__class_Opower(_308019), _308023), _308025), hAPP(hAPP(c_Power_Opower__class_Opower(_308019), _308021), _308025)))], (11058 ^ _113251) ^ [_308442, _308444, _308446, _308448] : [class_Divides_Osemiring__div(_308442), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_308442), _308444), _308446)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_308442), _308444), _308448)), 11069 ^ _113251 : [(11070 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_308442), c_Divides_Odiv__class_Odiv(_308442, _308446, _308444)), c_Divides_Odiv__class_Odiv(_308442, _308448, _308444))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_308442), _308446), _308448)))], (11076 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_308442), _308446), _308448)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_308442), c_Divides_Odiv__class_Odiv(_308442, _308446, _308444)), c_Divides_Odiv__class_Odiv(_308442, _308448, _308444))))]]], (11082 ^ _113251) ^ [_309220, _309222] : [class_Divides_Osemiring__div(_309220), -(c_Divides_Odiv__class_Odiv(_309220, _309222, c_Groups_Oone__class_Oone(_309220)) = _309222)], (11088 ^ _113251) ^ [_309454, _309456, _309458] : [class_Divides_Oring__div(_309454), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_309454), _309456), _309458)), -(c_Divides_Odiv__class_Odiv(_309454, _309458, c_Groups_Ouminus__class_Ouminus(_309454, _309456)) = c_Groups_Ouminus__class_Ouminus(_309454, c_Divides_Odiv__class_Odiv(_309454, _309458, _309456)))], (11098 ^ _113251) ^ [_309817, _309819, _309821] : [class_Divides_Oring__div(_309817), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_309817), _309819), _309821)), -(c_Divides_Odiv__class_Odiv(_309817, c_Groups_Ouminus__class_Ouminus(_309817, _309821), _309819) = c_Groups_Ouminus__class_Ouminus(_309817, c_Divides_Odiv__class_Odiv(_309817, _309821, _309819)))], (11108 ^ _113251) ^ [_310151, _310153] : [-(c_Divides_Odiv__class_Odiv(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _310151), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _310153)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint, _310151, _310153))], (11110 ^ _113251) ^ [_310259, _310261] : [-(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _310259, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _310261)) = c_Divides_Odiv__class_Odiv(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _310259), _310261))], (11112 ^ _113251) ^ [_310368] : [-(_310368 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _310368, _310368) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (11118 ^ _113251) ^ [_310583, _310585] : [class_Divides_Osemiring__div(_310583), -(_310585 = c_Groups_Ozero__class_Ozero(_310583)), -(c_Divides_Odiv__class_Odiv(_310583, _310585, _310585) = c_Groups_Oone__class_Oone(_310583))], (11128 ^ _113251) ^ [_310927, _310929, _310931, _310933] : [class_Divides_Osemiring__div(_310927), -(_310929 = c_Groups_Ozero__class_Ozero(_310927)), -(c_Divides_Odiv__class_Odiv(_310927, c_Groups_Oplus__class_Oplus(_310927, _310931, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_310927), _310929), _310933)), _310929) = c_Groups_Oplus__class_Oplus(_310927, _310933, c_Divides_Odiv__class_Odiv(_310927, _310931, _310929)))], (11138 ^ _113251) ^ [_311327, _311329, _311331, _311333] : [class_Divides_Osemiring__div(_311327), -(_311329 = c_Groups_Ozero__class_Ozero(_311327)), -(c_Divides_Odiv__class_Odiv(_311327, c_Groups_Oplus__class_Oplus(_311327, _311331, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_311327), _311333), _311329)), _311329) = c_Groups_Oplus__class_Oplus(_311327, _311333, c_Divides_Odiv__class_Odiv(_311327, _311331, _311329)))], (11148 ^ _113251) ^ [_311713, _311715, _311717] : [class_Divides_Osemiring__div(_311713), -(_311715 = c_Groups_Ozero__class_Ozero(_311713)), -(c_Divides_Odiv__class_Odiv(_311713, c_Groups_Oplus__class_Oplus(_311713, _311717, _311715), _311715) = c_Groups_Oplus__class_Oplus(_311713, c_Divides_Odiv__class_Odiv(_311713, _311717, _311715), c_Groups_Oone__class_Oone(_311713)))], (11158 ^ _113251) ^ [_312077, _312079, _312081] : [class_Divides_Osemiring__div(_312077), -(_312079 = c_Groups_Ozero__class_Ozero(_312077)), -(c_Divides_Odiv__class_Odiv(_312077, c_Groups_Oplus__class_Oplus(_312077, _312079, _312081), _312079) = c_Groups_Oplus__class_Oplus(_312077, c_Divides_Odiv__class_Odiv(_312077, _312081, _312079), c_Groups_Oone__class_Oone(_312077)))], (11168 ^ _113251) ^ [_312469, _312471, _312473, _312475, _312477] : [class_Divides_Osemiring__div(_312469), -(_312471 = c_Groups_Ozero__class_Ozero(_312469)), -(_312473 = c_Groups_Ozero__class_Ozero(_312469)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_312469), _312471), _312475)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_312469), _312473), _312477)), 11187 ^ _113251 : [(11188 ^ _113251) ^ [] : [c_Divides_Odiv__class_Odiv(_312469, _312475, _312471) = c_Divides_Odiv__class_Odiv(_312469, _312477, _312473), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_312469), _312475), _312473) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_312469), _312471), _312477))], (11194 ^ _113251) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_312469), _312475), _312473) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_312469), _312471), _312477), -(c_Divides_Odiv__class_Odiv(_312469, _312475, _312471) = c_Divides_Odiv__class_Odiv(_312469, _312477, _312473))]]], (11200 ^ _113251) ^ [_313521, _313523, _313525, _313527] : [class_Divides_Osemiring__div(_313521), -(_313523 = c_Groups_Ozero__class_Ozero(_313521)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_313521), _313523), _313525)), 11211 ^ _113251 : [(11212 ^ _113251) ^ [] : [c_Divides_Odiv__class_Odiv(_313521, _313525, _313523) = _313527, -(_313525 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_313521), _313527), _313523))], (11218 ^ _113251) ^ [] : [_313525 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_313521), _313527), _313523), -(c_Divides_Odiv__class_Odiv(_313521, _313525, _313523) = _313527)]]], (11270 ^ _113251) ^ [_315925, _315927, _315929] : [-(hBOOL(hAPP(_315925, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _315927, _315929)))), 11273 ^ _113251 : [(11274 ^ _113251) ^ [] : [-(_315929 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (11276 ^ _113251) ^ [] : [hBOOL(hAPP(_315925, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], 11279 ^ _113251 : [(11280 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _315929))], (11284 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), 11282 ^ [_315925, _315927, _315929]))], (11286 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, 11282 ^ [_315925, _315927, _315929], _315929))], (11288 ^ _113251) ^ [] : [-(_315927 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _315929), 11281 ^ [_315925, _315927, _315929]), 11282 ^ [_315925, _315927, _315929]))], (11290 ^ _113251) ^ [] : [hBOOL(hAPP(_315925, 11281 ^ [_315925, _315927, _315929]))]], 11291 ^ _113251 : [(11292 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _315929, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (11296 