%------------------------------------------------------------------------------
% File : nanoCoP---2.0
% Problem : SWW288+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : nanocop.sh %s %d
% Computer : n023.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 12:25:52 EDT 2023
% Result : Theorem 76.87s 74.89s
% Output : Proof 76.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : SWW288+1 : TPTP v8.1.2. Released v5.2.0.
% 0.04/0.12 % Command : nanocop.sh %s %d
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu May 18 22:24:14 EDT 2023
% 0.12/0.33 % CPUTime :
% 76.87/74.89
% 76.87/74.89 /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 76.87/74.89 Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 76.87/74.89 %-----------------------------------------------------
% 76.87/74.89 ncf(matrix, plain, [(13064 ^ _832576) ^ [] : [c_Polynomial_Odegree(t_a, v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], !, (5160 ^ _356604) ^ [_540865, _540867] : [class_Rings_Ocomm__semiring__1(_540865), -(c_Rings_Odvd__class_Odvd(_540865, c_Groups_Oone__class_Oone(_540865), _540867))], (1788 ^ _356604) ^ [_416732, _416734, _416736] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _416732, _416734), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _416732, _416736), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _416734, _416736)))], (2188 ^ _356604) ^ [_430644] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _430644))], (12648 ^ _356604) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (152 ^ _356604) ^ [_361622, _361624] : [-(class_Fields_Olinordered__field__inverse__zero(_361622)), _361624 = _361622, class_Fields_Olinordered__field__inverse__zero(_361624)], (1992 ^ _356604) ^ [_424021, _424023, _424025, _424027] : [class_Groups_Oab__semigroup__add(_424021), -(c_Groups_Oplus__class_Oplus(_424021, c_Groups_Oplus__class_Oplus(_424021, _424023, _424025), _424027) = c_Groups_Oplus__class_Oplus(_424021, _424023, c_Groups_Oplus__class_Oplus(_424021, _424025, _424027)))], (12672 ^ _356604) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (9717 ^ _356604) ^ [_700350, _700352] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _700350), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _700352), -(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), _700352), _700350)))], (3342 ^ _356604) ^ [_474380, _474382] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_474380)), _474382) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _474382, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _474380), _474382)))], (4158 ^ _356604) ^ [_503770, _503772, _503774] : [class_RealVector_Oreal__normed__algebra(_503770), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_503770), _503772), c_Groups_Ouminus__class_Ouminus(_503770, _503774)) = c_Groups_Ouminus__class_Ouminus(_503770, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_503770), _503772), _503774)))], (9707 ^ _356604) ^ [_700033, _700035] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _700033), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _700035), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _700033, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _700033), _700035)))], (618 ^ _356604) ^ [_375525, _375527] : [-(class_Rings_Osemiring(_375525)), _375527 = _375525, class_Rings_Osemiring(_375527)], (58 ^ _356604) ^ [_358607, _358609, _358611, _358613, _358615, _358617] : [-(c_Rings_Odvd__class_Odvd(_358615, _358611, _358607)), c_Rings_Odvd__class_Odvd(_358617, _358613, _358609), _358617 = _358615, _358613 = _358611, _358609 = _358607], (9755 ^ _356604) ^ [_701660, _701662, _701664] : [9756 ^ _356604 : [(9759 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _701662, _701664)], (9757 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _701660))]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _701660), _701662), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _701660), _701664)))], (5356 ^ _356604) ^ [_547814, _547816, _547818, _547820] : [class_Fields_Ofield(_547814), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_547814), _547816, _547818), -(_547820 = c_Groups_Ozero__class_Ozero(_547814)), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_547814), c_Polynomial_Osmult(_547814, _547820, _547816), _547818))], (12662 ^ _356604) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Nat_Onat))], (2887 ^ _356604) ^ [_457859, _457861, _457863, _457865] : [class_Orderings_Oord(_457859), c_Orderings_Oord__class_Oless__eq(_457859, _457861, _457863), _457863 = _457865, -(c_Orderings_Oord__class_Oless__eq(_457859, _457861, _457865))], (13002 ^ _356604) ^ [_808555] : [class_Groups_Oab__group__add(_808555), -(class_Groups_Ominus(tc_Polynomial_Opoly(_808555)))], (488 ^ _356604) ^ [_371690, _371692] : [-(class_Rings_Ocomm__semiring(_371690)), _371692 = _371690, class_Rings_Ocomm__semiring(_371692)], (7854 ^ _356604) ^ [_634171, _634173, _634175] : [class_Fields_Ofield(_634171), -(c_Polynomial_Opoly__gcd(_634171, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_634171), _634173), _634175) = c_Polynomial_Opoly__gcd(_634171, _634173, _634175))], (12602 ^ _356604) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (12046 ^ _356604) ^ [_779342, _779344, _779346, _779348] : [class_Fields_Olinordered__field__inverse__zero(_779342), 12049 ^ _356604 : [(12050 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_779342, c_Rings_Oinverse__class_Odivide(_779342, _779344, _779346), _779348), 12053 ^ _356604 : [(12060 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_779342, c_Groups_Ozero__class_Ozero(_779342), _779346)), 12063 ^ _356604 : [(12070 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_779342, _779346, c_Groups_Ozero__class_Ozero(_779342))), -(c_Orderings_Oord__class_Oless__eq(_779342, c_Groups_Ozero__class_Ozero(_779342), _779348))], (12064 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_779342, _779346, c_Groups_Ozero__class_Ozero(_779342)), -(c_Orderings_Oord__class_Oless__eq(_779342, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_779342), _779348), _779346), _779344))]]], (12054 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_779342, c_Groups_Ozero__class_Ozero(_779342), _779346), -(c_Orderings_Oord__class_Oless__eq(_779342, _779344, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_779342), _779348), _779346)))]]], (12076 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_779342, c_Rings_Oinverse__class_Odivide(_779342, _779344, _779346), _779348)), 12079 ^ _356604 : [(12082 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_779342, _779344, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_779342), _779348), _779346))], (12080 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_779342, c_Groups_Ozero__class_Ozero(_779342), _779346))]], 12083 ^ _356604 : [(12086 ^ _356604) ^ [] : [12087 ^ _356604 : [(12090 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_779342, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_779342), _779348), _779346), _779344)], (12088 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_779342, _779346, c_Groups_Ozero__class_Ozero(_779342)))]], 12091 ^ _356604 : [(12094 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_779342, c_Groups_Ozero__class_Ozero(_779342), _779348)], (12092 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_779342, _779346, c_Groups_Ozero__class_Ozero(_779342))]]], (12084 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_779342, c_Groups_Ozero__class_Ozero(_779342), _779346)]]]]], (1782 ^ _356604) ^ [_416490, _416492, _416494] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _416490, _416492), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _416490, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _416494, _416492)))], (12138 ^ _356604) ^ [_782324, _782326, _782328, _782330] : [class_Fields_Olinordered__field(_782324), c_Orderings_Oord__class_Oless(_782324, c_Groups_Ozero__class_Ozero(_782324), _782326), c_Orderings_Oord__class_Oless__eq(_782324, _782328, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_782324), _782330), _782326)), -(c_Orderings_Oord__class_Oless__eq(_782324, c_Rings_Oinverse__class_Odivide(_782324, _782328, _782326), _782330))], (3592 ^ _356604) ^ [_483091, _483093, _483095] : [class_Rings_Oordered__ring(_483091), c_Orderings_Oord__class_Oless__eq(_483091, _483093, c_Groups_Ozero__class_Ozero(_483091)), c_Orderings_Oord__class_Oless__eq(_483091, _483095, c_Groups_Ozero__class_Ozero(_483091)), -(c_Orderings_Oord__class_Oless__eq(_483091, c_Groups_Ozero__class_Ozero(_483091), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_483091), _483093), _483095)))], (1659 ^ _356604) ^ [_411478] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_411478)], (12792 ^ _356604) ^ [_801905] : [class_Rings_Olinordered__idom(_801905), -(class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(_801905)))], (10277 ^ _356604) ^ [_718600, _718602] : [_718600 = _718602, -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _718600, _718602))], (1671 ^ _356604) ^ [_412024, _412026, _412028, _412030, _412032] : [class_Rings_Ocomm__semiring__0(_412024), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_412024), _412026, c_Polynomial_Osmult(_412024, _412028, _412030)) = c_Polynomial_OpCons(_412024, _412032, _412030), 1678 ^ _356604 : [(1681 ^ _356604) ^ [] : [-(_412030 = c_Polynomial_Osynthetic__div(_412024, _412026, _412028))], (1679 ^ _356604) ^ [] : [-(_412032 = hAPP(c_Polynomial_Opoly(_412024, _412026), _412028))]]], (4934 ^ _356604) ^ [_532601, _532603, _532605, _532607] : [class_Groups_Omonoid__mult(_532601), -(hAPP(hAPP(c_Power_Opower__class_Opower(_532601), _532603), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _532605, _532607)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_532601), hAPP(hAPP(c_Power_Opower__class_Opower(_532601), _532603), _532605)), hAPP(hAPP(c_Power_Opower__class_Opower(_532601), _532603), _532607)))], (12374 ^ _356604) ^ [_789640] : [class_Rings_Oidom(_789640), -(class_Groups_Omonoid__add(_789640))], (12654 ^ _356604) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (4906 ^ _356604) ^ [_531462, _531464] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_531462), c_Groups_Ozero__class_Ozero(_531462)), c_Nat_OSuc(_531464)) = c_Groups_Ozero__class_Ozero(_531462)), class_Power_Opower(_531462), class_Rings_Osemiring__0(_531462)], (6230 ^ _356604) ^ [_579066, _579068, _579070] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _579066, _579068), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _579066, _579070), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _579068, _579070)))], (1000 ^ _356604) ^ [_388790, _388792, _388794, _388796, _388798, _388800] : [-(c_Polynomial_OpCons(_388800, _388796, _388792) = c_Polynomial_OpCons(_388798, _388794, _388790)), _388800 = _388798, _388796 = _388794, _388792 = _388790], (10197 ^ _356604) ^ [_716109, _716111] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _716109, _716111), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _716111, _716109), -(_716109 = _716111)], (6334 ^ _356604) ^ [_582867, _582869] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _582867, _582869)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _582869, c_Nat_OSuc(_582867)))], (9857 ^ _356604) ^ [_705235, _705237, _705239, _705241] : [class_Rings_Olinordered__semidom(_705235), hAPP(hAPP(c_Power_Opower__class_Opower(_705235), _705237), _705239) = hAPP(hAPP(c_Power_Opower__class_Opower(_705235), _705241), _705239), c_Orderings_Oord__class_Oless__eq(_705235, c_Groups_Ozero__class_Ozero(_705235), _705237), c_Orderings_Oord__class_Oless__eq(_705235, c_Groups_Ozero__class_Ozero(_705235), _705241), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _705239), -(_705237 = _705241)], (6462 ^ _356604) ^ [_587035, _587037] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _587035, _587037), _587035)], (5632 ^ _356604) ^ [_557547, _557549, _557551] : [class_Rings_Ocomm__ring__1(_557547), -(c_Groups_Ominus__class_Ominus(_557547, hAPP(hAPP(c_Power_Opower__class_Opower(_557547), _557549), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(hAPP(c_Power_Opower__class_Opower(_557547), _557551), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_557547), c_Groups_Ominus__class_Ominus(_557547, _557549, _557551)), c_Groups_Oplus__class_Oplus(_557547, _557549, _557551)))], (2404 ^ _356604) ^ [_438379, _438381, _438383, _438385] : [class_Rings_Ocomm__semiring__0(_438379), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_438379), c_Polynomial_Osmult(_438379, _438381, _438383), c_Polynomial_OpCons(_438379, _438385, _438383)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_438379)), -(_438383 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_438379)))], (7840 ^ _356604) ^ [_633717, _633719, _633721, _633723] : [class_Fields_Ofield(_633717), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_633717), _633719, _633721), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_633717), _633719, _633723), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_633717), _633719, c_Polynomial_Opoly__gcd(_633717, _633721, _633723)))], (3318 ^ _356604) ^ [_473550, _473552, _473554] : [class_Rings_Ocomm__semiring__0(_473550), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_473550, c_Polynomial_Opcompose(_473550, _473552, _473554)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Polynomial_Odegree(_473550, _473552)), c_Polynomial_Odegree(_473550, _473554))))], (2240 ^ _356604) ^ [_432659, _432661] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _432659, _432661), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_432659), c_Nat_OSuc(_432661)))], (4262 ^ _356604) ^ [_508124, _508126, _508128, _508130] : [class_Rings_Ocomm__semiring__1(_508124), -(hAPP(hAPP(c_Power_Opower__class_Opower(_508124), hAPP(hAPP(c_Power_Opower__class_Opower(_508124), _508126), _508128)), _508130) = hAPP(hAPP(c_Power_Opower__class_Opower(_508124), _508126), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _508128), _508130)))], (1617 ^ _356604) ^ [] : [-(c_Nat_Osize__class_Osize(tc_HOL_Obool, c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3835 ^ _356604) ^ [_492861, _492863] : [class_Rings_Ocomm__semiring__1(_492861), -(hAPP(c_Polynomial_Opoly(_492861, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_492861))), _492863) = c_Groups_Oone__class_Oone(_492861))], (8058 ^ _356604) ^ [_642441, _642443, _642445, _642447] : [class_Rings_Olinordered__ring__strict(_642441), c_Orderings_Oord__class_Oless(_642441, _642443, _642445), c_Orderings_Oord__class_Oless(_642441, _642447, c_Groups_Ozero__class_Ozero(_642441)), -(c_Orderings_Oord__class_Oless(_642441, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_642441), _642445), _642447), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_642441), _642443), _642447)))], (10135 ^ _356604) ^ [_714124, _714126] : [_714124 = _714126, c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _714124, _714126), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _714126, _714124))], (2637 ^ _356604) ^ [_448349, _448351, _448353, _448355, _448357] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_448349), 2640 ^ _356604 : [(2641 ^ _356604) ^ [] : [c_Groups_Oplus__class_Oplus(_448349, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_448349), _448351), _448355), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_448349), _448353), _448357)) = c_Groups_Oplus__class_Oplus(_448349, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_448349), _448351), _448357), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_448349), _448353), _448355)), -(_448351 = _448353), -(_448355 = _448357)], (2651 ^ _356604) ^ [] : [-(c_Groups_Oplus__class_Oplus(_448349, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_448349), _448351), _448355), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_448349), _448353), _448357)) = c_Groups_Oplus__class_Oplus(_448349, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_448349), _448351), _448357), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_448349), _448353), _448355))), 2654 ^ _356604 : [(2657 ^ _356604) ^ [] : [_448355 = _448357], (2655 ^ _356604) ^ [] : [_448351 = _448353]]]]], (6088 ^ _356604) ^ [_574135, _574137] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _574135, _574137), _574135) = _574137)], (2116 ^ _356604) ^ [_427971, _427973, _427975, _427977, _427979] : [class_Groups_Ocomm__monoid__add(_427971), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_427971), c_Polynomial_OpCons(_427971, _427973, _427975), c_Polynomial_OpCons(_427971, _427977, _427979)) = c_Polynomial_OpCons(_427971, c_Groups_Oplus__class_Oplus(_427971, _427973, _427977), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_427971), _427975, _427979)))], (4270 ^ _356604) ^ [_508524] : [class_Groups_Oab__group__add(_508524), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_508524), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_508524))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_508524)))], (3048 ^ _356604) ^ [_463568, _463570, _463572, _463574] : [class_Rings_Ocomm__semiring__1(_463568), -(c_Groups_Oplus__class_Oplus(_463568, _463570, c_Groups_Oplus__class_Oplus(_463568, _463572, _463574)) = c_Groups_Oplus__class_Oplus(_463568, _463572, c_Groups_Oplus__class_Oplus(_463568, _463570, _463574)))], (8086 ^ _356604) ^ [_643409, _643411, _643413, _643415] : [class_Rings_Olinordered__semiring__strict(_643409), c_Orderings_Oord__class_Oless(_643409, _643411, _643413), c_Orderings_Oord__class_Oless(_643409, c_Groups_Ozero__class_Ozero(_643409), _643415), -(c_Orderings_Oord__class_Oless(_643409, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_643409), _643415), _643411), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_643409), _643415), _643413)))], (12912 ^ _356604) ^ [_805705] : [class_Rings_Olinordered__idom(_805705), -(class_Orderings_Opreorder(tc_Polynomial_Opoly(_805705)))], (6076 ^ _356604) ^ [_573548, _573550] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _573548, _573550), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _573548, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _573550, _573548)))], (3288 ^ _356604) ^ [_472194, _472196, _472198] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _472194), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _472196, _472198)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _472194), _472196), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _472194), _472198)))], (2424 ^ _356604) ^ [_439097, _439099] : [_439097 = _439099, -(c_Nat_OSuc(_439097) = c_Nat_OSuc(_439099))], (11138 ^ _356604) ^ [_749038, _749040, _749042, _749044, _749046] : [class_Fields_Ofield__inverse__zero(_749038), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_749038), c_Rings_Oinverse__class_Odivide(_749038, _749040, _749042)), c_Rings_Oinverse__class_Odivide(_749038, _749044, _749046)) = c_Rings_Oinverse__class_Odivide(_749038, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_749038), _749040), _749044), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_749038), _749042), _749046)))], (2308 ^ _356604) ^ [_434995, _434997] : [class_Groups_Ocomm__monoid__add(_434995), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_434995), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_434995)), _434997) = _434997)], (4296 ^ _356604) ^ [_509524, _509526] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _509524), _509526) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _509524 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _509526 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (918 ^ _356604) ^ [_385790, _385792, _385794, _385796, _385798, _385800] : [-(c_Polynomial_Oorder(_385800, _385796, _385792) = c_Polynomial_Oorder(_385798, _385794, _385790)), _385800 = _385798, _385796 = _385794, _385792 = _385790], (8688 ^ _356604) ^ [_663487, _663489] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _663487, _663489), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _663489, _663487), _663487) = _663489)], (2807 ^ _356604) ^ [_455304, _455306, _455308, _455310, _455312] : [class_Orderings_Oord(_455304), c_Orderings_Oord__class_Oless__eq(tc_fun(_455306, _455304), _455308, _455310), -(c_Orderings_Oord__class_Oless__eq(_455304, hAPP(_455308, _455312), hAPP(_455310, _455312)))], (12504 ^ _356604) ^ [_793800, _793802] : [class_Groups_Ominus(_793800), -(class_Groups_Ominus(tc_fun(_793802, _793800)))], (1864 ^ _356604) ^ [_419536, _419538, _419540, _419542] : [class_Groups_Ocancel__semigroup__add(_419536), c_Groups_Oplus__class_Oplus(_419536, _419538, _419540) = c_Groups_Oplus__class_Oplus(_419536, _419542, _419540), -(_419538 = _419542)], (7058 ^ _356604) ^ [_607920, _607922, _607924] : [class_Orderings_Opreorder(_607920), c_Orderings_Oord__class_Oless(_607920, _607922, _607924), c_Orderings_Oord__class_Oless(_607920, _607924, _607922)], (8610 ^ _356604) ^ [_660528, _660530] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _660528, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _660528, _660530)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6496 ^ _356604) ^ [_588478, _588480, _588482, _588484] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _588478, _588480), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _588482, _588484), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _588478, _588482), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _588480, _588484)))], (4268 ^ _356604) ^ [_508403, _508405, _508407] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _508403), _508405)), _508407) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _508403), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _508405), _508407)))], (3564 ^ _356604) ^ [_482195, _482197, _482199] : [class_Rings_Oordered__cancel__semiring(_482195), c_Orderings_Oord__class_Oless__eq(_482195, c_Groups_Ozero__class_Ozero(_482195), _482197), c_Orderings_Oord__class_Oless__eq(_482195, _482199, c_Groups_Ozero__class_Ozero(_482195)), -(c_Orderings_Oord__class_Oless__eq(_482195, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_482195), _482199), _482197), c_Groups_Ozero__class_Ozero(_482195)))], (6576 ^ _356604) ^ [_591280, _591282] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _591280, _591282), -(_591280 = _591282), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _591280, _591282))], (9573 ^ _356604) ^ [_694513] : [class_Rings_Olinordered__semidom(_694513), -(c_Orderings_Oord__class_Oless(_694513, c_Groups_Ozero__class_Ozero(_694513), c_Groups_Oplus__class_Oplus(_694513, c_Groups_Oone__class_Oone(_694513), c_Groups_Oone__class_Oone(_694513))))], (5208 ^ _356604) ^ [_542631, _542633, _542635, _542637] : [class_Rings_Ocomm__semiring__1(_542631), c_Rings_Odvd__class_Odvd(_542631, _542633, _542635), c_Rings_Odvd__class_Odvd(_542631, _542635, _542637), -(c_Rings_Odvd__class_Odvd(_542631, _542633, _542637))], (4218 ^ _356604) ^ [_506379] : [class_Rings_Ozero__neq__one(_506379), c_Groups_Ozero__class_Ozero(_506379) = c_Groups_Oone__class_Oone(_506379)], (1665 ^ _356604) ^ [_411715] : [c_Nat_OSuc(_411715) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (1160 ^ _356604) ^ [_394756, _394758] : [hAPP(_394756, 1161 ^ [_394756, _394758]) = hAPP(_394758, 1161 ^ [_394756, _394758]), -(_394756 = _394758)], (8550 ^ _356604) ^ [_658417, _658419, _658421] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _658417, _658419), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _658417, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _658419, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _658417), _658421))))], (12542 ^ _356604) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (12320 ^ _356604) ^ [_787966] : [class_Rings_Oidom(_787966), -(class_Rings_Ono__zero__divisors(_787966))], (11040 ^ _356604) ^ [_745564, _745566, _745568, _745570] : [class_Rings_Odivision__ring(_745564), -(_745566 = c_Groups_Ozero__class_Ozero(_745564)), 11047 ^ _356604 : [(11054 ^ _356604) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_745564), _745568), _745566) = _745570, -(_745568 = c_Rings_Oinverse__class_Odivide(_745564, _745570, _745566))], (11048 ^ _356604) ^ [] : [_745568 = c_Rings_Oinverse__class_Odivide(_745564, _745570, _745566), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_745564), _745568), _745566) = _745570)]]], (12550 ^ _356604) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (2969 ^ _356604) ^ [_460483, _460485, _460487] : [class_Orderings_Oorder(_460483), 2972 ^ _356604 : [(2981 ^ _356604) ^ [] : [-(_460485 = _460487), c_Orderings_Oord__class_Oless__eq(_460483, _460485, _460487), c_Orderings_Oord__class_Oless__eq(_460483, _460487, _460485)], (2973 ^ _356604) ^ [] : [_460485 = _460487, 2976 ^ _356604 : [(2979 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_460483, _460487, _460485))], (2977 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_460483, _460485, _460487))]]]]], (12302 ^ _356604) ^ [_787408] : [class_Rings_Oidom(_787408), -(class_Groups_Oab__semigroup__mult(_787408))], (7872 ^ _356604) ^ [_634897, _634899] : [class_Fields_Ofield(_634897), -(c_Polynomial_Opoly__gcd(_634897, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_634897)), _634899) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_634897)))], (10868 ^ _356604) ^ [_739250, _739252] : [class_Rings_Odivision__ring__inverse__zero(_739250), -(c_Rings_Oinverse__class_Odivide(_739250, _739252, c_Groups_Ozero__class_Ozero(_739250)) = c_Groups_Ozero__class_Ozero(_739250))], (1794 ^ _356604) ^ [_416982, _416984, _416986] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _416982, _416984), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _416984, _416986), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _416982, _416986))], (10962 ^ _356604) ^ [_743010, _743012] : [class_Rings_Odivision__ring(_743010), -(_743012 = c_Groups_Ozero__class_Ozero(_743010)), -(c_Rings_Oinverse__class_Odivide(_743010, _743012, _743012) = c_Groups_Oone__class_Oone(_743010))], (8584 ^ _356604) ^ [_659666] : [_659666 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _659666, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (13058 ^ _356604) ^ [] : [-(hBOOL(c_fTrue))], (10856 ^ _356604) ^ [_738784, _738786, _738788] : [class_RealVector_Oreal__normed__field(_738784), -(c_Rings_Oinverse__class_Odivide(_738784, c_Groups_Ouminus__class_Ouminus(_738784, _738786), _738788) = c_Groups_Ouminus__class_Ouminus(_738784, c_Rings_Oinverse__class_Odivide(_738784, _738786, _738788)))], (12236 ^ _356604) ^ [_785362] : [class_Int_Oring__char__0(_785362), -(class_Groups_Ominus(_785362))], (6086 ^ _356604) ^ [_574023, _574025, _574027] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _574023, _574025), _574027) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _574023, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _574025, _574027)))], (7278 ^ _356604) ^ [_615091, _615093, _615095] : [class_Orderings_Oorder(_615091), 7281 ^ _356604 : [(7290 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_615091, _615093, _615095)), c_Orderings_Oord__class_Oless__eq(_615091, _615093, _615095), -(_615093 = _615095)], (7282 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_615091, _615093, _615095), 7285 ^ _356604 : [(7288 ^ _356604) ^ [] : [_615093 = _615095], (7286 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_615091, _615093, _615095))]]]]], (1619 ^ _356604) ^ [] : [-(c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1457 ^ _356604) ^ [_404084, _404086] : [class_Rings_Ocomm__semiring__0(_404084), -(hAPP(c_Polynomial_Opoly(_404084, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_404084))), _404086) = c_Groups_Ozero__class_Ozero(_404084))], (11950 ^ _356604) ^ [_776000, _776002, _776004, _776006] : [class_Fields_Ofield(_776000), -(_776002 = c_Groups_Ozero__class_Ozero(_776000)), -(c_Groups_Ominus__class_Ominus(_776000, c_Rings_Oinverse__class_Odivide(_776000, _776004, _776002), _776006) = c_Rings_Oinverse__class_Odivide(_776000, c_Groups_Ominus__class_Ominus(_776000, _776004, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_776000), _776002), _776006)), _776002))], (5126 ^ _356604) ^ [_539707, _539709, _539711, _539713] : [class_Rings_Ocomm__semiring__1(_539707), c_Rings_Odvd__class_Odvd(_539707, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_539707), _539709), _539711), _539713), -(c_Rings_Odvd__class_Odvd(_539707, _539709, _539713))], (7590 ^ _356604) ^ [_625127, _625129, _625131, _625133] : [class_RealVector_Oreal__normed__algebra(_625127), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_625127), c_Groups_Ominus__class_Ominus(_625127, _625129, _625131)), _625133) = c_Groups_Ominus__class_Ominus(_625127, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_625127), _625129), _625133), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_625127), _625131), _625133)))], (8949 ^ _356604) ^ [_672946, _672948, _672950] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _672946), _672948), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _672946), _672950))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _672946), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _672948, _672950)], (12720 ^ _356604) ^ [_799625] : [class_Rings_Olinordered__idom(_799625), -(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(_799625)))], (6194 ^ _356604) ^ [_577913, _577915] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _577913, _577915), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _577915), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _577913, _577915))], (12368 ^ _356604) ^ [_789454] : [class_Rings_Oidom(_789454), -(class_Rings_Ocomm__ring__1(_789454))], (12206 ^ _356604) ^ [_784432] : [class_Int_Oring__char__0(_784432), -(class_Groups_Ogroup__add(_784432))], (12638 ^ _356604) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (112 ^ _356604) ^ [_360442, _360444] : [-(class_RealVector_Oreal__normed__field(_360442)), _360444 = _360442, class_RealVector_Oreal__normed__field(_360444)], (4164 ^ _356604) ^ [_504042, _504044, _504046] : [class_RealVector_Oreal__normed__algebra(_504042), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_504042), _504044), c_Groups_Ouminus__class_Ouminus(_504042, _504046)) = c_Groups_Ouminus__class_Ouminus(_504042, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_504042), _504044), _504046)))], (3793 ^ _356604) ^ [_491033, _491035] : [class_Rings_Ocomm__semiring__1(_491033), -(hAPP(hAPP(c_Power_Opower__class_Opower(_491033), _491035), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _491035)], (9997 ^ _356604) ^ [_709959, _709961] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _709959, _709961), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _709961, _709959)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _709961, _709959), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _709959, _709961))], (2414 ^ _356604) ^ [_438710] : [_438710 = c_Nat_OSuc(_438710)], (5500 ^ _356604) ^ [_552856, _552858, _552860] : [class_Rings_Oidom(_552856), 5503 ^ _356604 : [(5510 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_552856), c_Polynomial_OpCons(_552856, c_Groups_Ouminus__class_Ouminus(_552856, _552860), c_Polynomial_OpCons(_552856, c_Groups_Oone__class_Oone(_552856), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_552856)))), _552858), -(hAPP(c_Polynomial_Opoly(_552856, _552858), _552860) = c_Groups_Ozero__class_Ozero(_552856))], (5504 ^ _356604) ^ [] : [hAPP(c_Polynomial_Opoly(_552856, _552858), _552860) = c_Groups_Ozero__class_Ozero(_552856), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_552856), c_Polynomial_OpCons(_552856, c_Groups_Ouminus__class_Ouminus(_552856, _552860), c_Polynomial_OpCons(_552856, c_Groups_Oone__class_Oone(_552856), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_552856)))), _552858))]]], (4244 ^ _356604) ^ [_507412, _507414] : [class_Groups_Omonoid__mult(_507412), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_507412), _507414), c_Groups_Oone__class_Oone(_507412)) = _507414)], (1667 ^ _356604) ^ [_411794] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_411794)], (3036 ^ _356604) ^ [_463008, _463010, _463012, _463014] : [class_Rings_Ocomm__semiring__1(_463008), -(c_Groups_Oplus__class_Oplus(_463008, c_Groups_Oplus__class_Oplus(_463008, _463010, _463012), _463014) = c_Groups_Oplus__class_Oplus(_463008, _463010, c_Groups_Oplus__class_Oplus(_463008, _463012, _463014)))], (8450 ^ _356604) ^ [_655245] : [class_Rings_Olinordered__semidom(_655245), -(c_Orderings_Oord__class_Oless(_655245, c_Groups_Ozero__class_Ozero(_655245), c_Groups_Oone__class_Oone(_655245)))], (8072 ^ _356604) ^ [_642925, _642927, _642929, _642931] : [class_Rings_Olinordered__comm__semiring__strict(_642925), c_Orderings_Oord__class_Oless(_642925, _642927, _642929), c_Orderings_Oord__class_Oless(_642925, c_Groups_Ozero__class_Ozero(_642925), _642931), -(c_Orderings_Oord__class_Oless(_642925, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_642925), _642931), _642927), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_642925), _642931), _642929)))], (12308 ^ _356604) ^ [_787594] : [class_Rings_Oidom(_787594), -(class_Groups_Ocomm__monoid__mult(_787594))], (5642 ^ _356604) ^ [_557990, _557992] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _557990, _557992), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_557990), c_Nat_OSuc(_557992)))], (4748 ^ _356604) ^ [_525587, _525589] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _525587)), _525589) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _525587), _525589)))], (3060 ^ _356604) ^ [_464078, _464080, _464082] : [class_Rings_Oidom(_464078), -(_464080 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_464078))), -(_464082 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_464078))), -(c_Polynomial_Odegree(_464078, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_464078)), _464080), _464082)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Polynomial_Odegree(_464078, _464080), c_Polynomial_Odegree(_464078, _464082)))], (7354 ^ _356604) ^ [_617400, _617402, _617404] : [class_Orderings_Olinorder(_617400), -(c_Orderings_Oord__class_Oless__eq(_617400, _617402, _617404)), -(c_Orderings_Oord__class_Oless(_617400, _617404, _617402))], (9407 ^ _356604) ^ [_689029, _689031, _689033, _689035] : [class_Rings_Olinordered__ring__strict(_689029), c_Orderings_Oord__class_Oless(_689029, _689031, c_Groups_Ozero__class_Ozero(_689029)), 9414 ^ _356604 : [(9421 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_689029, _689035, _689033), -(c_Orderings_Oord__class_Oless__eq(_689029, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_689029), _689031), _689033), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_689029), _689031), _689035)))], (9415 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_689029, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_689029), _689031), _689033), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_689029), _689031), _689035)), -(c_Orderings_Oord__class_Oless__eq(_689029, _689035, _689033))]]], (9077 ^ _356604) ^ [_677522, _677524] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _677522, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _677524, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _677522, _677524)), -(_677522 = _677524)], (1134 ^ _356604) ^ [_393650, _393652, _393654, _393656] : [-(c_fequal(_393656, _393652) = c_fequal(_393654, _393650)), _393656 = _393654, _393652 = _393650], (8624 ^ _356604) ^ [_661066, _661068] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _661066, _661068), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _661066, _661068) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5234 ^ _356604) ^ [_543539, _543541, _543543, _543545] : [class_Rings_Ocomm__semiring__1(_543539), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_543539), _543541, _543543), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_543539), _543541, c_Polynomial_Osmult(_543539, _543545, _543543)))], (3678 ^ _356604) ^ [_486542, _486544, _486546] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _486542), _486544)), _486546) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _486542), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _486544), _486546)))], (11638 ^ _356604) ^ [_765338, _765340, _765342, _765344] : [class_Fields_Olinordered__field__inverse__zero(_765338), 11641 ^ _356604 : [(11642 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_765338, _765340, c_Rings_Oinverse__class_Odivide(_765338, _765342, _765344)), 11645 ^ _356604 : [(11652 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_765338, c_Groups_Ozero__class_Ozero(_765338), _765344)), 11655 ^ _356604 : [(11662 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_765338, _765344, c_Groups_Ozero__class_Ozero(_765338))), -(c_Orderings_Oord__class_Oless(_765338, _765340, c_Groups_Ozero__class_Ozero(_765338)))], (11656 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_765338, _765344, c_Groups_Ozero__class_Ozero(_765338)), -(c_Orderings_Oord__class_Oless(_765338, _765342, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_765338), _765340), _765344)))]]], (11646 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_765338, c_Groups_Ozero__class_Ozero(_765338), _765344), -(c_Orderings_Oord__class_Oless(_765338, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_765338), _765340), _765344), _765342))]]], (11668 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_765338, _765340, c_Rings_Oinverse__class_Odivide(_765338, _765342, _765344))), 11671 ^ _356604 : [(11674 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_765338, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_765338), _765340), _765344), _765342)], (11672 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_765338, c_Groups_Ozero__class_Ozero(_765338), _765344))]], 11675 ^ _356604 : [(11678 ^ _356604) ^ [] : [11679 ^ _356604 : [(11682 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_765338, _765342, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_765338), _765340), _765344))], (11680 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_765338, _765344, c_Groups_Ozero__class_Ozero(_765338)))]], 11683 ^ _356604 : [(11686 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_765338, _765340, c_Groups_Ozero__class_Ozero(_765338))], (11684 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_765338, _765344, c_Groups_Ozero__class_Ozero(_765338))]]], (11676 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_765338, c_Groups_Ozero__class_Ozero(_765338), _765344)]]]]], (2597 ^ _356604) ^ [_446547, _446549, _446551, _446553] : [class_Rings_Ocomm__semiring__0(_446547), -(hAPP(c_Polynomial_Opoly(_446547, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_446547)), _446549), _446551)), _446553) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_446547), hAPP(c_Polynomial_Opoly(_446547, _446549), _446553)), hAPP(c_Polynomial_Opoly(_446547, _446551), _446553)))], (4176 ^ _356604) ^ [_504586, _504588, _504590] : [class_RealVector_Oreal__normed__algebra(_504586), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_504586), c_Groups_Ouminus__class_Ouminus(_504586, _504588)), _504590) = c_Groups_Ouminus__class_Ouminus(_504586, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_504586), _504588), _504590)))], (5032 ^ _356604) ^ [_536214, _536216] : [class_Rings_Ocomm__semiring__1(_536214), -(c_Rings_Odvd__class_Odvd(_536214, _536216, c_Groups_Ozero__class_Ozero(_536214)))], (3901 ^ _356604) ^ [_495183, _495185, _495187] : [class_Groups_Ogroup__add(_495183), 3904 ^ _356604 : [(3911 ^ _356604) ^ [] : [c_Groups_Ouminus__class_Ouminus(_495183, _495187) = _495185, -(c_Groups_Ouminus__class_Ouminus(_495183, _495185) = _495187)], (3905 ^ _356604) ^ [] : [c_Groups_Ouminus__class_Ouminus(_495183, _495185) = _495187, -(c_Groups_Ouminus__class_Ouminus(_495183, _495187) = _495185)]]], (5092 ^ _356604) ^ [_538471, _538473, _538475, _538477] : [class_Rings_Ocomm__semiring__1(_538471), c_Rings_Odvd__class_Odvd(_538471, _538473, _538475), -(c_Rings_Odvd__class_Odvd(_538471, _538473, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_538471), _538477), _538475)))], (11974 ^ _356604) ^ [_776958, _776960, _776962] : [class_Fields_Olinordered__field(_776958), c_Orderings_Oord__class_Oless(_776958, _776960, _776962), -(c_Orderings_Oord__class_Oless(_776958, c_Rings_Oinverse__class_Odivide(_776958, c_Groups_Oplus__class_Oplus(_776958, _776960, _776962), c_Groups_Oplus__class_Oplus(_776958, c_Groups_Oone__class_Oone(_776958), c_Groups_Oone__class_Oone(_776958))), _776962))], (2340 ^ _356604) ^ [_436186, _436188] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _436186, _436188) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 2341 ^ _356604 : [(2348 ^ _356604) ^ [] : [_436186 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _436188 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2342 ^ _356604) ^ [] : [_436186 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _436188 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (10373 ^ _356604) ^ [_721728, _721730, _721732, _721734] : [class_Groups_Omonoid__mult(_721728), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _721730, _721732), -(hAPP(hAPP(c_Power_Opower__class_Opower(_721728), _721734), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_721732), _721730)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_721728), hAPP(hAPP(c_Power_Opower__class_Opower(_721728), _721734), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _721732, _721730))), _721734))], (6934 ^ _356604) ^ [_604066, _604068] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _604066, _604068), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _604066, _604068))], (4048 ^ _356604) ^ [_499856] : [class_Rings_Ocomm__semiring__1(_499856), -(c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_499856)) = c_Polynomial_OpCons(_499856, c_Groups_Oone__class_Oone(_499856), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_499856))))], (4308 ^ _356604) ^ [_509950, _509952] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _509950), _509952), 4311 ^ _356604 : [(4314 ^ _356604) ^ [] : [-(_509952 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (4312 ^ _356604) ^ [] : [-(_509950 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (5076 ^ _356604) ^ [_537846, _537848, _537850] : [class_Rings_Ocomm__semiring__1(_537846), -(c_Rings_Odvd__class_Odvd(_537846, _537848, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_537846), _537850), _537848)))], (1918 ^ _356604) ^ [_421476, _421478, _421480, _421482] : [class_Groups_Oordered__ab__semigroup__add(_421476), c_Orderings_Oord__class_Oless__eq(_421476, _421478, _421480), -(c_Orderings_Oord__class_Oless__eq(_421476, c_Groups_Oplus__class_Oplus(_421476, _421478, _421482), c_Groups_Oplus__class_Oplus(_421476, _421480, _421482)))], (1607 ^ _356604) ^ [_409654, _409656, _409658, _409660] : [class_Rings_Ocomm__semiring__0(_409654), -(c_Polynomial_Osynthetic__div(_409654, c_Polynomial_OpCons(_409654, _409656, _409658), _409660) = c_Polynomial_OpCons(_409654, hAPP(c_Polynomial_Opoly(_409654, _409658), _409660), c_Polynomial_Osynthetic__div(_409654, _409658, _409660)))], (9503 ^ _356604) ^ [_692165, _692167, _692169] : [class_Groups_Oordered__comm__monoid__add(_692165), c_Orderings_Oord__class_Oless__eq(_692165, c_Groups_Ozero__class_Ozero(_692165), _692167), c_Orderings_Oord__class_Oless(_692165, c_Groups_Ozero__class_Ozero(_692165), _692169), -(c_Orderings_Oord__class_Oless(_692165, c_Groups_Ozero__class_Ozero(_692165), c_Groups_Oplus__class_Oplus(_692165, _692167, _692169)))], (5638 ^ _356604) ^ [_557804] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _557804))], (10307 ^ _356604) ^ [_719561, _719563] : [10314 ^ _356604 : [(10317 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _719563, _719561)], (10315 ^ _356604) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _719561, _719563))]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _719561, _719563), -(_719561 = _719563)], (5298 ^ _356604) ^ [_545779, _545781, _545783, _545785, _545787] : [class_Rings_Ocomm__semiring__1(_545779), c_Rings_Odvd__class_Odvd(_545779, hAPP(hAPP(c_Power_Opower__class_Opower(_545779), _545781), _545783), _545785), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _545787, _545783), -(c_Rings_Odvd__class_Odvd(_545779, hAPP(hAPP(c_Power_Opower__class_Opower(_545779), _545781), _545787), _545785))], (12392 ^ _356604) ^ [_790198] : [class_Rings_Oidom(_790198), -(class_Rings_Omult__zero(_790198))], (8865 ^ _356604) ^ [_670091, _670093] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _670091, c_Nat_OSuc(_670093)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _670091, _670093))], (7966 ^ _356604) ^ [_638795, _638797, _638799, _638801] : [class_Rings_Ocomm__ring(_638795), class_Rings_Odvd(_638795), c_Rings_Odvd__class_Odvd(_638795, _638797, _638799), 7977 ^ _356604 : [(7984 ^ _356604) ^ [_639436, _639438] : [c_Rings_Odvd__class_Odvd(_638795, _638797, c_Groups_Oplus__class_Oplus(_638795, c_Groups_Ominus__class_Ominus(_638795, _639438, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_638795), _639436), _638799)), _638801)), -(c_Rings_Odvd__class_Odvd(_638795, _638797, c_Groups_Oplus__class_Oplus(_638795, _639438, _638801)))], (7978 ^ _356604) ^ [_639198, _639200] : [c_Rings_Odvd__class_Odvd(_638795, _638797, c_Groups_Oplus__class_Oplus(_638795, _639200, _638801)), -(c_Rings_Odvd__class_Odvd(_638795, _638797, c_Groups_Oplus__class_Oplus(_638795, c_Groups_Ominus__class_Ominus(_638795, _639200, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_638795), _639198), _638799)), _638801)))]]], (12652 ^ _356604) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (12656 ^ _356604) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (2262 ^ _356604) ^ [_433415, _433417] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_433415), _433417), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _433415, _433417))], (12604 ^ _356604) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (10515 ^ _356604) ^ [_726626, _726628] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _726626), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _726628, _726626), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _726628))], (5244 ^ _356604) ^ [_543904, _543906, _543908, _543910] : [class_Rings_Ocomm__semiring__1(_543904), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_543904), c_Polynomial_Osmult(_543904, _543906, _543908), _543910), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_543904), _543908, _543910))], (2392 ^ _356604) ^ [_437833, _437835, _437837] : [class_Groups_Ozero(_437833), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_437833, c_Polynomial_Omonom(_437833, _437835, _437837)), _437837))], (3502 ^ _356604) ^ [_480250, _480252, _480254] : [class_Rings_Olinordered__ring__strict(_480250), 3505 ^ _356604 : [(3520 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_480250, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_480250), _480252), _480254), c_Groups_Ozero__class_Ozero(_480250))), 3521 ^ _356604 : [(3528 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_480250, _480252, c_Groups_Ozero__class_Ozero(_480250)), c_Orderings_Oord__class_Oless__eq(_480250, c_Groups_Ozero__class_Ozero(_480250), _480254)], (3522 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_480250, c_Groups_Ozero__class_Ozero(_480250), _480252), c_Orderings_Oord__class_Oless__eq(_480250, _480254, c_Groups_Ozero__class_Ozero(_480250))]]], (3506 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_480250, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_480250), _480252), _480254), c_Groups_Ozero__class_Ozero(_480250)), 3511 ^ _356604 : [(3514 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_480250, _480254, c_Groups_Ozero__class_Ozero(_480250)))], (3512 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_480250, c_Groups_Ozero__class_Ozero(_480250), _480252))]], 3515 ^ _356604 : [(3518 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_480250, c_Groups_Ozero__class_Ozero(_480250), _480254))], (3516 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_480250, _480252, c_Groups_Ozero__class_Ozero(_480250)))]]]]], (1247 ^ _356604) ^ [] : [-(c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12978 ^ _356604) ^ [_807795] : [class_Rings_Ocomm__semiring__0(_807795), -(class_Rings_Osemiring(tc_Polynomial_Opoly(_807795)))], (2709 ^ _356604) ^ [_451352, _451354, _451356, _451358] : [class_Rings_Ocomm__semiring__0(_451352), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_451352)), c_Polynomial_Osmult(_451352, _451354, _451356)), _451358) = c_Polynomial_Osmult(_451352, _451354, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_451352)), _451356), _451358)))], (5686 ^ _356604) ^ [_559614, _559616, _559618, _559620] : [class_Rings_Olinordered__semidom(_559614), c_Orderings_Oord__class_Oless(_559614, c_Groups_Oone__class_Oone(_559614), _559616), c_Orderings_Oord__class_Oless(_559614, hAPP(hAPP(c_Power_Opower__class_Opower(_559614), _559616), _559618), hAPP(hAPP(c_Power_Opower__class_Opower(_559614), _559616), _559620)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _559618, _559620))], (4276 ^ _356604) ^ [_508752, _508754] : [class_Groups_Oab__group__add(_508752), -(c_Polynomial_Odegree(_508752, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_508752), _508754)) = c_Polynomial_Odegree(_508752, _508754))], (12568 ^ _356604) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Int_Oint))], (9559 ^ _356604) ^ [_694071, _694073, _694075, _694077] : [class_Rings_Olinordered__semidom(_694071), c_Orderings_Oord__class_Oless(_694071, hAPP(hAPP(c_Power_Opower__class_Opower(_694071), _694073), _694075), hAPP(hAPP(c_Power_Opower__class_Opower(_694071), _694077), _694075)), c_Orderings_Oord__class_Oless__eq(_694071, c_Groups_Ozero__class_Ozero(_694071), _694077), -(c_Orderings_Oord__class_Oless(_694071, _694073, _694077))], (6326 ^ _356604) ^ [_582502] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _582502, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9955 ^ _356604) ^ [_708543, _708545, _708547] : [class_Power_Opower(_708543), 9958 ^ _356604 : [(9965 ^ _356604) ^ [] : [-(_708545 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_708543), _708547), _708545) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_708543), _708547), hAPP(hAPP(c_Power_Opower__class_Opower(_708543), _708547), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _708545, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (9959 ^ _356604) ^ [] : [_708545 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_708543), _708547), _708545) = c_Groups_Oone__class_Oone(_708543))]]], (9843 ^ _356604) ^ [_704751, _704753, _704755, _704757] : [class_Rings_Olinordered__semidom(_704751), c_Orderings_Oord__class_Oless(_704751, c_Groups_Oone__class_Oone(_704751), _704753), c_Orderings_Oord__class_Oless__eq(_704751, hAPP(hAPP(c_Power_Opower__class_Opower(_704751), _704753), _704755), hAPP(hAPP(c_Power_Opower__class_Opower(_704751), _704753), _704757)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _704755, _704757))], (9737 ^ _356604) ^ [_701001, _701003, _701005] : [9738 ^ _356604 : [(9741 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _701001, _701005)], (9739 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _701003))]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _701001), _701003), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _701005), _701003)))], (8836 ^ _356604) ^ [_668910, _668912] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _668910, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _668910, _668912))))], (8370 ^ _356604) ^ [_652640, _652642] : [class_Groups_Olinordered__ab__group__add(_652640), 8373 ^ _356604 : [(8380 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_652640, _652642, c_Groups_Ozero__class_Ozero(_652640)), -(c_Orderings_Oord__class_Oless(_652640, c_Groups_Oplus__class_Oplus(_652640, _652642, _652642), c_Groups_Ozero__class_Ozero(_652640)))], (8374 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_652640, c_Groups_Oplus__class_Oplus(_652640, _652642, _652642), c_Groups_Ozero__class_Ozero(_652640)), -(c_Orderings_Oord__class_Oless(_652640, _652642, c_Groups_Ozero__class_Ozero(_652640)))]]], (4846 ^ _356604) ^ [_529643, _529645, _529647] : [class_Groups_Ogroup__add(_529643), 4849 ^ _356604 : [(4856 ^ _356604) ^ [] : [_529647 = c_Groups_Ouminus__class_Ouminus(_529643, _529645), -(c_Groups_Oplus__class_Oplus(_529643, _529645, _529647) = c_Groups_Ozero__class_Ozero(_529643))], (4850 ^ _356604) ^ [] : [c_Groups_Oplus__class_Oplus(_529643, _529645, _529647) = c_Groups_Ozero__class_Ozero(_529643), -(_529647 = c_Groups_Ouminus__class_Ouminus(_529643, _529645))]]], (6376 ^ _356604) ^ [_584271, _584273] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _584271, _584273)), 6379 ^ _356604 : [(6386 ^ _356604) ^ [] : [_584271 = _584273, -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _584271, c_Nat_OSuc(_584273)))], (6380 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _584271, c_Nat_OSuc(_584273)), -(_584271 = _584273)]]], (1703 ^ _356604) ^ [_413250] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _413250, _413250))], (4466 ^ _356604) ^ [_515423, _515425, _515427, _515429] : [class_Rings_Ocomm__semiring__1(_515423), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_515423), hAPP(hAPP(c_Power_Opower__class_Opower(_515423), _515425), _515427)), hAPP(hAPP(c_Power_Opower__class_Opower(_515423), _515425), _515429)) = hAPP(hAPP(c_Power_Opower__class_Opower(_515423), _515425), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _515427, _515429)))], (11096 ^ _356604) ^ [_747596, _747598] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _747596, _747598), -(c_Nat__Transfer_Otsub(_747598, _747596) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _747598, _747596))], (9229 ^ _356604) ^ [_682933, _682935] : [class_Rings_Oring__1(_682933), -(c_Groups_Ominus__class_Ominus(_682933, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_682933), _682935), _682935), c_Groups_Oone__class_Oone(_682933)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_682933), c_Groups_Oplus__class_Oplus(_682933, _682935, c_Groups_Oone__class_Oone(_682933))), c_Groups_Ominus__class_Ominus(_682933, _682935, c_Groups_Oone__class_Oone(_682933))))], (8895 ^ _356604) ^ [_671118, _671120] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _671118, _671120), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_671118), _671120))], (4758 ^ _356604) ^ [_526118, _526120, _526122] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _526118, _526120)), _526122) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _526118), _526122), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _526120), _526122)))], (9903 ^ _356604) ^ [_706785, _706787, _706789] : [class_Rings_Ocomm__semiring__1(_706785), 9908 ^ _356604 : [(9911 ^ _356604) ^ [] : [_706789 = c_Groups_Oone__class_Oone(_706785)], (9909 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _706787)]], -(c_Rings_Odvd__class_Odvd(_706785, _706789, hAPP(hAPP(c_Power_Opower__class_Opower(_706785), _706789), _706787)))], (5336 ^ _356604) ^ [_547162, _547164, _547166, _547168] : [class_Fields_Ofield(_547162), -(_547164 = c_Groups_Ozero__class_Ozero(_547162)), 5343 ^ _356604 : [(5350 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_547162), _547166, _547168), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_547162), _547166, c_Polynomial_Osmult(_547162, _547164, _547168)))], (5344 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_547162), _547166, c_Polynomial_Osmult(_547162, _547164, _547168)), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_547162), _547166, _547168))]]], (6594 ^ _356604) ^ [_591874, _591876] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _591874, _591876), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _591874, _591876))], (6872 ^ _356604) ^ [_601652, _601654, _601656, _601658] : [class_Groups_Oab__group__add(_601652), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_601652, _601654), _601656), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_601652, _601658), _601656), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_601652, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_601652), _601654, _601658)), _601656))], (7480 ^ _356604) ^ [_621238, _621240, _621242] : [class_Orderings_Oorder(_621238), c_Orderings_Oord__class_Oless__eq(_621238, _621240, _621242), -(_621242 = _621240), -(c_Orderings_Oord__class_Oless(_621238, _621240, _621242))], (6528 ^ _356604) ^ [_589684, _589686, _589688] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _589684, _589686), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _589684, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _589688, _589686)))], (6098 ^ _356604) ^ [_574604, _574606] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _574604), c_Orderings_Oord__class_Oless(tc_Int_Oint, _574604, _574606), c_Rings_Odvd__class_Odvd(tc_Int_Oint, _574606, _574604)], (11280 ^ _356604) ^ [_753808, _753810, _753812] : [class_Fields_Olinordered__field(_753808), c_Orderings_Oord__class_Oless(_753808, _753810, c_Groups_Ozero__class_Ozero(_753808)), c_Orderings_Oord__class_Oless(_753808, _753812, c_Groups_Ozero__class_Ozero(_753808)), -(c_Orderings_Oord__class_Oless(_753808, c_Groups_Ozero__class_Ozero(_753808), c_Rings_Oinverse__class_Odivide(_753808, _753810, _753812)))], (5538 ^ _356604) ^ [_554296, _554298, _554300] : [class_Rings_Odvd(_554296), class_Rings_Osemiring__0(_554296), 5545 ^ _356604 : [(5555 ^ _356604) ^ [] : [-(hBOOL(hAPP(_554298, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_554296), _554300), 5562 ^ [_554296, _554298, _554300])))), 5556 ^ _356604 : [(5557 ^ _356604) ^ [_554945] : [c_Rings_Odvd__class_Odvd(_554296, _554300, c_Groups_Oplus__class_Oplus(_554296, _554945, c_Groups_Ozero__class_Ozero(_554296))), hBOOL(hAPP(_554298, _554945))]]], (5546 ^ _356604) ^ [] : [5547 ^ _356604 : [(5548 ^ _356604) ^ [_554605] : [hBOOL(hAPP(_554298, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_554296), _554300), _554605)))]], 5550 ^ _356604 : [(5553 ^ _356604) ^ [] : [-(hBOOL(hAPP(_554298, 5549 ^ [_554296, _554298, _554300])))], (5551 ^ _356604) ^ [] : [-(c_Rings_Odvd__class_Odvd(_554296, _554300, c_Groups_Oplus__class_Oplus(_554296, 5549 ^ [_554296, _554298, _554300], c_Groups_Ozero__class_Ozero(_554296))))]]]]], (1653 ^ _356604) ^ [_411262, _411264, _411266] : [class_Groups_Ozero(_411262), -(c_Polynomial_Omonom(_411262, _411264, c_Nat_OSuc(_411266)) = c_Polynomial_OpCons(_411262, c_Groups_Ozero__class_Ozero(_411262), c_Polynomial_Omonom(_411262, _411264, _411266)))], (11610 ^ _356604) ^ [_764444, _764446, _764448] : [class_Fields_Olinordered__field(_764444), c_Orderings_Oord__class_Oless__eq(_764444, _764446, c_Groups_Ozero__class_Ozero(_764444)), c_Orderings_Oord__class_Oless(_764444, c_Groups_Ozero__class_Ozero(_764444), _764448), -(c_Orderings_Oord__class_Oless__eq(_764444, c_Rings_Oinverse__class_Odivide(_764444, _764446, _764448), c_Groups_Ozero__class_Ozero(_764444)))], (3204 ^ _356604) ^ [_469196, _469198, _469200, _469202] : [class_Rings_Oordered__comm__semiring(_469196), c_Orderings_Oord__class_Oless__eq(_469196, _469198, _469200), c_Orderings_Oord__class_Oless__eq(_469196, c_Groups_Ozero__class_Ozero(_469196), _469202), -(c_Orderings_Oord__class_Oless__eq(_469196, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_469196), _469202), _469198), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_469196), _469202), _469200)))], (5892 ^ _356604) ^ [_567150, _567152, _567154] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _567150), _567152), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _567150), _567154)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _567150), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _567152, _567154))], (568 ^ _356604) ^ [_374050, _374052] : [-(class_Rings_Osemiring__0(_374050)), _374052 = _374050, class_Rings_Osemiring__0(_374052)], (12398 ^ _356604) ^ [_790384] : [class_Rings_Oidom(_790384), -(class_Rings_Ocomm__ring(_790384))], (12954 ^ _356604) ^ [_807035] : [class_Rings_Ocomm__semiring__0(_807035), -(class_Rings_Omult__zero(tc_Polynomial_Opoly(_807035)))], (8636 ^ _356604) ^ [_661567, _661569, _661571] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _661567), _661569), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _661567), _661571)), -(_661567 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _661569, _661571))], (6732 ^ _356604) ^ [_596589, _596591] : [-(_596589 = _596591), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _596589, _596591)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _596591, _596589))], (9385 ^ _356604) ^ [_688321, _688323, _688325, _688327, _688329] : [class_Rings_Olinordered__semiring__strict(_688321), c_Orderings_Oord__class_Oless(_688321, _688323, _688325), c_Orderings_Oord__class_Oless(_688321, _688327, _688329), c_Orderings_Oord__class_Oless(_688321, c_Groups_Ozero__class_Ozero(_688321), _688325), c_Orderings_Oord__class_Oless__eq(_688321, c_Groups_Ozero__class_Ozero(_688321), _688327), -(c_Orderings_Oord__class_Oless(_688321, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_688321), _688323), _688327), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_688321), _688325), _688329)))], (4404 ^ _356604) ^ [_513023, _513025] : [class_Groups_Ogroup__add(_513023), -(c_Groups_Oplus__class_Oplus(_513023, _513025, c_Groups_Ouminus__class_Ouminus(_513023, _513025)) = c_Groups_Ozero__class_Ozero(_513023))], (348 ^ _356604) ^ [_367560, _367562] : [-(class_Rings_Oring__no__zero__divisors(_367560)), _367562 = _367560, class_Rings_Oring__no__zero__divisors(_367562)], (9197 ^ _356604) ^ [_681581, _681583, _681585, _681587, _681589, _681591] : [class_Rings_Oordered__ring(_681581), 9200 ^ _356604 : [(9207 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_681581, c_Groups_Oplus__class_Oplus(_681581, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_681581), c_Groups_Ominus__class_Ominus(_681581, _681583, _681589)), _681585), _681587), _681591), -(c_Orderings_Oord__class_Oless__eq(_681581, c_Groups_Oplus__class_Oplus(_681581, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_681581), _681583), _681585), _681587), c_Groups_Oplus__class_Oplus(_681581, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_681581), _681589), _681585), _681591)))], (9201 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_681581, c_Groups_Oplus__class_Oplus(_681581, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_681581), _681583), _681585), _681587), c_Groups_Oplus__class_Oplus(_681581, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_681581), _681589), _681585), _681591)), -(c_Orderings_Oord__class_Oless__eq(_681581, c_Groups_Oplus__class_Oplus(_681581, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_681581), c_Groups_Ominus__class_Ominus(_681581, _681583, _681589)), _681585), _681587), _681591))]]], (4316 ^ _356604) ^ [_510199, _510201] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _510199), _510201)), _510199 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _510201 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (2122 ^ _356604) ^ [_428281, _428283, _428285, _428287] : [class_Rings_Ocomm__semiring__0(_428281), -(hAPP(c_Polynomial_Opoly(_428281, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_428281), _428283, _428285)), _428287) = c_Groups_Oplus__class_Oplus(_428281, hAPP(c_Polynomial_Opoly(_428281, _428283), _428287), hAPP(c_Polynomial_Opoly(_428281, _428285), _428287)))], (10898 ^ _356604) ^ [_740530, _740532, _740534, _740536] : [class_RealVector_Oreal__normed__field(_740530), -(c_Rings_Oinverse__class_Odivide(_740530, c_Groups_Oplus__class_Oplus(_740530, _740532, _740534), _740536) = c_Groups_Oplus__class_Oplus(_740530, c_Rings_Oinverse__class_Odivide(_740530, _740532, _740536), c_Rings_Oinverse__class_Odivide(_740530, _740534, _740536)))], (11184 ^ _356604) ^ [_750798, _750800, _750802] : [class_Fields_Olinordered__field__inverse__zero(_750798), 11187 ^ _356604 : [(11202 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_750798, c_Rings_Oinverse__class_Odivide(_750798, _750800, _750802), c_Groups_Ozero__class_Ozero(_750798))), 11203 ^ _356604 : [(11210 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_750798, _750800, c_Groups_Ozero__class_Ozero(_750798)), c_Orderings_Oord__class_Oless__eq(_750798, c_Groups_Ozero__class_Ozero(_750798), _750802)], (11204 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_750798, c_Groups_Ozero__class_Ozero(_750798), _750800), c_Orderings_Oord__class_Oless__eq(_750798, _750802, c_Groups_Ozero__class_Ozero(_750798))]]], (11188 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_750798, c_Rings_Oinverse__class_Odivide(_750798, _750800, _750802), c_Groups_Ozero__class_Ozero(_750798)), 11193 ^ _356604 : [(11196 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_750798, _750802, c_Groups_Ozero__class_Ozero(_750798)))], (11194 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_750798, c_Groups_Ozero__class_Ozero(_750798), _750800))]], 11197 ^ _356604 : [(11200 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_750798, c_Groups_Ozero__class_Ozero(_750798), _750802))], (11198 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_750798, _750800, c_Groups_Ozero__class_Ozero(_750798)))]]]]], (9809 ^ _356604) ^ [_703610, _703612, _703614] : [class_Rings_Olinordered__semidom(_703610), c_Orderings_Oord__class_Oless(_703610, c_Groups_Ozero__class_Ozero(_703610), _703612), c_Orderings_Oord__class_Oless(_703610, _703612, c_Groups_Oone__class_Oone(_703610)), -(c_Orderings_Oord__class_Oless(_703610, hAPP(hAPP(c_Power_Opower__class_Opower(_703610), _703612), c_Nat_OSuc(_703614)), c_Groups_Oone__class_Oone(_703610)))], (7536 ^ _356604) ^ [_623017, _623019, _623021, _623023] : [class_Orderings_Oorder(_623017), c_Orderings_Oord__class_Oless__eq(_623017, _623019, _623021), c_Orderings_Oord__class_Oless(_623017, _623023, _623019), -(c_Orderings_Oord__class_Oless(_623017, _623023, _623021))], (6090 ^ _356604) ^ [_574237, _574239] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _574237, _574239), _574239) = _574237)], (3817 ^ _356604) ^ [_492039, _492041, _492043] : [class_Rings_Ocomm__ring(_492039), -(hAPP(c_Polynomial_Opoly(_492039, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_492039), _492041)), _492043) = c_Groups_Ouminus__class_Ouminus(_492039, hAPP(c_Polynomial_Opoly(_492039, _492041), _492043)))], (10161 ^ _356604) ^ [_714952, _714954, _714956] : [_714952 = _714954, 10172 ^ _356604 : [(10175 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _714956, _714952)], (10173 ^ _356604) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _714952, _714956))]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _714954, _714956), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _714956, _714954))], (12242 ^ _356604) ^ [_785548] : [class_Int_Oring__char__0(_785548), -(class_Power_Opower(_785548))], (1401 ^ _356604) ^ [_402266, _402268, _402270] : [class_Groups_Ozero(_402266), 1404 ^ _356604 : [(1413 ^ _356604) ^ [] : [-(c_Polynomial_OpCons(_402266, _402268, _402270) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_402266))), _402268 = c_Groups_Ozero__class_Ozero(_402266), _402270 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_402266))], (1405 ^ _356604) ^ [] : [c_Polynomial_OpCons(_402266, _402268, _402270) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_402266)), 1408 ^ _356604 : [(1411 ^ _356604) ^ [] : [-(_402270 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_402266)))], (1409 ^ _356604) ^ [] : [-(_402268 = c_Groups_Ozero__class_Ozero(_402266))]]]]], (12326 ^ _356604) ^ [_788152] : [class_Rings_Oidom(_788152), -(class_Groups_Ocomm__monoid__add(_788152))], (2481 ^ _356604) ^ [_441387, _441389] : [class_Groups_Olinordered__ab__group__add(_441387), 2484 ^ _356604 : [(2491 ^ _356604) ^ [] : [_441389 = c_Groups_Ozero__class_Ozero(_441387), -(c_Groups_Oplus__class_Oplus(_441387, _441389, _441389) = c_Groups_Ozero__class_Ozero(_441387))], (2485 ^ _356604) ^ [] : [c_Groups_Oplus__class_Oplus(_441387, _441389, _441389) = c_Groups_Ozero__class_Ozero(_441387), -(_441389 = c_Groups_Ozero__class_Ozero(_441387))]]], (1279 ^ _356604) ^ [_398149, _398151] : [class_Rings_Ocomm__semiring__0(_398149), -(c_Polynomial_Osmult(_398149, _398151, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_398149))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_398149)))], (12416 ^ _356604) ^ [_790942] : [class_Rings_Oidom(_790942), -(class_Rings_Oring__1(_790942))], (2555 ^ _356604) ^ [_444575, _444577, _444579, _444581] : [class_Rings_Ocomm__semiring__1(_444575), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_444575), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_444575), _444577), _444579)), _444581) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_444575), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_444575), _444577), _444581)), _444579))], (2915 ^ _356604) ^ [_458751, _458753, _458755, _458757] : [class_Orderings_Oord(_458751), _458753 = _458755, c_Orderings_Oord__class_Oless__eq(_458751, _458755, _458757), -(c_Orderings_Oord__class_Oless__eq(_458751, _458753, _458757))], (1491 ^ _356604) ^ [_405335, _405337, _405339] : [c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(_405335, _405337, _405339), 1494 ^ _356604 : [(1495 ^ _356604) ^ [_405482, _405484] : [-(hAPP(_405339, _405484) = hAPP(_405339, _405482))]]], (6866 ^ _356604) ^ [_601360, _601362, _601364, _601366] : [class_Groups_Oab__group__add(_601360), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_601360), c_Polynomial_Omonom(_601360, _601362, _601364), c_Polynomial_Omonom(_601360, _601366, _601364)) = c_Polynomial_Omonom(_601360, c_Groups_Ominus__class_Ominus(_601360, _601362, _601366), _601364))], (7216 ^ _356604) ^ [_612947, _612949] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_612947), c_Nat_OSuc(_612949)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _612947, _612949))], (9643 ^ _356604) ^ [_697434, _697436, _697438, _697440, _697442] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _697434, _697436), 9646 ^ _356604 : [(9653 ^ _356604) ^ [] : [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, _697436, _697434)), _697438), _697440) = _697442, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _697436), _697438), _697440) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _697434), _697438), _697442))], (9647 ^ _356604) ^ [] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _697436), _697438), _697440) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _697434), _697438), _697442), -(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, _697436, _697434)), _697438), _697440) = _697442)]]], (12356 ^ _356604) ^ [_789082] : [class_Rings_Oidom(_789082), -(class_Rings_Ozero__neq__one(_789082))], (10121 ^ _356604) ^ [_713719, _713721] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _713719, _713721), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _713721, _713719)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _713721, _713719), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _713719, _713721))], (1663 ^ _356604) ^ [_411636] : [c_Nat_OSuc(_411636) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (8032 ^ _356604) ^ [_641443, _641445, _641447] : [class_Groups_Ogroup__add(_641443), -(c_Groups_Ominus__class_Ominus(_641443, _641445, c_Groups_Ouminus__class_Ouminus(_641443, _641447)) = c_Groups_Oplus__class_Oplus(_641443, _641445, _641447))], (9135 ^ _356604) ^ [_679406, _679408] : [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), _679406), _679408)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _679406)), -(_679408 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12212 ^ _356604) ^ [_784618] : [class_Int_Oring__char__0(_784618), -(class_Rings_Omult__zero(_784618))], (10567 ^ _356604) ^ [_728343, _728345] : [10568 ^ _356604 : [(10571 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _728343)], (10569 ^ _356604) ^ [] : [_728345 = 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), _728343), _728345)))], (1559 ^ _356604) ^ [_407842, _407844] : [class_Groups_Ozero(_407842), 1562 ^ _356604 : [(1569 ^ _356604) ^ [] : [_407844 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_407842)), -(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_407842, _407844) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1563 ^ _356604) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_407842, _407844) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_407844 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_407842)))]]], (2192 ^ _356604) ^ [_430843, _430845] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Nat_OSuc(_430843), _430845) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _430843, _430845)))], (12272 ^ _356604) ^ [_786478] : [class_Rings_Oidom(_786478), -(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_786478))], (9745 ^ _356604) ^ [_701369, _701371, _701373] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _701369), _701371), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _701369), _701373)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _701369), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _701371, _701373))], (12588 ^ _356604) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (12682 ^ _356604) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (268 ^ _356604) ^ [_365200, _365202] : [-(class_Rings_Olinordered__semiring__strict(_365200)), _365202 = _365200, class_Rings_Olinordered__semiring__strict(_365202)], (5042 ^ _356604) ^ [_536583, _536585] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _536583, _536585)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _536583), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _536585)))], (5254 ^ _356604) ^ [_544269, _544271, _544273, _544275] : [class_Rings_Oidom(_544269), 5257 ^ _356604 : [(5258 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(_544269, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_544269), _544271), _544273), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_544269), _544275), _544273)), -(_544273 = c_Groups_Ozero__class_Ozero(_544269)), -(c_Rings_Odvd__class_Odvd(_544269, _544271, _544275))], (5268 ^ _356604) ^ [] : [5269 ^ _356604 : [(5272 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(_544269, _544271, _544275)], (5270 ^ _356604) ^ [] : [_544273 = c_Groups_Ozero__class_Ozero(_544269)]], -(c_Rings_Odvd__class_Odvd(_544269, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_544269), _544271), _544273), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_544269), _544275), _544273)))]]], (8672 ^ _356604) ^ [_662985, _662987, _662989] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _662985, _662987), 8675 ^ _356604 : [(8682 ^ _356604) ^ [] : [_662987 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _662989, _662985), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _662987, _662985) = _662989)], (8676 ^ _356604) ^ [] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _662987, _662985) = _662989, -(_662987 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _662989, _662985))]]], (2549 ^ _356604) ^ [_444225, _444227, _444229, _444231, _444233] : [class_Rings_Ocomm__semiring__1(_444225), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_444225), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_444225), _444227), _444229)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_444225), _444231), _444233)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_444225), _444227), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_444225), _444229), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_444225), _444231), _444233))))], (3190 ^ _356604) ^ [_468712, _468714, _468716, _468718] : [class_Rings_Oordered__ring(_468712), c_Orderings_Oord__class_Oless__eq(_468712, _468714, _468716), c_Orderings_Oord__class_Oless__eq(_468712, _468718, c_Groups_Ozero__class_Ozero(_468712)), -(c_Orderings_Oord__class_Oless__eq(_468712, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_468712), _468716), _468718), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_468712), _468714), _468718)))], (11438 ^ _356604) ^ [_758892, _758894, _758896, _758898] : [class_Fields_Ofield__inverse__zero(_758892), -(_758894 = c_Groups_Ozero__class_Ozero(_758892)), -(c_Rings_Oinverse__class_Odivide(_758892, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_758892), _758896), _758894), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_758892), _758898), _758894)) = c_Rings_Oinverse__class_Odivide(_758892, _758896, _758898))], (11530 ^ _356604) ^ [_761886, _761888, _761890] : [class_Fields_Olinordered__field(_761886), c_Orderings_Oord__class_Oless__eq(_761886, c_Groups_Ozero__class_Ozero(_761886), _761888), c_Orderings_Oord__class_Oless(_761886, _761890, c_Groups_Ozero__class_Ozero(_761886)), -(c_Orderings_Oord__class_Oless__eq(_761886, c_Rings_Oinverse__class_Odivide(_761886, _761888, _761890), c_Groups_Ozero__class_Ozero(_761886)))], (10077 ^ _356604) ^ [_712392, _712394] : [_712394 = _712392, c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _712392, _712394), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _712394, _712392))], (3939 ^ _356604) ^ [_496463, _496465, _496467] : [class_Groups_Ozero(_496463), 3942 ^ _356604 : [(3949 ^ _356604) ^ [] : [hAPP(c_Polynomial_Ocoeff(_496463, _496465), 3950 ^ [_496463, _496465, _496467]) = hAPP(c_Polynomial_Ocoeff(_496463, _496467), 3950 ^ [_496463, _496465, _496467]), -(_496465 = _496467)], (3943 ^ _356604) ^ [] : [_496465 = _496467, 3946 ^ _356604 : [(3947 ^ _356604) ^ [_496711] : [-(hAPP(c_Polynomial_Ocoeff(_496463, _496465), _496711) = hAPP(c_Polynomial_Ocoeff(_496463, _496467), _496711))]]]]], (6534 ^ _356604) ^ [_589941, _589943] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _589941, _589943), 6537 ^ _356604 : [(6540 ^ _356604) ^ [] : [_589941 = _589943], (6538 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _589941, _589943))]]], (12380 ^ _356604) ^ [_789826] : [class_Rings_Oidom(_789826), -(class_Rings_Osemiring__0(_789826))], (7004 ^ _356604) ^ [_606255, _606257, _606259] : [class_Orderings_Olinorder(_606255), -(c_Orderings_Oord__class_Oless(_606255, _606257, _606259)), 7011 ^ _356604 : [(7018 ^ _356604) ^ [] : [_606259 = _606257, c_Orderings_Oord__class_Oless(_606255, _606259, _606257)], (7012 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_606255, _606259, _606257)), -(_606259 = _606257)]]], (4212 ^ _356604) ^ [_506182] : [class_Rings_Ozero__neq__one(_506182), c_Groups_Oone__class_Oone(_506182) = c_Groups_Ozero__class_Ozero(_506182)], (12756 ^ _356604) ^ [_800765] : [class_Rings_Olinordered__idom(_800765), -(class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(_800765)))], (10577 ^ _356604) ^ [_728684] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _728684, c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_728684 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_728684 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (1104 ^ _356604) ^ [_392585, _392587, _392589, _392591, _392593, _392595] : [-(c_Rings_Oinverse__class_Odivide(_392595, _392591, _392587) = c_Rings_Oinverse__class_Odivide(_392593, _392589, _392585)), _392595 = _392593, _392591 = _392589, _392587 = _392585], (2320 ^ _356604) ^ [_435479, _435481, _435483, _435485] : [class_Rings_Ocomm__semiring__0(_435479), -(c_Polynomial_Osmult(_435479, _435481, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_435479), _435483, _435485)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_435479), c_Polynomial_Osmult(_435479, _435481, _435483), c_Polynomial_Osmult(_435479, _435481, _435485)))], (2 ^ _356604) ^ [_356728] : [-(_356728 = _356728)], (20 ^ _356604) ^ [_357408, _357410, _357412, _357414, _357416, _357418] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(_357416, _357412, _357408)), c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(_357418, _357414, _357410), _357418 = _357416, _357414 = _357412, _357410 = _357408], (10820 ^ _356604) ^ [_737409, _737411, _737413, _737415, _737417, _737419, _737421] : [class_Fields_Ofield(_737409), c_Polynomial_Opdivmod__rel(_737409, _737411, _737413, _737415, _737417), -(_737413 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_737409))), _737419 = c_Rings_Oinverse__class_Odivide(_737409, hAPP(c_Polynomial_Ocoeff(_737409, c_Polynomial_OpCons(_737409, _737421, _737417)), c_Polynomial_Odegree(_737409, _737413)), hAPP(c_Polynomial_Ocoeff(_737409, _737413), c_Polynomial_Odegree(_737409, _737413))), -(c_Polynomial_Opdivmod__rel(_737409, c_Polynomial_OpCons(_737409, _737421, _737411), _737413, c_Polynomial_OpCons(_737409, _737419, _737415), c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_737409), c_Polynomial_OpCons(_737409, _737421, _737417), c_Polynomial_Osmult(_737409, _737419, _737413))))], (6022 ^ _356604) ^ [_571823, _571825, _571827] : [class_Groups_Oordered__ab__group__add(_571823), 6025 ^ _356604 : [(6032 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_571823, _571827, c_Groups_Ouminus__class_Ouminus(_571823, _571825)), -(c_Orderings_Oord__class_Oless(_571823, _571825, c_Groups_Ouminus__class_Ouminus(_571823, _571827)))], (6026 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_571823, _571825, c_Groups_Ouminus__class_Ouminus(_571823, _571827)), -(c_Orderings_Oord__class_Oless(_571823, _571827, c_Groups_Ouminus__class_Ouminus(_571823, _571825)))]]], (9681 ^ _356604) ^ [_699104, _699106, _699108, _699110, _699112] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _699104, _699106), 9684 ^ _356604 : [(9691 ^ _356604) ^ [] : [_699110 = 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, _699106, _699104)), _699108), _699112), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _699104), _699108), _699110) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _699106), _699108), _699112))], (9685 ^ _356604) ^ [] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _699104), _699108), _699110) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _699106), _699108), _699112), -(_699110 = 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, _699106, _699104)), _699108), _699112))]]], (8646 ^ _356604) ^ [_661857, _661859, _661861] : [8647 ^ _356604 : [(8650 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _661859, _661861)], (8648 ^ _356604) ^ [] : [_661857 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _661857), _661859), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _661857), _661861)))], (658 ^ _356604) ^ [_376705, _376707] : [-(class_Rings_Ocomm__ring__1(_376705)), _376707 = _376705, class_Rings_Ocomm__ring__1(_376707)], (12458 ^ _356604) ^ [_792244] : [class_Rings_Oidom(_792244), -(class_Groups_Ocancel__comm__monoid__add(_792244))], (7268 ^ _356604) ^ [_614765, _614767, _614769] : [class_Orderings_Olinorder(_614765), -(c_Orderings_Oord__class_Oless__eq(_614765, _614767, _614769)), -(c_Orderings_Oord__class_Oless(_614765, _614769, _614767))], (4438 ^ _356604) ^ [_514230, _514232, _514234] : [class_Groups_Ogroup__add(_514230), c_Groups_Oplus__class_Oplus(_514230, _514232, _514234) = c_Groups_Ozero__class_Ozero(_514230), -(c_Groups_Ouminus__class_Ouminus(_514230, _514232) = _514234)], (10886 ^ _356604) ^ [_739994, _739996] : [class_Rings_Odivision__ring(_739994), -(c_Rings_Oinverse__class_Odivide(_739994, _739996, c_Groups_Oone__class_Oone(_739994)) = _739996)], (990 ^ _356604) ^ [_388403, _388405, _388407, _388409] : [-(c_Polynomial_Ocoeff(_388409, _388405) = c_Polynomial_Ocoeff(_388407, _388403)), _388409 = _388407, _388405 = _388403], (9291 ^ _356604) ^ [_685173, _685175, _685177, _685179] : [class_Rings_Olinordered__semiring__strict(_685173), c_Orderings_Oord__class_Oless(_685173, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_685173), _685175), _685177), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_685173), _685179), _685177)), c_Orderings_Oord__class_Oless__eq(_685173, c_Groups_Ozero__class_Ozero(_685173), _685177), -(c_Orderings_Oord__class_Oless(_685173, _685175, _685179))], (8997 ^ _356604) ^ [_674666, _674668, _674670] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _674666), 9000 ^ _356604 : [(9007 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _674668, _674670), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _674666), _674668), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _674666), _674670)))], (9001 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _674666), _674668), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _674666), _674670)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _674668, _674670))]]], (6750 ^ _356604) ^ [_597189, _597191] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _597189, _597191), _597189 = _597191], (11150 ^ _356604) ^ [_749606, _749608, _749610] : [class_Fields_Ofield__inverse__zero(_749606), -(c_Groups_Ouminus__class_Ouminus(_749606, c_Rings_Oinverse__class_Odivide(_749606, _749608, _749610)) = c_Rings_Oinverse__class_Odivide(_749606, _749608, c_Groups_Ouminus__class_Ouminus(_749606, _749610)))], (9697 ^ _356604) ^ [_699716, _699718] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _699716), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _699718), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _699716, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _699718), _699716)))], (2949 ^ _356604) ^ [_459797, _459799, _459801, _459803, _459805] : [class_Orderings_Oord(_459797), c_Orderings_Oord__class_Oless__eq(tc_fun(_459799, _459797), _459801, _459803), -(c_Orderings_Oord__class_Oless__eq(_459797, hAPP(_459801, _459805), hAPP(_459803, _459805)))], (4460 ^ _356604) ^ [_515129, _515131, _515133] : [class_Rings_Ocomm__semiring__1(_515129), -(hAPP(hAPP(c_Power_Opower__class_Opower(_515129), _515131), c_Nat_OSuc(_515133)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_515129), _515131), hAPP(hAPP(c_Power_Opower__class_Opower(_515129), _515131), _515133)))], (10227 ^ _356604) ^ [_717056, _717058, _717060] : [_717056 = _717058, c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _717058, _717060), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _717056, _717060))], (4042 ^ _356604) ^ [_499654] : [class_Groups_Ogroup__add(_499654), -(c_Groups_Ouminus__class_Ouminus(_499654, c_Groups_Ozero__class_Ozero(_499654)) = c_Groups_Ozero__class_Ozero(_499654))], (12332 ^ _356604) ^ [_788338] : [class_Rings_Oidom(_788338), -(class_Rings_Ocomm__semiring__1(_788338))], (408 ^ _356604) ^ [_369330, _369332] : [-(class_Rings_Olinordered__semiring(_369330)), _369332 = _369330, class_Rings_Olinordered__semiring(_369332)], (378 ^ _356604) ^ [_368445, _368447] : [-(class_Groups_Oordered__ab__group__add(_368445)), _368447 = _368445, class_Groups_Oordered__ab__group__add(_368447)], (6370 ^ _356604) ^ [_584047, _584049] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _584047, _584049), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_584047), c_Nat_OSuc(_584049)))], (7632 ^ _356604) ^ [_626602, _626604, _626606] : [class_Groups_Oab__group__add(_626602), 7635 ^ _356604 : [(7642 ^ _356604) ^ [] : [c_Groups_Ominus__class_Ominus(_626602, _626604, _626606) = c_Groups_Ozero__class_Ozero(_626602), -(_626604 = _626606)], (7636 ^ _356604) ^ [] : [_626604 = _626606, -(c_Groups_Ominus__class_Ominus(_626602, _626604, _626606) = c_Groups_Ozero__class_Ozero(_626602))]]], (10936 ^ _356604) ^ [_742172, _742174, _742176] : [class_Rings_Odivision__ring(_742172), -(_742174 = c_Groups_Ozero__class_Ozero(_742172)), -(c_Rings_Oinverse__class_Odivide(_742172, c_Groups_Ouminus__class_Ouminus(_742172, _742176), c_Groups_Ouminus__class_Ouminus(_742172, _742174)) = c_Rings_Oinverse__class_Odivide(_742172, _742176, _742174))], (10746 ^ _356604) ^ [_734357, _734359] : [class_Fields_Ofield(_734357), -(c_Polynomial_Opdivmod__rel(_734357, _734359, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_734357)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_734357)), _734359))], (4916 ^ _356604) ^ [_531799, _531801, _531803] : [class_Power_Opower(_531799), -(hAPP(hAPP(c_Power_Opower__class_Opower(_531799), _531801), c_Nat_OSuc(_531803)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_531799), _531801), hAPP(hAPP(c_Power_Opower__class_Opower(_531799), _531801), _531803)))], (12586 ^ _356604) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (3332 ^ _356604) ^ [_474082, _474084] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _474082), _474084) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _474082 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _474084 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12486 ^ _356604) ^ [_793164, _793166] : [class_Orderings_Oorder(_793164), -(class_Orderings_Oorder(tc_fun(_793166, _793164)))], (7922 ^ _356604) ^ [_636645, _636647, _636649, _636651, _636653] : [class_Rings_Oring(_636645), -(c_Groups_Ominus__class_Ominus(_636645, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_636645), _636647), _636649), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_636645), _636651), _636653)) = c_Groups_Oplus__class_Oplus(_636645, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_636645), _636647), c_Groups_Ominus__class_Ominus(_636645, _636649, _636653)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_636645), c_Groups_Ominus__class_Ominus(_636645, _636647, _636651)), _636653)))], (12630 ^ _356604) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (4994 ^ _356604) ^ [_534829, _534831, _534833] : [class_Rings_Oidom(_534829), -(_534831 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_534829))), 5001 ^ _356604 : [(5004 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_534829), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_534829)), c_Polynomial_OpCons(_534829, c_Groups_Ouminus__class_Ouminus(_534829, _534833), c_Polynomial_OpCons(_534829, c_Groups_Oone__class_Oone(_534829), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_534829))))), c_Nat_OSuc(c_Polynomial_Oorder(_534829, _534833, _534831))), _534831)], (5002 ^ _356604) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_534829), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_534829)), c_Polynomial_OpCons(_534829, c_Groups_Ouminus__class_Ouminus(_534829, _534833), c_Polynomial_OpCons(_534829, c_Groups_Oone__class_Oone(_534829), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_534829))))), c_Polynomial_Oorder(_534829, _534833, _534831)), _534831))]]], (6772 ^ _356604) ^ [_598003, _598005, _598007] : [6773 ^ _356604 : [(6776 ^ _356604) ^ [] : [hBOOL(hAPP(hAPP(_598007, _598005), _598003))], (6774 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _598003, _598005))]], 6779 ^ _356604 : [(6782 ^ _356604) ^ [] : [hBOOL(hAPP(hAPP(_598007, _598005), _598003))], (6780 ^ _356604) ^ [] : [-(_598003 = _598005)]], 6785 ^ _356604 : [(6788 ^ _356604) ^ [] : [hBOOL(hAPP(hAPP(_598007, _598005), _598003))], (6786 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _598005, _598003))]], -(hBOOL(hAPP(hAPP(_598007, _598005), _598003)))], (6340 ^ _356604) ^ [_583040, _583042] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _583042, c_Nat_OSuc(_583040)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _583040, _583042)], (4432 ^ _356604) ^ [_513990, _513992] : [class_Groups_Oab__group__add(_513990), -(c_Groups_Oplus__class_Oplus(_513990, c_Groups_Ouminus__class_Ouminus(_513990, _513992), _513992) = c_Groups_Ozero__class_Ozero(_513990))], (9013 ^ _356604) ^ [_675200, _675202, _675204] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _675200), 9016 ^ _356604 : [(9023 ^ _356604) ^ [] : [_675202 = _675204, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _675200), _675202) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _675200), _675204))], (9017 ^ _356604) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _675200), _675202) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _675200), _675204), -(_675202 = _675204)]]], (9637 ^ _356604) ^ [_697078, _697080, _697082, _697084, _697086] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _697078, _697080), -(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), _697080), _697082), _697084), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _697078), _697082), _697086)) = 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, _697080, _697078)), _697082), _697084), _697086))], (2148 ^ _356604) ^ [_429327, _429329] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _429327, _429329) = _429327, -(_429329 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7048 ^ _356604) ^ [_607594, _607596, _607598] : [class_Orderings_Opreorder(_607594), c_Orderings_Oord__class_Oless(_607594, _607596, _607598), c_Orderings_Oord__class_Oless(_607594, _607598, _607596)], (190 ^ _356604) ^ [_362877, _362879, _362881, _362883, _362885, _362887] : [-(c_Orderings_Oord__class_Oless__eq(_362885, _362881, _362877)), c_Orderings_Oord__class_Oless__eq(_362887, _362883, _362879), _362887 = _362885, _362883 = _362881, _362879 = _362877], (5200 ^ _356604) ^ [_542138] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _542138, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _542138)], (5402 ^ _356604) ^ [_549307, _549309, _549311, _549313] : [class_Fields_Ofield(_549307), 5405 ^ _356604 : [(5406 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_549307), c_Polynomial_Osmult(_549307, _549309, _549311), _549313), 5409 ^ _356604 : [(5416 ^ _356604) ^ [] : [-(_549309 = c_Groups_Ozero__class_Ozero(_549307)), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_549307), _549311, _549313))], (5410 ^ _356604) ^ [] : [_549309 = c_Groups_Ozero__class_Ozero(_549307), -(_549313 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_549307)))]]], (5422 ^ _356604) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_549307), c_Polynomial_Osmult(_549307, _549309, _549311), _549313)), 5425 ^ _356604 : [(5428 ^ _356604) ^ [] : [_549313 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_549307))], (5426 ^ _356604) ^ [] : [-(_549309 = c_Groups_Ozero__class_Ozero(_549307))]], 5429 ^ _356604 : [(5432 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_549307), _549311, _549313)], (5430 ^ _356604) ^ [] : [_549309 = c_Groups_Ozero__class_Ozero(_549307)]]]]], (5228 ^ _356604) ^ [_543275, _543277, _543279] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _543275, _543277), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _543279, _543275), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _543279, _543277)))], (5714 ^ _356604) ^ [_560583, _560585] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _560583, _560585), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _560583, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _560585)))], (2859 ^ _356604) ^ [_456981, _456983, _456985] : [class_Orderings_Oorder(_456981), c_Orderings_Oord__class_Oless__eq(_456981, _456983, _456985), c_Orderings_Oord__class_Oless__eq(_456981, _456985, _456983), -(_456983 = _456985)], (12314 ^ _356604) ^ [_787780] : [class_Rings_Oidom(_787780), -(class_Groups_Oab__semigroup__add(_787780))], (8218 ^ _356604) ^ [_647726, _647728, _647730] : [class_Rings_Olinordered__semiring__strict(_647726), c_Orderings_Oord__class_Oless(_647726, c_Groups_Ozero__class_Ozero(_647726), _647728), c_Orderings_Oord__class_Oless(_647726, c_Groups_Ozero__class_Ozero(_647726), _647730), -(c_Orderings_Oord__class_Oless(_647726, c_Groups_Ozero__class_Ozero(_647726), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_647726), _647728), _647730)))], (162 ^ _356604) ^ [_361917, _361919] : [-(class_Fields_Olinordered__field(_361917)), _361919 = _361917, class_Fields_Olinordered__field(_361919)], (8232 ^ _356604) ^ [_648188, _648190, _648192, _648194] : [class_Rings_Olinordered__ring__strict(_648188), c_Orderings_Oord__class_Oless(_648188, c_Groups_Ozero__class_Ozero(_648188), _648190), 8239 ^ _356604 : [(8246 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_648188, _648192, _648194), -(c_Orderings_Oord__class_Oless(_648188, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_648188), _648190), _648192), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_648188), _648190), _648194)))], (8240 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_648188, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_648188), _648190), _648192), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_648188), _648190), _648194)), -(c_Orderings_Oord__class_Oless(_648188, _648192, _648194))]]], (2679 ^ _356604) ^ [_450130, _450132] : [class_Rings_Ocomm__semiring__0(_450130), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_450130)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_450130))), _450132) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_450130)))], (2475 ^ _356604) ^ [_441159, _441161, _441163] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _441159, _441161), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _441159, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _441163, _441161)))], (10513 ^ _356604) ^ [_726518] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _726518))], (5046 ^ _356604) ^ [] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (10261 ^ _356604) ^ [_718135, _718137] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _718135, _718137), 10264 ^ _356604 : [(10271 ^ _356604) ^ [] : [_718137 = _718135, -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _718137, _718135))], (10265 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _718137, _718135), -(_718137 = _718135)]]], (3308 ^ _356604) ^ [_473187, _473189, _473191, _473193] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _473187, _473189), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _473191, _473193), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _473187), _473191), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _473189), _473193)))], (5466 ^ _356604) ^ [_551576, _551578, _551580] : [class_Lattices_Oab__semigroup__idem__mult(_551576), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_551576), _551578), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_551576), _551578), _551580)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_551576), _551578), _551580))], (12164 ^ _356604) ^ [_783130] : [class_Int_Oring__char__0(_783130), -(class_Groups_Oab__semigroup__add(_783130))], (12640 ^ _356604) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (4768 ^ _356604) ^ [_526629, _526631, _526633] : [class_Rings_Oring__1__no__zero__divisors(_526629), -(_526631 = c_Groups_Ozero__class_Ozero(_526629)), hAPP(hAPP(c_Power_Opower__class_Opower(_526629), _526631), _526633) = c_Groups_Ozero__class_Ozero(_526629)], (10587 ^ _356604) ^ [] : [-(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)))], (3956 ^ _356604) ^ [_497074, _497076] : [class_Groups_Oone(_497074), 3959 ^ _356604 : [(3966 ^ _356604) ^ [] : [_497076 = c_Groups_Oone__class_Oone(_497074), -(c_Groups_Oone__class_Oone(_497074) = _497076)], (3960 ^ _356604) ^ [] : [c_Groups_Oone__class_Oone(_497074) = _497076, -(_497076 = c_Groups_Oone__class_Oone(_497074))]]], (12942 ^ _356604) ^ [_806655] : [class_Rings_Ocomm__semiring__0(_806655), -(class_Rings_Osemiring__0(tc_Polynomial_Opoly(_806655)))], (3344 ^ _356604) ^ [_474492, _474494] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _474492), c_Nat_OSuc(_474494)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _474492, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _474492), _474494)))], (12870 ^ _356604) ^ [_804375] : [class_Rings_Olinordered__idom(_804375), -(class_Rings_Olinordered__idom(tc_Polynomial_Opoly(_804375)))], (13026 ^ _356604) ^ [_809315] : [class_Rings_Oidom(_809315), -(class_Rings_Oidom(tc_Polynomial_Opoly(_809315)))], (12344 ^ _356604) ^ [_788710] : [class_Rings_Oidom(_788710), -(class_Rings_Ocomm__semiring(_788710))], (8977 ^ _356604) ^ [_673960, _673962, _673964] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _673960, _673962), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _673964), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _673960), _673964), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _673962), _673964)))], (3536 ^ _356604) ^ [_481299, _481301, _481303] : [class_Rings_Oordered__cancel__semiring(_481299), c_Orderings_Oord__class_Oless__eq(_481299, c_Groups_Ozero__class_Ozero(_481299), _481301), c_Orderings_Oord__class_Oless__eq(_481299, c_Groups_Ozero__class_Ozero(_481299), _481303), -(c_Orderings_Oord__class_Oless__eq(_481299, c_Groups_Ozero__class_Ozero(_481299), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_481299), _481301), _481303)))], (7710 ^ _356604) ^ [_629185] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _629185), -(c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _629185, c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _629185)], (6714 ^ _356604) ^ [_596039, _596041] : [-(_596039 = _596041), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _596039, _596041)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _596041, _596039))], (1028 ^ _356604) ^ [_389766, _389768] : [_389768 = _389766, -(c_Power_Opower__class_Opower(_389768) = c_Power_Opower__class_Opower(_389766))], (12732 ^ _356604) ^ [_800005] : [class_Rings_Olinordered__idom(_800005), -(class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(_800005)))], (12512 ^ _356604) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (4140 ^ _356604) ^ [_502954, _502956, _502958] : [class_Rings_Oring(_502954), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_502954), c_Groups_Ouminus__class_Ouminus(_502954, _502956)), _502958) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_502954), _502956), c_Groups_Ouminus__class_Ouminus(_502954, _502958)))], (7192 ^ _356604) ^ [_612226, _612228, _612230] : [class_Orderings_Opreorder(_612226), c_Orderings_Oord__class_Oless(_612226, _612228, _612230), c_Orderings_Oord__class_Oless(_612226, _612230, _612228)], (10916 ^ _356604) ^ [_741414, _741416, _741418, _741420] : [class_Fields_Ofield(_741414), -(_741416 = c_Groups_Ozero__class_Ozero(_741414)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_741414), c_Rings_Oinverse__class_Odivide(_741414, _741418, _741416)), _741420) = c_Rings_Oinverse__class_Odivide(_741414, hAPP(hAPP(c_Power_Opower__class_Opower(_741414), _741418), _741420), hAPP(hAPP(c_Power_Opower__class_Opower(_741414), _741416), _741420)))], (1707 ^ _356604) ^ [_413442, _413444] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _413442, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _413442, _413444)))], (9427 ^ _356604) ^ [_689704, _689706, _689708, _689710] : [class_Rings_Olinordered__ring__strict(_689704), c_Orderings_Oord__class_Oless(_689704, c_Groups_Ozero__class_Ozero(_689704), _689706), 9434 ^ _356604 : [(9441 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_689704, _689708, _689710), -(c_Orderings_Oord__class_Oless__eq(_689704, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_689704), _689706), _689708), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_689704), _689706), _689710)))], (9435 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_689704, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_689704), _689706), _689708), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_689704), _689706), _689710)), -(c_Orderings_Oord__class_Oless__eq(_689704, _689708, _689710))]]], (956 ^ _356604) ^ [_387181, _387183, _387185, _387187, _387189, _387191] : [-(c_Polynomial_Osynthetic__div(_387191, _387187, _387183) = c_Polynomial_Osynthetic__div(_387189, _387185, _387181)), _387191 = _387189, _387187 = _387185, _387183 = _387181], (8740 ^ _356604) ^ [_665462, _665464, _665466] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _665462, _665464), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _665466, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _665464, _665462)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _665466, _665462), _665464))], (598 ^ _356604) ^ [_374935, _374937] : [-(class_Orderings_Oorder(_374935)), _374937 = _374935, class_Orderings_Oorder(_374937)], (12634 ^ _356604) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (4928 ^ _356604) ^ [_532345, _532347] : [class_Power_Opower(_532345), -(hAPP(hAPP(c_Power_Opower__class_Opower(_532345), _532347), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_532345))], (3462 ^ _356604) ^ [_478957, _478959] : [class_Rings_Olinordered__ring(_478957), -(c_Orderings_Oord__class_Oless__eq(_478957, c_Groups_Ozero__class_Ozero(_478957), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_478957), _478959), _478959)))], (11020 ^ _356604) ^ [_744906, _744908, _744910, _744912] : [class_Rings_Odivision__ring(_744906), -(_744908 = c_Groups_Ozero__class_Ozero(_744906)), 11027 ^ _356604 : [(11034 ^ _356604) ^ [] : [_744910 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_744906), _744912), _744908), -(c_Rings_Oinverse__class_Odivide(_744906, _744910, _744908) = _744912)], (11028 ^ _356604) ^ [] : [c_Rings_Oinverse__class_Odivide(_744906, _744910, _744908) = _744912, -(_744910 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_744906), _744912), _744908))]]], (1976 ^ _356604) ^ [_423479, _423481, _423483, _423485] : [class_Groups_Ocancel__semigroup__add(_423479), 1979 ^ _356604 : [(1986 ^ _356604) ^ [] : [_423483 = _423485, -(c_Groups_Oplus__class_Oplus(_423479, _423481, _423483) = c_Groups_Oplus__class_Oplus(_423479, _423481, _423485))], (1980 ^ _356604) ^ [] : [c_Groups_Oplus__class_Oplus(_423479, _423481, _423483) = c_Groups_Oplus__class_Oplus(_423479, _423481, _423485), -(_423483 = _423485)]]], (6136 ^ _356604) ^ [_575958, _575960, _575962, _575964, _575966] : [class_Groups_Ominus(_575958), -(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_575960, _575958), _575962, _575964), _575966) = c_Groups_Ominus__class_Ominus(_575958, hAPP(_575962, _575966), hAPP(_575964, _575966)))], (3578 ^ _356604) ^ [_482643, _482645, _482647] : [class_Rings_Oordered__cancel__semiring(_482643), c_Orderings_Oord__class_Oless__eq(_482643, _482645, c_Groups_Ozero__class_Ozero(_482643)), c_Orderings_Oord__class_Oless__eq(_482643, c_Groups_Ozero__class_Ozero(_482643), _482647), -(c_Orderings_Oord__class_Oless__eq(_482643, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_482643), _482645), _482647), c_Groups_Ozero__class_Ozero(_482643)))], (9029 ^ _356604) ^ [_675757, _675759, _675761] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_675757)), _675759), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_675757)), _675761)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _675759, _675761))], (8764 ^ _356604) ^ [_666397] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _666397), -(_666397 = c_Nat_OSuc(8767 ^ [_666397]))], (10283 ^ _356604) ^ [_718812, _718814] : [-(_718812 = _718814), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _718812, _718814), 10290 ^ _356604 : [(10293 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _718814, _718812)], (10291 ^ _356604) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _718812, _718814))]]], (8789 ^ _356604) ^ [_667256, _667258] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _667256, c_Nat_OSuc(_667258)), -(_667256 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 8797 ^ _356604 : [(8800 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 8796 ^ [_667256, _667258], _667258))], (8798 ^ _356604) ^ [] : [-(_667256 = c_Nat_OSuc(8796 ^ [_667256, _667258]))]]], (12706 ^ _356604) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (5370 ^ _356604) ^ [_548283, _548285, _548287, _548289] : [class_Fields_Ofield(_548283), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_548283), _548285, c_Polynomial_Osmult(_548283, _548287, _548289)), -(_548287 = c_Groups_Ozero__class_Ozero(_548283)), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_548283), _548285, _548289))], (7860 ^ _356604) ^ [_634425, _634427, _634429] : [class_Fields_Ofield(_634425), -(c_Polynomial_Opoly__gcd(_634425, _634427, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_634425), _634429)) = c_Polynomial_Opoly__gcd(_634425, _634427, _634429))], (3670 ^ _356604) ^ [_486205, _486207] : [class_RealVector_Oreal__normed__algebra(_486205), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_486205), c_Groups_Ozero__class_Ozero(_486205)), _486207) = c_Groups_Ozero__class_Ozero(_486205))], (8128 ^ _356604) ^ [_644811, _644813, _644815] : [class_Rings_Olinordered__semiring__strict(_644811), c_Orderings_Oord__class_Oless(_644811, _644813, c_Groups_Ozero__class_Ozero(_644811)), c_Orderings_Oord__class_Oless(_644811, c_Groups_Ozero__class_Ozero(_644811), _644815), -(c_Orderings_Oord__class_Oless(_644811, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_644811), _644813), _644815), c_Groups_Ozero__class_Ozero(_644811)))], (12428 ^ _356604) ^ [_791314] : [class_Rings_Oidom(_791314), -(class_Power_Opower(_791314))], (10740 ^ _356604) ^ [_734119, _734121] : [class_Fields_Ofield(_734119), -(c_Polynomial_Opdivmod__rel(_734119, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_734119)), _734121, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_734119)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_734119))))], (2525 ^ _356604) ^ [_442843, _442845, _442847, _442849] : [class_Rings_Ocomm__semiring__0(_442843), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_442843)), _442845), c_Polynomial_OpCons(_442843, _442847, _442849)) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_442843), c_Polynomial_Osmult(_442843, _442847, _442845), c_Polynomial_OpCons(_442843, c_Groups_Ozero__class_Ozero(_442843), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_442843)), _442845), _442849))))], (9609 ^ _356604) ^ [_695846, _695848, _695850] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _695846, _695848), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _695850, c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _695848, _695846))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _695850, _695846), c_Nat_OSuc(_695848)))], (12548 ^ _356604) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (12260 ^ _356604) ^ [_786106] : [class_Int_Oring__char__0(_786106), -(class_Groups_Oone(_786106))], (6296 ^ _356604) ^ [_581388, _581390, _581392] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _581388, _581390)), _581392) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _581388), _581392), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _581390), _581392)))], (13020 ^ _356604) ^ [_809125] : [class_Rings_Ocomm__ring(_809125), -(class_Rings_Oring(tc_Polynomial_Opoly(_809125)))], (1337 ^ _356604) ^ [_400083, _400085, _400087] : [class_Rings_Ocomm__semiring__0(_400083), 1340 ^ _356604 : [(1347 ^ _356604) ^ [] : [_400085 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_400083)), -(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_400083, _400085, _400087) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_400083)))], (1341 ^ _356604) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_400083, _400085, _400087) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_400083)), -(_400085 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_400083)))]]], (12644 ^ _356604) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (438 ^ _356604) ^ [_370215, _370217] : [-(class_Groups_Ocomm__monoid__mult(_370215)), _370217 = _370215, class_Groups_Ocomm__monoid__mult(_370217)], (1144 ^ _356604) ^ [_394009, _394011, _394013, _394015] : [-(c_Polynomial_Odegree(_394015, _394011) = c_Polynomial_Odegree(_394013, _394009)), _394015 = _394013, _394011 = _394009], (3923 ^ _356604) ^ [_495957, _495959, _495961] : [class_Groups_Ogroup__add(_495957), 3926 ^ _356604 : [(3933 ^ _356604) ^ [] : [_495961 = c_Groups_Ouminus__class_Ouminus(_495957, _495959), -(_495959 = c_Groups_Ouminus__class_Ouminus(_495957, _495961))], (3927 ^ _356604) ^ [] : [_495959 = c_Groups_Ouminus__class_Ouminus(_495957, _495961), -(_495961 = c_Groups_Ouminus__class_Ouminus(_495957, _495959))]]], (10 ^ _356604) ^ [_357039, _357041, _357043] : [-(_357043 = _357039), _357043 = _357041, _357041 = _357039], (4576 ^ _356604) ^ [_519937, _519939, _519941] : [class_Rings_Olinordered__idom(_519937), c_Orderings_Oord__class_Oless__eq(_519937, c_Groups_Ozero__class_Ozero(_519937), _519939), c_Orderings_Oord__class_Oless__eq(_519937, c_Groups_Ozero__class_Ozero(_519937), _519941), c_Orderings_Oord__class_Oless__eq(_519937, _519941, c_Groups_Oone__class_Oone(_519937)), -(c_Orderings_Oord__class_Oless__eq(_519937, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_519937), _519939), _519941), _519939))], (7760 ^ _356604) ^ [_630806, _630808] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _630806), 7763 ^ _356604 : [(7770 ^ _356604) ^ [] : [_630808 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _630806), _630808), _630806))], (7764 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _630806), _630808), _630806), -(_630808 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (1331 ^ _356604) ^ [_399815, _399817, _399819] : [class_Rings_Ocomm__semiring__0(_399815), -(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_399815, c_Polynomial_OpCons(_399815, _399817, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_399815))), _399819) = c_Polynomial_OpCons(_399815, _399817, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_399815))))], (10511 ^ _356604) ^ [_726439] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _726439, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (11336 ^ _356604) ^ [_755568, _755570, _755572] : [class_Fields_Olinordered__field__inverse__zero(_755568), 11339 ^ _356604 : [(11354 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_755568, c_Rings_Oinverse__class_Odivide(_755568, _755570, _755572), c_Groups_Ozero__class_Ozero(_755568))), 11355 ^ _356604 : [(11362 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_755568, _755570, c_Groups_Ozero__class_Ozero(_755568)), c_Orderings_Oord__class_Oless(_755568, c_Groups_Ozero__class_Ozero(_755568), _755572)], (11356 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_755568, c_Groups_Ozero__class_Ozero(_755568), _755570), c_Orderings_Oord__class_Oless(_755568, _755572, c_Groups_Ozero__class_Ozero(_755568))]]], (11340 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_755568, c_Rings_Oinverse__class_Odivide(_755568, _755570, _755572), c_Groups_Ozero__class_Ozero(_755568)), 11345 ^ _356604 : [(11348 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_755568, _755572, c_Groups_Ozero__class_Ozero(_755568)))], (11346 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_755568, c_Groups_Ozero__class_Ozero(_755568), _755570))]], 11349 ^ _356604 : [(11352 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_755568, c_Groups_Ozero__class_Ozero(_755568), _755572))], (11350 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_755568, _755570, c_Groups_Ozero__class_Ozero(_755568)))]]]]], (4816 ^ _356604) ^ [_528516, _528518, _528520, _528522] : [class_Groups_Omonoid__mult(_528516), -(hAPP(hAPP(c_Power_Opower__class_Opower(_528516), _528518), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _528520), _528522)) = hAPP(hAPP(c_Power_Opower__class_Opower(_528516), hAPP(hAPP(c_Power_Opower__class_Opower(_528516), _528518), _528520)), _528522))], (6688 ^ _356604) ^ [_595177, _595179, _595181] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _595177, _595179), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _595181, _595177), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _595177, _595181), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _595179, _595181)))], (11428 ^ _356604) ^ [_758492, _758494, _758496, _758498] : [class_Fields_Ofield__inverse__zero(_758492), -(_758494 = c_Groups_Ozero__class_Ozero(_758492)), -(c_Rings_Oinverse__class_Odivide(_758492, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_758492), _758494), _758496), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_758492), _758494), _758498)) = c_Rings_Oinverse__class_Odivide(_758492, _758496, _758498))], (2194 ^ _356604) ^ [_430949, _430951] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Nat_OSuc(_430949), _430951) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _430949, c_Nat_OSuc(_430951)))], (9675 ^ _356604) ^ [_698748, _698750, _698752, _698754, _698756] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _698748, _698750), -(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), _698748), _698752), _698754), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _698750), _698752), _698756)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _698754, 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, _698750, _698748)), _698752), _698756)))], (1716 ^ _356604) ^ [_413818, _413820] : [1717 ^ _356604 : [(1718 ^ _356604) ^ [_413893] : [_413820 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _413818, _413893)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _413818, _413820))], (6356 ^ _356604) ^ [_583550, _583552] : [6357 ^ _356604 : [(6360 ^ _356604) ^ [] : [_583550 = _583552], (6358 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _583550, _583552)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _583550, c_Nat_OSuc(_583552)))], (12522 ^ _356604) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (748 ^ _356604) ^ [_379360, _379362] : [-(class_Rings_Ocomm__semiring__1(_379360)), _379362 = _379360, class_Rings_Ocomm__semiring__1(_379362)], (4548 ^ _356604) ^ [_518835] : [class_Rings_Ocomm__semiring__1(_518835), -(c_Polynomial_Odegree(_518835, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_518835))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7792 ^ _356604) ^ [_631991, _631993, _631995, _631997, _631999] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _631991, _631993), 7795 ^ _356604 : [(7802 ^ _356604) ^ [] : [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, _631993, _631991)), _631995), _631997), _631999), -(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), _631993), _631995), _631997), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _631991), _631995), _631999)))], (7796 ^ _356604) ^ [] : [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), _631993), _631995), _631997), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _631991), _631995), _631999)), -(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, _631993, _631991)), _631995), _631997), _631999))]]], (6826 ^ _356604) ^ [_600038, _600040, _600042, _600044, _600046] : [class_Groups_Oab__group__add(_600038), c_Groups_Ominus__class_Ominus(_600038, _600040, _600042) = c_Groups_Ominus__class_Ominus(_600038, _600044, _600046), 6833 ^ _356604 : [(6840 ^ _356604) ^ [] : [_600044 = _600046, -(_600040 = _600042)], (6834 ^ _356604) ^ [] : [_600040 = _600042, -(_600044 = _600046)]]], (5804 ^ _356604) ^ [_563861, _563863, _563865, _563867, _563869, _563871] : [class_Rings_Oordered__ring(_563861), 5807 ^ _356604 : [(5814 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_563861, _563867, c_Groups_Oplus__class_Oplus(_563861, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_563861), c_Groups_Ominus__class_Ominus(_563861, _563869, _563863)), _563865), _563871)), -(c_Orderings_Oord__class_Oless(_563861, c_Groups_Oplus__class_Oplus(_563861, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_563861), _563863), _563865), _563867), c_Groups_Oplus__class_Oplus(_563861, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_563861), _563869), _563865), _563871)))], (5808 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_563861, c_Groups_Oplus__class_Oplus(_563861, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_563861), _563863), _563865), _563867), c_Groups_Oplus__class_Oplus(_563861, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_563861), _563869), _563865), _563871)), -(c_Orderings_Oord__class_Oless(_563861, _563867, c_Groups_Oplus__class_Oplus(_563861, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_563861), c_Groups_Ominus__class_Ominus(_563861, _563869, _563863)), _563865), _563871)))]]], (6402 ^ _356604) ^ [_585055, _585057] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _585055, _585057), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _585055, c_Nat_OSuc(_585057)))], (4206 ^ _356604) ^ [_505948, _505950, _505952] : [class_Groups_Oab__group__add(_505948), -(c_Groups_Ouminus__class_Ouminus(_505948, c_Groups_Oplus__class_Oplus(_505948, _505950, _505952)) = c_Groups_Oplus__class_Oplus(_505948, c_Groups_Ouminus__class_Ouminus(_505948, _505950), c_Groups_Ouminus__class_Ouminus(_505948, _505952)))], (778 ^ _356604) ^ [_380245, _380247] : [-(class_Int_Oring__char__0(_380245)), _380247 = _380245, class_Int_Oring__char__0(_380247)], (10926 ^ _356604) ^ [_741816, _741818, _741820] : [class_Rings_Odivision__ring(_741816), -(_741818 = c_Groups_Ozero__class_Ozero(_741816)), -(c_Groups_Ouminus__class_Ouminus(_741816, c_Rings_Oinverse__class_Odivide(_741816, _741820, _741818)) = c_Rings_Oinverse__class_Odivide(_741816, _741820, c_Groups_Ouminus__class_Ouminus(_741816, _741818)))], (5662 ^ _356604) ^ [_558748] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(_558748)))], (2959 ^ _356604) ^ [_460160, _460162, _460164] : [class_Orderings_Opreorder(_460160), _460162 = _460164, -(c_Orderings_Oord__class_Oless__eq(_460160, _460162, _460164))], (8987 ^ _356604) ^ [_674313, _674315, _674317] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _674313, _674315), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _674317), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _674317), _674313), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _674317), _674315)))], (9035 ^ _356604) ^ [_675961, _675963, _675965] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _675963, _675965), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_675961)), _675963), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_675961)), _675965)))], (5516 ^ _356604) ^ [_553428, _553430, _553432] : [class_Rings_Oidom(_553428), 5519 ^ _356604 : [(5526 ^ _356604) ^ [] : [hAPP(c_Polynomial_Opoly(_553428, _553432), c_Groups_Ouminus__class_Ouminus(_553428, _553430)) = c_Groups_Ozero__class_Ozero(_553428), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_553428), c_Polynomial_OpCons(_553428, _553430, c_Polynomial_OpCons(_553428, c_Groups_Oone__class_Oone(_553428), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_553428)))), _553432))], (5520 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_553428), c_Polynomial_OpCons(_553428, _553430, c_Polynomial_OpCons(_553428, c_Groups_Oone__class_Oone(_553428), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_553428)))), _553432), -(hAPP(c_Polynomial_Opoly(_553428, _553432), c_Groups_Ouminus__class_Ouminus(_553428, _553430)) = c_Groups_Ozero__class_Ozero(_553428))]]], (5726 ^ _356604) ^ [_561006, _561008] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _561006, _561008), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _561006), _561008))], (12888 ^ _356604) ^ [_804945] : [class_Rings_Ocomm__semiring__0(_804945), -(class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(_804945)))], (3823 ^ _356604) ^ [_492321, _492323, _492325, _492327] : [class_Rings_Ocomm__semiring__1(_492321), -(hAPP(c_Polynomial_Opoly(_492321, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_492321)), _492323), _492325)), _492327) = hAPP(hAPP(c_Power_Opower__class_Opower(_492321), hAPP(c_Polynomial_Opoly(_492321, _492323), _492327)), _492325))], (2585 ^ _356604) ^ [_446055, _446057] : [class_Rings_Ocomm__semiring__1(_446055), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_446055), c_Groups_Ozero__class_Ozero(_446055)), _446057) = c_Groups_Ozero__class_Ozero(_446055))], (12762 ^ _356604) ^ [_800955] : [class_Groups_Ocancel__comm__monoid__add(_800955), -(class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(_800955)))], (1118 ^ _356604) ^ [_393073, _393075, _393077, _393079] : [-(tc_fun(_393079, _393075) = tc_fun(_393077, _393073)), _393079 = _393077, _393075 = _393073], (9145 ^ _356604) ^ [_679674, _679676] : [9146 ^ _356604 : [(9149 ^ _356604) ^ [] : [_679676 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (9147 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _679674)]], -(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), _679674), _679676)))], (5656 ^ _356604) ^ [_558549, _558551, _558553] : [class_Fields_Ofield(_558549), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_558549), c_Polynomial_Opoly__gcd(_558549, _558551, _558553), _558553))], (3228 ^ _356604) ^ [_469981, _469983, _469985] : [3229 ^ _356604 : [(3232 ^ _356604) ^ [] : [_469983 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3230 ^ _356604) ^ [] : [_469981 = _469985]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _469981), _469983) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _469985), _469983))], (5478 ^ _356604) ^ [_552086, _552088, _552090, _552092] : [class_Groups_Ouminus(_552086), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_552088, _552086), _552090), _552092) = c_Groups_Ouminus__class_Ouminus(_552086, hAPP(_552090, _552092)))], (12592 ^ _356604) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (3917 ^ _356604) ^ [_495689, _495691, _495693] : [class_Groups_Oab__group__add(_495689), -(hAPP(c_Polynomial_Ocoeff(_495689, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_495689), _495691)), _495693) = c_Groups_Ouminus__class_Ouminus(_495689, hAPP(c_Polynomial_Ocoeff(_495689, _495691), _495693)))], (7990 ^ _356604) ^ [_639763, _639765, _639767, _639769] : [class_Rings_Ocomm__ring(_639763), class_Rings_Odvd(_639763), c_Rings_Odvd__class_Odvd(_639763, _639765, _639767), 8001 ^ _356604 : [(8008 ^ _356604) ^ [_640404, _640406] : [c_Rings_Odvd__class_Odvd(_639763, _639765, c_Groups_Oplus__class_Oplus(_639763, c_Groups_Ominus__class_Ominus(_639763, _640406, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_639763), _640404), _639767)), _639769)), -(c_Rings_Odvd__class_Odvd(_639763, _639765, c_Groups_Oplus__class_Oplus(_639763, _640406, _639769)))], (8002 ^ _356604) ^ [_640166, _640168] : [c_Rings_Odvd__class_Odvd(_639763, _639765, c_Groups_Oplus__class_Oplus(_639763, _640168, _639769)), -(c_Rings_Odvd__class_Odvd(_639763, _639765, c_Groups_Oplus__class_Oplus(_639763, c_Groups_Ominus__class_Ominus(_639763, _640168, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_639763), _640166), _639767)), _639769)))]]], (6170 ^ _356604) ^ [_577126, _577128, _577130] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _577126, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _577128, _577130)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _577126, _577130), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _577130, _577128), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _577126, _577128))], (1353 ^ _356604) ^ [_400621, _400623, _400625, _400627] : [class_Groups_Ozero(_400621), 1356 ^ _356604 : [(1363 ^ _356604) ^ [] : [_400623 = _400627, -(c_Polynomial_Omonom(_400621, _400623, _400625) = c_Polynomial_Omonom(_400621, _400627, _400625))], (1357 ^ _356604) ^ [] : [c_Polynomial_Omonom(_400621, _400623, _400625) = c_Polynomial_Omonom(_400621, _400627, _400625), -(_400623 = _400627)]]], (5738 ^ _356604) ^ [_561429, _561431] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _561429, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _561431, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _561429, _561431))], (10061 ^ _356604) ^ [_711899, _711901, _711903] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _711899, _711901), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _711901, _711899)), _711901 = _711903, 10072 ^ _356604 : [(10075 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _711903, _711899)], (10073 ^ _356604) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _711899, _711903))]]], (11960 ^ _356604) ^ [_776414, _776416, _776418, _776420, _776422] : [class_Fields_Ofield(_776414), -(_776416 = c_Groups_Ozero__class_Ozero(_776414)), -(_776418 = c_Groups_Ozero__class_Ozero(_776414)), -(c_Groups_Ominus__class_Ominus(_776414, c_Rings_Oinverse__class_Odivide(_776414, _776420, _776416), c_Rings_Oinverse__class_Odivide(_776414, _776422, _776418)) = c_Rings_Oinverse__class_Odivide(_776414, c_Groups_Ominus__class_Ominus(_776414, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_776414), _776420), _776418), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_776414), _776422), _776416)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_776414), _776416), _776418)))], (11482 ^ _356604) ^ [_760376, _760378, _760380, _760382] : [class_Fields_Ofield__inverse__zero(_760376), 11485 ^ _356604 : [(11486 ^ _356604) ^ [] : [_760378 = c_Rings_Oinverse__class_Odivide(_760376, _760380, _760382), 11489 ^ _356604 : [(11496 ^ _356604) ^ [] : [_760382 = c_Groups_Ozero__class_Ozero(_760376), -(_760378 = c_Groups_Ozero__class_Ozero(_760376))], (11490 ^ _356604) ^ [] : [-(_760382 = c_Groups_Ozero__class_Ozero(_760376)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_760376), _760378), _760382) = _760380)]]], (11502 ^ _356604) ^ [] : [-(_760378 = c_Rings_Oinverse__class_Odivide(_760376, _760380, _760382)), 11505 ^ _356604 : [(11508 ^ _356604) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_760376), _760378), _760382) = _760380], (11506 ^ _356604) ^ [] : [_760382 = c_Groups_Ozero__class_Ozero(_760376)]], 11509 ^ _356604 : [(11512 ^ _356604) ^ [] : [_760378 = c_Groups_Ozero__class_Ozero(_760376)], (11510 ^ _356604) ^ [] : [-(_760382 = c_Groups_Ozero__class_Ozero(_760376))]]]]], (13060 ^ _356604) ^ [] : [-(class_Int_Oring__char__0(t_a))], (6012 ^ _356604) ^ [_571472, _571474, _571476, _571478] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_571472), c_Orderings_Oord__class_Oless(_571472, c_Groups_Oplus__class_Oplus(_571472, _571474, _571476), c_Groups_Oplus__class_Oplus(_571472, _571474, _571478)), -(c_Orderings_Oord__class_Oless(_571472, _571476, _571478))], (798 ^ _356604) ^ [_381247, _381249] : [_381249 = _381247, -(c_HOL_Obool_Obool__size(_381249) = c_HOL_Obool_Obool__size(_381247))], (3074 ^ _356604) ^ [_464574, _464576, _464578, _464580] : [class_Rings_Ocomm__semiring__0(_464574), -(hAPP(c_Polynomial_Opoly(_464574, c_Polynomial_OpCons(_464574, _464576, _464578)), _464580) = c_Groups_Oplus__class_Oplus(_464574, _464576, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_464574), _464580), hAPP(c_Polynomial_Opoly(_464574, _464578), _464580))))], (7024 ^ _356604) ^ [_606846, _606848, _606850] : [class_Orderings_Olinorder(_606846), -(_606848 = _606850), -(c_Orderings_Oord__class_Oless(_606846, _606848, _606850)), -(c_Orderings_Oord__class_Oless(_606846, _606850, _606848))], (6142 ^ _356604) ^ [_576252, _576254, _576256, _576258] : [class_Rings_Ocomm__ring__1(_576252), c_Rings_Odvd__class_Odvd(_576252, _576254, _576256), c_Rings_Odvd__class_Odvd(_576252, _576254, _576258), -(c_Rings_Odvd__class_Odvd(_576252, _576254, c_Groups_Ominus__class_Ominus(_576252, _576256, _576258)))], (5952 ^ _356604) ^ [_569337, _569339, _569341, _569343] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_569337), 5955 ^ _356604 : [(5962 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_569337, _569341, _569343), -(c_Orderings_Oord__class_Oless(_569337, c_Groups_Oplus__class_Oplus(_569337, _569339, _569341), c_Groups_Oplus__class_Oplus(_569337, _569339, _569343)))], (5956 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_569337, c_Groups_Oplus__class_Oplus(_569337, _569339, _569341), c_Groups_Oplus__class_Oplus(_569337, _569339, _569343)), -(c_Orderings_Oord__class_Oless(_569337, _569341, _569343))]]], (5040 ^ _356604) ^ [_536484] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _536484), _536484) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (6082 ^ _356604) ^ [_573771, _573773, _573775] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _573771, _573773), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _573775, _573773)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _573771, _573775))], (6272 ^ _356604) ^ [_580514, _580516, _580518] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _580514, _580516), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _580514, _580518), 6279 ^ _356604 : [(6286 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _580516, _580518), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _580516, _580514), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _580518, _580514)))], (6280 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _580516, _580514), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _580518, _580514)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _580516, _580518))]]], (8286 ^ _356604) ^ [_649966, _649968, _649970, _649972] : [class_Rings_Olinordered__ring__strict(_649966), 8289 ^ _356604 : [(8304 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_649966, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_649966), _649968), _649970), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_649966), _649972), _649970))), 8305 ^ _356604 : [(8312 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_649966, _649970, c_Groups_Ozero__class_Ozero(_649966)), c_Orderings_Oord__class_Oless(_649966, _649972, _649968)], (8306 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_649966, c_Groups_Ozero__class_Ozero(_649966), _649970), c_Orderings_Oord__class_Oless(_649966, _649968, _649972)]]], (8290 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_649966, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_649966), _649968), _649970), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_649966), _649972), _649970)), 8295 ^ _356604 : [(8298 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_649966, _649968, _649972))], (8296 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_649966, c_Groups_Ozero__class_Ozero(_649966), _649970))]], 8299 ^ _356604 : [(8302 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_649966, _649972, _649968))], (8300 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_649966, _649970, c_Groups_Ozero__class_Ozero(_649966)))]]]]], (12158 ^ _356604) ^ [_782944] : [class_Int_Oring__char__0(_782944), -(class_Groups_Ocancel__semigroup__add(_782944))], (4096 ^ _356604) ^ [_501461, _501463, _501465] : [class_Groups_Oordered__ab__group__add(_501461), 4099 ^ _356604 : [(4106 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_501461, _501465, c_Groups_Ouminus__class_Ouminus(_501461, _501463)), -(c_Orderings_Oord__class_Oless__eq(_501461, _501463, c_Groups_Ouminus__class_Ouminus(_501461, _501465)))], (4100 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_501461, _501463, c_Groups_Ouminus__class_Ouminus(_501461, _501465)), -(c_Orderings_Oord__class_Oless__eq(_501461, _501465, c_Groups_Ouminus__class_Ouminus(_501461, _501463)))]]], (10844 ^ _356604) ^ [_738291, _738293] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _738291, _738293)), -(c_Nat__Transfer_Otsub(_738293, _738291) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (6892 ^ _356604) ^ [_602422, _602424, _602426, _602428] : [class_Rings_Ocomm__ring(_602422), -(hAPP(c_Polynomial_Opoly(_602422, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_602422), _602424, _602426)), _602428) = c_Groups_Ominus__class_Ominus(_602422, hAPP(c_Polynomial_Opoly(_602422, _602424), _602428), hAPP(c_Polynomial_Opoly(_602422, _602426), _602428)))], (548 ^ _356604) ^ [_373460, _373462] : [-(class_Groups_Ocomm__monoid__add(_373460)), _373462 = _373460, class_Groups_Ocomm__monoid__add(_373462)], (9249 ^ _356604) ^ [_683721, _683723, _683725, _683727] : [class_Rings_Olinordered__semiring__strict(_683721), c_Orderings_Oord__class_Oless__eq(_683721, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_683721), _683723), _683725), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_683721), _683727), _683725)), c_Orderings_Oord__class_Oless(_683721, c_Groups_Ozero__class_Ozero(_683721), _683725), -(c_Orderings_Oord__class_Oless__eq(_683721, _683723, _683727))], (12984 ^ _356604) ^ [_807985] : [class_Rings_Olinordered__idom(_807985), -(class_Orderings_Oord(tc_Polynomial_Opoly(_807985)))], (4256 ^ _356604) ^ [_507868, _507870] : [class_Groups_Omonoid__mult(_507868), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_507868), c_Groups_Oone__class_Oone(_507868)), _507870) = _507870)], (3444 ^ _356604) ^ [_478065, _478067] : [class_Rings_Omult__zero(_478065), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_478065), c_Groups_Ozero__class_Ozero(_478065)), _478067) = c_Groups_Ozero__class_Ozero(_478065))], (2561 ^ _356604) ^ [_444887, _444889, _444891, _444893] : [class_Rings_Ocomm__semiring__1(_444887), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_444887), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_444887), _444889), _444891)), _444893) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_444887), _444889), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_444887), _444891), _444893)))], (9319 ^ _356604) ^ [_686155, _686157, _686159, _686161, _686163] : [class_Rings_Olinordered__semiring__strict(_686155), c_Orderings_Oord__class_Oless__eq(_686155, _686157, _686159), c_Orderings_Oord__class_Oless(_686155, _686161, _686163), c_Orderings_Oord__class_Oless(_686155, c_Groups_Ozero__class_Ozero(_686155), _686157), c_Orderings_Oord__class_Oless__eq(_686155, c_Groups_Ozero__class_Ozero(_686155), _686161), -(c_Orderings_Oord__class_Oless(_686155, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_686155), _686157), _686161), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_686155), _686159), _686163)))], (2356 ^ _356604) ^ [_436687, _436689] : [c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _436687, _436689), 2361 ^ _356604 : [(2364 ^ _356604) ^ [] : [-(_436689 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2362 ^ _356604) ^ [] : [-(_436687 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 2365 ^ _356604 : [(2368 ^ _356604) ^ [] : [-(_436689 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (2366 ^ _356604) ^ [] : [-(_436687 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (3346 ^ _356604) ^ [_474662, _474664, _474666] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_474662)), _474664), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_474662)), _474666)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _474664, _474666))], (5276 ^ _356604) ^ [_545017, _545019, _545021, _545023] : [class_Rings_Oidom(_545017), 5279 ^ _356604 : [(5280 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(_545017, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_545017), _545019), _545021), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_545017), _545019), _545023)), -(_545019 = c_Groups_Ozero__class_Ozero(_545017)), -(c_Rings_Odvd__class_Odvd(_545017, _545021, _545023))], (5290 ^ _356604) ^ [] : [5291 ^ _356604 : [(5294 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(_545017, _545021, _545023)], (5292 ^ _356604) ^ [] : [_545019 = c_Groups_Ozero__class_Ozero(_545017)]], -(c_Rings_Odvd__class_Odvd(_545017, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_545017), _545019), _545021), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_545017), _545019), _545023)))]]], (428 ^ _356604) ^ [_369920, _369922] : [-(class_Groups_Oab__semigroup__mult(_369920)), _369922 = _369920, class_Groups_Oab__semigroup__mult(_369922)], (698 ^ _356604) ^ [_377885, _377887] : [-(class_Power_Opower(_377885)), _377887 = _377885, class_Power_Opower(_377887)], (11448 ^ _356604) ^ [_759292, _759294, _759296, _759298] : [class_Fields_Ofield__inverse__zero(_759292), 11451 ^ _356604 : [(11452 ^ _356604) ^ [] : [c_Rings_Oinverse__class_Odivide(_759292, _759294, _759296) = _759298, 11455 ^ _356604 : [(11462 ^ _356604) ^ [] : [_759296 = c_Groups_Ozero__class_Ozero(_759292), -(_759298 = c_Groups_Ozero__class_Ozero(_759292))], (11456 ^ _356604) ^ [] : [-(_759296 = c_Groups_Ozero__class_Ozero(_759292)), -(_759294 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_759292), _759298), _759296))]]], (11468 ^ _356604) ^ [] : [-(c_Rings_Oinverse__class_Odivide(_759292, _759294, _759296) = _759298), 11471 ^ _356604 : [(11474 ^ _356604) ^ [] : [_759294 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_759292), _759298), _759296)], (11472 ^ _356604) ^ [] : [_759296 = c_Groups_Ozero__class_Ozero(_759292)]], 11475 ^ _356604 : [(11478 ^ _356604) ^ [] : [_759298 = c_Groups_Ozero__class_Ozero(_759292)], (11476 ^ _356604) ^ [] : [-(_759296 = c_Groups_Ozero__class_Ozero(_759292))]]]]], (2296 ^ _356604) ^ [_434555, _434557] : [class_Groups_Ocomm__monoid__add(_434555), -(c_Groups_Oplus__class_Oplus(_434555, c_Groups_Ozero__class_Ozero(_434555), _434557) = _434557)], (10319 ^ _356604) ^ [_719976, _719978] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _719976, _719978), 10324 ^ _356604 : [(10327 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _719978, _719976)], (10325 ^ _356604) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _719976, _719978))]], -(_719976 = _719978)], (6968 ^ _356604) ^ [_605175, _605177, _605179] : [class_Orderings_Olinorder(_605175), 6971 ^ _356604 : [(6972 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_605175, _605177, _605179)), -(c_Orderings_Oord__class_Oless(_605175, _605179, _605177)), -(_605177 = _605179)], (6982 ^ _356604) ^ [] : [6983 ^ _356604 : [(6986 ^ _356604) ^ [] : [_605177 = _605179], (6984 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_605175, _605179, _605177)]], c_Orderings_Oord__class_Oless(_605175, _605177, _605179)]]], (12828 ^ _356604) ^ [_803045] : [class_Rings_Ocomm__semiring__0(_803045), -(class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(_803045)))], (2216 ^ _356604) ^ [_431894, _431896] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _431894, c_Nat_OSuc(_431896)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _431894, _431896)), -(_431894 = c_Nat_OSuc(_431896))], (12936 ^ _356604) ^ [_806465] : [class_Groups_Ocomm__monoid__add(_806465), -(class_Groups_Omonoid__add(tc_Polynomial_Opoly(_806465)))], (8100 ^ _356604) ^ [_643893, _643895, _643897, _643899] : [class_Rings_Olinordered__semiring__strict(_643893), c_Orderings_Oord__class_Oless(_643893, _643895, _643897), c_Orderings_Oord__class_Oless(_643893, c_Groups_Ozero__class_Ozero(_643893), _643899), -(c_Orderings_Oord__class_Oless(_643893, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_643893), _643895), _643899), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_643893), _643897), _643899)))], (7896 ^ _356604) ^ [_635726, _635728, _635730] : [class_Groups_Omonoid__mult(_635726), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _635728), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_635726), hAPP(hAPP(c_Power_Opower__class_Opower(_635726), _635730), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _635728, c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _635730) = hAPP(hAPP(c_Power_Opower__class_Opower(_635726), _635730), _635728))], (5102 ^ _356604) ^ [_538850, _538852, _538854, _538856, _538858] : [class_Rings_Ocomm__semiring__1(_538850), c_Rings_Odvd__class_Odvd(_538850, _538852, _538854), c_Rings_Odvd__class_Odvd(_538850, _538856, _538858), -(c_Rings_Odvd__class_Odvd(_538850, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_538850), _538852), _538856), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_538850), _538854), _538858)))], (6300 ^ _356604) ^ [_581647] : [-(_581647 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _581647))], (3550 ^ _356604) ^ [_481747, _481749, _481751] : [class_Rings_Oordered__cancel__semiring(_481747), c_Orderings_Oord__class_Oless__eq(_481747, c_Groups_Ozero__class_Ozero(_481747), _481749), c_Orderings_Oord__class_Oless__eq(_481747, _481751, c_Groups_Ozero__class_Ozero(_481747)), -(c_Orderings_Oord__class_Oless__eq(_481747, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_481747), _481749), _481751), c_Groups_Ozero__class_Ozero(_481747)))], (5048 ^ _356604) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (9589 ^ _356604) ^ [_695116, _695118, _695120] : [class_Rings_Olinordered__semidom(_695116), c_Orderings_Oord__class_Oless(_695116, c_Groups_Oone__class_Oone(_695116), _695118), -(c_Orderings_Oord__class_Oless(_695116, hAPP(hAPP(c_Power_Opower__class_Opower(_695116), _695118), _695120), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_695116), _695118), hAPP(hAPP(c_Power_Opower__class_Opower(_695116), _695118), _695120))))], (2302 ^ _356604) ^ [_434775, _434777] : [class_Groups_Omonoid__add(_434775), -(c_Groups_Oplus__class_Oplus(_434775, c_Groups_Ozero__class_Ozero(_434775), _434777) = _434777)], (6466 ^ _356604) ^ [_587290, _587292, _587294] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _587290, _587292), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _587290, _587294)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _587292, _587294))], (2456 ^ _356604) ^ [_440426, _440428] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _440426, _440428), -(_440428 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _440426, 2459 ^ [_440426, _440428]))], (13032 ^ _356604) ^ [_809505] : [class_Rings_Ocomm__semiring__1(_809505), -(class_Groups_Oone(tc_Polynomial_Opoly(_809505)))], (1722 ^ _356604) ^ [_414047, _414049] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _414047, _414049) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _414049, _414047))], (1014 ^ _356604) ^ [_389306, _389308, _389310, _389312, _389314, _389316] : [-(c_Polynomial_Osmult(_389316, _389312, _389308) = c_Polynomial_Osmult(_389314, _389310, _389306)), _389316 = _389314, _389312 = _389310, _389308 = _389306], (2519 ^ _356604) ^ [_442595, _442597] : [class_Rings_Ocomm__semiring__1(_442595), -(c_Groups_Oplus__class_Oplus(_442595, c_Groups_Ozero__class_Ozero(_442595), _442597) = _442597)], (628 ^ _356604) ^ [_375820, _375822] : [-(class_Rings_Olinordered__idom(_375820)), _375822 = _375820, class_Rings_Olinordered__idom(_375822)], (7150 ^ _356604) ^ [_610898, _610900, _610902, _610904] : [class_Orderings_Oorder(_610898), c_Orderings_Oord__class_Oless(_610898, _610900, _610902), _610900 = _610904, -(c_Orderings_Oord__class_Oless(_610898, _610904, _610902))], (528 ^ _356604) ^ [_372870, _372872] : [-(class_Orderings_Olinorder(_372870)), _372872 = _372870, class_Orderings_Olinorder(_372872)], (5902 ^ _356604) ^ [_567503, _567505, _567507] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _567503), 5905 ^ _356604 : [(5912 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _567505, _567507), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _567503), _567505), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _567503), _567507)))], (5906 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _567503), _567505), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _567503), _567507)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _567505, _567507))]]], (3092 ^ _356604) ^ [_465512, _465514, _465516] : [class_Rings_Oordered__cancel__semiring(_465512), -(c_Orderings_Oord__class_Oless__eq(_465512, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_465512), _465514), _465516), c_Groups_Ozero__class_Ozero(_465512))), 3097 ^ _356604 : [(3104 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_465512, _465514, c_Groups_Ozero__class_Ozero(_465512)), c_Orderings_Oord__class_Oless__eq(_465512, c_Groups_Ozero__class_Ozero(_465512), _465516)], (3098 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_465512, c_Groups_Ozero__class_Ozero(_465512), _465514), c_Orderings_Oord__class_Oless__eq(_465512, _465516, c_Groups_Ozero__class_Ozero(_465512))]]], (2398 ^ _356604) ^ [_438091, _438093, _438095, _438097] : [class_Rings_Ocomm__semiring__0(_438091), -(hAPP(c_Polynomial_Opoly(_438091, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_438091, _438093, _438095)), _438097) = hAPP(c_Polynomial_Opoly(_438091, _438093), c_Groups_Oplus__class_Oplus(_438091, _438095, _438097)))], (3236 ^ _356604) ^ [_470342, _470344, _470346] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _470342), _470344) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _470342), _470346), -(_470344 = _470346), -(_470342 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12528 ^ _356604) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (8356 ^ _356604) ^ [_652214, _652216, _652218] : [class_Groups_Oordered__comm__monoid__add(_652214), c_Orderings_Oord__class_Oless(_652214, c_Groups_Ozero__class_Ozero(_652214), _652216), c_Orderings_Oord__class_Oless(_652214, c_Groups_Ozero__class_Ozero(_652214), _652218), -(c_Orderings_Oord__class_Oless(_652214, c_Groups_Ozero__class_Ozero(_652214), c_Groups_Oplus__class_Oplus(_652214, _652216, _652218)))], (1311 ^ _356604) ^ [_399216, _399218, _399220] : [class_Int_Oring__char__0(_399216), class_Rings_Oidom(_399216), 1318 ^ _356604 : [(1325 ^ _356604) ^ [] : [_399218 = _399220, -(c_Polynomial_Opoly(_399216, _399218) = c_Polynomial_Opoly(_399216, _399220))], (1319 ^ _356604) ^ [] : [c_Polynomial_Opoly(_399216, _399218) = c_Polynomial_Opoly(_399216, _399220), -(_399218 = _399220)]]], (2418 ^ _356604) ^ [_438927, _438929] : [c_Nat_OSuc(_438927) = c_Nat_OSuc(_438929), -(_438927 = _438929)], (1944 ^ _356604) ^ [_422389, _422391, _422393, _422395] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_422389), 1947 ^ _356604 : [(1954 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_422389, _422391, _422395), -(c_Orderings_Oord__class_Oless__eq(_422389, c_Groups_Oplus__class_Oplus(_422389, _422391, _422393), c_Groups_Oplus__class_Oplus(_422389, _422395, _422393)))], (1948 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_422389, c_Groups_Oplus__class_Oplus(_422389, _422391, _422393), c_Groups_Oplus__class_Oplus(_422389, _422395, _422393)), -(c_Orderings_Oord__class_Oless__eq(_422389, _422391, _422395))]]], (12540 ^ _356604) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (518 ^ _356604) ^ [_372575, _372577] : [-(class_Orderings_Opreorder(_372575)), _372577 = _372575, class_Orderings_Opreorder(_372577)], (688 ^ _356604) ^ [_377590, _377592] : [-(class_Groups_Ominus(_377590)), _377592 = _377590, class_Groups_Ominus(_377592)], (12618 ^ _356604) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (9129 ^ _356604) ^ [_679139, _679141] : [class_Groups_Oab__group__add(_679139), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_679139), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_679139)), _679141) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_679139), _679141))], (3863 ^ _356604) ^ [_493879, _493881, _493883] : [class_Rings_Ocomm__semiring__1(_493879), -(hAPP(c_Polynomial_Ocoeff(_493879, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_493879)), c_Polynomial_OpCons(_493879, _493881, c_Polynomial_OpCons(_493879, c_Groups_Oone__class_Oone(_493879), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_493879))))), _493883)), _493883) = c_Groups_Oone__class_Oone(_493879))], (3030 ^ _356604) ^ [_462728, _462730, _462732, _462734] : [class_Rings_Ocomm__semiring__1(_462728), -(c_Groups_Oplus__class_Oplus(_462728, c_Groups_Oplus__class_Oplus(_462728, _462730, _462732), _462734) = c_Groups_Oplus__class_Oplus(_462728, c_Groups_Oplus__class_Oplus(_462728, _462730, _462734), _462732))], (12750 ^ _356604) ^ [_800575] : [class_Rings_Olinordered__idom(_800575), -(class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(_800575)))], (1199 ^ _356604) ^ [_395965, _395967, _395969] : [class_Rings_Oidom(_395965), 1202 ^ _356604 : [(1209 ^ _356604) ^ [] : [-(_395967 = c_Groups_Ozero__class_Ozero(_395965)), -(c_Polynomial_Odegree(_395965, c_Polynomial_Osmult(_395965, _395967, _395969)) = c_Polynomial_Odegree(_395965, _395969))], (1203 ^ _356604) ^ [] : [_395967 = c_Groups_Ozero__class_Ozero(_395965), -(c_Polynomial_Odegree(_395965, c_Polynomial_Osmult(_395965, _395967, _395969)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (7122 ^ _356604) ^ [_610006, _610008, _610010, _610012] : [class_Orderings_Oorder(_610006), _610008 = _610010, c_Orderings_Oord__class_Oless(_610006, _610012, _610010), -(c_Orderings_Oord__class_Oless(_610006, _610012, _610008))], (7098 ^ _356604) ^ [_609220, _609222, _609224] : [class_Orderings_Oorder(_609220), c_Orderings_Oord__class_Oless(_609220, _609222, _609224), c_Orderings_Oord__class_Oless(_609220, _609224, _609222)], (10557 ^ _356604) ^ [_728075, _728077] : [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), _728075), _728077)), -(_728077 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _728075))], (12876 ^ _356604) ^ [_804565] : [class_Rings_Ocomm__semiring__1(_804565), -(class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(_804565)))], (6928 ^ _356604) ^ [_603892, _603894] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _603892, _603894), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _603892, _603894), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (1746 ^ _356604) ^ [_415135, _415137, _415139] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _415135, _415137) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _415139, _415137), -(_415135 = _415139)], (3634 ^ _356604) ^ [_484521, _484523, _484525, _484527] : [class_RealVector_Oreal__normed__algebra(_484521), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_484521), _484523), c_Groups_Oplus__class_Oplus(_484521, _484525, _484527)) = c_Groups_Oplus__class_Oplus(_484521, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_484521), _484523), _484525), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_484521), _484523), _484527)))], (9447 ^ _356604) ^ [_690365, _690367, _690369] : [class_Groups_Oordered__comm__monoid__add(_690365), c_Orderings_Oord__class_Oless__eq(_690365, _690367, c_Groups_Ozero__class_Ozero(_690365)), c_Orderings_Oord__class_Oless(_690365, _690369, c_Groups_Ozero__class_Ozero(_690365)), -(c_Orderings_Oord__class_Oless(_690365, c_Groups_Oplus__class_Oplus(_690365, _690367, _690369), c_Groups_Ozero__class_Ozero(_690365)))], (8014 ^ _356604) ^ [_640703, _640705] : [class_Groups_Ogroup__add(_640703), -(c_Groups_Ominus__class_Ominus(_640703, c_Groups_Ozero__class_Ozero(_640703), _640705) = c_Groups_Ouminus__class_Ouminus(_640703, _640705))], (3024 ^ _356604) ^ [_462426, _462428, _462430, _462432, _462434] : [class_Rings_Ocomm__semiring__1(_462426), -(c_Groups_Oplus__class_Oplus(_462426, c_Groups_Oplus__class_Oplus(_462426, _462428, _462430), c_Groups_Oplus__class_Oplus(_462426, _462432, _462434)) = c_Groups_Oplus__class_Oplus(_462426, c_Groups_Oplus__class_Oplus(_462426, _462428, _462432), c_Groups_Oplus__class_Oplus(_462426, _462430, _462434)))], (12248 ^ _356604) ^ [_785734] : [class_Int_Oring__char__0(_785734), -(class_Groups_Ozero(_785734))], (12480 ^ _356604) ^ [_792952, _792954] : [class_Orderings_Opreorder(_792952), -(class_Orderings_Opreorder(tc_fun(_792954, _792952)))], (9795 ^ _356604) ^ [_703134, _703136, _703138] : [class_Rings_Olinordered__semidom(_703134), c_Orderings_Oord__class_Oless(_703134, c_Groups_Ozero__class_Ozero(_703134), _703136), c_Orderings_Oord__class_Oless(_703134, _703136, c_Groups_Oone__class_Oone(_703134)), -(c_Orderings_Oord__class_Oless(_703134, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_703134), _703136), hAPP(hAPP(c_Power_Opower__class_Opower(_703134), _703136), _703138)), hAPP(hAPP(c_Power_Opower__class_Opower(_703134), _703136), _703138)))], (12278 ^ _356604) ^ [_786664] : [class_Rings_Oidom(_786664), -(class_Groups_Ocancel__ab__semigroup__add(_786664))], (7452 ^ _356604) ^ [_620398, _620400, _620402] : [class_Orderings_Oorder(_620398), c_Orderings_Oord__class_Oless__eq(_620398, _620400, _620402), -(c_Orderings_Oord__class_Oless(_620398, _620400, _620402)), -(_620400 = _620402)], (890 ^ _356604) ^ [_384758, _384760, _384762, _384764, _384766, _384768] : [-(c_Polynomial_Opcompose(_384768, _384764, _384760) = c_Polynomial_Opcompose(_384766, _384762, _384758)), _384768 = _384766, _384764 = _384762, _384760 = _384758], (12556 ^ _356604) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (10806 ^ _356604) ^ [_736799, _736801, _736803, _736805, _736807, _736809, _736811, _736813] : [class_Fields_Ofield(_736799), c_Polynomial_Opdivmod__rel(_736799, _736801, _736803, _736805, _736807), c_Polynomial_Opdivmod__rel(_736799, _736805, _736809, _736811, _736813), -(c_Polynomial_Opdivmod__rel(_736799, _736801, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_736799)), _736803), _736809), _736811, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_736799), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_736799)), _736803), _736813), _736807)))], (9823 ^ _356604) ^ [_704076, _704078, _704080, _704082] : [class_Rings_Olinordered__semidom(_704076), c_Orderings_Oord__class_Oless(_704076, c_Groups_Oone__class_Oone(_704076), _704078), 9830 ^ _356604 : [(9837 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _704080, _704082), -(c_Orderings_Oord__class_Oless__eq(_704076, hAPP(hAPP(c_Power_Opower__class_Opower(_704076), _704078), _704080), hAPP(hAPP(c_Power_Opower__class_Opower(_704076), _704078), _704082)))], (9831 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_704076, hAPP(hAPP(c_Power_Opower__class_Opower(_704076), _704078), _704080), hAPP(hAPP(c_Power_Opower__class_Opower(_704076), _704078), _704082)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _704080, _704082))]]], (10187 ^ _356604) ^ [_715794, _715796, _715798] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _715794, _715796), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _715796, _715798), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _715794, _715798))], (6724 ^ _356604) ^ [_596298, _596300] : [6725 ^ _356604 : [(6728 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _596300, _596298)], (6726 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _596298, _596300)]], _596298 = _596300], (5452 ^ _356604) ^ [_550971, _550973, _550975, _550977, _550979] : [-(hAPP(hAPP(c_Power_Opower_Opower(_550971, _550973, _550975), _550977), c_Nat_OSuc(_550979)) = hAPP(hAPP(_550975, _550977), hAPP(hAPP(c_Power_Opower_Opower(_550971, _550973, _550975), _550977), _550979)))], (1661 ^ _356604) ^ [_411557] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_411557)], (1804 ^ _356604) ^ [_417297, _417299] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _417297, _417299), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _417299, _417297), -(_417297 = _417299)], (1591 ^ _356604) ^ [_409092, _409094, _409096] : [class_Groups_Ozero(_409092), 1594 ^ _356604 : [(1601 ^ _356604) ^ [] : [-(_409094 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_409092))), -(c_Polynomial_Odegree(_409092, c_Polynomial_OpCons(_409092, _409096, _409094)) = c_Nat_OSuc(c_Polynomial_Odegree(_409092, _409094)))], (1595 ^ _356604) ^ [] : [_409094 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_409092)), -(c_Polynomial_Odegree(_409092, c_Polynomial_OpCons(_409092, _409096, _409094)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (398 ^ _356604) ^ [_369035, _369037] : [-(class_Groups_Ocancel__semigroup__add(_369035)), _369037 = _369035, class_Groups_Ocancel__semigroup__add(_369037)], (3799 ^ _356604) ^ [_491257, _491259] : [class_Rings_Ocomm__semiring__1(_491257), -(hAPP(hAPP(c_Power_Opower__class_Opower(_491257), _491259), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_491257))], (11830 ^ _356604) ^ [_771591, _771593, _771595, _771597] : [class_Fields_Olinordered__field(_771591), c_Orderings_Oord__class_Oless(_771591, _771593, c_Groups_Ozero__class_Ozero(_771591)), 11837 ^ _356604 : [(11844 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_771591, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_771591), _771597), _771593), _771595), -(c_Orderings_Oord__class_Oless(_771591, c_Rings_Oinverse__class_Odivide(_771591, _771595, _771593), _771597))], (11838 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_771591, c_Rings_Oinverse__class_Odivide(_771591, _771595, _771593), _771597), -(c_Orderings_Oord__class_Oless(_771591, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_771591), _771597), _771593), _771595))]]], (7068 ^ _356604) ^ [_608246, _608248, _608250] : [class_Orderings_Oorder(_608246), c_Orderings_Oord__class_Oless(_608246, _608248, _608250), _608248 = _608250], (7744 ^ _356604) ^ [_630323, _630325] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _630323), 7747 ^ _356604 : [(7754 ^ _356604) ^ [] : [_630325 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _630325), _630323), _630323))], (7748 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _630325), _630323), _630323), -(_630325 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (4756 ^ _356604) ^ [_525984, _525986, _525988] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _525984), _525986)), _525988) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _525984), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _525986), _525988)))], (8572 ^ _356604) ^ [_659271, _659273] : [class_Rings_Olinordered__semidom(_659271), -(c_Orderings_Oord__class_Oless(_659271, _659273, c_Groups_Oplus__class_Oplus(_659271, _659273, c_Groups_Oone__class_Oone(_659271))))], (9531 ^ _356604) ^ [_693045, _693047, _693049] : [class_Rings_Olinordered__ring__strict(_693045), 9534 ^ _356604 : [(9535 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_693045, c_Groups_Ozero__class_Ozero(_693045), c_Groups_Oplus__class_Oplus(_693045, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_693045), _693047), _693047), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_693045), _693049), _693049))), _693047 = c_Groups_Ozero__class_Ozero(_693045), _693049 = c_Groups_Ozero__class_Ozero(_693045)], (9545 ^ _356604) ^ [] : [9546 ^ _356604 : [(9549 ^ _356604) ^ [] : [-(_693049 = c_Groups_Ozero__class_Ozero(_693045))], (9547 ^ _356604) ^ [] : [-(_693047 = c_Groups_Ozero__class_Ozero(_693045))]], -(c_Orderings_Oord__class_Oless(_693045, c_Groups_Ozero__class_Ozero(_693045), c_Groups_Oplus__class_Oplus(_693045, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_693045), _693047), _693047), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_693045), _693049), _693049))))]]], (11404 ^ _356604) ^ [_757670, _757672, _757674, _757676, _757678] : [class_Fields_Ofield(_757670), -(_757672 = c_Groups_Ozero__class_Ozero(_757670)), -(_757674 = c_Groups_Ozero__class_Ozero(_757670)), 11415 ^ _356604 : [(11422 ^ _356604) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_757670), _757676), _757674) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_757670), _757678), _757672), -(c_Rings_Oinverse__class_Odivide(_757670, _757676, _757672) = c_Rings_Oinverse__class_Odivide(_757670, _757678, _757674))], (11416 ^ _356604) ^ [] : [c_Rings_Oinverse__class_Odivide(_757670, _757676, _757672) = c_Rings_Oinverse__class_Odivide(_757670, _757678, _757674), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_757670), _757676), _757674) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_757670), _757678), _757672))]]], (7666 ^ _356604) ^ [_627746] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _627746), -(c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _627746, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _627746)], (8456 ^ _356604) ^ [_655457, _655459] : [class_Rings_Olinordered__idom(_655457), 8459 ^ _356604 : [(8466 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_655457, _655459, c_Groups_Ozero__class_Ozero(_655457)), -(c_Orderings_Oord__class_Oless(_655457, _655459, c_Groups_Ouminus__class_Ouminus(_655457, _655459)))], (8460 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_655457, _655459, c_Groups_Ouminus__class_Ouminus(_655457, _655459)), -(c_Orderings_Oord__class_Oless(_655457, _655459, c_Groups_Ozero__class_Ozero(_655457)))]]], (4026 ^ _356604) ^ [_499189, _499191] : [class_Groups_Ogroup__add(_499189), 4029 ^ _356604 : [(4036 ^ _356604) ^ [] : [c_Groups_Ozero__class_Ozero(_499189) = _499191, -(c_Groups_Ozero__class_Ozero(_499189) = c_Groups_Ouminus__class_Ouminus(_499189, _499191))], (4030 ^ _356604) ^ [] : [c_Groups_Ozero__class_Ozero(_499189) = c_Groups_Ouminus__class_Ouminus(_499189, _499191), -(c_Groups_Ozero__class_Ozero(_499189) = _499191)]]], (6092 ^ _356604) ^ [_574368, _574370, _574372] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _574368, _574370), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _574368, _574372), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _574370, _574372)))], (3450 ^ _356604) ^ [_478325, _478327, _478329, _478331] : [class_Rings_Ocomm__semiring(_478325), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_478325), c_Groups_Oplus__class_Oplus(_478325, _478327, _478329)), _478331) = c_Groups_Oplus__class_Oplus(_478325, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_478325), _478327), _478331), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_478325), _478329), _478331)))], (8883 ^ _356604) ^ [_670680, _670682] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _670680, _670682), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_670680), _670682))], (1251 ^ _356604) ^ [_397438] : [-(c_String_Ochar_Ochar__size(_397438) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8612 ^ _356604) ^ [_660645, _660647] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _660645, _660647), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _660645, _660647) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4054 ^ _356604) ^ [_500100, _500102, _500104] : [class_Groups_Oordered__ab__group__add(_500100), c_Orderings_Oord__class_Oless__eq(_500100, _500102, _500104), -(c_Orderings_Oord__class_Oless__eq(_500100, c_Groups_Ouminus__class_Ouminus(_500100, _500104), c_Groups_Ouminus__class_Ouminus(_500100, _500102)))], (12284 ^ _356604) ^ [_786850] : [class_Rings_Oidom(_786850), -(class_Rings_Oring__1__no__zero__divisors(_786850))], (9987 ^ _356604) ^ [_709636, _709638, _709640] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _709636, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _709638, _709640)), c_Rings_Odvd__class_Odvd(tc_Int_Oint, _709636, _709640), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _709636, _709638))], (10650 ^ _356604) ^ [_731153, _731155, _731157, _731159, _731161] : [class_Fields_Ofield(_731153), 10653 ^ _356604 : [(10654 ^ _356604) ^ [] : [c_Polynomial_Opdivmod__rel(_731153, _731155, _731157, _731159, _731161), 10657 ^ _356604 : [(10666 ^ _356604) ^ [] : [-(_731157 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_731153))), -(_731161 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_731153))), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_731153, _731161), c_Polynomial_Odegree(_731153, _731157)))], (10660 ^ _356604) ^ [] : [_731157 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_731153)), -(_731159 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_731153)))], (10658 ^ _356604) ^ [] : [-(_731155 = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_731153), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_731153)), _731159), _731157), _731161))]]], (10676 ^ _356604) ^ [] : [-(c_Polynomial_Opdivmod__rel(_731153, _731155, _731157, _731159, _731161)), _731155 = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_731153), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_731153)), _731159), _731157), _731161), 10683 ^ _356604 : [(10686 ^ _356604) ^ [] : [_731159 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_731153))], (10684 ^ _356604) ^ [] : [-(_731157 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_731153)))]], 10687 ^ _356604 : [(10692 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_731153, _731161), c_Polynomial_Odegree(_731153, _731157))], (10690 ^ _356604) ^ [] : [_731161 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_731153))], (10688 ^ _356604) ^ [] : [_731157 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_731153))]]]]], (7928 ^ _356604) ^ [_637009, _637011, _637013, _637015, _637017] : [class_RealVector_Oreal__normed__algebra(_637009), -(c_Groups_Ominus__class_Ominus(_637009, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_637009), _637011), _637013), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_637009), _637015), _637017)) = c_Groups_Oplus__class_Oplus(_637009, c_Groups_Oplus__class_Oplus(_637009, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_637009), c_Groups_Ominus__class_Ominus(_637009, _637011, _637015)), c_Groups_Ominus__class_Ominus(_637009, _637013, _637017)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_637009), c_Groups_Ominus__class_Ominus(_637009, _637011, _637015)), _637017)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_637009), _637015), c_Groups_Ominus__class_Ominus(_637009, _637013, _637017))))], (12446 ^ _356604) ^ [_791872] : [class_Rings_Oidom(_791872), -(class_Groups_Oone(_791872))], (3869 ^ _356604) ^ [_494171, _494173, _494175] : [class_Groups_Ogroup__add(_494171), 3872 ^ _356604 : [(3879 ^ _356604) ^ [] : [_494173 = _494175, -(c_Groups_Ouminus__class_Ouminus(_494171, _494173) = c_Groups_Ouminus__class_Ouminus(_494171, _494175))], (3873 ^ _356604) ^ [] : [c_Groups_Ouminus__class_Ouminus(_494171, _494173) = c_Groups_Ouminus__class_Ouminus(_494171, _494175), -(_494173 = _494175)]]], (9971 ^ _356604) ^ [_709113, _709115, _709117] : [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), _709113), _709115), _709117)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _709117, _709113), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _709113), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _709115))], (12972 ^ _356604) ^ [_807605] : [class_Rings_Olinordered__idom(_807605), -(class_Int_Oring__char__0(tc_Polynomial_Opoly(_807605)))], (9153 ^ _356604) ^ [_679990, _679992, _679994] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _679990), c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _679990), _679992), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _679990), _679994)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _679992, _679994))], (1235 ^ _356604) ^ [_396952, _396954, _396956] : [class_Groups_Ozero(_396952), -(_396954 = c_Groups_Ozero__class_Ozero(_396952)), -(c_Polynomial_Odegree(_396952, c_Polynomial_Omonom(_396952, _396954, _396956)) = _396956)], (12558 ^ _356604) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (4752 ^ _356604) ^ [_525769] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _525769) = _525769)], (76 ^ _356604) ^ [_359272, _359274, _359276, _359278, _359280, _359282, _359284, _359286, _359288, _359290] : [-(c_Polynomial_Opdivmod__rel(_359288, _359284, _359280, _359276, _359272)), c_Polynomial_Opdivmod__rel(_359290, _359286, _359282, _359278, _359274), _359290 = _359288, _359286 = _359284, _359282 = _359280, _359278 = _359276, _359274 = _359272], (9779 ^ _356604) ^ [_702533, _702535, _702537] : [class_Groups_Ozero(_702533), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_702533, _702535), _702537), -(hAPP(c_Polynomial_Ocoeff(_702533, _702535), _702537) = c_Groups_Ozero__class_Ozero(_702533))], (6744 ^ _356604) ^ [_596976, _596978] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _596976, _596978), _596978 = _596976], (6392 ^ _356604) ^ [_584745, _584747] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _584745, _584747)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _584745, c_Nat_OSuc(_584747)), -(_584747 = _584745)], (12688 ^ _356604) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (6236 ^ _356604) ^ [_579302, _579304] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _579302, _579304), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _579304, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _579304, _579302)) = _579302)], (8416 ^ _356604) ^ [_654118, _654120, _654122, _654124, _654126] : [class_Groups_Oordered__cancel__ab__semigroup__add(_654118), c_Orderings_Oord__class_Oless(_654118, _654120, _654122), c_Orderings_Oord__class_Oless__eq(_654118, _654124, _654126), -(c_Orderings_Oord__class_Oless(_654118, c_Groups_Oplus__class_Oplus(_654118, _654120, _654124), c_Groups_Oplus__class_Oplus(_654118, _654122, _654126)))], (1830 ^ _356604) ^ [_418225, _418227, _418229] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _418225, _418227), _418229), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _418225, _418229))], (12514 ^ _356604) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (10752 ^ _356604) ^ [_734643, _734645, _734647, _734649, _734651, _734653] : [class_Fields_Ofield(_734643), c_Polynomial_Opdivmod__rel(_734643, _734645, _734647, _734649, _734651), -(c_Polynomial_Opdivmod__rel(_734643, c_Polynomial_Osmult(_734643, _734653, _734645), _734647, c_Polynomial_Osmult(_734643, _734653, _734649), c_Polynomial_Osmult(_734643, _734653, _734651)))], (11984 ^ _356604) ^ [_777315, _777317, _777319] : [class_Fields_Olinordered__field(_777315), c_Orderings_Oord__class_Oless(_777315, _777317, _777319), -(c_Orderings_Oord__class_Oless(_777315, _777317, c_Rings_Oinverse__class_Odivide(_777315, c_Groups_Oplus__class_Oplus(_777315, _777317, _777319), c_Groups_Oplus__class_Oplus(_777315, c_Groups_Oone__class_Oone(_777315), c_Groups_Oone__class_Oone(_777315)))))], (6124 ^ _356604) ^ [_575490, _575492, _575494] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _575490, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _575492, _575494)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _575490, _575494), _575492))], (12930 ^ _356604) ^ [_806275] : [class_Rings_Ocomm__ring__1(_806275), -(class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(_806275)))], (7432 ^ _356604) ^ [_619810, _619812, _619814] : [class_Orderings_Olinorder(_619810), c_Orderings_Oord__class_Oless__eq(_619810, _619812, _619814), 7439 ^ _356604 : [(7446 ^ _356604) ^ [] : [_619812 = _619814, c_Orderings_Oord__class_Oless(_619810, _619812, _619814)], (7440 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_619810, _619812, _619814)), -(_619812 = _619814)]]], (12470 ^ _356604) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat))], (3416 ^ _356604) ^ [_477153, _477155, _477157] : [class_Rings_Oring__no__zero__divisors(_477153), 3419 ^ _356604 : [(3420 ^ _356604) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_477153), _477155), _477157) = c_Groups_Ozero__class_Ozero(_477153), -(_477155 = c_Groups_Ozero__class_Ozero(_477153)), -(_477157 = c_Groups_Ozero__class_Ozero(_477153))], (3430 ^ _356604) ^ [] : [3431 ^ _356604 : [(3434 ^ _356604) ^ [] : [_477157 = c_Groups_Ozero__class_Ozero(_477153)], (3432 ^ _356604) ^ [] : [_477155 = c_Groups_Ozero__class_Ozero(_477153)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_477153), _477155), _477157) = c_Groups_Ozero__class_Ozero(_477153))]]], (2659 ^ _356604) ^ [_449185, _449187, _449189, _449191] : [class_Rings_Ocomm__semiring__1(_449185), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_449185), _449187), c_Groups_Oplus__class_Oplus(_449185, _449189, _449191)) = c_Groups_Oplus__class_Oplus(_449185, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_449185), _449187), _449189), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_449185), _449187), _449191)))], (2196 ^ _356604) ^ [_431098, _431100, _431102, _431104] : [class_Groups_Ocomm__monoid__add(_431098), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_431098), c_Polynomial_Omonom(_431098, _431100, _431102), c_Polynomial_Omonom(_431098, _431104, _431102)) = c_Polynomial_Omonom(_431098, c_Groups_Oplus__class_Oplus(_431098, _431100, _431104), _431102))], (7364 ^ _356604) ^ [_617728, _617730, _617732] : [class_Orderings_Olinorder(_617728), -(c_Orderings_Oord__class_Oless(_617728, _617730, _617732)), 7371 ^ _356604 : [(7378 ^ _356604) ^ [] : [_617730 = _617732, -(c_Orderings_Oord__class_Oless__eq(_617728, _617730, _617732))], (7372 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_617728, _617730, _617732), -(_617730 = _617732)]]], (4448 ^ _356604) ^ [_514569, _514571, _514573] : [class_Rings_Ocomm__semiring__1(_514569), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_514569), hAPP(hAPP(c_Power_Opower__class_Opower(_514569), _514571), _514573)), _514571) = hAPP(hAPP(c_Power_Opower__class_Opower(_514569), _514571), c_Nat_OSuc(_514573)))], (458 ^ _356604) ^ [_370805, _370807] : [-(class_Rings_Oordered__semiring(_370805)), _370807 = _370805, class_Rings_Oordered__semiring(_370807)], (12200 ^ _356604) ^ [_784246] : [class_Int_Oring__char__0(_784246), -(class_Rings_Osemiring__0(_784246))], (13014 ^ _356604) ^ [_808935] : [class_Groups_Ozero(_808935), -(class_Groups_Ozero(tc_Polynomial_Opoly(_808935)))], (2246 ^ _356604) ^ [_432883, _432885] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _432883, _432885), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _432883, c_Nat_OSuc(_432885)))], (2416 ^ _356604) ^ [_438789] : [c_Nat_OSuc(_438789) = _438789], (7572 ^ _356604) ^ [_624191, _624193, _624195, _624197] : [class_RealVector_Oreal__normed__algebra(_624191), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_624191), _624193), c_Groups_Ominus__class_Ominus(_624191, _624195, _624197)) = c_Groups_Ominus__class_Ominus(_624191, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_624191), _624193), _624195), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_624191), _624193), _624197)))], (10363 ^ _356604) ^ [_721395, _721397] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _721395, _721397)), -(_721395 = _721397), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _721397, _721395))], (2210 ^ _356604) ^ [_431644, _431646] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_431646), _431644), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _431644, _431646)], (10874 ^ _356604) ^ [_739474, _739476] : [class_RealVector_Oreal__normed__field(_739474), -(c_Rings_Oinverse__class_Odivide(_739474, c_Groups_Ozero__class_Ozero(_739474), _739476) = c_Groups_Ozero__class_Ozero(_739474))], (12554 ^ _356604) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (1621 ^ _356604) ^ [_410158, _410160] : [class_Groups_Ozero(_410158), 1624 ^ _356604 : [(1631 ^ _356604) ^ [] : [-(_410160 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_410158))), -(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_410158, _410160) = c_Nat_OSuc(c_Polynomial_Odegree(_410158, _410160)))], (1625 ^ _356604) ^ [] : [_410160 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_410158)), -(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_410158, _410160) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (2845 ^ _356604) ^ [_456547, _456549, _456551, _456553] : [class_Orderings_Opreorder(_456547), c_Orderings_Oord__class_Oless__eq(_456547, _456549, _456551), c_Orderings_Oord__class_Oless__eq(_456547, _456551, _456553), -(c_Orderings_Oord__class_Oless__eq(_456547, _456549, _456553))], (2769 ^ _356604) ^ [_453941, _453943, _453945] : [class_Rings_Olinordered__ring__strict(_453941), 2772 ^ _356604 : [(2781 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_453941, c_Groups_Oplus__class_Oplus(_453941, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_453941), _453943), _453943), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_453941), _453945), _453945)), c_Groups_Ozero__class_Ozero(_453941))), _453943 = c_Groups_Ozero__class_Ozero(_453941), _453945 = c_Groups_Ozero__class_Ozero(_453941)], (2773 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_453941, c_Groups_Oplus__class_Oplus(_453941, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_453941), _453943), _453943), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_453941), _453945), _453945)), c_Groups_Ozero__class_Ozero(_453941)), 2776 ^ _356604 : [(2779 ^ _356604) ^ [] : [-(_453945 = c_Groups_Ozero__class_Ozero(_453941))], (2777 ^ _356604) ^ [] : [-(_453943 = c_Groups_Ozero__class_Ozero(_453941))]]]]], (10097 ^ _356604) ^ [_713006, _713008] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _713006, _713008), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _713008, _713006)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _713008, _713006), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _713006, _713008))], (3652 ^ _356604) ^ [_485457, _485459, _485461, _485463] : [class_RealVector_Oreal__normed__algebra(_485457), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_485457), c_Groups_Oplus__class_Oplus(_485457, _485459, _485461)), _485463) = c_Groups_Oplus__class_Oplus(_485457, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_485457), _485459), _485463), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_485457), _485461), _485463)))], (4328 ^ _356604) ^ [_510593, _510595] : [class_Rings_Ocomm__semiring__1(_510593), -(c_Polynomial_Osmult(_510593, c_Groups_Oone__class_Oone(_510593), _510595) = _510595)], (4426 ^ _356604) ^ [_513764, _513766] : [class_Groups_Ogroup__add(_513764), -(c_Groups_Oplus__class_Oplus(_513764, c_Groups_Ouminus__class_Ouminus(_513764, _513766), _513766) = c_Groups_Ozero__class_Ozero(_513764))], (1088 ^ _356604) ^ [_391980, _391982, _391984, _391986] : [-(hAPP(_391986, _391982) = hAPP(_391984, _391980)), _391986 = _391984, _391982 = _391980], (10453 ^ _356604) ^ [_724554, _724556, _724558, _724560, _724562] : [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), _724554), _724556), _724558), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _724554), _724560), _724562)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _724558), c_Orderings_Oord__class_Oless(tc_Int_Oint, _724558, _724554), c_Orderings_Oord__class_Oless(tc_Int_Oint, _724562, _724554), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _724556, _724560))], (6222 ^ _356604) ^ [_578688, _578690] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _578688, _578690), _578688))], (1543 ^ _356604) ^ [_407335, _407337, _407339] : [class_Rings_Ocomm__semiring__0(_407335), 1546 ^ _356604 : [(1553 ^ _356604) ^ [] : [c_Polynomial_Odegree(_407335, _407337) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Polynomial_Osynthetic__div(_407335, _407337, _407339) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_407335)))], (1547 ^ _356604) ^ [] : [c_Polynomial_Osynthetic__div(_407335, _407337, _407339) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_407335)), -(c_Polynomial_Odegree(_407335, _407337) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (2274 ^ _356604) ^ [_433853, _433855] : [class_Groups_Omonoid__add(_433853), -(c_Groups_Oplus__class_Oplus(_433853, _433855, c_Groups_Ozero__class_Ozero(_433853)) = _433855)], (6418 ^ _356604) ^ [_585601, _585603, _585605] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _585601, _585603), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _585603, _585605), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_585601), _585605))], (4654 ^ _356604) ^ [_522493, _522495, _522497, _522499] : [class_Rings_Olinordered__semidom(_522493), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _522495, _522497), c_Orderings_Oord__class_Oless__eq(_522493, c_Groups_Ozero__class_Ozero(_522493), _522499), c_Orderings_Oord__class_Oless__eq(_522493, _522499, c_Groups_Oone__class_Oone(_522493)), -(c_Orderings_Oord__class_Oless__eq(_522493, hAPP(hAPP(c_Power_Opower__class_Opower(_522493), _522499), _522497), hAPP(hAPP(c_Power_Opower__class_Opower(_522493), _522499), _522495)))], (6990 ^ _356604) ^ [_605835, _605837, _605839] : [class_Orderings_Olinorder(_605835), -(c_Orderings_Oord__class_Oless(_605835, _605837, _605839)), -(_605837 = _605839), -(c_Orderings_Oord__class_Oless(_605835, _605839, _605837))], (12714 ^ _356604) ^ [_799435] : [class_Rings_Olinordered__idom(_799435), -(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(_799435)))], (2625 ^ _356604) ^ [_447711, _447713, _447715, _447717] : [class_Rings_Ocomm__semiring__1(_447711), -(c_Groups_Oplus__class_Oplus(_447711, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_447711), _447713), _447715), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_447711), _447717), _447715)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_447711), c_Groups_Oplus__class_Oplus(_447711, _447713, _447717)), _447715))], (8444 ^ _356604) ^ [_655046] : [class_Rings_Olinordered__semidom(_655046), c_Orderings_Oord__class_Oless(_655046, c_Groups_Oone__class_Oone(_655046), c_Groups_Ozero__class_Ozero(_655046))], (1814 ^ _356604) ^ [_417628, _417630, _417632, _417634] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _417628, _417630), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _417632, _417634), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _417628, _417632), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _417630, _417634)))], (10535 ^ _356604) ^ [_727299, _727301, _727303] : [-(_727299 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 10538 ^ _356604 : [(10545 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _727301, _727303), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _727301), _727299), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _727303), _727299)))], (10539 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _727301), _727299), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _727303), _727299)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _727301, _727303))]]], (5182 ^ _356604) ^ [_541596, _541598, _541600] : [class_Rings_Ocomm__ring__1(_541596), 5185 ^ _356604 : [(5192 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(_541596, _541598, _541600), -(c_Rings_Odvd__class_Odvd(_541596, c_Groups_Ouminus__class_Ouminus(_541596, _541598), _541600))], (5186 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(_541596, c_Groups_Ouminus__class_Ouminus(_541596, _541598), _541600), -(c_Rings_Odvd__class_Odvd(_541596, _541598, _541600))]]], (880 ^ _356604) ^ [_384371, _384373, _384375, _384377] : [-(c_Nat_Osize__class_Osize(_384377, _384373) = c_Nat_Osize__class_Osize(_384375, _384371)), _384377 = _384375, _384373 = _384371], (4946 ^ _356604) ^ [_533147, _533149, _533151, _533153] : [class_Rings_Olinordered__semidom(_533147), c_Orderings_Oord__class_Oless__eq(_533147, hAPP(hAPP(c_Power_Opower__class_Opower(_533147), _533149), c_Nat_OSuc(_533151)), hAPP(hAPP(c_Power_Opower__class_Opower(_533147), _533153), c_Nat_OSuc(_533151))), c_Orderings_Oord__class_Oless__eq(_533147, c_Groups_Ozero__class_Ozero(_533147), _533153), -(c_Orderings_Oord__class_Oless__eq(_533147, _533149, _533153))], (8694 ^ _356604) ^ [_663729, _663731, _663733] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _663729, _663731), 8697 ^ _356604 : [(8704 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _663733, _663729), _663731), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _663733, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _663731, _663729)))], (8698 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _663733, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _663731, _663729)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _663733, _663729), _663731))]]], (5016 ^ _356604) ^ [_535716, _535718, _535720] : [class_Lattices_Oboolean__algebra(_535716), 5019 ^ _356604 : [(5026 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_535716, _535720, _535718), -(c_Orderings_Oord__class_Oless__eq(_535716, c_Groups_Ouminus__class_Ouminus(_535716, _535718), c_Groups_Ouminus__class_Ouminus(_535716, _535720)))], (5020 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_535716, c_Groups_Ouminus__class_Ouminus(_535716, _535718), c_Groups_Ouminus__class_Ouminus(_535716, _535720)), -(c_Orderings_Oord__class_Oless__eq(_535716, _535720, _535718))]]], (1724 ^ _356604) ^ [_414164, _414166] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _414164, _414166)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _414166, _414164))], (2448 ^ _356604) ^ [_440097, _440099] : [class_Orderings_Opreorder(_440097), -(c_Orderings_Oord__class_Oless__eq(_440097, _440099, _440099))], (4796 ^ _356604) ^ [_527787] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _527787) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (12698 ^ _356604) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (38 ^ _356604) ^ [_357961, _357963] : [-(class_Lattices_Oab__semigroup__idem__mult(_357961)), _357963 = _357961, class_Lattices_Oab__semigroup__idem__mult(_357963)], (12834 ^ _356604) ^ [_803235] : [class_Rings_Ocomm__semiring__1(_803235), -(class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(_803235)))], (6522 ^ _356604) ^ [_589442, _589444, _589446] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _589442, _589444), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _589442, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _589444, _589446)))], (10343 ^ _356604) ^ [_720723, _720725] : [_720723 = _720725, 10346 ^ _356604 : [(10349 ^ _356604) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _720725, _720723))], (10347 ^ _356604) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _720723, _720725))]]], (608 ^ _356604) ^ [_375230, _375232] : [-(class_Rings_Ocomm__semiring__0(_375230)), _375232 = _375230, class_Rings_Ocomm__semiring__0(_375232)], (12692 ^ _356604) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (4152 ^ _356604) ^ [_503498, _503500, _503502] : [class_Rings_Oring(_503498), -(c_Groups_Ouminus__class_Ouminus(_503498, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_503498), _503500), _503502)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_503498), _503500), c_Groups_Ouminus__class_Ouminus(_503498, _503502)))], (4188 ^ _356604) ^ [_505186, _505188, _505190] : [class_Groups_Ogroup__add(_505186), -(c_Groups_Oplus__class_Oplus(_505186, c_Groups_Ouminus__class_Ouminus(_505186, _505188), c_Groups_Oplus__class_Oplus(_505186, _505188, _505190)) = _505190)], (7508 ^ _356604) ^ [_622121, _622123, _622125, _622127] : [class_Orderings_Oorder(_622121), c_Orderings_Oord__class_Oless(_622121, _622123, _622125), c_Orderings_Oord__class_Oless__eq(_622121, _622127, _622123), -(c_Orderings_Oord__class_Oless(_622121, _622127, _622125))], (13050 ^ _356604) ^ [_810115, _810117] : [_810115 = _810117, -(hBOOL(c_fequal(_810115, _810117)))], (8783 ^ _356604) ^ [_667019] : [_667019 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _667019, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (1423 ^ _356604) ^ [_402932] : [class_Groups_Ozero(_402932), -(c_Polynomial_OpCons(_402932, c_Groups_Ozero__class_Ozero(_402932), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_402932))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_402932)))], (11544 ^ _356604) ^ [_762354, _762356, _762358, _762360, _762362] : [class_Fields_Olinordered__field(_762354), c_Orderings_Oord__class_Oless(_762354, c_Groups_Ozero__class_Ozero(_762354), _762356), c_Orderings_Oord__class_Oless__eq(_762354, _762356, _762358), c_Orderings_Oord__class_Oless(_762354, c_Groups_Ozero__class_Ozero(_762354), _762360), c_Orderings_Oord__class_Oless(_762354, _762360, _762362), -(c_Orderings_Oord__class_Oless(_762354, c_Rings_Oinverse__class_Odivide(_762354, _762356, _762362), c_Rings_Oinverse__class_Odivide(_762354, _762358, _762360)))], (10910 ^ _356604) ^ [_741116, _741118, _741120] : [class_Fields_Ofield__inverse__zero(_741116), -(c_Rings_Oinverse__class_Odivide(_741116, c_Groups_Oone__class_Oone(_741116), hAPP(hAPP(c_Power_Opower__class_Opower(_741116), _741118), _741120)) = hAPP(hAPP(c_Power_Opower__class_Opower(_741116), c_Rings_Oinverse__class_Odivide(_741116, c_Groups_Oone__class_Oone(_741116), _741118)), _741120))], (12960 ^ _356604) ^ [_807225] : [class_Rings_Ocomm__ring(_807225), -(class_Rings_Ocomm__ring(tc_Polynomial_Opoly(_807225)))], (12572 ^ _356604) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (3706 ^ _356604) ^ [_487730, _487732, _487734] : [class_Rings_Ocomm__semiring__0(_487730), -(hAPP(c_Polynomial_Ocoeff(_487730, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_487730)), _487732), _487734)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Polynomial_Odegree(_487730, _487732), c_Polynomial_Odegree(_487730, _487734))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_487730), hAPP(c_Polynomial_Ocoeff(_487730, _487732), c_Polynomial_Odegree(_487730, _487732))), hAPP(c_Polynomial_Ocoeff(_487730, _487734), c_Polynomial_Odegree(_487730, _487734))))], (3994 ^ _356604) ^ [_498237, _498239] : [class_Groups_Ogroup__add(_498237), 3997 ^ _356604 : [(4004 ^ _356604) ^ [] : [_498239 = c_Groups_Ozero__class_Ozero(_498237), -(c_Groups_Ouminus__class_Ouminus(_498237, _498239) = c_Groups_Ozero__class_Ozero(_498237))], (3998 ^ _356604) ^ [] : [c_Groups_Ouminus__class_Ouminus(_498237, _498239) = c_Groups_Ozero__class_Ozero(_498237), -(_498239 = c_Groups_Ozero__class_Ozero(_498237))]]], (2603 ^ _356604) ^ [_446881, _446883, _446885, _446887, _446889] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_446881), 2606 ^ _356604 : [(2607 ^ _356604) ^ [] : [c_Groups_Oplus__class_Oplus(_446881, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_446881), _446883), _446885), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_446881), _446887), _446889)) = c_Groups_Oplus__class_Oplus(_446881, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_446881), _446883), _446889), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_446881), _446887), _446885)), -(_446883 = _446887), -(_446885 = _446889)], (2617 ^ _356604) ^ [] : [2618 ^ _356604 : [(2621 ^ _356604) ^ [] : [_446885 = _446889], (2619 ^ _356604) ^ [] : [_446883 = _446887]], -(c_Groups_Oplus__class_Oplus(_446881, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_446881), _446883), _446885), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_446881), _446887), _446889)) = c_Groups_Oplus__class_Oplus(_446881, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_446881), _446883), _446889), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_446881), _446887), _446885)))]]], (11624 ^ _356604) ^ [_764884, _764886, _764888] : [class_Fields_Olinordered__field(_764884), c_Orderings_Oord__class_Oless__eq(_764884, _764886, c_Groups_Ozero__class_Ozero(_764884)), c_Orderings_Oord__class_Oless(_764884, _764888, c_Groups_Ozero__class_Ozero(_764884)), -(c_Orderings_Oord__class_Oless__eq(_764884, c_Groups_Ozero__class_Ozero(_764884), c_Rings_Oinverse__class_Odivide(_764884, _764886, _764888)))], (6484 ^ _356604) ^ [_587972, _587974, _587976] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _587972, _587974), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _587972, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _587976, _587974)))], (6820 ^ _356604) ^ [_599744, _599746, _599748, _599750] : [class_Fields_Ofield(_599744), -(c_Polynomial_Opoly__gcd(_599744, c_Polynomial_Opoly__gcd(_599744, _599746, _599748), _599750) = c_Polynomial_Opoly__gcd(_599744, _599746, c_Polynomial_Opoly__gcd(_599744, _599748, _599750)))], (3688 ^ _356604) ^ [_487112, _487114, _487116] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _487112), _487114) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _487112), _487116), -(_487112 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_487114 = _487116)], (9897 ^ _356604) ^ [_706516, _706518] : [-(_706516 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _706516), _706518) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _706518, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _706516, c_Groups_Oone__class_Oone(tc_Nat_Onat))), _706518)))], (8326 ^ _356604) ^ [_651272, _651274] : [class_Rings_Olinordered__idom(_651272), 8329 ^ _356604 : [(8336 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_651272, _651274, c_Groups_Ozero__class_Ozero(_651272)), -(c_Orderings_Oord__class_Oless(_651272, c_Groups_Oplus__class_Oplus(_651272, _651274, _651274), c_Groups_Ozero__class_Ozero(_651272)))], (8330 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_651272, c_Groups_Oplus__class_Oplus(_651272, _651274, _651274), c_Groups_Ozero__class_Ozero(_651272)), -(c_Orderings_Oord__class_Oless(_651272, _651274, c_Groups_Ozero__class_Ozero(_651272)))]]], (9059 ^ _356604) ^ [_676873, _676875] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _676873, c_Groups_Oone__class_Oone(tc_Int_Oint)), _676875), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _676873, _676875))], (12780 ^ _356604) ^ [_801525] : [class_Rings_Olinordered__idom(_801525), -(class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(_801525)))], (4532 ^ _356604) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (12452 ^ _356604) ^ [_792058] : [class_Rings_Oidom(_792058), -(class_Rings_Odvd(_792058))], (6516 ^ _356604) ^ [_589200, _589202, _589204] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _589200, _589202), _589204), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _589200, _589204))], (11940 ^ _356604) ^ [_775600, _775602, _775604, _775606] : [class_Fields_Ofield(_775600), -(_775602 = c_Groups_Ozero__class_Ozero(_775600)), -(c_Groups_Ominus__class_Ominus(_775600, _775604, c_Rings_Oinverse__class_Odivide(_775600, _775606, _775602)) = c_Rings_Oinverse__class_Odivide(_775600, c_Groups_Ominus__class_Ominus(_775600, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_775600), _775602), _775604), _775606), _775602))], (3664 ^ _356604) ^ [_485973, _485975] : [class_RealVector_Oreal__normed__algebra(_485973), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_485973), _485975), c_Groups_Ozero__class_Ozero(_485973)) = c_Groups_Ozero__class_Ozero(_485973))], (8504 ^ _356604) ^ [_656906, _656908] : [class_Groups_Olinordered__ab__group__add(_656906), 8507 ^ _356604 : [(8514 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_656906, c_Groups_Ozero__class_Ozero(_656906), _656908), -(c_Orderings_Oord__class_Oless(_656906, c_Groups_Ouminus__class_Ouminus(_656906, _656908), _656908))], (8508 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_656906, c_Groups_Ouminus__class_Ouminus(_656906, _656908), _656908), -(c_Orderings_Oord__class_Oless(_656906, c_Groups_Ozero__class_Ozero(_656906), _656908))]]], (7322 ^ _356604) ^ [_616414, _616416, _616418] : [class_Orderings_Oorder(_616414), 7325 ^ _356604 : [(7326 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_616414, _616416, _616418), -(c_Orderings_Oord__class_Oless(_616414, _616416, _616418)), -(_616416 = _616418)], (7336 ^ _356604) ^ [] : [7337 ^ _356604 : [(7340 ^ _356604) ^ [] : [_616416 = _616418], (7338 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_616414, _616416, _616418)]], -(c_Orderings_Oord__class_Oless__eq(_616414, _616416, _616418))]]], (10551 ^ _356604) ^ [_727820, _727822] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _727820), -(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), _727820), _727822)))], (5720 ^ _356604) ^ [_560755, _560757] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _560755, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _560757)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _560755, _560757))], (12194 ^ _356604) ^ [_784060] : [class_Int_Oring__char__0(_784060), -(class_Groups_Omonoid__add(_784060))], (5436 ^ _356604) ^ [_550377, _550379, _550381] : [class_Rings_Oidom(_550377), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_550377), _550379, _550381), -(_550381 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_550377))), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_550377, _550379), c_Polynomial_Odegree(_550377, _550381)))], (6346 ^ _356604) ^ [_583290, _583292] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _583290, c_Nat_OSuc(_583292)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _583290, _583292)), -(_583290 = _583292)], (11218 ^ _356604) ^ [_751835, _751837, _751839] : [class_Fields_Olinordered__field__inverse__zero(_751835), 11221 ^ _356604 : [(11236 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_751835, c_Groups_Ozero__class_Ozero(_751835), c_Rings_Oinverse__class_Odivide(_751835, _751837, _751839))), 11237 ^ _356604 : [(11244 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_751835, _751837, c_Groups_Ozero__class_Ozero(_751835)), c_Orderings_Oord__class_Oless__eq(_751835, _751839, c_Groups_Ozero__class_Ozero(_751835))], (11238 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_751835, c_Groups_Ozero__class_Ozero(_751835), _751837), c_Orderings_Oord__class_Oless__eq(_751835, c_Groups_Ozero__class_Ozero(_751835), _751839)]]], (11222 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_751835, c_Groups_Ozero__class_Ozero(_751835), c_Rings_Oinverse__class_Odivide(_751835, _751837, _751839)), 11227 ^ _356604 : [(11230 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_751835, c_Groups_Ozero__class_Ozero(_751835), _751839))], (11228 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_751835, c_Groups_Ozero__class_Ozero(_751835), _751837))]], 11231 ^ _356604 : [(11234 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_751835, _751839, c_Groups_Ozero__class_Ozero(_751835)))], (11232 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_751835, _751837, c_Groups_Ozero__class_Ozero(_751835)))]]]]], (7906 ^ _356604) ^ [_636105, _636107, _636109] : [class_Groups_Oordered__ab__group__add(_636105), 7909 ^ _356604 : [(7916 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_636105, c_Groups_Ominus__class_Ominus(_636105, _636107, _636109), c_Groups_Ozero__class_Ozero(_636105)), -(c_Orderings_Oord__class_Oless__eq(_636105, _636107, _636109))], (7910 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_636105, _636107, _636109), -(c_Orderings_Oord__class_Oless__eq(_636105, c_Groups_Ominus__class_Ominus(_636105, _636107, _636109), c_Groups_Ozero__class_Ozero(_636105)))]]], (9305 ^ _356604) ^ [_685657, _685659, _685661, _685663] : [class_Rings_Olinordered__semiring(_685657), c_Orderings_Oord__class_Oless(_685657, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_685657), _685659), _685661), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_685657), _685663), _685661)), c_Orderings_Oord__class_Oless__eq(_685657, c_Groups_Ozero__class_Ozero(_685657), _685661), -(c_Orderings_Oord__class_Oless(_685657, _685659, _685663))], (1511 ^ _356604) ^ [_406160, _406162, _406164] : [class_Rings_Oidom(_406160), 1514 ^ _356604 : [(1515 ^ _356604) ^ [] : [hAPP(c_Polynomial_Opoly(_406160, _406162), _406164) = c_Groups_Ozero__class_Ozero(_406160), -(_406162 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_406160))), c_Polynomial_Oorder(_406160, _406164, _406162) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (1525 ^ _356604) ^ [] : [1526 ^ _356604 : [(1529 ^ _356604) ^ [] : [-(c_Polynomial_Oorder(_406160, _406164, _406162) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1527 ^ _356604) ^ [] : [_406162 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_406160))]], -(hAPP(c_Polynomial_Opoly(_406160, _406162), _406164) = c_Groups_Ozero__class_Ozero(_406160))]]], (6108 ^ _356604) ^ [_574910, _574912] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _574910), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _574910, _574912), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _574912, _574910)], (12774 ^ _356604) ^ [_801335] : [class_Rings_Olinordered__idom(_801335), -(class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(_801335)))], (6638 ^ _356604) ^ [_593606, _593608] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _593606, _593608)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _593606, _593608), -(_593606 = _593608)], (2721 ^ _356604) ^ [_451960, _451962, _451964, _451966] : [class_Rings_Ocomm__semiring__0(_451960), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_451960)), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_451960), _451962, _451964)), _451966) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_451960), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_451960)), _451962), _451966), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_451960)), _451964), _451966)))], (7164 ^ _356604) ^ [_611344, _611346, _611348, _611350] : [class_Orderings_Opreorder(_611344), c_Orderings_Oord__class_Oless(_611344, _611346, _611348), c_Orderings_Oord__class_Oless(_611344, _611348, _611350), -(c_Orderings_Oord__class_Oless(_611344, _611346, _611350))], (5648 ^ _356604) ^ [_558183] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _558183, c_Nat_OSuc(_558183)))], (6038 ^ _356604) ^ [_572335, _572337, _572339] : [class_Groups_Oordered__ab__group__add(_572335), 6041 ^ _356604 : [(6048 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_572335, c_Groups_Ouminus__class_Ouminus(_572335, _572339), _572337), -(c_Orderings_Oord__class_Oless(_572335, c_Groups_Ouminus__class_Ouminus(_572335, _572337), _572339))], (6042 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_572335, c_Groups_Ouminus__class_Ouminus(_572335, _572337), _572339), -(c_Orderings_Oord__class_Oless(_572335, c_Groups_Ouminus__class_Ouminus(_572335, _572339), _572337))]]], (9163 ^ _356604) ^ [_680343, _680345, _680347] : [class_Groups_Ocomm__monoid__add(_680343), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_680343, _680345), c_Polynomial_Odegree(_680343, _680347)), -(c_Polynomial_Odegree(_680343, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_680343), _680347, _680345)) = c_Polynomial_Odegree(_680343, _680347))], (9927 ^ _356604) ^ [_707659, _707661, _707663] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _707659), _707659 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _707661, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _707659), _707663)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _707661, _707659), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _707663))], (10011 ^ _356604) ^ [_710378, _710380, _710382] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _710378, _710380), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _710380, _710378)), 10026 ^ _356604 : [(10029 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _710382, _710378)], (10027 ^ _356604) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _710378, _710382))]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _710380, _710382), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _710382, _710380))], (6906 ^ _356604) ^ [_603152, _603154] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _603152, _603154)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _603154, _603152))], (7108 ^ _356604) ^ [_609560, _609562, _609564, _609566] : [class_Orderings_Oord(_609560), _609562 = _609564, c_Orderings_Oord__class_Oless(_609560, _609564, _609566), -(c_Orderings_Oord__class_Oless(_609560, _609562, _609566))], (6886 ^ _356604) ^ [_602130, _602132, _602134, _602136] : [class_Rings_Ocomm__ring(_602130), -(c_Polynomial_Osmult(_602130, c_Groups_Ominus__class_Ominus(_602130, _602132, _602134), _602136) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_602130), c_Polynomial_Osmult(_602130, _602132, _602136), c_Polynomial_Osmult(_602130, _602134, _602136)))], (3620 ^ _356604) ^ [_484037, _484039, _484041, _484043] : [class_Rings_Oordered__semiring(_484037), c_Orderings_Oord__class_Oless__eq(_484037, _484039, _484041), c_Orderings_Oord__class_Oless__eq(_484037, c_Groups_Ozero__class_Ozero(_484037), _484043), -(c_Orderings_Oord__class_Oless__eq(_484037, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_484037), _484043), _484039), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_484037), _484043), _484041)))], (788 ^ _356604) ^ [_380520, _380522] : [-(class_Rings_Oidom(_380520)), _380522 = _380520, class_Rings_Oidom(_380522)], (10850 ^ _356604) ^ [_738528, _738530, _738532] : [class_Rings_Odivision__ring(_738528), -(c_Groups_Ouminus__class_Ouminus(_738528, c_Rings_Oinverse__class_Odivide(_738528, _738530, _738532)) = c_Rings_Oinverse__class_Odivide(_738528, c_Groups_Ouminus__class_Ouminus(_738528, _738530), _738532))], (6156 ^ _356604) ^ [_576694, _576696, _576698] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _576694, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _576696, _576698)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _576694, _576696), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _576698, _576696), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _576694, _576698))], (12574 ^ _356604) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (5206 ^ _356604) ^ [_542476, _542478, _542480] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _542476, _542478), _542480) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _542476, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _542478, _542480)))], (1740 ^ _356604) ^ [_414858, _414860, _414862] : [_414860 = _414862, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _414858, _414860) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _414858, _414862))], (4750 ^ _356604) ^ [_525685] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _525685), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _525685)], (1291 ^ _356604) ^ [_398613, _398615] : [class_Int_Oring__char__0(_398613), class_Rings_Oidom(_398613), 1298 ^ _356604 : [(1305 ^ _356604) ^ [] : [_398615 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_398613)), -(c_Polynomial_Opoly(_398613, _398615) = c_Polynomial_Opoly(_398613, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_398613))))], (1299 ^ _356604) ^ [] : [c_Polynomial_Opoly(_398613, _398615) = c_Polynomial_Opoly(_398613, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_398613))), -(_398615 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_398613)))]]], (3218 ^ _356604) ^ [_469695, _469697, _469699] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _469695), _469697) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _469699), _469697), -(_469695 = _469699), -(_469697 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10045 ^ _356604) ^ [_711390, _711392, _711394] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _711390, _711392), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _711392, _711390)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _711392, _711394), 10056 ^ _356604 : [(10059 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _711394, _711390)], (10057 ^ _356604) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _711390, _711394))]]], (1637 ^ _356604) ^ [_410660, _410662] : [class_Rings_Ocomm__semiring__0(_410660), -(c_Polynomial_Osynthetic__div(_410660, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_410660)), _410662) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_410660)))], (9213 ^ _356604) ^ [_682285, _682287, _682289, _682291, _682293, _682295] : [class_Rings_Oordered__ring(_682285), 9216 ^ _356604 : [(9223 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_682285, _682291, c_Groups_Oplus__class_Oplus(_682285, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_682285), c_Groups_Ominus__class_Ominus(_682285, _682293, _682287)), _682289), _682295)), -(c_Orderings_Oord__class_Oless__eq(_682285, c_Groups_Oplus__class_Oplus(_682285, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_682285), _682287), _682289), _682291), c_Groups_Oplus__class_Oplus(_682285, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_682285), _682293), _682289), _682295)))], (9217 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_682285, c_Groups_Oplus__class_Oplus(_682285, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_682285), _682287), _682289), _682291), c_Groups_Oplus__class_Oplus(_682285, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_682285), _682293), _682289), _682295)), -(c_Orderings_Oord__class_Oless__eq(_682285, _682291, c_Groups_Oplus__class_Oplus(_682285, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_682285), c_Groups_Ominus__class_Ominus(_682285, _682293, _682287)), _682289), _682295)))]]], (9579 ^ _356604) ^ [_694751, _694753, _694755] : [class_Rings_Olinordered__semidom(_694751), c_Orderings_Oord__class_Oless(_694751, c_Groups_Oone__class_Oone(_694751), _694753), -(c_Orderings_Oord__class_Oless(_694751, c_Groups_Oone__class_Oone(_694751), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_694751), _694753), hAPP(hAPP(c_Power_Opower__class_Opower(_694751), _694753), _694755))))], (4410 ^ _356604) ^ [_513263, _513265, _513267] : [class_Groups_Ogroup__add(_513263), 4413 ^ _356604 : [(4420 ^ _356604) ^ [] : [c_Groups_Oplus__class_Oplus(_513263, _513265, _513267) = c_Groups_Ozero__class_Ozero(_513263), -(_513265 = c_Groups_Ouminus__class_Ouminus(_513263, _513267))], (4414 ^ _356604) ^ [] : [_513265 = c_Groups_Ouminus__class_Ouminus(_513263, _513267), -(c_Groups_Oplus__class_Oplus(_513263, _513265, _513267) = c_Groups_Ozero__class_Ozero(_513263))]]], (4182 ^ _356604) ^ [_504872, _504874, _504876, _504878] : [class_Rings_Ocomm__semiring__1(_504872), -(hAPP(hAPP(c_Power_Opower__class_Opower(_504872), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_504872), _504874), _504876)), _504878) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_504872), hAPP(hAPP(c_Power_Opower__class_Opower(_504872), _504874), _504878)), hAPP(hAPP(c_Power_Opower__class_Opower(_504872), _504876), _504878)))], (5650 ^ _356604) ^ [_558307, _558309, _558311] : [class_Fields_Ofield(_558307), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_558307), c_Polynomial_Opoly__gcd(_558307, _558309, _558311), _558309))], (4960 ^ _356604) ^ [_533639, _533641, _533643, _533645] : [class_Rings_Olinordered__semidom(_533639), hAPP(hAPP(c_Power_Opower__class_Opower(_533639), _533641), c_Nat_OSuc(_533643)) = hAPP(hAPP(c_Power_Opower__class_Opower(_533639), _533645), c_Nat_OSuc(_533643)), c_Orderings_Oord__class_Oless__eq(_533639, c_Groups_Ozero__class_Ozero(_533639), _533641), c_Orderings_Oord__class_Oless__eq(_533639, c_Groups_Ozero__class_Ozero(_533639), _533645), -(_533641 = _533645)], (5136 ^ _356604) ^ [_540072, _540074, _540076, _540078] : [class_Rings_Ocomm__semiring__1(_540072), c_Rings_Odvd__class_Odvd(_540072, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_540072), _540074), _540076), _540078), -(c_Rings_Odvd__class_Odvd(_540072, _540076, _540078))], (7808 ^ _356604) ^ [_632623, _632625, _632627] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _632623), _632625), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _632623), _632627)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _632623), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _632625, _632627))], (6898 ^ _356604) ^ [_602740, _602742, _602744, _602746, _602748] : [class_Groups_Oab__group__add(_602740), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_602740), c_Polynomial_OpCons(_602740, _602742, _602744), c_Polynomial_OpCons(_602740, _602746, _602748)) = c_Polynomial_OpCons(_602740, c_Groups_Ominus__class_Ominus(_602740, _602742, _602746), c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_602740), _602744, _602748)))], (11170 ^ _356604) ^ [_750344, _750346, _750348, _750350] : [class_Fields_Olinordered__field__inverse__zero(_750344), c_Orderings_Oord__class_Oless__eq(_750344, _750346, _750348), c_Orderings_Oord__class_Oless__eq(_750344, c_Groups_Ozero__class_Ozero(_750344), _750350), -(c_Orderings_Oord__class_Oless__eq(_750344, c_Rings_Oinverse__class_Odivide(_750344, _750346, _750350), c_Rings_Oinverse__class_Odivide(_750344, _750348, _750350)))], (12570 ^ _356604) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (810 ^ _356604) ^ [_381767, _381769, _381771, _381773, _381775, _381777, _381779, _381781] : [-(c_If(_381781, _381777, _381773, _381769) = c_If(_381779, _381775, _381771, _381767)), _381781 = _381779, _381777 = _381775, _381773 = _381771, _381769 = _381767], (768 ^ _356604) ^ [_379950, _379952] : [-(hBOOL(_379950)), _379952 = _379950, hBOOL(_379952)], (7616 ^ _356604) ^ [_626096, _626098, _626100] : [class_Groups_Ogroup__add(_626096), 7619 ^ _356604 : [(7626 ^ _356604) ^ [] : [_626098 = _626100, -(c_Groups_Ominus__class_Ominus(_626096, _626098, _626100) = c_Groups_Ozero__class_Ozero(_626096))], (7620 ^ _356604) ^ [] : [c_Groups_Ominus__class_Ominus(_626096, _626098, _626100) = c_Groups_Ozero__class_Ozero(_626096), -(_626098 = _626100)]]], (12576 ^ _356604) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (7494 ^ _356604) ^ [_621673, _621675, _621677, _621679] : [class_Orderings_Opreorder(_621673), c_Orderings_Oord__class_Oless(_621673, _621675, _621677), c_Orderings_Oord__class_Oless__eq(_621673, _621677, _621679), -(c_Orderings_Oord__class_Oless(_621673, _621675, _621679))], (7934 ^ _356604) ^ [_637427, _637429, _637431, _637433, _637435, _637437] : [class_Rings_Oring(_637427), 7937 ^ _356604 : [(7944 ^ _356604) ^ [] : [_637433 = c_Groups_Oplus__class_Oplus(_637427, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_637427), c_Groups_Ominus__class_Ominus(_637427, _637435, _637429)), _637431), _637437), -(c_Groups_Oplus__class_Oplus(_637427, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_637427), _637429), _637431), _637433) = c_Groups_Oplus__class_Oplus(_637427, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_637427), _637435), _637431), _637437))], (7938 ^ _356604) ^ [] : [c_Groups_Oplus__class_Oplus(_637427, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_637427), _637429), _637431), _637433) = c_Groups_Oplus__class_Oplus(_637427, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_637427), _637435), _637431), _637437), -(_637433 = c_Groups_Oplus__class_Oplus(_637427, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_637427), c_Groups_Ominus__class_Ominus(_637427, _637435, _637429)), _637431), _637437))]]], (2430 ^ _356604) ^ [_439317, _439319] : [c_Nat_OSuc(_439317) = c_Nat_OSuc(_439319), -(_439317 = _439319)], (7344 ^ _356604) ^ [_617072, _617074, _617076] : [class_Orderings_Olinorder(_617072), -(c_Orderings_Oord__class_Oless(_617072, _617074, _617076)), -(c_Orderings_Oord__class_Oless__eq(_617072, _617076, _617074))], (2030 ^ _356604) ^ [_425263, _425265, _425267] : [class_Groups_Oordered__comm__monoid__add(_425263), c_Orderings_Oord__class_Oless__eq(_425263, c_Groups_Ozero__class_Ozero(_425263), _425265), c_Orderings_Oord__class_Oless__eq(_425263, c_Groups_Ozero__class_Ozero(_425263), _425267), -(c_Orderings_Oord__class_Oless__eq(_425263, c_Groups_Ozero__class_Ozero(_425263), c_Groups_Oplus__class_Oplus(_425263, _425265, _425267)))], (8771 ^ _356604) ^ [_666612] : [8772 ^ _356604 : [(8773 ^ _356604) ^ [_666683] : [_666612 = c_Nat_OSuc(_666683)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _666612))], (12966 ^ _356604) ^ [_807415] : [class_Rings_Olinordered__idom(_807415), -(class_Orderings_Oorder(tc_Polynomial_Opoly(_807415)))], (3378 ^ _356604) ^ [_475928, _475930] : [-(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), _475928), _475930))), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _475928), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _475930)], (1249 ^ _356604) ^ [_397357] : [-(c_Nat_Osize__class_Osize(tc_String_Oliteral, _397357) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8038 ^ _356604) ^ [_641693, _641695, _641697] : [class_Rings_Ocomm__ring__1(_641693), -(c_Groups_Ominus__class_Ominus(_641693, _641695, _641697) = c_Groups_Oplus__class_Oplus(_641693, _641695, c_Groups_Ouminus__class_Ouminus(_641693, _641697)))], (12990 ^ _356604) ^ [_808175] : [class_Groups_Oab__group__add(_808175), -(class_Groups_Ouminus(tc_Polynomial_Opoly(_808175)))], (12600 ^ _356604) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (1613 ^ _356604) ^ [_409889] : [-(c_Nat_Osize__class_Osize(tc_String_Ochar, _409889) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3001 ^ _356604) ^ [_461481, _461483, _461485, _461487] : [class_Orderings_Oord(_461481), 3004 ^ _356604 : [(3011 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_461481, hAPP(_461485, 3012 ^ [_461481, _461483, _461485, _461487]), hAPP(_461487, 3012 ^ [_461481, _461483, _461485, _461487])), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_461483, _461481), _461485, _461487))], (3005 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_461483, _461481), _461485, _461487), 3008 ^ _356604 : [(3009 ^ _356604) ^ [_461740] : [-(c_Orderings_Oord__class_Oless__eq(_461481, hAPP(_461485, _461740), hAPP(_461487, _461740)))]]]]], (3054 ^ _356604) ^ [_463834, _463836, _463838] : [class_Rings_Ocomm__semiring__1(_463834), -(c_Groups_Oplus__class_Oplus(_463834, _463836, _463838) = c_Groups_Oplus__class_Oplus(_463834, _463838, _463836))], (11322 ^ _356604) ^ [_755128, _755130, _755132] : [class_Fields_Olinordered__field(_755128), c_Orderings_Oord__class_Oless(_755128, c_Groups_Ozero__class_Ozero(_755128), _755130), c_Orderings_Oord__class_Oless(_755128, c_Groups_Ozero__class_Ozero(_755128), _755132), -(c_Orderings_Oord__class_Oless(_755128, c_Groups_Ozero__class_Ozero(_755128), c_Rings_Oinverse__class_Odivide(_755128, _755130, _755132)))], (10031 ^ _356604) ^ [_710971, _710973] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _710971, _710973), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _710973, _710971)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _710973, _710971), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _710971, _710973))], (11896 ^ _356604) ^ [_773828, _773830, _773832, _773834] : [class_Fields_Ofield(_773828), -(_773830 = c_Groups_Ozero__class_Ozero(_773828)), -(c_Groups_Oplus__class_Oplus(_773828, _773832, c_Rings_Oinverse__class_Odivide(_773828, _773834, _773830)) = c_Rings_Oinverse__class_Odivide(_773828, c_Groups_Oplus__class_Oplus(_773828, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_773828), _773830), _773832), _773834), _773830))], (5978 ^ _356604) ^ [_570250, _570252, _570254, _570256] : [class_Groups_Oordered__cancel__ab__semigroup__add(_570250), c_Orderings_Oord__class_Oless(_570250, _570252, _570254), -(c_Orderings_Oord__class_Oless(_570250, c_Groups_Oplus__class_Oplus(_570250, _570256, _570252), c_Groups_Oplus__class_Oplus(_570250, _570256, _570254)))], (7704 ^ _356604) ^ [_628981] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _628981), -(_628981 = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _628981, c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (5044 ^ _356604) ^ [_536680] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _536680)) = _536680)], (11926 ^ _356604) ^ [_775042, _775044, _775046, _775048, _775050] : [class_Fields_Ofield(_775042), -(_775044 = c_Groups_Ozero__class_Ozero(_775042)), -(_775046 = c_Groups_Ozero__class_Ozero(_775042)), -(c_Groups_Oplus__class_Oplus(_775042, c_Rings_Oinverse__class_Odivide(_775042, _775048, _775044), c_Rings_Oinverse__class_Odivide(_775042, _775050, _775046)) = c_Rings_Oinverse__class_Odivide(_775042, c_Groups_Oplus__class_Oplus(_775042, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_775042), _775048), _775046), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_775042), _775050), _775044)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_775042), _775044), _775046)))], (8901 ^ _356604) ^ [_671336, _671338] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _671336, _671338), 8904 ^ _356604 : [(8911 ^ _356604) ^ [] : [_671338 = _671336, -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _671338, c_Nat_OSuc(_671336)))], (8905 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _671338, c_Nat_OSuc(_671336)), -(_671338 = _671336)]]], (4526 ^ _356604) ^ [_518060, _518062, _518064, _518066] : [class_Groups_Ozero(_518060), -(hAPP(c_Polynomial_Ocoeff(_518060, c_Polynomial_OpCons(_518060, _518062, _518064)), c_Nat_OSuc(_518066)) = hAPP(c_Polynomial_Ocoeff(_518060, _518064), _518066))], (2831 ^ _356604) ^ [_456115, _456117, _456119] : [class_Orderings_Oorder(_456115), c_Orderings_Oord__class_Oless__eq(_456115, _456117, _456119), c_Orderings_Oord__class_Oless__eq(_456115, _456119, _456117), -(_456119 = _456117)], (6846 ^ _356604) ^ [_600703, _600705, _600707, _600709, _600711] : [class_Groups_Oordered__ab__group__add(_600703), c_Groups_Ominus__class_Ominus(_600703, _600705, _600707) = c_Groups_Ominus__class_Ominus(_600703, _600709, _600711), 6853 ^ _356604 : [(6860 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_600703, _600709, _600711), -(c_Orderings_Oord__class_Oless(_600703, _600705, _600707))], (6854 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_600703, _600705, _600707), -(c_Orderings_Oord__class_Oless(_600703, _600709, _600711))]]], (448 ^ _356604) ^ [_370510, _370512] : [-(class_Groups_Oab__semigroup__add(_370510)), _370512 = _370510, class_Groups_Oab__semigroup__add(_370512)], (8556 ^ _356604) ^ [_658701, _658703, _658705, _658707, _658709] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _658701, _658703), 8559 ^ _356604 : [(8566 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _658701, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _658705, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _658709), _658703)), _658707)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _658701, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _658705, _658707)))], (8560 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _658701, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _658705, _658707)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _658701, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _658705, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _658709), _658703)), _658707)))]]], (1836 ^ _356604) ^ [_418467, _418469, _418471] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _418467, _418469), _418471), 1839 ^ _356604 : [(1842 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _418469, _418471))], (1840 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _418467, _418471))]]], (3972 ^ _356604) ^ [_497544, _497546] : [class_Groups_Ogroup__add(_497544), -(c_Groups_Ouminus__class_Ouminus(_497544, c_Groups_Ouminus__class_Ouminus(_497544, _497546)) = _497546)], (12660 ^ _356604) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (10207 ^ _356604) ^ [_716412, _716414] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _716412, _716414), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _716414, _716412), -(_716412 = _716414)], (12596 ^ _356604) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (12566 ^ _356604) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (10946 ^ _356604) ^ [_742514, _742516] : [class_Rings_Odivision__ring__inverse__zero(_742514), 10949 ^ _356604 : [(10956 ^ _356604) ^ [] : [-(_742516 = c_Groups_Ozero__class_Ozero(_742514)), -(c_Rings_Oinverse__class_Odivide(_742514, _742516, _742516) = c_Groups_Oone__class_Oone(_742514))], (10950 ^ _356604) ^ [] : [_742516 = c_Groups_Ozero__class_Ozero(_742514), -(c_Rings_Oinverse__class_Odivide(_742514, _742516, _742516) = c_Groups_Ozero__class_Ozero(_742514))]]], (6428 ^ _356604) ^ [_585920, _585922] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _585920, c_Nat_OSuc(_585922)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _585920, _585922)), -(_585920 = _585922)], (4502 ^ _356604) ^ [_516920, _516922] : [class_Groups_Ozero(_516920), -(hAPP(c_Polynomial_Ocoeff(_516920, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_516920))), _516922) = c_Groups_Ozero__class_Ozero(_516920))], (12552 ^ _356604) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (5988 ^ _356604) ^ [_570629, _570631, _570633, _570635, _570637] : [class_Groups_Oordered__cancel__ab__semigroup__add(_570629), c_Orderings_Oord__class_Oless(_570629, _570631, _570633), c_Orderings_Oord__class_Oless(_570629, _570635, _570637), -(c_Orderings_Oord__class_Oless(_570629, c_Groups_Oplus__class_Oplus(_570629, _570631, _570635), c_Groups_Oplus__class_Oplus(_570629, _570633, _570637)))], (48 ^ _356604) ^ [_358256, _358258] : [-(class_RealVector_Oreal__normed__algebra(_358256)), _358258 = _358256, class_RealVector_Oreal__normed__algebra(_358258)], (12704 ^ _356604) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (9475 ^ _356604) ^ [_691259, _691261, _691263, _691265] : [class_Groups_Oordered__comm__monoid__add(_691259), c_Orderings_Oord__class_Oless__eq(_691259, c_Groups_Ozero__class_Ozero(_691259), _691261), c_Orderings_Oord__class_Oless(_691259, _691263, _691265), -(c_Orderings_Oord__class_Oless(_691259, _691263, c_Groups_Oplus__class_Oplus(_691259, _691261, _691265)))], (4754 ^ _356604) ^ [_525864, _525866] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _525864), _525866) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _525866), _525864))], (12498 ^ _356604) ^ [_793588, _793590] : [class_Groups_Ouminus(_793588), -(class_Groups_Ouminus(tc_fun(_793590, _793588)))], (8488 ^ _356604) ^ [_656421, _656423] : [class_Groups_Oordered__ab__group__add(_656421), 8491 ^ _356604 : [(8498 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_656421, c_Groups_Ozero__class_Ozero(_656421), _656423), -(c_Orderings_Oord__class_Oless(_656421, c_Groups_Ouminus__class_Ouminus(_656421, _656423), c_Groups_Ozero__class_Ozero(_656421)))], (8492 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_656421, c_Groups_Ouminus__class_Ouminus(_656421, _656423), c_Groups_Ozero__class_Ozero(_656421)), -(c_Orderings_Oord__class_Oless(_656421, c_Groups_Ozero__class_Ozero(_656421), _656423))]]], (328 ^ _356604) ^ [_366970, _366972] : [-(class_Rings_Oordered__cancel__semiring(_366970)), _366972 = _366970, class_Rings_Oordered__cancel__semiring(_366972)], (5116 ^ _356604) ^ [_539344, _539346, _539348, _539350] : [class_Rings_Odvd(_539344), _539346 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_539344), _539348), _539350), -(c_Rings_Odvd__class_Odvd(_539344, _539348, _539346))], (12560 ^ _356604) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (638 ^ _356604) ^ [_376115, _376117] : [-(class_Orderings_Oord(_376115)), _376117 = _376115, class_Orderings_Oord(_376117)], (9891 ^ _356604) ^ [_706342, _706344] : [_706342 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _706342), _706344) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2817 ^ _356604) ^ [_455681, _455683, _455685, _455687] : [class_Orderings_Oorder(_455681), c_Orderings_Oord__class_Oless__eq(_455681, _455683, _455685), c_Orderings_Oord__class_Oless__eq(_455681, _455687, _455683), -(c_Orderings_Oord__class_Oless__eq(_455681, _455687, _455685))], (4628 ^ _356604) ^ [_521631, _521633] : [class_Groups_Ozero(_521631), -(_521633 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_521631))), hAPP(c_Polynomial_Ocoeff(_521631, _521633), c_Polynomial_Odegree(_521631, _521633)) = c_Groups_Ozero__class_Ozero(_521631)], (12464 ^ _356604) ^ [_792430] : [class_Groups_Ocancel__comm__monoid__add(_792430), -(class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(_792430)))], (946 ^ _356604) ^ [_386794, _386796, _386798, _386800] : [-(c_Polynomial_Opoly(_386800, _386796) = c_Polynomial_Opoly(_386798, _386794)), _386800 = _386798, _386796 = _386794], (5640 ^ _356604) ^ [_557882] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _557882, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9363 ^ _356604) ^ [_687599, _687601, _687603, _687605, _687607] : [class_Rings_Olinordered__semiring__strict(_687599), c_Orderings_Oord__class_Oless(_687599, _687601, _687603), c_Orderings_Oord__class_Oless(_687599, _687605, _687607), c_Orderings_Oord__class_Oless__eq(_687599, c_Groups_Ozero__class_Ozero(_687599), _687601), c_Orderings_Oord__class_Oless__eq(_687599, c_Groups_Ozero__class_Ozero(_687599), _687605), -(c_Orderings_Oord__class_Oless(_687599, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_687599), _687601), _687605), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_687599), _687603), _687607)))], (298 ^ _356604) ^ [_366085, _366087] : [-(class_Groups_Olinordered__ab__group__add(_366085)), _366087 = _366085, class_Groups_Olinordered__ab__group__add(_366087)], (12492 ^ _356604) ^ [_793376, _793378] : [class_Orderings_Oord(_793376), -(class_Orderings_Oord(tc_fun(_793378, _793376)))], (12152 ^ _356604) ^ [_782758] : [class_Int_Oring__char__0(_782758), -(class_Groups_Ocancel__ab__semigroup__add(_782758))], (4490 ^ _356604) ^ [_516406, _516408, _516410] : [class_Rings_Ocomm__semiring__1(_516406), -(c_Groups_Oplus__class_Oplus(_516406, _516408, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_516406), _516410), _516408)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_516406), c_Groups_Oplus__class_Oplus(_516406, _516410, c_Groups_Oone__class_Oone(_516406))), _516408))], (3759 ^ _356604) ^ [_489854, _489856, _489858, _489860] : [class_Rings_Ocomm__semiring__1(_489854), -(hAPP(c_Polynomial_Opoly(_489854, c_Polynomial_Omonom(_489854, _489856, _489858)), _489860) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_489854), _489856), hAPP(hAPP(c_Power_Opower__class_Opower(_489854), _489860), _489858)))], (2567 ^ _356604) ^ [_445199, _445201, _445203, _445205] : [class_Rings_Ocomm__semiring__1(_445199), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_445199), _445201), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_445199), _445203), _445205)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_445199), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_445199), _445201), _445203)), _445205))], (12386 ^ _356604) ^ [_790012] : [class_Rings_Oidom(_790012), -(class_Groups_Ogroup__add(_790012))], (3640 ^ _356604) ^ [_484833, _484835, _484837, _484839] : [class_RealVector_Oreal__normed__algebra(_484833), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_484833), _484835), c_Groups_Oplus__class_Oplus(_484833, _484837, _484839)) = c_Groups_Oplus__class_Oplus(_484833, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_484833), _484835), _484837), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_484833), _484835), _484839)))], (12098 ^ _356604) ^ [_780998, _781000, _781002, _781004] : [class_Fields_Olinordered__field(_780998), c_Orderings_Oord__class_Oless(_780998, c_Groups_Ozero__class_Ozero(_780998), _781000), 12105 ^ _356604 : [(12112 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_780998, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_780998), _781002), _781000), _781004), -(c_Orderings_Oord__class_Oless__eq(_780998, _781002, c_Rings_Oinverse__class_Odivide(_780998, _781004, _781000)))], (12106 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_780998, _781002, c_Rings_Oinverse__class_Odivide(_780998, _781004, _781000)), -(c_Orderings_Oord__class_Oless__eq(_780998, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_780998), _781002), _781000), _781004))]]], (9553 ^ _356604) ^ [_693782, _693784, _693786] : [class_Rings_Olinordered__ring(_693782), c_Orderings_Oord__class_Oless(_693782, c_Groups_Oplus__class_Oplus(_693782, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_693782), _693784), _693784), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_693782), _693786), _693786)), c_Groups_Ozero__class_Ozero(_693782))], (1215 ^ _356604) ^ [] : [-(c_Polynomial_Odegree(t_a, v_p) = c_Polynomial_Odegree(t_a, c_Polynomial_OpCons(t_a, hAPP(c_Polynomial_Opoly(t_a, v_p), c_Groups_Ozero__class_Ozero(t_a)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))), class_Int_Oring__char__0(t_a), class_Rings_Oidom(t_a)], (12894 ^ _356604) ^ [_805135] : [class_Groups_Oab__group__add(_805135), -(class_Groups_Oab__group__add(tc_Polynomial_Opoly(_805135)))], (1998 ^ _356604) ^ [_424273, _424275] : [class_Groups_Olinordered__ab__group__add(_424273), 2001 ^ _356604 : [(2008 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_424273, c_Groups_Ozero__class_Ozero(_424273), _424275), -(c_Orderings_Oord__class_Oless__eq(_424273, c_Groups_Ozero__class_Ozero(_424273), c_Groups_Oplus__class_Oplus(_424273, _424275, _424275)))], (2002 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_424273, c_Groups_Ozero__class_Ozero(_424273), c_Groups_Oplus__class_Oplus(_424273, _424275, _424275)), -(c_Orderings_Oord__class_Oless__eq(_424273, c_Groups_Ozero__class_Ozero(_424273), _424275))]]], (1575 ^ _356604) ^ [_408377, _408379, _408381, _408383, _408385, _408387] : [class_Groups_Ozero(_408377), -(c_Polynomial_Opoly__rec(_408379, _408377, _408381, _408383, c_Polynomial_OpCons(_408377, _408385, _408387)) = hAPP(hAPP(hAPP(_408383, _408385), _408387), c_If(_408379, c_fequal(_408387, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_408377))), _408381, c_Polynomial_Opoly__rec(_408379, _408377, _408381, _408383, _408387))))], (12474 ^ _356604) ^ [_792740, _792742] : [class_Lattices_Oboolean__algebra(_792740), -(class_Lattices_Oboolean__algebra(tc_fun(_792742, _792740)))], (4112 ^ _356604) ^ [_501973, _501975, _501977] : [class_Rings_Oidom(_501973), 4115 ^ _356604 : [(4116 ^ _356604) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_501973), _501975), _501975) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_501973), _501977), _501977), -(_501975 = _501977), -(_501975 = c_Groups_Ouminus__class_Ouminus(_501973, _501977))], (4126 ^ _356604) ^ [] : [4127 ^ _356604 : [(4130 ^ _356604) ^ [] : [_501975 = c_Groups_Ouminus__class_Ouminus(_501973, _501977)], (4128 ^ _356604) ^ [] : [_501975 = _501977]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_501973), _501975), _501975) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_501973), _501977), _501977))]]], (12846 ^ _356604) ^ [_803615] : [class_Rings_Olinordered__idom(_803615), -(class_Rings_Oordered__semiring(tc_Polynomial_Opoly(_803615)))], (2749 ^ _356604) ^ [_453022, _453024, _453026, _453028] : [class_Rings_Ocomm__semiring__0(_453022), -(c_Polynomial_Osmult(_453022, _453024, c_Polynomial_OpCons(_453022, _453026, _453028)) = c_Polynomial_OpCons(_453022, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_453022), _453024), _453026), c_Polynomial_Osmult(_453022, _453024, _453028)))], (2044 ^ _356604) ^ [_425703, _425705, _425707] : [class_Groups_Oordered__comm__monoid__add(_425703), c_Orderings_Oord__class_Oless__eq(_425703, c_Groups_Ozero__class_Ozero(_425703), _425705), c_Orderings_Oord__class_Oless__eq(_425703, c_Groups_Ozero__class_Ozero(_425703), _425707), 2055 ^ _356604 : [(2064 ^ _356604) ^ [] : [-(c_Groups_Oplus__class_Oplus(_425703, _425705, _425707) = c_Groups_Ozero__class_Ozero(_425703)), _425705 = c_Groups_Ozero__class_Ozero(_425703), _425707 = c_Groups_Ozero__class_Ozero(_425703)], (2056 ^ _356604) ^ [] : [c_Groups_Oplus__class_Oplus(_425703, _425705, _425707) = c_Groups_Ozero__class_Ozero(_425703), 2059 ^ _356604 : [(2062 ^ _356604) ^ [] : [-(_425707 = c_Groups_Ozero__class_Ozero(_425703))], (2060 ^ _356604) ^ [] : [-(_425705 = c_Groups_Ozero__class_Ozero(_425703))]]]]], (6552 ^ _356604) ^ [_590520, _590522] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _590520, _590522), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _590520, _590522)), -(_590520 = _590522)], (11994 ^ _356604) ^ [_777686, _777688, _777690, _777692] : [class_Fields_Olinordered__field__inverse__zero(_777686), 11997 ^ _356604 : [(11998 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_777686, _777688, c_Rings_Oinverse__class_Odivide(_777686, _777690, _777692)), 12001 ^ _356604 : [(12008 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_777686, c_Groups_Ozero__class_Ozero(_777686), _777692)), 12011 ^ _356604 : [(12018 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_777686, _777692, c_Groups_Ozero__class_Ozero(_777686))), -(c_Orderings_Oord__class_Oless__eq(_777686, _777688, c_Groups_Ozero__class_Ozero(_777686)))], (12012 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_777686, _777692, c_Groups_Ozero__class_Ozero(_777686)), -(c_Orderings_Oord__class_Oless__eq(_777686, _777690, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_777686), _777688), _777692)))]]], (12002 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_777686, c_Groups_Ozero__class_Ozero(_777686), _777692), -(c_Orderings_Oord__class_Oless__eq(_777686, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_777686), _777688), _777692), _777690))]]], (12024 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_777686, _777688, c_Rings_Oinverse__class_Odivide(_777686, _777690, _777692))), 12027 ^ _356604 : [(12030 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_777686, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_777686), _777688), _777692), _777690)], (12028 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_777686, c_Groups_Ozero__class_Ozero(_777686), _777692))]], 12031 ^ _356604 : [(12034 ^ _356604) ^ [] : [12035 ^ _356604 : [(12038 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_777686, _777690, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_777686), _777688), _777692))], (12036 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_777686, _777692, c_Groups_Ozero__class_Ozero(_777686)))]], 12039 ^ _356604 : [(12042 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_777686, _777688, c_Groups_Ozero__class_Ozero(_777686))], (12040 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_777686, _777692, c_Groups_Ozero__class_Ozero(_777686))]]], (12032 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_777686, c_Groups_Ozero__class_Ozero(_777686), _777692)]]]]], (7234 ^ _356604) ^ [_613648] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _613648) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (228 ^ _356604) ^ [_364020, _364022] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_364020)), _364022 = _364020, class_Groups_Oordered__cancel__ab__semigroup__add(_364022)], (4862 ^ _356604) ^ [_530158, _530160, _530162] : [class_Rings_Olinordered__semidom(_530158), c_Orderings_Oord__class_Oless__eq(_530158, c_Groups_Oone__class_Oone(_530158), _530160), -(c_Orderings_Oord__class_Oless__eq(_530158, c_Groups_Oone__class_Oone(_530158), hAPP(hAPP(c_Power_Opower__class_Opower(_530158), _530160), _530162)))], (3676 ^ _356604) ^ [_486422, _486424] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _486422), _486424) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _486424), _486422))], (8853 ^ _356604) ^ [_669672, _669674] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _669672, _669674), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_669672), _669674))], (8716 ^ _356604) ^ [_664501, _664503] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _664501, _664503), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _664501, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _664503, _664501)) = _664503)], (1263 ^ _356604) ^ [] : [-(v_p = c_Polynomial_OpCons(t_a, hAPP(c_Polynomial_Opoly(t_a, v_p), c_Groups_Ozero__class_Ozero(t_a)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))), class_Int_Oring__char__0(t_a), class_Rings_Oidom(t_a)], (1960 ^ _356604) ^ [_422937, _422939, _422941, _422943] : [class_Groups_Ocancel__semigroup__add(_422937), 1963 ^ _356604 : [(1970 ^ _356604) ^ [] : [_422939 = _422943, -(c_Groups_Oplus__class_Oplus(_422937, _422939, _422941) = c_Groups_Oplus__class_Oplus(_422937, _422943, _422941))], (1964 ^ _356604) ^ [] : [c_Groups_Oplus__class_Oplus(_422937, _422939, _422941) = c_Groups_Oplus__class_Oplus(_422937, _422943, _422941), -(_422939 = _422943)]]], (5384 ^ _356604) ^ [_548738, _548740, _548742] : [class_Rings_Oidom(_548738), hAPP(c_Polynomial_Ocoeff(_548738, _548740), c_Polynomial_Odegree(_548738, _548740)) = hAPP(c_Polynomial_Ocoeff(_548738, _548742), c_Polynomial_Odegree(_548738, _548742)), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_548738), _548740, _548742), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_548738), _548742, _548740), -(_548740 = _548742)], (1854 ^ _356604) ^ [_419171, _419173, _419175, _419177] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_419171), c_Orderings_Oord__class_Oless__eq(_419171, c_Groups_Oplus__class_Oplus(_419171, _419173, _419175), c_Groups_Oplus__class_Oplus(_419171, _419177, _419175)), -(c_Orderings_Oord__class_Oless__eq(_419171, _419173, _419177))], (12628 ^ _356604) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (1669 ^ _356604) ^ [_411873] : [c_Nat_OSuc(_411873) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (10217 ^ _356604) ^ [_716729, _716731, _716733] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _716729, _716731), _716731 = _716733, -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _716729, _716733))], (12690 ^ _356604) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (1245 ^ _356604) ^ [] : [-(c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9087 ^ _356604) ^ [_677786, _677788] : [9088 ^ _356604 : [(9091 ^ _356604) ^ [] : [_677786 = _677788], (9089 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _677786, _677788)]], -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _677786, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _677788, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (6478 ^ _356604) ^ [_587730, _587732, _587734] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _587730, _587732), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _587730, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _587732, _587734)))], (6616 ^ _356604) ^ [_592765, _592767, _592769, _592771] : [class_Groups_Oab__group__add(_592765), -(hAPP(c_Polynomial_Ocoeff(_592765, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_592765), _592767, _592769)), _592771) = c_Groups_Ominus__class_Ominus(_592765, hAPP(c_Polynomial_Ocoeff(_592765, _592767), _592771), hAPP(c_Polynomial_Ocoeff(_592765, _592769), _592771)))], (4356 ^ _356604) ^ [_511580, _511582] : [class_Groups_Olinordered__ab__group__add(_511580), 4359 ^ _356604 : [(4366 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_511580, _511582, c_Groups_Ozero__class_Ozero(_511580)), -(c_Orderings_Oord__class_Oless__eq(_511580, _511582, c_Groups_Ouminus__class_Ouminus(_511580, _511582)))], (4360 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_511580, _511582, c_Groups_Ouminus__class_Ouminus(_511580, _511582)), -(c_Orderings_Oord__class_Oless__eq(_511580, _511582, c_Groups_Ozero__class_Ozero(_511580)))]]], (2280 ^ _356604) ^ [_434073, _434075] : [class_Groups_Olinordered__ab__group__add(_434073), 2283 ^ _356604 : [(2290 ^ _356604) ^ [] : [_434075 = c_Groups_Ozero__class_Ozero(_434073), -(c_Groups_Ozero__class_Ozero(_434073) = c_Groups_Oplus__class_Oplus(_434073, _434075, _434075))], (2284 ^ _356604) ^ [] : [c_Groups_Ozero__class_Ozero(_434073) = c_Groups_Oplus__class_Oplus(_434073, _434075, _434075), -(_434075 = c_Groups_Ozero__class_Ozero(_434073))]]], (102 ^ _356604) ^ [_360147, _360149] : [-(class_Rings_Odivision__ring__inverse__zero(_360147)), _360149 = _360147, class_Rings_Odivision__ring__inverse__zero(_360149)], (12622 ^ _356604) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (12676 ^ _356604) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (10383 ^ _356604) ^ [_722171, _722173, _722175, _722177, _722179, _722181] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _722171), _722173), _722175) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _722177), _722179), _722181), 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), _722177), _722179), _722181), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _722175, _722171), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _722181), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _722177), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _722177, _722171), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _722179, _722173))], (2667 ^ _356604) ^ [_449592, _449594, _449596, _449598, _449600] : [class_Rings_Ocomm__semiring__0(_449592), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_449592)), c_Polynomial_Omonom(_449592, _449594, _449596)), c_Polynomial_Omonom(_449592, _449598, _449600)) = c_Polynomial_Omonom(_449592, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_449592), _449594), _449598), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _449596, _449600)))], (8748 ^ _356604) ^ [_665781, _665783] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _665781, c_Nat_OSuc(_665783)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _665781, c_Groups_Oone__class_Oone(tc_Nat_Onat)), _665783))], (6456 ^ _356604) ^ [_586843] : [_586843 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _586843, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (12188 ^ _356604) ^ [_783874] : [class_Int_Oring__char__0(_783874), -(class_Groups_Omonoid__mult(_783874))], (1497 ^ _356604) ^ [_405560, _405562, _405564] : [hAPP(_405564, 1498 ^ [_405560, _405562, _405564]) = hAPP(_405564, 1499 ^ [_405560, _405562, _405564]), -(c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(_405560, _405562, _405564))], (1752 ^ _356604) ^ [_415319, _415321, _415323] : [_415319 = _415323, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _415319, _415321) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _415323, _415321))], (2176 ^ _356604) ^ [_430307] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _430307, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_430307 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12614 ^ _356604) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (5756 ^ _356604) ^ [_562002] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _562002), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _562002))], (3352 ^ _356604) ^ [_474866, _474868, _474870] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _474868, _474870), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_474866)), _474868), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_474866)), _474870)))], (368 ^ _356604) ^ [_368150, _368152] : [-(class_Rings_Olinordered__semiring__1(_368150)), _368152 = _368150, class_Rings_Olinordered__semiring__1(_368152)], (4340 ^ _356604) ^ [_511095, _511097] : [class_Groups_Oordered__ab__group__add(_511095), 4343 ^ _356604 : [(4350 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_511095, _511097, c_Groups_Ozero__class_Ozero(_511095)), -(c_Orderings_Oord__class_Oless__eq(_511095, c_Groups_Ozero__class_Ozero(_511095), c_Groups_Ouminus__class_Ouminus(_511095, _511097)))], (4344 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_511095, c_Groups_Ozero__class_Ozero(_511095), c_Groups_Ouminus__class_Ouminus(_511095, _511097)), -(c_Orderings_Oord__class_Oless__eq(_511095, _511097, c_Groups_Ozero__class_Ozero(_511095)))]]], (7522 ^ _356604) ^ [_622569, _622571, _622573, _622575] : [class_Orderings_Opreorder(_622569), c_Orderings_Oord__class_Oless__eq(_622569, _622571, _622573), c_Orderings_Oord__class_Oless(_622569, _622573, _622575), -(c_Orderings_Oord__class_Oless(_622569, _622571, _622575))], (12182 ^ _356604) ^ [_783688] : [class_Int_Oring__char__0(_783688), -(class_Rings_Ozero__neq__one(_783688))], (2513 ^ _356604) ^ [_442375, _442377] : [class_Rings_Ocomm__semiring__1(_442375), -(c_Groups_Oplus__class_Oplus(_442375, _442377, c_Groups_Ozero__class_Ozero(_442375)) = _442377)], (7422 ^ _356604) ^ [_619485, _619487, _619489] : [class_Orderings_Opreorder(_619485), c_Orderings_Oord__class_Oless(_619485, _619487, _619489), -(c_Orderings_Oord__class_Oless__eq(_619485, _619487, _619489))], (9183 ^ _356604) ^ [_681075, _681077, _681079, _681081] : [class_Groups_Ocomm__monoid__add(_681075), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_681075, _681077), _681079), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_681075, _681081), _681079), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_681075, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_681075), _681077, _681081)), _681079))], (1369 ^ _356604) ^ [_401177, _401179, _401181, _401183, _401185] : [class_Groups_Ozero(_401177), 1372 ^ _356604 : [(1381 ^ _356604) ^ [] : [-(c_Polynomial_OpCons(_401177, _401179, _401181) = c_Polynomial_OpCons(_401177, _401183, _401185)), _401179 = _401183, _401181 = _401185], (1373 ^ _356604) ^ [] : [c_Polynomial_OpCons(_401177, _401179, _401181) = c_Polynomial_OpCons(_401177, _401183, _401185), 1376 ^ _356604 : [(1379 ^ _356604) ^ [] : [-(_401181 = _401185)], (1377 ^ _356604) ^ [] : [-(_401179 = _401183)]]]]], (2791 ^ _356604) ^ [_454674, _454676, _454678] : [class_Rings_Olinordered__ring(_454674), -(c_Orderings_Oord__class_Oless__eq(_454674, c_Groups_Ozero__class_Ozero(_454674), c_Groups_Oplus__class_Oplus(_454674, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_454674), _454676), _454676), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_454674), _454678), _454678))))], (728 ^ _356604) ^ [_378770, _378772] : [-(class_Rings_Oring(_378770)), _378772 = _378770, class_Rings_Oring(_378772)], (5006 ^ _356604) ^ [_535379, _535381, _535383] : [class_Lattices_Oboolean__algebra(_535379), c_Orderings_Oord__class_Oless__eq(_535379, _535381, _535383), -(c_Orderings_Oord__class_Oless__eq(_535379, c_Groups_Ouminus__class_Ouminus(_535379, _535383), c_Groups_Ouminus__class_Ouminus(_535379, _535381)))], (5750 ^ _356604) ^ [_561842] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _561842), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _561842))], (12918 ^ _356604) ^ [_805895] : [class_Rings_Olinordered__idom(_805895), -(class_Orderings_Olinorder(tc_Polynomial_Opoly(_805895)))], (1285 ^ _356604) ^ [_398381, _398383] : [class_Groups_Ozero(_398381), -(c_Polynomial_Omonom(_398381, _398383, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Polynomial_OpCons(_398381, _398383, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_398381))))], (508 ^ _356604) ^ [_372280, _372282] : [-(class_Rings_Oordered__ring(_372280)), _372282 = _372280, class_Rings_Oordered__ring(_372282)], (10471 ^ _356604) ^ [_725149, _725151, _725153] : [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), _725149), _725151), _725153), 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), _725153), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _725149), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _725151, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (12632 ^ _356604) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (5222 ^ _356604) ^ [_543051, _543053] : [class_Rings_Ocomm__semiring__1(_543051), -(c_Rings_Odvd__class_Odvd(_543051, _543053, _543053))], (12612 ^ _356604) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (8871 ^ _356604) ^ [_670261, _670263] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _670261, _670263), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _670261, c_Nat_OSuc(_670263)))], (9041 ^ _356604) ^ [_676201] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _676201), -(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), _676201)))], (2755 ^ _356604) ^ [_453318, _453320, _453322, _453324] : [class_Rings_Ocomm__semiring__0(_453318), -(hAPP(c_Polynomial_Opoly(_453318, c_Polynomial_Osmult(_453318, _453320, _453322)), _453324) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_453318), _453320), hAPP(c_Polynomial_Opoly(_453318, _453322), _453324)))], (10696 ^ _356604) ^ [_732693, _732695, _732697, _732699] : [class_Fields_Ofield(_732693), 10699 ^ _356604 : [(10708 ^ _356604) ^ [] : [-(c_Polynomial_Opdivmod__rel(_732693, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_732693)), _732695, _732697, _732699)), _732697 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_732693)), _732699 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_732693))], (10700 ^ _356604) ^ [] : [c_Polynomial_Opdivmod__rel(_732693, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_732693)), _732695, _732697, _732699), 10703 ^ _356604 : [(10706 ^ _356604) ^ [] : [-(_732699 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_732693)))], (10704 ^ _356604) ^ [] : [-(_732697 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_732693)))]]]]], (6314 ^ _356604) ^ [_582162] : [-(_582162 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _582162))], (4762 ^ _356604) ^ [_526391, _526393] : [class_Groups_Omonoid__mult(_526391), -(hAPP(hAPP(c_Power_Opower__class_Opower(_526391), _526393), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _526393)], (7878 ^ _356604) ^ [_635157, _635159, _635161, _635163] : [class_Rings_Olinordered__semidom(_635157), c_Orderings_Oord__class_Oless(_635157, _635159, _635161), c_Orderings_Oord__class_Oless__eq(_635157, c_Groups_Ozero__class_Ozero(_635157), _635159), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _635163), -(c_Orderings_Oord__class_Oless(_635157, hAPP(hAPP(c_Power_Opower__class_Opower(_635157), _635159), _635163), hAPP(hAPP(c_Power_Opower__class_Opower(_635157), _635161), _635163)))], (5532 ^ _356604) ^ [_554000, _554002, _554004] : [class_Rings_Oidom(_554000), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_554000), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_554000)), c_Polynomial_OpCons(_554000, c_Groups_Ouminus__class_Ouminus(_554000, _554002), c_Polynomial_OpCons(_554000, c_Groups_Oone__class_Oone(_554000), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_554000))))), c_Polynomial_Oorder(_554000, _554002, _554004)), _554004))], (132 ^ _356604) ^ [_361032, _361034] : [-(class_Fields_Ofield__inverse__zero(_361032)), _361034 = _361032, class_Fields_Ofield__inverse__zero(_361034)], (12230 ^ _356604) ^ [_785176] : [class_Int_Oring__char__0(_785176), -(class_Rings_Oring__1(_785176))], (1167 ^ _356604) ^ [] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(t_a, t_a, c_Polynomial_Opoly(t_a, v_p))), class_Int_Oring__char__0(t_a), class_Rings_Oidom(t_a)], (4454 ^ _356604) ^ [_514849, _514851, _514853] : [class_Rings_Ocomm__semiring__1(_514849), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_514849), _514851), hAPP(hAPP(c_Power_Opower__class_Opower(_514849), _514851), _514853)) = hAPP(hAPP(c_Power_Opower__class_Opower(_514849), _514851), c_Nat_OSuc(_514853)))], (12678 ^ _356604) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (5312 ^ _356604) ^ [_546287, _546289, _546291, _546293, _546295] : [class_Rings_Ocomm__semiring__1(_546287), c_Rings_Odvd__class_Odvd(_546287, _546289, _546291), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _546293, _546295), -(c_Rings_Odvd__class_Odvd(_546287, hAPP(hAPP(c_Power_Opower__class_Opower(_546287), _546289), _546293), hAPP(hAPP(c_Power_Opower__class_Opower(_546287), _546291), _546295)))], (11906 ^ _356604) ^ [_774228, _774230, _774232, _774234] : [class_Fields_Ofield__inverse__zero(_774228), -(_774230 = c_Groups_Ozero__class_Ozero(_774228)), -(c_Groups_Oplus__class_Oplus(_774228, c_Rings_Oinverse__class_Odivide(_774228, _774232, _774230), _774234) = c_Rings_Oinverse__class_Odivide(_774228, c_Groups_Oplus__class_Oplus(_774228, _774232, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_774228), _774234), _774230)), _774230))], (2436 ^ _356604) ^ [_439549, _439551, _439553] : [class_Groups_Ozero(_439549), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_439549, c_Polynomial_OpCons(_439549, _439551, _439553)), c_Nat_OSuc(c_Polynomial_Odegree(_439549, _439553))))], (12670 ^ _356604) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (4508 ^ _356604) ^ [_517180, _517182, _517184, _517186] : [class_Rings_Ocomm__ring__1(_517180), -(hAPP(c_Polynomial_Opoly(_517180, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_517180)), c_Polynomial_Omonom(_517180, c_Groups_Oone__class_Oone(_517180), _517182)), _517184)), _517186) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_517180), hAPP(hAPP(c_Power_Opower__class_Opower(_517180), _517186), _517182)), hAPP(c_Polynomial_Opoly(_517180, _517184), _517186)))], (12526 ^ _356604) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (278 ^ _356604) ^ [_365495, _365497] : [-(class_Groups_Oordered__ab__semigroup__add(_365495)), _365497 = _365495, class_Groups_Oordered__ab__semigroup__add(_365497)], (8959 ^ _356604) ^ [_673330, _673332, _673334] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _673330), _673332), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _673334), _673332)), 8962 ^ _356604 : [(8965 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _673330, _673334))], (8963 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _673332))]]], (3456 ^ _356604) ^ [_478651, _478653, _478655, _478657, _478659] : [class_Rings_Osemiring(_478651), -(c_Groups_Oplus__class_Oplus(_478651, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_478651), _478653), _478655), c_Groups_Oplus__class_Oplus(_478651, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_478651), _478657), _478655), _478659)) = c_Groups_Oplus__class_Oplus(_478651, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_478651), c_Groups_Oplus__class_Oplus(_478651, _478653, _478657)), _478655), _478659))], (7384 ^ _356604) ^ [_618317, _618319, _618321] : [class_Orderings_Oorder(_618317), -(_618319 = _618321), c_Orderings_Oord__class_Oless__eq(_618317, _618319, _618321), -(c_Orderings_Oord__class_Oless(_618317, _618319, _618321))], (12530 ^ _356604) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (4334 ^ _356604) ^ [_510827, _510829, _510831] : [class_Rings_Ocomm__semiring__1(_510827), -(c_Polynomial_Odegree(_510827, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_510827)), c_Polynomial_OpCons(_510827, _510829, c_Polynomial_OpCons(_510827, c_Groups_Oone__class_Oone(_510827), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_510827))))), _510831)) = _510831)], (7038 ^ _356604) ^ [_607270, _607272, _607274] : [class_Orderings_Oorder(_607270), c_Orderings_Oord__class_Oless(_607270, _607272, _607274), _607272 = _607274], (12266 ^ _356604) ^ [_786292] : [class_Int_Oring__char__0(_786292), -(class_Groups_Ocancel__comm__monoid__add(_786292))], (12906 ^ _356604) ^ [_805515] : [class_Rings_Olinordered__idom(_805515), -(class_Rings_Oordered__ring(tc_Polynomial_Opoly(_805515)))], (12564 ^ _356604) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (3292 ^ _356604) ^ [_472438] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _472438, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _472438), _472438)))], (10111 ^ _356604) ^ [_713411, _713413] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _713411, _713413)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _713411, _713413), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _713413, _713411))], (11916 ^ _356604) ^ [_774628, _774630, _774632, _774634] : [class_Fields_Ofield(_774628), -(_774630 = c_Groups_Ozero__class_Ozero(_774628)), -(c_Groups_Oplus__class_Oplus(_774628, c_Rings_Oinverse__class_Odivide(_774628, _774632, _774630), _774634) = c_Rings_Oinverse__class_Odivide(_774628, c_Groups_Oplus__class_Oplus(_774628, _774632, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_774628), _774630), _774634)), _774630))], (8342 ^ _356604) ^ [_651774, _651776, _651778] : [class_Groups_Oordered__comm__monoid__add(_651774), c_Orderings_Oord__class_Oless(_651774, _651776, c_Groups_Ozero__class_Ozero(_651774)), c_Orderings_Oord__class_Oless(_651774, _651778, c_Groups_Ozero__class_Ozero(_651774)), -(c_Orderings_Oord__class_Oless(_651774, c_Groups_Oplus__class_Oplus(_651774, _651776, _651778), c_Groups_Ozero__class_Ozero(_651774)))], (7202 ^ _356604) ^ [_612552, _612554, _612556] : [class_Orderings_Olinorder(_612552), -(c_Orderings_Oord__class_Oless(_612552, _612554, _612556)), -(_612554 = _612556), -(c_Orderings_Oord__class_Oless(_612552, _612556, _612554))], (8710 ^ _356604) ^ [_664251, _664253, _664255] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _664251, _664253), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _664255, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _664253, _664251)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _664255, _664253), _664251))], (12218 ^ _356604) ^ [_784804] : [class_Int_Oring__char__0(_784804), -(class_Rings_Osemiring(_784804))], (1533 ^ _356604) ^ [_406904, _406906, _406908, _406910, _406912, _406914] : [class_Groups_Ozero(_406904), hAPP(hAPP(hAPP(_406906, c_Groups_Ozero__class_Ozero(_406904)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_406904))), _406908) = _406908, -(c_Polynomial_Opoly__rec(_406910, _406904, _406908, _406906, c_Polynomial_OpCons(_406904, _406912, _406914)) = hAPP(hAPP(hAPP(_406906, _406912), _406914), c_Polynomial_Opoly__rec(_406910, _406904, _406908, _406906, _406914)))], (12224 ^ _356604) ^ [_784990] : [class_Int_Oring__char__0(_784990), -(class_Groups_Ouminus(_784990))], (4798 ^ _356604) ^ [_527926, _527928] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _527926), _527928) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_527928 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_527926 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10718 ^ _356604) ^ [_733426, _733428, _733430, _733432] : [class_Fields_Ofield(_733426), 10721 ^ _356604 : [(10730 ^ _356604) ^ [] : [-(c_Polynomial_Opdivmod__rel(_733426, _733428, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_733426)), _733430, _733432)), _733430 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_733426)), _733432 = _733428], (10722 ^ _356604) ^ [] : [c_Polynomial_Opdivmod__rel(_733426, _733428, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_733426)), _733430, _733432), 10725 ^ _356604 : [(10728 ^ _356604) ^ [] : [-(_733432 = _733428)], (10726 ^ _356604) ^ [] : [-(_733430 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_733426)))]]]]], (12882 ^ _356604) ^ [_804755] : [class_Rings_Ocomm__semiring__0(_804755), -(class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(_804755)))], (1824 ^ _356604) ^ [_417983, _417985, _417987] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _417983, _417985), _417987), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _417985, _417987))], (7220 ^ _356604) ^ [_613198, _613200] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _613198, _613200) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _613200, _613198) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_613198 = _613200)], (758 ^ _356604) ^ [_379655, _379657] : [-(class_Rings_Odvd(_379655)), _379657 = _379655, class_Rings_Odvd(_379657)], (9789 ^ _356604) ^ [_702878, _702880, _702882] : [class_Rings_Ocomm__semiring__0(_702878), -(c_Polynomial_Odegree(_702878, c_Polynomial_Osynthetic__div(_702878, _702880, _702882)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Polynomial_Odegree(_702878, _702880), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (1485 ^ _356604) ^ [_405062, _405064] : [class_Groups_Ozero(_405062), -(c_Polynomial_Odegree(_405062, c_Polynomial_OpCons(_405062, _405064, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_405062)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4282 ^ _356604) ^ [_508996, _508998, _509000] : [class_Rings_Ocomm__ring(_508996), -(c_Polynomial_Osmult(_508996, _508998, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_508996), _509000)) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_508996), c_Polynomial_Osmult(_508996, _508998, _509000)))], (3468 ^ _356604) ^ [_479201, _479203, _479205] : [class_Rings_Olinordered__ring__strict(_479201), 3471 ^ _356604 : [(3486 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_479201, c_Groups_Ozero__class_Ozero(_479201), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_479201), _479203), _479205))), 3487 ^ _356604 : [(3494 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_479201, _479203, c_Groups_Ozero__class_Ozero(_479201)), c_Orderings_Oord__class_Oless__eq(_479201, _479205, c_Groups_Ozero__class_Ozero(_479201))], (3488 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_479201, c_Groups_Ozero__class_Ozero(_479201), _479203), c_Orderings_Oord__class_Oless__eq(_479201, c_Groups_Ozero__class_Ozero(_479201), _479205)]]], (3472 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_479201, c_Groups_Ozero__class_Ozero(_479201), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_479201), _479203), _479205)), 3477 ^ _356604 : [(3480 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_479201, c_Groups_Ozero__class_Ozero(_479201), _479205))], (3478 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_479201, c_Groups_Ozero__class_Ozero(_479201), _479203))]], 3481 ^ _356604 : [(3484 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_479201, _479205, c_Groups_Ozero__class_Ozero(_479201)))], (3482 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_479201, _479203, c_Groups_Ozero__class_Ozero(_479201)))]]]]], (6054 ^ _356604) ^ [_572847, _572849, _572851] : [class_Groups_Oordered__ab__group__add(_572847), 6057 ^ _356604 : [(6064 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_572847, _572851, _572849), -(c_Orderings_Oord__class_Oless(_572847, c_Groups_Ouminus__class_Ouminus(_572847, _572849), c_Groups_Ouminus__class_Ouminus(_572847, _572851)))], (6058 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_572847, c_Groups_Ouminus__class_Ouminus(_572847, _572849), c_Groups_Ouminus__class_Ouminus(_572847, _572851)), -(c_Orderings_Oord__class_Oless(_572847, _572851, _572849))]]], (12816 ^ _356604) ^ [_802665] : [class_Rings_Olinordered__idom(_802665), -(class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(_802665)))], (1643 ^ _356604) ^ [_410906, _410908, _410910] : [class_Groups_Ozero(_410906), -(_410908 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_410906))), -(c_Polynomial_Odegree(_410906, c_Polynomial_OpCons(_410906, _410910, _410908)) = c_Nat_OSuc(c_Polynomial_Odegree(_410906, _410908)))], (12948 ^ _356604) ^ [_806845] : [class_Groups_Oab__group__add(_806845), -(class_Groups_Ogroup__add(tc_Polynomial_Opoly(_806845)))], (6742 ^ _356604) ^ [_596868] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _596868, _596868)], (4306 ^ _356604) ^ [_509808] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _509808), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _509808)], (2901 ^ _356604) ^ [_458305, _458307, _458309, _458311] : [class_Orderings_Oorder(_458305), _458307 = _458309, c_Orderings_Oord__class_Oless__eq(_458305, _458311, _458309), -(c_Orderings_Oord__class_Oless__eq(_458305, _458311, _458307))], (12996 ^ _356604) ^ [_808365] : [class_Rings_Ocomm__ring__1(_808365), -(class_Rings_Oring__1(tc_Polynomial_Opoly(_808365)))], (12624 ^ _356604) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (6262 ^ _356604) ^ [_580155, _580157, _580159] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _580155, _580157), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _580155, _580159), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _580157, _580155), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _580159, _580155)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _580157, _580159))], (8402 ^ _356604) ^ [_653644, _653646, _653648, _653650] : [class_Rings_Olinordered__semidom(_653644), c_Orderings_Oord__class_Oless(_653644, c_Groups_Ozero__class_Ozero(_653644), _653646), c_Orderings_Oord__class_Oless(_653644, _653648, _653650), -(c_Orderings_Oord__class_Oless(_653644, _653648, c_Groups_Oplus__class_Oplus(_653644, _653646, _653650)))], (12620 ^ _356604) ^ [] : [-(class_Rings_Odvd(tc_Int_Oint))], (9615 ^ _356604) ^ [_696118, _696120, _696122] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _696118, _696120), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _696120, _696118)), _696122) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_696120), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _696118, _696122)))], (2174 ^ _356604) ^ [_430181] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _430181) = _430181)], (6306 ^ _356604) ^ [_581856, _581858] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _581856, _581858), _581858 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (4514 ^ _356604) ^ [_517502, _517504, _517506] : [class_Groups_Ozero(_517502), -(hAPP(c_Polynomial_Ocoeff(_517502, c_Polynomial_OpCons(_517502, _517504, _517506)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _517504)], (6610 ^ _356604) ^ [_592469, _592471, _592473, _592475] : [class_Rings_Ocomm__ring(_592469), -(c_Polynomial_Osmult(_592469, _592471, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_592469), _592473, _592475)) = c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_592469), c_Polynomial_Osmult(_592469, _592471, _592473), c_Polynomial_Osmult(_592469, _592471, _592475)))], (3712 ^ _356604) ^ [_488104, _488106, _488108, _488110, _488112, _488114] : [class_Rings_Olinordered__semiring__1(_488104), c_Orderings_Oord__class_Oless__eq(_488104, _488106, _488108), c_Orderings_Oord__class_Oless__eq(_488104, _488110, _488108), c_Orderings_Oord__class_Oless__eq(_488104, c_Groups_Ozero__class_Ozero(_488104), _488112), c_Orderings_Oord__class_Oless__eq(_488104, c_Groups_Ozero__class_Ozero(_488104), _488114), c_Groups_Oplus__class_Oplus(_488104, _488112, _488114) = c_Groups_Oone__class_Oone(_488104), -(c_Orderings_Oord__class_Oless__eq(_488104, c_Groups_Oplus__class_Oplus(_488104, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_488104), _488112), _488106), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_488104), _488114), _488110)), _488108))], (12686 ^ _356604) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (8520 ^ _356604) ^ [_657399, _657401, _657403] : [class_Rings_Olinordered__semidom(_657399), c_Orderings_Oord__class_Oless(_657399, c_Groups_Oone__class_Oone(_657399), _657401), c_Orderings_Oord__class_Oless(_657399, c_Groups_Oone__class_Oone(_657399), _657403), -(c_Orderings_Oord__class_Oless(_657399, c_Groups_Oone__class_Oone(_657399), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_657399), _657401), _657403)))], (8777 ^ _356604) ^ [_666861] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _666861, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_666861 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2469 ^ _356604) ^ [_440917, _440919, _440921] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _440917, _440919), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _440917, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _440919, _440921)))], (3302 ^ _356604) ^ [_472915, _472917, _472919] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _472915, _472917), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _472919), _472915), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _472919), _472917)))], (6130 ^ _356604) ^ [_575678, _575680, _575682] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _575678, _575682), _575680), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _575678, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _575680, _575682)))], (2685 ^ _356604) ^ [_450402, _450404, _450406, _450408] : [class_Rings_Ocomm__semiring__0(_450402), -(c_Polynomial_Osmult(_450402, _450404, c_Polynomial_Osmult(_450402, _450406, _450408)) = c_Polynomial_Osmult(_450402, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_450402), _450404), _450406), _450408))], (13044 ^ _356604) ^ [_809899, _809901] : [hBOOL(c_fequal(_809899, _809901)), -(_809899 = _809901)], (3438 ^ _356604) ^ [_477833, _477835] : [class_Rings_Omult__zero(_477833), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_477833), _477835), c_Groups_Ozero__class_Ozero(_477833)) = c_Groups_Ozero__class_Ozero(_477833))], (6624 ^ _356604) ^ [_593120, _593122] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _593120, _593122)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _593122, _593120))], (6084 ^ _356604) ^ [_573897, _573899, _573901] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _573897, _573899), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _573897, _573901)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _573899, _573901))], (12694 ^ _356604) ^ [] : [-(class_Rings_Odvd(tc_Nat_Onat))], (13056 ^ _356604) ^ [] : [hBOOL(c_fFalse)], (3811 ^ _356604) ^ [_491769, _491771, _491773] : [class_Groups_Oab__group__add(_491769), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_491769), c_Polynomial_OpCons(_491769, _491771, _491773)) = c_Polynomial_OpCons(_491769, c_Groups_Ouminus__class_Ouminus(_491769, _491771), c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_491769), _491773)))], (3738 ^ _356604) ^ [_488959, _488961, _488963, _488965] : [class_Orderings_Oorder(_488959), c_Orderings_Oord__class_Oless__eq(_488959, hAPP(_488961, 3743 ^ [_488959, _488961, _488963, _488965]), hAPP(_488961, c_Nat_OSuc(3743 ^ [_488959, _488961, _488963, _488965]))), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _488963, _488965), -(c_Orderings_Oord__class_Oless__eq(_488959, hAPP(_488961, _488963), hAPP(_488961, _488965)))], (3805 ^ _356604) ^ [_491499, _491501, _491503] : [class_Groups_Oab__group__add(_491499), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_491499), c_Polynomial_OpCons(_491499, _491501, _491503)) = c_Polynomial_OpCons(_491499, c_Groups_Ouminus__class_Ouminus(_491499, _491501), c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_491499), _491503)))], (8746 ^ _356604) ^ [_665683] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_665683), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _665683)], (2268 ^ _356604) ^ [_433633, _433635] : [class_Groups_Ocomm__monoid__add(_433633), -(c_Groups_Oplus__class_Oplus(_433633, _433635, c_Groups_Ozero__class_Ozero(_433633)) = _433635)], (4922 ^ _356604) ^ [_532079, _532081, _532083] : [class_Groups_Omonoid__mult(_532079), -(hAPP(hAPP(c_Power_Opower__class_Opower(_532079), _532081), c_Nat_OSuc(_532083)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_532079), hAPP(hAPP(c_Power_Opower__class_Opower(_532079), _532081), _532083)), _532081))], (7690 ^ _356604) ^ [_628565, _628567, _628569] : [class_Rings_Olinordered__semidom(_628565), c_Orderings_Oord__class_Oless(_628565, c_Groups_Oone__class_Oone(_628565), _628567), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _628569), -(c_Orderings_Oord__class_Oless(_628565, c_Groups_Oone__class_Oone(_628565), hAPP(hAPP(c_Power_Opower__class_Opower(_628565), _628567), _628569)))], (5326 ^ _356604) ^ [_546781, _546783, _546785, _546787] : [class_Rings_Ocomm__semiring__1(_546781), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _546783, _546785), -(c_Rings_Odvd__class_Odvd(_546781, hAPP(hAPP(c_Power_Opower__class_Opower(_546781), _546787), _546783), hAPP(hAPP(c_Power_Opower__class_Opower(_546781), _546787), _546785)))], (8931 ^ _356604) ^ [_672309, _672311] : [-(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), _672309), _672311))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _672309), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _672311)], (1701 ^ _356604) ^ [_413171] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _413171))], (6294 ^ _356604) ^ [_581252, _581254, _581256] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _581252), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _581254, _581256)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _581252), _581254), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _581252), _581256)))], (7660 ^ _356604) ^ [_627534, _627536] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _627534), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _627534, c_Nat_OSuc(_627536)), _627534))], (3606 ^ _356604) ^ [_483553, _483555, _483557, _483559] : [class_Rings_Oordered__semiring(_483553), c_Orderings_Oord__class_Oless__eq(_483553, _483555, _483557), c_Orderings_Oord__class_Oless__eq(_483553, c_Groups_Ozero__class_Ozero(_483553), _483559), -(c_Orderings_Oord__class_Oless__eq(_483553, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_483553), _483555), _483559), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_483553), _483557), _483559)))], (5070 ^ _356604) ^ [_537600, _537602, _537604] : [class_Rings_Ocomm__semiring__1(_537600), -(c_Rings_Odvd__class_Odvd(_537600, _537602, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_537600), _537602), _537604)))], (3246 ^ _356604) ^ [_470628, _470630, _470632] : [3247 ^ _356604 : [(3250 ^ _356604) ^ [] : [_470628 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3248 ^ _356604) ^ [] : [_470630 = _470632]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _470628), _470630) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _470628), _470632))], (12664 ^ _356604) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (8859 ^ _356604) ^ [_669842, _669844] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_669842), _669844), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _669842, _669844))], (718 ^ _356604) ^ [_378475, _378477] : [-(class_Rings_Ocomm__ring(_378475)), _378477 = _378475, class_Rings_Ocomm__ring(_378477)], (12840 ^ _356604) ^ [_803425] : [class_Groups_Ocomm__monoid__add(_803425), -(class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(_803425)))], (12674 ^ _356604) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (1844 ^ _356604) ^ [_418806, _418808, _418810, _418812] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_418806), c_Orderings_Oord__class_Oless__eq(_418806, c_Groups_Oplus__class_Oplus(_418806, _418808, _418810), c_Groups_Oplus__class_Oplus(_418806, _418808, _418812)), -(c_Orderings_Oord__class_Oless__eq(_418806, _418810, _418812))], (358 ^ _356604) ^ [_367855, _367857] : [-(class_Rings_Oordered__comm__semiring(_367855)), _367857 = _367855, class_Rings_Oordered__comm__semiring(_367857)], (3112 ^ _356604) ^ [_466141, _466143, _466145] : [class_Rings_Oordered__ring(_466141), -(c_Orderings_Oord__class_Oless__eq(_466141, c_Groups_Ozero__class_Ozero(_466141), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_466141), _466143), _466145))), 3117 ^ _356604 : [(3124 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_466141, _466143, c_Groups_Ozero__class_Ozero(_466141)), c_Orderings_Oord__class_Oless__eq(_466141, _466145, c_Groups_Ozero__class_Ozero(_466141))], (3118 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_466141, c_Groups_Ozero__class_Ozero(_466141), _466143), c_Orderings_Oord__class_Oless__eq(_466141, c_Groups_Ozero__class_Ozero(_466141), _466145)]]], (1908 ^ _356604) ^ [_421111, _421113, _421115, _421117] : [class_Groups_Oordered__ab__semigroup__add(_421111), c_Orderings_Oord__class_Oless__eq(_421111, _421113, _421115), -(c_Orderings_Oord__class_Oless__eq(_421111, c_Groups_Oplus__class_Oplus(_421111, _421117, _421113), c_Groups_Oplus__class_Oplus(_421111, _421117, _421115)))], (1479 ^ _356604) ^ [_404834, _404836] : [class_Groups_Ozero(_404834), -(c_Polynomial_Omonom(_404834, c_Groups_Ozero__class_Ozero(_404834), _404836) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_404834)))], (498 ^ _356604) ^ [_371985, _371987] : [-(class_Rings_Ozero__neq__one(_371985)), _371987 = _371985, class_Rings_Ozero__neq__one(_371987)], (11294 ^ _356604) ^ [_754248, _754250, _754252] : [class_Fields_Olinordered__field(_754248), c_Orderings_Oord__class_Oless(_754248, _754250, c_Groups_Ozero__class_Ozero(_754248)), c_Orderings_Oord__class_Oless(_754248, c_Groups_Ozero__class_Ozero(_754248), _754252), -(c_Orderings_Oord__class_Oless(_754248, c_Rings_Oinverse__class_Odivide(_754248, _754250, _754252), c_Groups_Ozero__class_Ozero(_754248)))], (6658 ^ _356604) ^ [_594243, _594245] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _594243, _594245), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _594245, _594243), -(_594243 = _594245)], (3294 ^ _356604) ^ [_472523] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _472523, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _472523), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _472523), _472523))))], (4534 ^ _356604) ^ [_518340] : [-(c_Nat_OSuc(_518340) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _518340, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (8190 ^ _356604) ^ [_646830, _646832, _646834] : [class_Rings_Olinordered__semiring__strict(_646830), c_Orderings_Oord__class_Oless(_646830, c_Groups_Ozero__class_Ozero(_646830), _646832), c_Orderings_Oord__class_Oless(_646830, _646834, c_Groups_Ozero__class_Ozero(_646830)), -(c_Orderings_Oord__class_Oless(_646830, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_646830), _646834), _646832), c_Groups_Ozero__class_Ozero(_646830)))], (6562 ^ _356604) ^ [_590776, _590778] : [6563 ^ _356604 : [(6566 ^ _356604) ^ [] : [_590776 = _590778], (6564 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _590776, _590778)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _590776, _590778))], (2543 ^ _356604) ^ [_443861, _443863, _443865, _443867, _443869] : [class_Rings_Ocomm__semiring__1(_443861), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_443861), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_443861), _443863), _443865)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_443861), _443867), _443869)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_443861), _443867), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_443861), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_443861), _443863), _443865)), _443869)))], (2088 ^ _356604) ^ [_427057, _427059, _427061, _427063] : [class_Groups_Oordered__comm__monoid__add(_427057), c_Orderings_Oord__class_Oless__eq(_427057, c_Groups_Ozero__class_Ozero(_427057), _427059), c_Orderings_Oord__class_Oless__eq(_427057, _427061, _427063), -(c_Orderings_Oord__class_Oless__eq(_427057, _427061, c_Groups_Oplus__class_Oplus(_427057, _427063, _427059)))], (7236 ^ _356604) ^ [_613773, _613775, _613777] : [class_Orderings_Olinorder(_613773), 7239 ^ _356604 : [(7246 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_613773, _613777, _613775), c_Orderings_Oord__class_Oless(_613773, _613775, _613777)], (7240 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_613773, _613775, _613777)), -(c_Orderings_Oord__class_Oless__eq(_613773, _613777, _613775))]]], (3358 ^ _356604) ^ [_475120, _475122] : [class_Rings_Ocomm__semiring__0(_475120), -(c_Polynomial_Opcompose(_475120, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_475120)), _475122) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_475120)))], (4478 ^ _356604) ^ [_515900] : [class_Rings_Olinordered__semidom(_515900), -(c_Orderings_Oord__class_Oless__eq(_515900, c_Groups_Ozero__class_Ozero(_515900), c_Groups_Oone__class_Oone(_515900)))], (6648 ^ _356604) ^ [_593928, _593930, _593932] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _593928, _593930), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _593930, _593932), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _593928, _593932))], (5202 ^ _356604) ^ [_542234, _542236] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _542234, _542236) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _542236, _542234))], (3698 ^ _356604) ^ [_487398, _487400, _487402] : [3699 ^ _356604 : [(3702 ^ _356604) ^ [] : [_487400 = _487402], (3700 ^ _356604) ^ [] : [_487398 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _487398), _487400) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _487398), _487402))], (8838 ^ _356604) ^ [_669011, _669013] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _669011, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _669013, _669011))))], (7776 ^ _356604) ^ [_631331, _631333, _631335, _631337, _631339] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _631331, _631333), 7779 ^ _356604 : [(7786 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _631337, 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, _631333, _631331)), _631335), _631339)), -(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), _631331), _631335), _631337), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _631333), _631335), _631339)))], (7780 ^ _356604) ^ [] : [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), _631331), _631335), _631337), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _631333), _631335), _631339)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _631337, 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, _631333, _631331)), _631335), _631339)))]]], (8114 ^ _356604) ^ [_644363, _644365, _644367] : [class_Rings_Olinordered__ring__strict(_644363), c_Orderings_Oord__class_Oless(_644363, _644365, c_Groups_Ozero__class_Ozero(_644363)), c_Orderings_Oord__class_Oless(_644363, _644367, c_Groups_Ozero__class_Ozero(_644363)), -(c_Orderings_Oord__class_Oless(_644363, c_Groups_Ozero__class_Ozero(_644363), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_644363), _644365), _644367)))], (1154 ^ _356604) ^ [_394320, _394322] : [_394322 = _394320, -(c_Groups_Ozero__class_Ozero(_394322) = c_Groups_Ozero__class_Ozero(_394320))], (1034 ^ _356604) ^ [_390012, _390014, _390016, _390018] : [-(c_Nat__Transfer_Otsub(_390018, _390014) = c_Nat__Transfer_Otsub(_390016, _390012)), _390018 = _390016, _390014 = _390012], (1683 ^ _356604) ^ [_412494, _412496, _412498] : [class_Rings_Ocomm__semiring__0(_412494), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_412494), _412496, c_Polynomial_Osmult(_412494, _412498, c_Polynomial_Osynthetic__div(_412494, _412496, _412498))) = c_Polynomial_OpCons(_412494, hAPP(c_Polynomial_Opoly(_412494, _412496), _412498), c_Polynomial_Osynthetic__div(_412494, _412496, _412498)))], (338 ^ _356604) ^ [_367265, _367267] : [-(class_Rings_Olinordered__ring__strict(_367265)), _367267 = _367265, class_Rings_Olinordered__ring__strict(_367267)], (11072 ^ _356604) ^ [_746798, _746800, _746802, _746804] : [class_Fields_Ofield(_746798), -(_746800 = c_Groups_Ozero__class_Ozero(_746798)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _746802, _746804), -(hAPP(hAPP(c_Power_Opower__class_Opower(_746798), _746800), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _746804, _746802)) = c_Rings_Oinverse__class_Odivide(_746798, hAPP(hAPP(c_Power_Opower__class_Opower(_746798), _746800), _746804), hAPP(hAPP(c_Power_Opower__class_Opower(_746798), _746800), _746802)))], (11850 ^ _356604) ^ [_772254, _772256, _772258, _772260] : [class_Fields_Olinordered__field(_772254), c_Orderings_Oord__class_Oless(_772254, _772256, _772258), c_Orderings_Oord__class_Oless(_772254, c_Groups_Ozero__class_Ozero(_772254), _772260), c_Orderings_Oord__class_Oless(_772254, c_Groups_Ozero__class_Ozero(_772254), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_772254), _772258), _772256)), -(c_Orderings_Oord__class_Oless(_772254, c_Rings_Oinverse__class_Odivide(_772254, _772260, _772258), c_Rings_Oinverse__class_Odivide(_772254, _772260, _772256)))], (4554 ^ _356604) ^ [_519079, _519081, _519083, _519085] : [class_Groups_Ozero(_519079), 4557 ^ _356604 : [(4564 ^ _356604) ^ [] : [-(_519081 = _519083), -(hAPP(c_Polynomial_Ocoeff(_519079, c_Polynomial_Omonom(_519079, _519085, _519081)), _519083) = c_Groups_Ozero__class_Ozero(_519079))], (4558 ^ _356604) ^ [] : [_519081 = _519083, -(hAPP(c_Polynomial_Ocoeff(_519079, c_Polynomial_Omonom(_519079, _519085, _519081)), _519083) = _519085)]]], (9065 ^ _356604) ^ [_677047, _677049] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _677047, _677049), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _677047, c_Groups_Oone__class_Oone(tc_Int_Oint)), _677049))], (10249 ^ _356604) ^ [_717753, _717755] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _717753, _717755), 10254 ^ _356604 : [(10257 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _717755, _717753)], (10255 ^ _356604) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _717753, _717755))]], -(_717753 = _717755)], (12864 ^ _356604) ^ [_804185] : [class_Rings_Olinordered__idom(_804185), -(class_Rings_Olinordered__ring(tc_Polynomial_Opoly(_804185)))], (4686 ^ _356604) ^ [_523514, _523516, _523518] : [class_Rings_Oidom(_523514), 4689 ^ _356604 : [(4690 ^ _356604) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_523514), _523516), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(_523514), _523518), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_523516 = _523518), -(_523516 = c_Groups_Ouminus__class_Ouminus(_523514, _523518))], (4700 ^ _356604) ^ [] : [4701 ^ _356604 : [(4704 ^ _356604) ^ [] : [_523516 = c_Groups_Ouminus__class_Ouminus(_523514, _523518)], (4702 ^ _356604) ^ [] : [_523516 = _523518]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_523514), _523516), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(_523514), _523518), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))]]], (8176 ^ _356604) ^ [_646382, _646384, _646386] : [class_Rings_Olinordered__semiring__strict(_646382), c_Orderings_Oord__class_Oless(_646382, c_Groups_Ozero__class_Ozero(_646382), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_646382), _646384), _646386)), c_Orderings_Oord__class_Oless(_646382, c_Groups_Ozero__class_Ozero(_646382), _646384), -(c_Orderings_Oord__class_Oless(_646382, c_Groups_Ozero__class_Ozero(_646382), _646386))], (8941 ^ _356604) ^ [_672671, _672673, _672675] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _672671), _672673), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _672671), _672675)), 8944 ^ _356604 : [(8947 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _672673, _672675))], (8945 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _672671))]]], (12536 ^ _356604) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (904 ^ _356604) ^ [_385274, _385276, _385278, _385280, _385282, _385284] : [-(c_Power_Opower_Opower(_385284, _385280, _385276) = c_Power_Opower_Opower(_385282, _385278, _385274)), _385284 = _385282, _385280 = _385278, _385276 = _385274], (3132 ^ _356604) ^ [_466798, _466800, _466802, _466804, _466806] : [class_Rings_Oordered__semiring(_466798), c_Orderings_Oord__class_Oless__eq(_466798, _466800, _466802), c_Orderings_Oord__class_Oless__eq(_466798, _466804, _466806), c_Orderings_Oord__class_Oless__eq(_466798, c_Groups_Ozero__class_Ozero(_466798), _466802), c_Orderings_Oord__class_Oless__eq(_466798, c_Groups_Ozero__class_Ozero(_466798), _466804), -(c_Orderings_Oord__class_Oless__eq(_466798, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_466798), _466800), _466804), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_466798), _466802), _466806)))], (7738 ^ _356604) ^ [_630089] : [class_Fields_Ofield(_630089), -(c_Polynomial_Opoly__gcd(_630089, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_630089)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_630089))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_630089)))], (12702 ^ _356604) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (6918 ^ _356604) ^ [_603550, _603552] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _603550), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _603552), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _603552, _603550), _603552))], (6904 ^ _356604) ^ [_603007, _603009] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _603007, _603009), c_Nat_OSuc(_603007)))], (4672 ^ _356604) ^ [_523066, _523068, _523070] : [class_Rings_Olinordered__semidom(_523066), c_Orderings_Oord__class_Oless__eq(_523066, c_Groups_Ozero__class_Ozero(_523066), _523068), c_Orderings_Oord__class_Oless__eq(_523066, _523068, c_Groups_Oone__class_Oone(_523066)), -(c_Orderings_Oord__class_Oless__eq(_523066, hAPP(hAPP(c_Power_Opower__class_Opower(_523066), _523068), c_Nat_OSuc(_523070)), _523068))], (7596 ^ _356604) ^ [_625453, _625455, _625457, _625459, _625461] : [class_Groups_Oordered__ab__group__add(_625453), c_Groups_Ominus__class_Ominus(_625453, _625455, _625457) = c_Groups_Ominus__class_Ominus(_625453, _625459, _625461), 7603 ^ _356604 : [(7610 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_625453, _625459, _625461), -(c_Orderings_Oord__class_Oless__eq(_625453, _625455, _625457))], (7604 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_625453, _625455, _625457), -(c_Orderings_Oord__class_Oless__eq(_625453, _625459, _625461))]]], (3787 ^ _356604) ^ [_490793, _490795] : [class_Rings_Ocomm__ring__1(_490793), -(c_Groups_Ouminus__class_Ouminus(_490793, _490795) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_490793), c_Groups_Ouminus__class_Ouminus(_490793, c_Groups_Oone__class_Oone(_490793))), _490795))], (9071 ^ _356604) ^ [_677271, _677273] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _677271, _677273), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _677271, c_Groups_Oone__class_Oone(tc_Int_Oint)), _677273))], (4978 ^ _356604) ^ [_534188] : [class_Power_Opower(_534188), -(c_Power_Opower__class_Opower(_534188) = c_Power_Opower_Opower(_534188, c_Groups_Oone__class_Oone(_534188), c_Groups_Otimes__class_Otimes(_534188)))], (8923 ^ _356604) ^ [_672054, _672056] : [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), _672054), _672056)), 8926 ^ _356604 : [(8929 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _672056))], (8927 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _672054))]]], (2691 ^ _356604) ^ [_450718, _450720, _450722, _450724, _450726, _450728] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_450718), -(_450720 = c_Groups_Ozero__class_Ozero(_450718)), c_Groups_Oplus__class_Oplus(_450718, _450722, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_450718), _450720), _450726)) = c_Groups_Oplus__class_Oplus(_450718, _450724, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_450718), _450720), _450728)), _450722 = _450724, -(_450726 = _450728)], (1709 ^ _356604) ^ [_413585, _413587] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _413585, _413587), -(_413587 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _413585, 1712 ^ [_413585, _413587]))], (4760 ^ _356604) ^ [_526254, _526256, _526258] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _526254), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _526256, _526258)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _526254), _526256), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _526254), _526258)))], (1505 ^ _356604) ^ [_405930] : [class_Groups_Ozero(_405930), -(c_Polynomial_Odegree(_405930, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_405930))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (860 ^ _356604) ^ [_383609, _383611] : [_383611 = _383609, -(c_Nat_Onat_Onat__size(_383611) = c_Nat_Onat_Onat__size(_383609))], (218 ^ _356604) ^ [_363725, _363727] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_363725)), _363727 = _363725, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_363727)], (12170 ^ _356604) ^ [_783316] : [class_Int_Oring__char__0(_783316), -(class_Groups_Ocomm__monoid__add(_783316))], (2226 ^ _356604) ^ [_432158, _432160] : [2227 ^ _356604 : [(2230 ^ _356604) ^ [] : [_432158 = c_Nat_OSuc(_432160)], (2228 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _432158, _432160)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _432158, c_Nat_OSuc(_432160)))], (4326 ^ _356604) ^ [_510483] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _510483) = _510483)], (10495 ^ _356604) ^ [_725947, _725949, _725951] : [-(_725947 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 10498 ^ _356604 : [(10505 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _725949, _725951), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _725949), _725947), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _725951), _725947)))], (10499 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _725949), _725947), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _725951), _725947)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _725949, _725951))]]], (12924 ^ _356604) ^ [_806085] : [class_Rings_Ocomm__semiring__1(_806085), -(class_Groups_Omonoid__mult(tc_Polynomial_Opoly(_806085)))], (3324 ^ _356604) ^ [_473833, _473835] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _473833), _473835) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 3327 ^ _356604 : [(3330 ^ _356604) ^ [] : [-(_473835 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (3328 ^ _356604) ^ [] : [-(_473833 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (6224 ^ _356604) ^ [_578816, _578818, _578820] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _578816, _578818), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _578820, _578818), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _578820, _578816)))], (12538 ^ _356604) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (1776 ^ _356604) ^ [_416248, _416250, _416252] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _416248, _416250), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _416248, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _416250, _416252)))], (11086 ^ _356604) ^ [_747285, _747287] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _747285), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _747287), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Nat__Transfer_Otsub(_747285, _747287)))], (12900 ^ _356604) ^ [_805325] : [class_Rings_Ocomm__semiring__1(_805325), -(class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(_805325)))], (9107 ^ _356604) ^ [_678501, _678503] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _678501), 9110 ^ _356604 : [(9119 ^ _356604) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _678501), _678503) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _678501 = c_Groups_Oone__class_Oone(tc_Int_Oint), _678503 = c_Groups_Oone__class_Oone(tc_Int_Oint)], (9111 ^ _356604) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _678501), _678503) = c_Groups_Oone__class_Oone(tc_Int_Oint), 9114 ^ _356604 : [(9117 ^ _356604) ^ [] : [-(_678503 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (9115 ^ _356604) ^ [] : [-(_678501 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]]]], (3080 ^ _356604) ^ [_464878, _464880, _464882, _464884] : [class_Rings_Ocomm__semiring__0(_464878), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_464878)), c_Polynomial_OpCons(_464878, _464880, _464882)), _464884) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_464878), c_Polynomial_Osmult(_464878, _464880, _464884), c_Polynomial_OpCons(_464878, c_Groups_Ozero__class_Ozero(_464878), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_464878)), _464882), _464884))))], (8204 ^ _356604) ^ [_647278, _647280, _647282] : [class_Rings_Olinordered__semiring__strict(_647278), c_Orderings_Oord__class_Oless(_647278, c_Groups_Ozero__class_Ozero(_647278), _647280), c_Orderings_Oord__class_Oless(_647278, _647282, c_Groups_Ozero__class_Ozero(_647278)), -(c_Orderings_Oord__class_Oless(_647278, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_647278), _647280), _647282), c_Groups_Ozero__class_Ozero(_647278)))], (12594 ^ _356604) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (4822 ^ _356604) ^ [_528824, _528826, _528828, _528830] : [class_Rings_Olinordered__semidom(_528824), c_Orderings_Oord__class_Oless__eq(_528824, _528826, _528828), c_Orderings_Oord__class_Oless__eq(_528824, c_Groups_Ozero__class_Ozero(_528824), _528826), -(c_Orderings_Oord__class_Oless__eq(_528824, hAPP(hAPP(c_Power_Opower__class_Opower(_528824), _528826), _528830), hAPP(hAPP(c_Power_Opower__class_Opower(_528824), _528828), _528830)))], (248 ^ _356604) ^ [_364610, _364612] : [-(class_Rings_Olinordered__comm__semiring__strict(_364610)), _364612 = _364610, class_Rings_Olinordered__comm__semiring__strict(_364612)], (4080 ^ _356604) ^ [_500949, _500951, _500953] : [class_Groups_Oordered__ab__group__add(_500949), 4083 ^ _356604 : [(4090 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_500949, c_Groups_Ouminus__class_Ouminus(_500949, _500953), _500951), -(c_Orderings_Oord__class_Oless__eq(_500949, c_Groups_Ouminus__class_Ouminus(_500949, _500951), _500953))], (4084 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_500949, c_Groups_Ouminus__class_Ouminus(_500949, _500951), _500953), -(c_Orderings_Oord__class_Oless__eq(_500949, c_Groups_Ouminus__class_Ouminus(_500949, _500953), _500951))]]], (5744 ^ _356604) ^ [_561603, _561605] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _561603, _561605), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _561603, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _561605, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (9879 ^ _356604) ^ [_705909, _705911] : [_705909 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _705909, _705911) = _705911)], (9235 ^ _356604) ^ [_683237, _683239, _683241, _683243] : [class_Rings_Olinordered__semiring__strict(_683237), c_Orderings_Oord__class_Oless__eq(_683237, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_683237), _683239), _683241), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_683237), _683239), _683243)), c_Orderings_Oord__class_Oless(_683237, c_Groups_Ozero__class_Ozero(_683237), _683239), -(c_Orderings_Oord__class_Oless__eq(_683237, _683241, _683243))], (8847 ^ _356604) ^ [_669395, _669397] : [8848 ^ _356604 : [(8849 ^ _356604) ^ [_669472] : [_669397 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _669395, _669472))]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _669395, _669397))], (8750 ^ _356604) ^ [_665932, _665934, _665936, _665938] : [class_Groups_Oab__group__add(_665932), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_665932, _665934), _665936), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_665932, _665938), _665936), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_665932, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_665932), _665934, _665938)), _665936))], (3276 ^ _356604) ^ [_471745, _471747, _471749] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_471745)), _471747) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_471745)), _471749), -(_471747 = _471749)], (1082 ^ _356604) ^ [_391734, _391736] : [_391736 = _391734, -(c_Groups_Oone__class_Oone(_391736) = c_Groups_Oone__class_Oone(_391734))], (6698 ^ _356604) ^ [_595522, _595524, _595526] : [class_Rings_Olinordered__idom(_595522), -(_595524 = _595526), -(c_Orderings_Oord__class_Oless(_595522, _595524, _595526)), -(c_Orderings_Oord__class_Oless(_595522, _595526, _595524))], (7866 ^ _356604) ^ [_634665, _634667] : [class_Fields_Ofield(_634665), -(c_Polynomial_Opoly__gcd(_634665, _634667, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_634665))) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_634665)))], (9263 ^ _356604) ^ [_684205, _684207, _684209, _684211] : [class_Rings_Olinordered__semiring__strict(_684205), c_Orderings_Oord__class_Oless(_684205, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_684205), _684207), _684209), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_684205), _684207), _684211)), c_Orderings_Oord__class_Oless__eq(_684205, c_Groups_Ozero__class_Ozero(_684205), _684207), -(c_Orderings_Oord__class_Oless(_684205, _684209, _684211))], (4064 ^ _356604) ^ [_500437, _500439, _500441] : [class_Groups_Oordered__ab__group__add(_500437), 4067 ^ _356604 : [(4074 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_500437, _500441, _500439), -(c_Orderings_Oord__class_Oless__eq(_500437, c_Groups_Ouminus__class_Ouminus(_500437, _500439), c_Groups_Ouminus__class_Ouminus(_500437, _500441)))], (4068 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_500437, c_Groups_Ouminus__class_Ouminus(_500437, _500439), c_Groups_Ouminus__class_Ouminus(_500437, _500441)), -(c_Orderings_Oord__class_Oless__eq(_500437, _500441, _500439))]]], (2797 ^ _356604) ^ [_454948, _454950, _454952] : [class_Orderings_Olinorder(_454948), -(c_Orderings_Oord__class_Oless__eq(_454948, _454950, _454952)), -(c_Orderings_Oord__class_Oless__eq(_454948, _454952, _454950))], (9101 ^ _356604) ^ [_678275] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _678275, 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), _678275), _678275), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (9727 ^ _356604) ^ [_700710, _700712, _700714] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _700710), _700712), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _700714), _700712)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _700712), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _700710, _700714))], (11588 ^ _356604) ^ [_763766, _763768, _763770, _763772, _763774] : [class_Fields_Olinordered__field(_763766), c_Orderings_Oord__class_Oless__eq(_763766, c_Groups_Ozero__class_Ozero(_763766), _763768), c_Orderings_Oord__class_Oless__eq(_763766, _763768, _763770), c_Orderings_Oord__class_Oless(_763766, c_Groups_Ozero__class_Ozero(_763766), _763772), c_Orderings_Oord__class_Oless__eq(_763766, _763772, _763774), -(c_Orderings_Oord__class_Oless__eq(_763766, c_Rings_Oinverse__class_Odivide(_763766, _763768, _763774), c_Rings_Oinverse__class_Odivide(_763766, _763770, _763772)))], (1581 ^ _356604) ^ [_408711, _408713, _408715, _408717] : [class_Groups_Ozero(_408711), hAPP(hAPP(hAPP(_408713, c_Groups_Ozero__class_Ozero(_408711)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_408711))), _408715) = _408715, -(c_Polynomial_Opoly__rec(_408717, _408711, _408715, _408713, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_408711))) = _408715)], (558 ^ _356604) ^ [_373755, _373757] : [-(class_Groups_Omonoid__add(_373755)), _373757 = _373755, class_Groups_Omonoid__add(_373757)], (9885 ^ _356604) ^ [_706079, _706081] : [-(_706079 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _706079, _706081) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _706079, c_Groups_Oone__class_Oone(tc_Nat_Onat)), _706081)))], (6490 ^ _356604) ^ [_588214, _588216, _588218] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _588214, _588216), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _588214, _588218), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _588216, _588218)))], (12176 ^ _356604) ^ [_783502] : [class_Int_Oring__char__0(_783502), -(class_Groups_Oab__group__add(_783502))], (1177 ^ _356604) ^ [_395233, _395235] : [class_Groups_Ozero(_395233), 1180 ^ _356604 : [(1187 ^ _356604) ^ [] : [_395235 = c_Groups_Ozero__class_Ozero(_395233), -(c_Groups_Ozero__class_Ozero(_395233) = _395235)], (1181 ^ _356604) ^ [] : [c_Groups_Ozero__class_Ozero(_395233) = _395235, -(_395235 = c_Groups_Ozero__class_Ozero(_395233))]]], (5146 ^ _356604) ^ [_540437, _540439, _540441, _540443] : [class_Rings_Ocomm__semiring__1(_540437), c_Rings_Odvd__class_Odvd(_540437, _540439, _540441), c_Rings_Odvd__class_Odvd(_540437, _540439, _540443), -(c_Rings_Odvd__class_Odvd(_540437, _540439, c_Groups_Oplus__class_Oplus(_540437, _540441, _540443)))], (2128 ^ _356604) ^ [_428585, _428587, _428589, _428591] : [class_Groups_Ocomm__monoid__add(_428585), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_428585, _428587), _428589), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_428585, _428591), _428589), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_428585, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_428585), _428587, _428591)), _428589))], (12810 ^ _356604) ^ [_802475] : [class_Groups_Ocancel__comm__monoid__add(_802475), -(class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(_802475)))], (4536 ^ _356604) ^ [_518424] : [-(c_Nat_OSuc(_518424) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _518424))], (1770 ^ _356604) ^ [_416022, _416024] : [_416022 = _416024, -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _416022, _416024))], (3978 ^ _356604) ^ [_497764, _497766] : [class_Groups_Olinordered__ab__group__add(_497764), 3981 ^ _356604 : [(3988 ^ _356604) ^ [] : [_497766 = c_Groups_Ozero__class_Ozero(_497764), -(c_Groups_Ouminus__class_Ouminus(_497764, _497766) = _497766)], (3982 ^ _356604) ^ [] : [c_Groups_Ouminus__class_Ouminus(_497764, _497766) = _497766, -(_497766 = c_Groups_Ozero__class_Ozero(_497764))]]], (2873 ^ _356604) ^ [_457413, _457415, _457417, _457419] : [class_Orderings_Oorder(_457413), c_Orderings_Oord__class_Oless__eq(_457413, _457415, _457417), _457415 = _457419, -(c_Orderings_Oord__class_Oless__eq(_457413, _457419, _457417))], (3885 ^ _356604) ^ [_494677, _494679, _494681] : [class_Groups_Ozero(_494677), 3888 ^ _356604 : [(3895 ^ _356604) ^ [] : [_494679 = _494681, -(c_Polynomial_Ocoeff(_494677, _494679) = c_Polynomial_Ocoeff(_494677, _494681))], (3889 ^ _356604) ^ [] : [c_Polynomial_Ocoeff(_494677, _494679) = c_Polynomial_Ocoeff(_494677, _494681), -(_494679 = _494681)]]], (3753 ^ _356604) ^ [_489510, _489512, _489514] : [class_Rings_Ocomm__ring__1(_489510), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_489510), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_489510)), c_Polynomial_OpCons(_489510, c_Groups_Ouminus__class_Ouminus(_489510, _489512), c_Polynomial_OpCons(_489510, c_Groups_Oone__class_Oone(_489510), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_489510))))), c_Polynomial_Osynthetic__div(_489510, _489514, _489512)), c_Polynomial_OpCons(_489510, hAPP(c_Polynomial_Opoly(_489510, _489514), _489512), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_489510)))) = _489514)], (12404 ^ _356604) ^ [_790570] : [class_Rings_Oidom(_790570), -(class_Rings_Osemiring(_790570))], (9659 ^ _356604) ^ [_698088, _698090, _698092, _698094, _698096] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _698088, _698090), 9662 ^ _356604 : [(9669 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _698094, 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, _698090, _698088)), _698092), _698096)), -(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), _698088), _698092), _698094), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _698090), _698092), _698096)))], (9663 ^ _356604) ^ [] : [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), _698088), _698092), _698094), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _698090), _698092), _698096)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _698094, 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, _698090, _698088)), _698092), _698096)))]]], (976 ^ _356604) ^ [_387915, _387917, _387919, _387921, _387923, _387925] : [-(c_Polynomial_Opoly__gcd(_387925, _387921, _387917) = c_Polynomial_Opoly__gcd(_387923, _387919, _387915)), _387925 = _387923, _387921 = _387919, _387917 = _387915], (10880 ^ _356604) ^ [_739726, _739728, _739730, _739732] : [class_Rings_Odivision__ring(_739726), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_739726), _739728), c_Rings_Oinverse__class_Odivide(_739726, _739730, _739732)) = c_Rings_Oinverse__class_Odivide(_739726, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_739726), _739728), _739730), _739732))], (2631 ^ _356604) ^ [_448023, _448025, _448027, _448029] : [class_Rings_Ocomm__semiring__1(_448023), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_448023), c_Groups_Oplus__class_Oplus(_448023, _448025, _448027)), _448029) = c_Groups_Oplus__class_Oplus(_448023, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_448023), _448025), _448029), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_448023), _448027), _448029)))], (8578 ^ _356604) ^ [_659508] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _659508, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_659508 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (3264 ^ _356604) ^ [_471239, _471241] : [3265 ^ _356604 : [(3268 ^ _356604) ^ [] : [_471241 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3266 ^ _356604) ^ [] : [_471239 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _471239), _471241) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2715 ^ _356604) ^ [_451656, _451658, _451660, _451662] : [class_Rings_Ocomm__semiring__0(_451656), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_451656)), _451658), c_Polynomial_Osmult(_451656, _451660, _451662)) = c_Polynomial_Osmult(_451656, _451660, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_451656)), _451658), _451662)))], (5198 ^ _356604) ^ [_542056] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _542056) = _542056)], (4194 ^ _356604) ^ [_505436, _505438, _505440] : [class_Groups_Ogroup__add(_505436), -(c_Groups_Oplus__class_Oplus(_505436, _505438, c_Groups_Oplus__class_Oplus(_505436, c_Groups_Ouminus__class_Ouminus(_505436, _505438), _505440)) = _505440)], (8142 ^ _356604) ^ [_645273, _645275, _645277, _645279] : [class_Rings_Olinordered__ring__strict(_645273), c_Orderings_Oord__class_Oless(_645273, _645275, c_Groups_Ozero__class_Ozero(_645273)), 8149 ^ _356604 : [(8156 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_645273, _645279, _645277), -(c_Orderings_Oord__class_Oless(_645273, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_645273), _645275), _645277), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_645273), _645275), _645279)))], (8150 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_645273, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_645273), _645275), _645277), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_645273), _645275), _645279)), -(c_Orderings_Oord__class_Oless(_645273, _645279, _645277))]]], (11266 ^ _356604) ^ [_753354, _753356, _753358, _753360] : [class_Fields_Olinordered__field(_753354), c_Orderings_Oord__class_Oless(_753354, _753356, _753358), c_Orderings_Oord__class_Oless(_753354, c_Groups_Ozero__class_Ozero(_753354), _753360), -(c_Orderings_Oord__class_Oless(_753354, c_Rings_Oinverse__class_Odivide(_753354, _753356, _753360), c_Rings_Oinverse__class_Odivide(_753354, _753358, _753360)))], (5700 ^ _356604) ^ [_560098, _560100, _560102, _560104] : [class_Rings_Olinordered__semidom(_560098), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _560100, _560102), c_Orderings_Oord__class_Oless(_560098, c_Groups_Oone__class_Oone(_560098), _560104), -(c_Orderings_Oord__class_Oless(_560098, hAPP(hAPP(c_Power_Opower__class_Opower(_560098), _560104), _560100), hAPP(hAPP(c_Power_Opower__class_Opower(_560098), _560104), _560102)))], (7818 ^ _356604) ^ [_632990, _632992, _632994, _632996] : [class_Fields_Ofield(_632990), 7821 ^ _356604 : [(7830 ^ _356604) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_632990), _632992, c_Polynomial_Opoly__gcd(_632990, _632994, _632996))), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_632990), _632992, _632994), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_632990), _632992, _632996)], (7822 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_632990), _632992, c_Polynomial_Opoly__gcd(_632990, _632994, _632996)), 7825 ^ _356604 : [(7828 ^ _356604) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_632990), _632992, _632996))], (7826 ^ _356604) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_632990), _632992, _632994))]]]]], (1734 ^ _356604) ^ [_414674, _414676, _414678] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _414674, _414676) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _414674, _414678), -(_414676 = _414678)], (8818 ^ _356604) ^ [_668359, _668361] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _668359, _668361)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _668359)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _668361))], (4472 ^ _356604) ^ [_515701] : [class_Rings_Olinordered__semidom(_515701), c_Orderings_Oord__class_Oless__eq(_515701, c_Groups_Oone__class_Oone(_515701), c_Groups_Ozero__class_Ozero(_515701))], (10361 ^ _356604) ^ [_721268, _721270, _721272] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _721268, _721270), _721272) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _721268, _721272), _721270))], (12798 ^ _356604) ^ [_802095] : [class_Rings_Olinordered__idom(_802095), -(class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(_802095)))], (9941 ^ _356604) ^ [_708101, _708103, _708105] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _708101), _708101 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _708103, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _708101), _708105)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _708103), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _708105, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (11810 ^ _356604) ^ [_770928, _770930, _770932, _770934] : [class_Fields_Olinordered__field(_770928), c_Orderings_Oord__class_Oless(_770928, _770930, c_Groups_Ozero__class_Ozero(_770928)), 11817 ^ _356604 : [(11824 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_770928, _770934, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_770928), _770932), _770930)), -(c_Orderings_Oord__class_Oless(_770928, _770932, c_Rings_Oinverse__class_Odivide(_770928, _770934, _770930)))], (11818 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_770928, _770932, c_Rings_Oinverse__class_Odivide(_770928, _770934, _770930)), -(c_Orderings_Oord__class_Oless(_770928, _770934, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_770928), _770932), _770930)))]]], (11060 ^ _356604) ^ [_746222, _746224, _746226, _746228] : [class_RealVector_Oreal__normed__field(_746222), -(c_Rings_Oinverse__class_Odivide(_746222, c_Groups_Ominus__class_Ominus(_746222, _746224, _746226), _746228) = c_Groups_Ominus__class_Ominus(_746222, c_Rings_Oinverse__class_Odivide(_746222, _746224, _746228), c_Rings_Oinverse__class_Odivide(_746222, _746226, _746228)))], (11566 ^ _356604) ^ [_763060, _763062, _763064, _763066, _763068] : [class_Fields_Olinordered__field(_763060), c_Orderings_Oord__class_Oless__eq(_763060, c_Groups_Ozero__class_Ozero(_763060), _763062), c_Orderings_Oord__class_Oless(_763060, _763062, _763064), c_Orderings_Oord__class_Oless(_763060, c_Groups_Ozero__class_Ozero(_763060), _763066), c_Orderings_Oord__class_Oless__eq(_763060, _763066, _763068), -(c_Orderings_Oord__class_Oless(_763060, c_Rings_Oinverse__class_Odivide(_763060, _763062, _763068), c_Rings_Oinverse__class_Odivide(_763060, _763064, _763066)))], (2761 ^ _356604) ^ [_453614, _453616, _453618, _453620] : [class_Rings_Ocomm__semiring__0(_453614), -(c_Polynomial_Osmult(_453614, _453616, c_Polynomial_Omonom(_453614, _453618, _453620)) = c_Polynomial_Omonom(_453614, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_453614), _453616), _453618), _453620))], (12642 ^ _356604) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (9985 ^ _356604) ^ [_709514] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _709514, _709514))], (7398 ^ _356604) ^ [_618738, _618740, _618742] : [class_Orderings_Oorder(_618738), -(_618740 = _618742), c_Orderings_Oord__class_Oless__eq(_618738, _618742, _618740), -(c_Orderings_Oord__class_Oless(_618738, _618742, _618740))], (11006 ^ _356604) ^ [_744433, _744435, _744437, _744439] : [class_Rings_Odivision__ring(_744433), -(_744435 = c_Groups_Ozero__class_Ozero(_744433)), _744437 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_744433), _744439), _744435), -(c_Rings_Oinverse__class_Odivide(_744433, _744437, _744435) = _744439)], (9053 ^ _356604) ^ [_676620, _676622] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _676620, _676622), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _676620, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _676622, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (10992 ^ _356604) ^ [_743960, _743962, _743964, _743966] : [class_Rings_Odivision__ring(_743960), -(_743962 = c_Groups_Ozero__class_Ozero(_743960)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_743960), _743964), _743962) = _743966, -(_743964 = c_Rings_Oinverse__class_Odivide(_743960, _743966, _743962))], (12584 ^ _356604) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (3765 ^ _356604) ^ [_490126, _490128] : [class_Rings_Oring__1__no__zero__divisors(_490126), 3768 ^ _356604 : [(3769 ^ _356604) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_490126), _490128), _490128) = c_Groups_Oone__class_Oone(_490126), -(_490128 = c_Groups_Oone__class_Oone(_490126)), -(_490128 = c_Groups_Ouminus__class_Ouminus(_490126, c_Groups_Oone__class_Oone(_490126)))], (3779 ^ _356604) ^ [] : [3780 ^ _356604 : [(3783 ^ _356604) ^ [] : [_490128 = c_Groups_Ouminus__class_Ouminus(_490126, c_Groups_Oone__class_Oone(_490126))], (3781 ^ _356604) ^ [] : [_490128 = c_Groups_Oone__class_Oone(_490126)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_490126), _490128), _490128) = c_Groups_Oone__class_Oone(_490126))]]], (318 ^ _356604) ^ [_366675, _366677] : [-(class_Rings_Oring__1__no__zero__divisors(_366675)), _366677 = _366675, class_Rings_Oring__1__no__zero__divisors(_366677)], (7950 ^ _356604) ^ [_638125, _638127, _638129, _638131, _638133, _638135] : [class_Rings_Oring(_638125), 7953 ^ _356604 : [(7960 ^ _356604) ^ [] : [c_Groups_Oplus__class_Oplus(_638125, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_638125), c_Groups_Ominus__class_Ominus(_638125, _638127, _638133)), _638129), _638131) = _638135, -(c_Groups_Oplus__class_Oplus(_638125, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_638125), _638127), _638129), _638131) = c_Groups_Oplus__class_Oplus(_638125, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_638125), _638133), _638129), _638135))], (7954 ^ _356604) ^ [] : [c_Groups_Oplus__class_Oplus(_638125, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_638125), _638127), _638129), _638131) = c_Groups_Oplus__class_Oplus(_638125, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_638125), _638133), _638129), _638135), -(c_Groups_Oplus__class_Oplus(_638125, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_638125), c_Groups_Ominus__class_Ominus(_638125, _638127, _638133)), _638129), _638131) = _638135)]]], (4940 ^ _356604) ^ [_532893, _532895] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _532893), -(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), _532893), _532895)))], (142 ^ _356604) ^ [_361327, _361329] : [-(class_Fields_Ofield(_361327)), _361329 = _361327, class_Fields_Ofield(_361329)], (7716 ^ _356604) ^ [_629417, _629419, _629421] : [class_Fields_Ofield(_629417), 7719 ^ _356604 : [(7728 ^ _356604) ^ [] : [-(c_Polynomial_Opoly__gcd(_629417, _629419, _629421) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_629417))), _629419 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_629417)), _629421 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_629417))], (7720 ^ _356604) ^ [] : [c_Polynomial_Opoly__gcd(_629417, _629419, _629421) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_629417)), 7723 ^ _356604 : [(7726 ^ _356604) ^ [] : [-(_629421 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_629417)))], (7724 ^ _356604) ^ [] : [-(_629419 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_629417)))]]]]], (12362 ^ _356604) ^ [_789268] : [class_Rings_Oidom(_789268), -(class_Groups_Omonoid__mult(_789268))], (4288 ^ _356604) ^ [_509275, _509277] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _509275), _509277) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 4291 ^ _356604 : [(4294 ^ _356604) ^ [] : [-(_509277 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (4292 ^ _356604) ^ [] : [-(_509275 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (8320 ^ _356604) ^ [_651041, _651043] : [class_Rings_Olinordered__ring(_651041), c_Orderings_Oord__class_Oless(_651041, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_651041), _651043), _651043), c_Groups_Ozero__class_Ozero(_651041))], (5204 ^ _356604) ^ [_542350, _542352, _542354] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _542350, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _542352, _542354)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _542352, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _542350, _542354)))], (5851 ^ _356604) ^ [_565705, _565707, _565709] : [hBOOL(hAPP(_565705, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _565707, _565709))), 5854 ^ _356604 : [(5861 ^ _356604) ^ [_566043] : [_565707 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _565709, _566043), -(hBOOL(hAPP(_565705, _566043)))], (5855 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _565707, _565709), -(hBOOL(hAPP(_565705, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (6586 ^ _356604) ^ [_591586, _591588] : [6587 ^ _356604 : [(6590 ^ _356604) ^ [] : [_591586 = _591588], (6588 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _591586, _591588)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _591586, _591588))], (2463 ^ _356604) ^ [_440659, _440661] : [2464 ^ _356604 : [(2465 ^ _356604) ^ [_440734] : [_440661 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _440659, _440734)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _440659, _440661))], (12726 ^ _356604) ^ [_799815] : [class_Rings_Olinordered__idom(_799815), -(class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(_799815)))], (10295 ^ _356604) ^ [_719225, _719227] : [10302 ^ _356604 : [(10305 ^ _356604) ^ [] : [_719225 = _719227], (10303 ^ _356604) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _719225, _719227))]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _719225, _719227), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _719227, _719225))], (1429 ^ _356604) ^ [_403176, _403178, _403180] : [class_Rings_Oidom(_403176), 1432 ^ _356604 : [(1433 ^ _356604) ^ [] : [c_Polynomial_Osmult(_403176, _403178, _403180) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_403176)), -(_403178 = c_Groups_Ozero__class_Ozero(_403176)), -(_403180 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_403176)))], (1443 ^ _356604) ^ [] : [1444 ^ _356604 : [(1447 ^ _356604) ^ [] : [_403180 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_403176))], (1445 ^ _356604) ^ [] : [_403178 = c_Groups_Ozero__class_Ozero(_403176)]], -(c_Polynomial_Osmult(_403176, _403178, _403180) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_403176)))]]], (12598 ^ _356604) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (5882 ^ _356604) ^ [_566831, _566833] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _566831, _566833), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _566833), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _566831, _566833))], (208 ^ _356604) ^ [_363430, _363432] : [-(class_Lattices_Oboolean__algebra(_363430)), _363432 = _363430, class_Lattices_Oboolean__algebra(_363432)], (6364 ^ _356604) ^ [_583873, _583875] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_583873), c_Nat_OSuc(_583875)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _583873, _583875))], (10525 ^ _356604) ^ [_726945, _726947, _726949] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _726945), _726947), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _726949), _726947)), -(_726947 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _726945, _726949))], (7300 ^ _356604) ^ [_615751, _615753, _615755] : [class_Orderings_Opreorder(_615751), 7303 ^ _356604 : [(7312 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_615751, _615753, _615755)), c_Orderings_Oord__class_Oless__eq(_615751, _615753, _615755), -(c_Orderings_Oord__class_Oless__eq(_615751, _615755, _615753))], (7304 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_615751, _615753, _615755), 7307 ^ _356604 : [(7310 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_615751, _615755, _615753)], (7308 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_615751, _615753, _615755))]]]]], (5566 ^ _356604) ^ [_555344, _555346, _555348] : [class_Fields_Ofield(_555344), 5569 ^ _356604 : [(5570 ^ _356604) ^ [] : [-(hAPP(c_Polynomial_Ocoeff(_555344, c_Polynomial_Opoly__gcd(_555344, _555346, _555348)), c_Polynomial_Odegree(_555344, c_Polynomial_Opoly__gcd(_555344, _555346, _555348))) = c_Groups_Ozero__class_Ozero(_555344)), _555346 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_555344)), _555348 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_555344))], (5580 ^ _356604) ^ [] : [5581 ^ _356604 : [(5584 ^ _356604) ^ [] : [-(_555348 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_555344)))], (5582 ^ _356604) ^ [] : [-(_555346 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_555344)))]], -(hAPP(c_Polynomial_Ocoeff(_555344, c_Polynomial_Opoly__gcd(_555344, _555346, _555348)), c_Polynomial_Odegree(_555344, c_Polynomial_Opoly__gcd(_555344, _555346, _555348))) = c_Groups_Oone__class_Oone(_555344))]]], (5588 ^ _356604) ^ [_556116, _556118, _556120] : [class_Groups_Ozero(_556116), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_556116, _556118), _556120), hAPP(c_Polynomial_Ocoeff(_556116, _556118), _556120) = c_Groups_Ozero__class_Ozero(_556116), -(_556118 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_556116))), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_556116, _556118), _556120))], (2665 ^ _356604) ^ [_449440] : [-(c_Nat_Osize__class_Osize(tc_Nat_Onat, _449440) = _449440)], (3296 ^ _356604) ^ [_472657, _472659, _472661] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _472657, _472659), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _472657), _472661), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _472659), _472661)))], (6808 ^ _356604) ^ [_599206, _599208, _599210] : [class_Fields_Ofield(_599206), -(c_Polynomial_Opoly__gcd(_599206, _599208, _599210) = c_Polynomial_Opoly__gcd(_599206, _599210, _599208))], (3829 ^ _356604) ^ [_492615, _492617, _492619] : [class_Rings_Ocomm__ring(_492615), -(c_Polynomial_Osmult(_492615, c_Groups_Ouminus__class_Ouminus(_492615, _492617), _492619) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_492615), c_Polynomial_Osmult(_492615, _492617, _492619)))], (1225 ^ _356604) ^ [_396658] : [-(hAPP(c_Polynomial_Opoly(t_a, v_p), _396658) = hAPP(c_Polynomial_Opoly(t_a, v_p), c_Groups_Ozero__class_Ozero(t_a))), class_Int_Oring__char__0(t_a), class_Rings_Oidom(t_a)], (5038 ^ _356604) ^ [_536398] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _536398), _536398) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (12254 ^ _356604) ^ [_785920] : [class_Int_Oring__char__0(_785920), -(class_Rings_Oring(_785920))], (9341 ^ _356604) ^ [_686877, _686879, _686881, _686883, _686885] : [class_Rings_Olinordered__semiring__strict(_686877), c_Orderings_Oord__class_Oless(_686877, _686879, _686881), c_Orderings_Oord__class_Oless__eq(_686877, _686883, _686885), c_Orderings_Oord__class_Oless__eq(_686877, c_Groups_Ozero__class_Ozero(_686877), _686879), c_Orderings_Oord__class_Oless(_686877, c_Groups_Ozero__class_