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _315929, 11294 ^ [_315925, _315927, _315929]))], (11298 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, 11294 ^ [_315925, _315927, _315929], c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (11300 ^ _113251) ^ [] : [-(_315927 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _315929), 11293 ^ [_315925, _315927, _315929]), 11294 ^ [_315925, _315927, _315929]))], (11302 ^ _113251) ^ [] : [hBOOL(hAPP(_315925, 11293 ^ [_315925, _315927, _315929]))]]], (11224 ^ _113251) ^ [_314305, _314307, _314309] : [hBOOL(hAPP(_314305, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _314307, _314309))), 11227 ^ _113251 : [(11228 ^ _113251) ^ [] : [_314309 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_314305, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (11234 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _314309), 11237 ^ _113251 : [(11238 ^ _113251) ^ [_314826] : [-(hBOOL(hAPP(_314305, _314826))), 11239 ^ _113251 : [(11240 ^ _113251) ^ [_314948] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _314948), c_Orderings_Oord__class_Oless(tc_Int_Oint, _314948, _314309), _314307 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _314309), _314826), _314948)]]]]], (11252 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _314309, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 11255 ^ _113251 : [(11256 ^ _113251) ^ [_315420] : [-(hBOOL(hAPP(_314305, _315420))), 11257 ^ _113251 : [(11258 ^ _113251) ^ [_315542] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _314309, _315542), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _315542, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _314307 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _314309), _315420), _315542)]]]]]]], (11306 ^ _113251) ^ [_317574, _317576, _317578, _317580] : [_317574 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _317576), _317578), _317580), -(_317576 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _317574, _317576) = _317578), 11313 ^ _113251 : [(11314 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _317576))], (11316 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _317580), c_Orderings_Oord__class_Oless(tc_Int_Oint, _317580, _317576)]], 11321 ^ _113251 : [(11322 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _317576)], (11324 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _317576, _317580), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _317580, c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (11336 ^ _113251) ^ [_318505, _318507] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _318505), -(c_SMT_Oz3div(_318507, _318505) = c_Divides_Odiv__class_Odiv(tc_Int_Oint, _318507, _318505))], (11342 ^ _113251) ^ [_318683, _318685] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _318683)), -(c_SMT_Oz3div(_318685, _318683) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _318685, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _318683))))], (11348 ^ _113251) ^ [_318946, _318948] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _318946, _318948), -(c_Nat__Transfer_Otsub(_318948, _318946) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _318948, _318946))], (11354 ^ _113251) ^ [_319124, _319126] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _319124, _319126)), -(c_Nat__Transfer_Otsub(_319126, _319124) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (11360 ^ _113251) ^ [_319361, _319363, _319365] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _319361), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _319361, _319363), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _319365, _319363), c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _319365, _319361)))], (11370 ^ _113251) ^ [_319692, _319694] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _319692), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _319692), _319694), _319692) = _319694)], (11376 ^ _113251) ^ [_319924, _319926] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _319924), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _319926), _319924), _319924) = _319926)], (11382 ^ _113251) ^ [_320170, _320172, _320174] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _320170), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _320170), _320172), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _320170), _320174)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _320172, _320174))], (11388 ^ _113251) ^ [_320428, _320430] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _320428), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _320430), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _320430, _320428), _320430))], (11398 ^ _113251) ^ [_320726, _320728] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _320726, _320728), _320726))], (11400 ^ _113251) ^ [_320854, _320856, _320858] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _320854, _320856), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _320854, _320858), c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _320856, _320858)))], (11406 ^ _113251) ^ [_321061] : [-(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _321061, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _321061)], (11408 ^ _113251) ^ [_321172, _321174] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _321172, _321174), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _321172, _321174) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11414 ^ _113251) ^ [_321391, _321393, _321395] : [-(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _321391, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _321393), _321395)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _321391, _321393), _321395))], (11416 ^ _113251) ^ [_321534, _321536, _321538] : [class_Fields_Ofield(_321534), -(c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_321534), _321536, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_321534), _321538)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_321534), c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_321534), _321536, _321538)))], (11422 ^ _113251) ^ [_321806, _321808, _321810] : [class_Fields_Ofield(_321806), -(c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_321806), c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_321806), _321808), _321810) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_321806), c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_321806), _321808, _321810)))], (11428 ^ _113251) ^ [_322092, _322094, _322096, _322098] : [class_Fields_Ofield(_322092), -(c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_322092), _322094, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_322092)), _322096), _322098)) = c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_322092), c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_322092), _322094, _322096), _322098))], (11434 ^ _113251) ^ [_322402, _322404, _322406] : [_322402 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _322402), _322404), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _322402), _322406)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11440 ^ _113251) ^ [_322602, _322604, _322606] : [-(_322602 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _322602), _322604), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _322602), _322606)) = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _322604, _322606))], (11446 ^ _113251) ^ [_322905, _322907, _322909, _322911, _322913] : [class_Fields_Ofield(_322905), c_Polynomial_Opdivmod__rel(_322905, _322907, _322909, _322911, _322913), -(c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_322905), _322907, _322909) = _322911)], (11456 ^ _113251) ^ [_323264, _323266, _323268] : [class_Fields_Ofield(_323264), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_323264, _323266), c_Polynomial_Odegree(_323264, _323268)), -(c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(_323264), _323266, _323268) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_323264)))], (11466 ^ _113251) ^ [_323605, _323607] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _323605), 11469 ^ _113251 : [(11470 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _323607, _323605), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _323607, _323605) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11476 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _323607, _323605)), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _323607, _323605) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _323607, _323605), _323605)))]]], (11482 ^ _113251) ^ [_324113, _324115] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _324113), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _324115, _324113)), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _324115, _324113) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _324115, _324113), _324113)))], (11516 ^ _113251) ^ [_325269, _325271, _325273] : [-(hBOOL(hAPP(_325269, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _325271, _325273)))), 11519 ^ _113251 : [(11520 ^ _113251) ^ [] : [-(_325273 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11522 ^ _113251) ^ [] : [hBOOL(hAPP(_325269, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 11523 ^ _113251 : [(11524 ^ _113251) ^ [] : [_325273 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11528 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 11526 ^ [_325269, _325271, _325273], _325273))], (11530 ^ _113251) ^ [] : [-(_325271 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _325273), 11525 ^ [_325269, _325271, _325273]), 11526 ^ [_325269, _325271, _325273]))], (11532 ^ _113251) ^ [] : [hBOOL(hAPP(_325269, 11525 ^ [_325269, _325271, _325273]))]]], (11492 ^ _113251) ^ [_324490, _324492, _324494] : [hBOOL(hAPP(_324490, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _324492, _324494))), 11495 ^ _113251 : [(11496 ^ _113251) ^ [] : [_324494 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_324490, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (11502 ^ _113251) ^ [] : [-(_324494 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 11505 ^ _113251 : [(11506 ^ _113251) ^ [_324944, _324946] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _324944, _324494), _324492 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _324494), _324946), _324944), -(hBOOL(hAPP(_324490, _324946)))]]]]], (11536 ^ _113251) ^ [_326189, _326191, _326193] : [hBOOL(hAPP(_326189, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _326191, _326193))), 11541 ^ _113251 : [(11542 ^ _113251) ^ [] : [-(_326193 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (11544 ^ _113251) ^ [] : [-(hBOOL(hAPP(_326189, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]], 11546 ^ _113251 : [(11547 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _326193), 11545 ^ [_326189, _326191, _326193]), _326191))], (11549 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _326191, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _326193), c_Nat_OSuc(11545 ^ [_326189, _326191, _326193]))))], (11551 ^ _113251) ^ [] : [-(hBOOL(hAPP(_326189, 11545 ^ [_326189, _326191, _326193])))]]], (11553 ^ _113251) ^ [_326844, _326846, _326848] : [-(hBOOL(hAPP(_326844, c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _326846, _326848)))), 11554 ^ _113251 : [(11555 ^ _113251) ^ [] : [_326848 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_326844, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (11561 ^ _113251) ^ [_327138] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _326848), _327138), _326846), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _326846, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _326848), c_Nat_OSuc(_327138))), hBOOL(hAPP(_326844, _327138))]]], (11573 ^ _113251) ^ [_327575, _327577, _327579] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _327575), 11576 ^ _113251 : [(11587 ^ _113251) ^ [] : [_327577 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _327579, _327575), 11590 ^ _113251 : [(11591 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _327575), _327577), _327579))], (11593 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _327579, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _327575), c_Nat_OSuc(_327577))))]]], (11577 ^ _113251) ^ [] : [-(_327577 = c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _327579, _327575)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _327575), _327577), _327579), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _327579, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _327575), c_Nat_OSuc(_327577)))]]], (11595 ^ _113251) ^ [_328277, _328279] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _328277), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _328277, _328279), -(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, _328279, _328277) = c_Nat_OSuc(c_Divides_Odiv__class_Odiv(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _328279, _328277), _328277)))], (11605 ^ _113251) ^ [_328608, _328610] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _328608), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _328610), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Nat__Transfer_Otsub(_328608, _328610)))], (11615 ^ _113251) ^ [_328919, _328921] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _328919, _328921), -(c_Nat__Transfer_Otsub(_328921, _328919) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _328921, _328919))], (11621 ^ _113251) ^ [_329187, _329189, _329191, _329193, _329195] : [class_Groups_Oab__group__add(_329187), -(c_Groups_Ominus__class_Ominus(_329187, c_Groups_Oplus__class_Oplus(_329187, _329189, _329191), c_Groups_Oplus__class_Oplus(_329187, _329193, _329195)) = c_Groups_Oplus__class_Oplus(_329187, c_Groups_Ominus__class_Ominus(_329187, _329189, _329193), c_Groups_Ominus__class_Ominus(_329187, _329191, _329195)))], (11627 ^ _113251) ^ [_329461, _329463] : [class_Rings_Olinordered__idom(_329461), 11630 ^ _113251 : [(11631 ^ _113251) ^ [] : [_329463 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_329461)), -(c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(_329461), _329463) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_329461)))], (11637 ^ _113251) ^ [] : [-(_329463 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_329461))), 11640 ^ _113251 : [(11641 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_329461), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_329461)), _329463), -(c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(_329461), _329463) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_329461)))], (11647 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_329461), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_329461)), _329463)), -(c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(_329461), _329463) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_329461), c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_329461))))]]]]], (11653 ^ _113251) ^ [_330289, _330291] : [class_RealVector_Oreal__normed__vector(_330289), -(c_Groups_Osgn__class_Osgn(_330289, c_Groups_Ouminus__class_Ouminus(_330289, _330291)) = c_Groups_Ouminus__class_Ouminus(_330289, c_Groups_Osgn__class_Osgn(_330289, _330291)))], (11659 ^ _113251) ^ [_330507] : [class_RealVector_Oreal__normed__algebra__1(_330507), -(c_Groups_Osgn__class_Osgn(_330507, c_Groups_Oone__class_Oone(_330507)) = c_Groups_Oone__class_Oone(_330507))], (11665 ^ _113251) ^ [_330723, _330725] : [class_Rings_Olinordered__idom(_330723), -(c_Groups_Osgn__class_Osgn(_330723, c_Groups_Osgn__class_Osgn(_330723, _330725)) = c_Groups_Osgn__class_Osgn(_330723, _330725))], (11671 ^ _113251) ^ [_330963, _330965, _330967] : [class_RealVector_Oreal__normed__div__algebra(_330963), -(c_Groups_Osgn__class_Osgn(_330963, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_330963), _330965), _330967)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_330963), c_Groups_Osgn__class_Osgn(_330963, _330965)), c_Groups_Osgn__class_Osgn(_330963, _330967)))], (11677 ^ _113251) ^ [_331241, _331243, _331245] : [class_Rings_Olinordered__idom(_331241), -(c_Groups_Osgn__class_Osgn(_331241, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_331241), _331243), _331245)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_331241), c_Groups_Osgn__class_Osgn(_331241, _331243)), c_Groups_Osgn__class_Osgn(_331241, _331245)))], (11683 ^ _113251) ^ [_331491] : [class_Groups_Osgn__if(_331491), -(c_Groups_Osgn__class_Osgn(_331491, c_Groups_Ozero__class_Ozero(_331491)) = c_Groups_Ozero__class_Ozero(_331491))], (11689 ^ _113251) ^ [_331693] : [class_RealVector_Oreal__normed__vector(_331693), -(c_Groups_Osgn__class_Osgn(_331693, c_Groups_Ozero__class_Ozero(_331693)) = c_Groups_Ozero__class_Ozero(_331693))], (11695 ^ _113251) ^ [_331909, _331911] : [class_RealVector_Oreal__normed__vector(_331909), 11698 ^ _113251 : [(11699 ^ _113251) ^ [] : [c_Groups_Osgn__class_Osgn(_331909, _331911) = c_Groups_Ozero__class_Ozero(_331909), -(_331911 = c_Groups_Ozero__class_Ozero(_331909))], (11705 ^ _113251) ^ [] : [_331911 = c_Groups_Ozero__class_Ozero(_331909), -(c_Groups_Osgn__class_Osgn(_331909, _331911) = c_Groups_Ozero__class_Ozero(_331909))]]], (11711 ^ _113251) ^ [_332388, _332390] : [class_Rings_Olinordered__idom(_332388), 11714 ^ _113251 : [(11715 ^ _113251) ^ [] : [c_Groups_Osgn__class_Osgn(_332388, _332390) = c_Groups_Ozero__class_Ozero(_332388), -(_332390 = c_Groups_Ozero__class_Ozero(_332388))], (11721 ^ _113251) ^ [] : [_332390 = c_Groups_Ozero__class_Ozero(_332388), -(c_Groups_Osgn__class_Osgn(_332388, _332390) = c_Groups_Ozero__class_Ozero(_332388))]]], (11727 ^ _113251) ^ [_332867, _332869] : [class_Rings_Olinordered__idom(_332867), 11730 ^ _113251 : [(11731 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_332867, c_Groups_Ozero__class_Ozero(_332867), c_Groups_Osgn__class_Osgn(_332867, _332869)), -(c_Orderings_Oord__class_Oless(_332867, c_Groups_Ozero__class_Ozero(_332867), _332869))], (11737 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_332867, c_Groups_Ozero__class_Ozero(_332867), _332869), -(c_Orderings_Oord__class_Oless(_332867, c_Groups_Ozero__class_Ozero(_332867), c_Groups_Osgn__class_Osgn(_332867, _332869)))]]], (11743 ^ _113251) ^ [_333352, _333354] : [class_Rings_Olinordered__idom(_333352), 11746 ^ _113251 : [(11747 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_333352, c_Groups_Osgn__class_Osgn(_333352, _333354), c_Groups_Ozero__class_Ozero(_333352)), -(c_Orderings_Oord__class_Oless(_333352, _333354, c_Groups_Ozero__class_Ozero(_333352)))], (11753 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_333352, _333354, c_Groups_Ozero__class_Ozero(_333352)), -(c_Orderings_Oord__class_Oless(_333352, c_Groups_Osgn__class_Osgn(_333352, _333354), c_Groups_Ozero__class_Ozero(_333352)))]]], (11759 ^ _113251) ^ [_333837, _333839] : [class_Rings_Olinordered__idom(_333837), 11762 ^ _113251 : [(11763 ^ _113251) ^ [] : [c_Groups_Osgn__class_Osgn(_333837, _333839) = c_Groups_Oone__class_Oone(_333837), -(c_Orderings_Oord__class_Oless(_333837, c_Groups_Ozero__class_Ozero(_333837), _333839))], (11769 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_333837, c_Groups_Ozero__class_Ozero(_333837), _333839), -(c_Groups_Osgn__class_Osgn(_333837, _333839) = c_Groups_Oone__class_Oone(_333837))]]], (11775 ^ _113251) ^ [_334319, _334321] : [class_Rings_Olinordered__idom(_334319), c_Orderings_Oord__class_Oless(_334319, c_Groups_Ozero__class_Ozero(_334319), _334321), -(c_Groups_Osgn__class_Osgn(_334319, _334321) = c_Groups_Oone__class_Oone(_334319))], (11785 ^ _113251) ^ [_334632, _334634] : [class_Groups_Osgn__if(_334632), 11788 ^ _113251 : [(11789 ^ _113251) ^ [] : [_334634 = c_Groups_Ozero__class_Ozero(_334632), -(c_Groups_Osgn__class_Osgn(_334632, _334634) = c_Groups_Ozero__class_Ozero(_334632))], (11795 ^ _113251) ^ [] : [-(_334634 = c_Groups_Ozero__class_Ozero(_334632)), 11798 ^ _113251 : [(11799 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_334632, c_Groups_Ozero__class_Ozero(_334632), _334634), -(c_Groups_Osgn__class_Osgn(_334632, _334634) = c_Groups_Oone__class_Oone(_334632))], (11805 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(_334632, c_Groups_Ozero__class_Ozero(_334632), _334634)), -(c_Groups_Osgn__class_Osgn(_334632, _334634) = c_Groups_Ouminus__class_Ouminus(_334632, c_Groups_Oone__class_Oone(_334632)))]]]]], (11811 ^ _113251) ^ [_335408, _335410] : [class_Rings_Olinordered__idom(_335408), 11814 ^ _113251 : [(11815 ^ _113251) ^ [] : [c_Groups_Osgn__class_Osgn(_335408, _335410) = c_Groups_Ouminus__class_Ouminus(_335408, c_Groups_Oone__class_Oone(_335408)), -(c_Orderings_Oord__class_Oless(_335408, _335410, c_Groups_Ozero__class_Ozero(_335408)))], (11821 ^ _113251) ^ [] : [c_Orderings_Oord__class_Oless(_335408, _335410, c_Groups_Ozero__class_Ozero(_335408)), -(c_Groups_Osgn__class_Osgn(_335408, _335410) = c_Groups_Ouminus__class_Ouminus(_335408, c_Groups_Oone__class_Oone(_335408)))]]], (11827 ^ _113251) ^ [_335899, _335901] : [class_Rings_Olinordered__idom(_335899), c_Orderings_Oord__class_Oless(_335899, _335901, c_Groups_Ozero__class_Ozero(_335899)), -(c_Groups_Osgn__class_Osgn(_335899, _335901) = c_Groups_Ouminus__class_Ouminus(_335899, c_Groups_Oone__class_Oone(_335899)))], (11837 ^ _113251) ^ [_336232, _336234, _336236] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _336232), 11843 ^ _113251 : [(11844 ^ _113251) ^ [] : [-(hBOOL(hAPP(_336234, 11842 ^ [_336232, _336234, _336236])))], (11846 ^ _113251) ^ [] : [hBOOL(hAPP(_336234, c_Groups_Ominus__class_Ominus(tc_Int_Oint, 11842 ^ [_336232, _336234, _336236], _336232)))]], c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _336236), 11851 ^ _113251 : [(11852 ^ _113251) ^ [_336747] : [hBOOL(hAPP(_336234, _336747)), -(hBOOL(hAPP(_336234, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _336747, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _336236), _336232)))))]]], (11858 ^ _113251) ^ [_337031, _337033, _337035] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _337031, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 11861 ^ _113251 : [(11880 ^ _113251) ^ [] : [11883 ^ _113251 : [(11884 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _337031, 11882 ^ [_337031, _337033, _337035]))], (11886 ^ _113251) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, 11882 ^ [_337031, _337033, _337035], c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (11888 ^ _113251) ^ [] : [-(_337035 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _337031), 11881 ^ [_337031, _337033, _337035]), 11882 ^ [_337031, _337033, _337035]))], (11890 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(_337033, 11881 ^ [_337031, _337033, _337035]), 11882 ^ [_337031, _337033, _337035]))]], -(hBOOL(hAPP(hAPP(_337033, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _337035, _337031)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _337035, _337031))))], (11862 ^ _113251) ^ [] : [hBOOL(hAPP(hAPP(_337033, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _337035, _337031)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _337035, _337031))), 11865 ^ _113251 : [(11866 ^ _113251) ^ [_337366, _337368] : [-(hBOOL(hAPP(hAPP(_337033, _337368), _337366))), c_Orderings_Oord__class_Oless(tc_Int_Oint, _337031, _337366), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _337366, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _337035 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _337031), _337368), _337366)]]]]], (11894 ^ _113251) ^ [_338501, _338503, _338505, _338507] : [class_Divides_Osemiring__div(_338501), -(c_Groups_Oplus__class_Oplus(_338501, c_Groups_Oplus__class_Oplus(_338501, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_338501), c_Divides_Odiv__class_Odiv(_338501, _338503, _338505)), _338505), c_Divides_Odiv__class_Omod(_338501, _338503, _338505)), _338507) = c_Groups_Oplus__class_Oplus(_338501, _338503, _338507))], (11900 ^ _113251) ^ [_338805, _338807, _338809, _338811] : [class_Divides_Osemiring__div(_338805), -(c_Groups_Oplus__class_Oplus(_338805, c_Groups_Oplus__class_Oplus(_338805, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_338805), _338807), c_Divides_Odiv__class_Odiv(_338805, _338809, _338807)), c_Divides_Odiv__class_Omod(_338805, _338809, _338807)), _338811) = c_Groups_Oplus__class_Oplus(_338805, _338809, _338811))], (11906 ^ _113251) ^ [_339095, _339097, _339099] : [class_Divides_Osemiring__div(_339095), -(c_Groups_Oplus__class_Oplus(_339095, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339095), c_Divides_Odiv__class_Odiv(_339095, _339097, _339099)), _339099), c_Divides_Odiv__class_Omod(_339095, _339097, _339099)) = _339097)], (11912 ^ _113251) ^ [_339363, _339365, _339367] : [class_Divides_Osemiring__div(_339363), -(c_Groups_Oplus__class_Oplus(_339363, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339363), _339365), c_Divides_Odiv__class_Odiv(_339363, _339367, _339365)), c_Divides_Odiv__class_Omod(_339363, _339367, _339365)) = _339367)], (11918 ^ _113251) ^ [_339631, _339633, _339635] : [class_Divides_Osemiring__div(_339631), -(c_Groups_Oplus__class_Oplus(_339631, c_Divides_Odiv__class_Omod(_339631, _339633, _339635), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_339631), c_Divides_Odiv__class_Odiv(_339631, _339633, _339635)), _339635)) = _339633)], (11924 ^ _113251) ^ [_339884, _339886, _339888] : [-(c_Divides_Odiv__class_Odiv(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _339884, _339886), _339888) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Divides_Odiv__class_Odiv(tc_Int_Oint, _339884, _339888), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _339886, _339888)), c_Divides_Odiv__class_Odiv(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Divides_Odiv__class_Omod(tc_Int_Oint, _339884, _339888), c_Divides_Odiv__class_Omod(tc_Int_Oint, _339886, _339888)), _339888)))], (11926 ^ _113251) ^ [_340020, _340022] : [-(c_Divides_Odiv__class_Odiv(tc_Int_Oint, c_Divides_Odiv__class_Omod(tc_Int_Oint, _340020, _340022), _340022) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (11928 ^ _113251) ^ [_340151, _340153, _340155] : [class_Divides_Osemiring__div(_340151), -(c_Divides_Odiv__class_Odiv(_340151, c_Divides_Odiv__class_Omod(_340151, _340153, _340155), _340155) = c_Groups_Ozero__class_Ozero(_340151))], (11934 ^ _113251) ^ [_340376] : [-(c_Divides_Odiv__class_Odiv(tc_Int_Oint, _340376, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (11936 ^ _113251) ^ [_340424] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _340424, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _340424)], (11938 ^ _113251) ^ [_340522, _340524] : [-(_340522 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _340524), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _340522, _340524)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _340522, _340524)))], (11940 ^ _113251) ^ [_340648, _340650, _340652] : [-(c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _340648), _340650), _340652) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _340648), c_Divides_Odiv__class_Odiv(tc_Int_Oint, _340650, _340652)), c_Divides_Odiv__class_Odiv(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _340648), c_Divides_Odiv__class_Omod(tc_Int_Oint, _340650, _340652)), _340652)))], (11942 ^ _113251) ^ [_340783] : [class_Groups_Ocancel__comm__monoid__add(_340783), -(class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(_340783)))], (11948 ^ _113251) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex))], (11950 ^ _113251) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat))], (11952 ^ _113251) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint))], (11954 ^ _113251) ^ [_341146, _341148] : [class_Lattices_Oboolean__algebra(_341146), -(class_Lattices_Oboolean__algebra(tc_fun(_341148, _341146)))], (11960 ^ _113251) ^ [_341358, _341360] : [class_Orderings_Opreorder(_341358), -(class_Orderings_Opreorder(tc_fun(_341360, _341358)))], (11966 ^ _113251) ^ [_341570, _341572] : [class_Orderings_Oorder(_341570), -(class_Orderings_Oorder(tc_fun(_341572, _341570)))], (11972 ^ _113251) ^ [_341782, _341784] : [class_Orderings_Oord(_341782), -(class_Orderings_Oord(tc_fun(_341784, _341782)))], (11978 ^ _113251) ^ [_341994, _341996] : [class_Groups_Ouminus(_341994), -(class_Groups_Ouminus(tc_fun(_341996, _341994)))], (11984 ^ _113251) ^ [_342206, _342208] : [class_Groups_Ominus(_342206), -(class_Groups_Ominus(tc_fun(_342208, _342206)))], (11990 ^ _113251) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (11992 ^ _113251) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (11994 ^ _113251) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (11996 ^ _113251) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (11998 ^ _113251) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (12000 ^ _113251) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (12002 ^ _113251) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (12004 ^ _113251) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (12006 ^ _113251) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (12008 ^ _113251) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (12010 ^ _113251) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (12012 ^ _113251) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (12014 ^ _113251) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (12016 ^ _113251) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (12018 ^ _113251) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (12020 ^ _113251) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (12022 ^ _113251) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (12024 ^ _113251) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (12026 ^ _113251) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (12028 ^ _113251) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (12030 ^ _113251) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (12032 ^ _113251) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (12034 ^ _113251) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (12036 ^ _113251) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (12038 ^ _113251) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (12040 ^ _113251) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (12042 ^ _113251) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (12044 ^ _113251) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (12046 ^ _113251) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (12048 ^ _113251) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Int_Oint))], (12050 ^ _113251) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (12052 ^ _113251) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (12054 ^ _113251) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (12056 ^ _113251) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (12058 ^ _113251) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (12060 ^ _113251) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (12062 ^ _113251) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (12064 ^ _113251) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (12066 ^ _113251) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (12068 ^ _113251) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (12070 ^ _113251) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (12072 ^ _113251) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (12074 ^ _113251) ^ [] : [-(class_Divides_Oring__div(tc_Int_Oint))], (12076 ^ _113251) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (12078 ^ _113251) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (12080 ^ _113251) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (12082 ^ _113251) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (12084 ^ _113251) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (12086 ^ _113251) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (12088 ^ _113251) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (12090 ^ _113251) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (12092 ^ _113251) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (12094 ^ _113251) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (12096 ^ _113251) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (12098 ^ _113251) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (12100 ^ _113251) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (12102 ^ _113251) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (12104 ^ _113251) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (12106 ^ _113251) ^ [] : [-(class_Rings_Odvd(tc_Int_Oint))], (12108 ^ _113251) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (12110 ^ _113251) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (12112 ^ _113251) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (12114 ^ _113251) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (12116 ^ _113251) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (12118 ^ _113251) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (12120 ^ _113251) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (12122 ^ _113251) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (12124 ^ _113251) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (12126 ^ _113251) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (12128 ^ _113251) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (12130 ^ _113251) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (12132 ^ _113251) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (12134 ^ _113251) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (12136 ^ _113251) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (12138 ^ _113251) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (12140 ^ _113251) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (12142 ^ _113251) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (12144 ^ _113251) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (12146 ^ _113251) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (12148 ^ _113251) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Nat_Onat))], (12150 ^ _113251) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (12152 ^ _113251) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (12154 ^ _113251) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (12156 ^ _113251) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (12158 ^ _113251) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (12160 ^ _113251) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (12162 ^ _113251) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (12164 ^ _113251) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (12166 ^ _113251) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (12168 ^ _113251) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (12170 ^ _113251) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (12172 ^ _113251) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (12174 ^ _113251) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (12176 ^ _113251) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (12178 ^ _113251) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (12180 ^ _113251) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (12182 ^ _113251) ^ [] : [-(class_Rings_Odvd(tc_Nat_Onat))], (12184 ^ _113251) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (12186 ^ _113251) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (12188 ^ _113251) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (12190 ^ _113251) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (12192 ^ _113251) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (12194 ^ _113251) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (12196 ^ _113251) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex))], (12198 ^ _113251) ^ [] : [-(class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex))], (12200 ^ _113251) ^ [] : [-(class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex))], (12202 ^ _113251) ^ [] : [-(class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex))], (12204 ^ _113251) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex))], (12206 ^ _113251) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex))], (12208 ^ _113251) ^ [] : [-(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex))], (12210 ^ _113251) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex))], (12212 ^ _113251) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex))], (12214 ^ _113251) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex))], (12216 ^ _113251) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex))], (12218 ^ _113251) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex))], (12220 ^ _113251) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex))], (12222 ^ _113251) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex))], (12224 ^ _113251) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex))], (12226 ^ _113251) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex))], (12228 ^ _113251) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Complex_Ocomplex))], (12230 ^ _113251) ^ [] : [-(class_Groups_Oab__group__add(tc_Complex_Ocomplex))], (12232 ^ _113251) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Complex_Ocomplex))], (12234 ^ _113251) ^ [] : [-(class_Groups_Omonoid__mult(tc_Complex_Ocomplex))], (12236 ^ _113251) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex))], (12238 ^ _113251) ^ [] : [-(class_Groups_Omonoid__add(tc_Complex_Ocomplex))], (12240 ^ _113251) ^ [] : [-(class_Rings_Osemiring__0(tc_Complex_Ocomplex))], (12242 ^ _113251) ^ [] : [-(class_Groups_Ogroup__add(tc_Complex_Ocomplex))], (12244 ^ _113251) ^ [] : [-(class_Rings_Omult__zero(tc_Complex_Ocomplex))], (12246 ^ _113251) ^ [] : [-(class_Rings_Ocomm__ring(tc_Complex_Ocomplex))], (12248 ^ _113251) ^ [] : [-(class_Int_Oring__char__0(tc_Complex_Ocomplex))], (12250 ^ _113251) ^ [] : [-(class_Rings_Osemiring(tc_Complex_Ocomplex))], (12252 ^ _113251) ^ [] : [-(class_Groups_Ouminus(tc_Complex_Ocomplex))], (12254 ^ _113251) ^ [] : [-(class_Rings_Oring__1(tc_Complex_Ocomplex))], (12256 ^ _113251) ^ [] : [-(class_Groups_Ominus(tc_Complex_Ocomplex))], (12258 ^ _113251) ^ [] : [-(class_Fields_Ofield(tc_Complex_Ocomplex))], (12260 ^ _113251) ^ [] : [-(class_Power_Opower(tc_Complex_Ocomplex))], (12262 ^ _113251) ^ [] : [-(class_Groups_Ozero(tc_Complex_Ocomplex))], (12264 ^ _113251) ^ [] : [-(class_Rings_Oring(tc_Complex_Ocomplex))], (12266 ^ _113251) ^ [] : [-(class_Rings_Oidom(tc_Complex_Ocomplex))], (12268 ^ _113251) ^ [] : [-(class_Groups_Oone(tc_Complex_Ocomplex))], (12270 ^ _113251) ^ [] : [-(class_Rings_Odvd(tc_Complex_Ocomplex))], (12272 ^ _113251) ^ [_349877] : [class_Rings_Oidom(_349877), -(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(_349877)))], (12278 ^ _113251) ^ [_350067] : [class_Rings_Olinordered__idom(_350067), -(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(_350067)))], (12284 ^ _113251) ^ [_350257] : [class_Rings_Olinordered__idom(_350257), -(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(_350257)))], (12290 ^ _113251) ^ [_350447] : [class_Rings_Olinordered__idom(_350447), -(class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(_350447)))], (12296 ^ _113251) ^ [_350637] : [class_Rings_Olinordered__idom(_350637), -(class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(_350637)))], (12302 ^ _113251) ^ [_350827] : [class_Rings_Olinordered__idom(_350827), -(class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(_350827)))], (12308 ^ _113251) ^ [_351017] : [class_Rings_Olinordered__idom(_351017), -(class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(_351017)))], (12314 ^ _113251) ^ [_351207] : [class_Rings_Olinordered__idom(_351207), -(class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(_351207)))], (12320 ^ _113251) ^ [_351397] : [class_Rings_Olinordered__idom(_351397), -(class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(_351397)))], (12326 ^ _113251) ^ [_351587] : [class_Groups_Ocancel__comm__monoid__add(_351587), -(class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(_351587)))], (12332 ^ _113251) ^ [_351777] : [class_Rings_Oidom(_351777), -(class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(_351777)))], (12338 ^ _113251) ^ [_351967] : [class_Rings_Olinordered__idom(_351967), -(class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(_351967)))], (12344 ^ _113251) ^ [_352157] : [class_Rings_Olinordered__idom(_352157), -(class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(_352157)))], (12350 ^ _113251) ^ [_352347] : [class_Rings_Oidom(_352347), -(class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(_352347)))], (12356 ^ _113251) ^ [_352537] : [class_Rings_Olinordered__idom(_352537), -(class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(_352537)))], (12362 ^ _113251) ^ [_352727] : [class_Rings_Olinordered__idom(_352727), -(class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(_352727)))], (12368 ^ _113251) ^ [_352917] : [class_Rings_Olinordered__idom(_352917), -(class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(_352917)))], (12374 ^ _113251) ^ [_353107] : [class_Groups_Ocancel__comm__monoid__add(_353107), -(class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(_353107)))], (12380 ^ _113251) ^ [_353297] : [class_Rings_Olinordered__idom(_353297), -(class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(_353297)))], (12386 ^ _113251) ^ [_353487] : [class_Rings_Olinordered__idom(_353487), -(class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(_353487)))], (12392 ^ _113251) ^ [_353677] : [class_Rings_Ocomm__semiring__0(_353677), -(class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(_353677)))], (12398 ^ _113251) ^ [_353867] : [class_Rings_Ocomm__semiring__1(_353867), -(class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(_353867)))], (12404 ^ _113251) ^ [_354057] : [class_Groups_Ocomm__monoid__add(_354057), -(class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(_354057)))], (12410 ^ _113251) ^ [_354247] : [class_Rings_Olinordered__idom(_354247), -(class_Rings_Oordered__semiring(tc_Polynomial_Opoly(_354247)))], (12416 ^ _113251) ^ [_354437] : [class_Rings_Oidom(_354437), -(class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(_354437)))], (12422 ^ _113251) ^ [_354627] : [class_Groups_Ocomm__monoid__add(_354627), -(class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(_354627)))], (12428 ^ _113251) ^ [_354817] : [class_Rings_Olinordered__idom(_354817), -(class_Rings_Olinordered__ring(tc_Polynomial_Opoly(_354817)))], (12434 ^ _113251) ^ [_355007] : [class_Rings_Olinordered__idom(_355007), -(class_Rings_Olinordered__idom(tc_Polynomial_Opoly(_355007)))], (12440 ^ _113251) ^ [_355197] : [class_Rings_Ocomm__semiring__1(_355197), -(class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(_355197)))], (12446 ^ _113251) ^ [_355387] : [class_Rings_Ocomm__semiring__0(_355387), -(class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(_355387)))], (12452 ^ _113251) ^ [_355577] : [class_Fields_Ofield(_355577), -(class_Divides_Osemiring__div(tc_Polynomial_Opoly(_355577)))], (12458 ^ _113251) ^ [_355767] : [class_Rings_Ocomm__semiring__0(_355767), -(class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(_355767)))], (12464 ^ _113251) ^ [_355957] : [class_Groups_Oab__group__add(_355957), -(class_Groups_Oab__group__add(tc_Polynomial_Opoly(_355957)))], (12470 ^ _113251) ^ [_356147] : [class_Rings_Ocomm__semiring__1(_356147), -(class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(_356147)))], (12476 ^ _113251) ^ [_356337] : [class_Rings_Olinordered__idom(_356337), -(class_Rings_Oordered__ring(tc_Polynomial_Opoly(_356337)))], (12482 ^ _113251) ^ [_356527] : [class_Rings_Olinordered__idom(_356527), -(class_Orderings_Opreorder(tc_Polynomial_Opoly(_356527)))], (12488 ^ _113251) ^ [_356717] : [class_Rings_Olinordered__idom(_356717), -(class_Orderings_Olinorder(tc_Polynomial_Opoly(_356717)))], (12494 ^ _113251) ^ [_356907] : [class_Rings_Ocomm__semiring__1(_356907), -(class_Groups_Omonoid__mult(tc_Polynomial_Opoly(_356907)))], (12500 ^ _113251) ^ [_357097] : [class_Rings_Ocomm__ring__1(_357097), -(class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(_357097)))], (12506 ^ _113251) ^ [_357287] : [class_Groups_Ocomm__monoid__add(_357287), -(class_Groups_Omonoid__add(tc_Polynomial_Opoly(_357287)))], (12512 ^ _113251) ^ [_357477] : [class_Rings_Ocomm__semiring__0(_357477), -(class_Rings_Osemiring__0(tc_Polynomial_Opoly(_357477)))], (12518 ^ _113251) ^ [_357667] : [class_Groups_Oab__group__add(_357667), -(class_Groups_Ogroup__add(tc_Polynomial_Opoly(_357667)))], (12524 ^ _113251) ^ [_357857] : [class_Fields_Ofield(_357857), -(class_Divides_Oring__div(tc_Polynomial_Opoly(_357857)))], (12530 ^ _113251) ^ [_358047] : [class_Rings_Ocomm__semiring__0(_358047), -(class_Rings_Omult__zero(tc_Polynomial_Opoly(_358047)))], (12536 ^ _113251) ^ [_358237] : [class_Rings_Ocomm__ring(_358237), -(class_Rings_Ocomm__ring(tc_Polynomial_Opoly(_358237)))], (12542 ^ _113251) ^ [_358427] : [class_Rings_Olinordered__idom(_358427), -(class_Orderings_Oorder(tc_Polynomial_Opoly(_358427)))], (12548 ^ _113251) ^ [_358617] : [class_Rings_Olinordered__idom(_358617), -(class_Int_Oring__char__0(tc_Polynomial_Opoly(_358617)))], (12554 ^ _113251) ^ [_358807] : [class_Rings_Ocomm__semiring__0(_358807), -(class_Rings_Osemiring(tc_Polynomial_Opoly(_358807)))], (12560 ^ _113251) ^ [_358997] : [class_Rings_Olinordered__idom(_358997), -(class_Orderings_Oord(tc_Polynomial_Opoly(_358997)))], (12566 ^ _113251) ^ [_359187] : [class_Groups_Oab__group__add(_359187), -(class_Groups_Ouminus(tc_Polynomial_Opoly(_359187)))], (12572 ^ _113251) ^ [_359377] : [class_Rings_Olinordered__idom(_359377), -(class_Groups_Osgn__if(tc_Polynomial_Opoly(_359377)))], (12578 ^ _113251) ^ [_359567] : [class_Rings_Ocomm__ring__1(_359567), -(class_Rings_Oring__1(tc_Polynomial_Opoly(_359567)))], (12584 ^ _113251) ^ [_359757] : [class_Groups_Oab__group__add(_359757), -(class_Groups_Ominus(tc_Polynomial_Opoly(_359757)))], (12590 ^ _113251) ^ [_359947] : [class_Rings_Ocomm__semiring__1(_359947), -(class_Power_Opower(tc_Polynomial_Opoly(_359947)))], (12596 ^ _113251) ^ [_360137] : [class_Groups_Ozero(_360137), -(class_Groups_Ozero(tc_Polynomial_Opoly(_360137)))], (12602 ^ _113251) ^ [_360327] : [class_Rings_Ocomm__ring(_360327), -(class_Rings_Oring(tc_Polynomial_Opoly(_360327)))], (12608 ^ _113251) ^ [_360517] : [class_Rings_Oidom(_360517), -(class_Rings_Oidom(tc_Polynomial_Opoly(_360517)))], (12614 ^ _113251) ^ [_360707] : [class_Rings_Ocomm__semiring__1(_360707), -(class_Groups_Oone(tc_Polynomial_Opoly(_360707)))], (12620 ^ _113251) ^ [_360897] : [class_Rings_Ocomm__semiring__1(_360897), -(class_Rings_Odvd(tc_Polynomial_Opoly(_360897)))], (12626 ^ _113251) ^ [_361101, _361103] : [hBOOL(c_fequal(_361101, _361103)), -(_361101 = _361103)], (12632 ^ _113251) ^ [_361317, _361319] : [_361317 = _361319, -(hBOOL(c_fequal(_361317, _361319)))], (12638 ^ _113251) ^ [] : [12639 ^ _113251 : [(12640 ^ _113251) ^ [_361513] : [v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), _361513)]], -(v_thesis____)]], input).
% 140.44/136.03  ncf('1',plain,[v_thesis____],start(12644 ^ 0)).
% 140.44/136.03  ncf('1.1',plain,[-(v_thesis____), 12640 : v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex), v_qa____, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))))],extension(12638 ^ 1,bind([[_361513], [c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex), v_qa____, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))]]))).
% 140.44/136.03  ncf('1.1.1',plain,[-(v_qa____ = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex), v_qa____, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex), v_qa____, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))) = v_qa____],extension(4 ^ 4,bind([[_113304, _113306], [v_qa____, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex), v_qa____, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))))]]))).
% 140.44/136.03  ncf('1.1.1.1',plain,[-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), c_Divides_Odiv__class_Odiv(tc_Polynomial_Opoly(tc_Complex_Ocomplex), v_qa____, c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))))) = v_qa____), class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), v_qa____))],extension(10932 ^ 5,bind([[_303860, _303862, _303864], [tc_Polynomial_Opoly(tc_Complex_Ocomplex), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))), v_qa____]]))).
% 140.44/136.03  ncf('1.1.1.1.1',plain,[-(class_Divides_Osemiring__div(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), class_Fields_Ofield(tc_Complex_Ocomplex)],extension(12452 ^ 6,bind([[_355577], [tc_Complex_Ocomplex]]))).
% 140.44/136.03  ncf('1.1.1.1.1.1',plain,[-(class_Fields_Ofield(tc_Complex_Ocomplex))],extension(12258 ^ 7)).
% 140.44/136.03  ncf('1.1.1.1.2',plain,[-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(tc_Complex_Ocomplex)), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex, v_a____), c_Polynomial_OpCons(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))))), v_qa____)))],extension(1153 ^ 6)).
% 140.44/136.03  %-----------------------------------------------------
% 140.44/136.03  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------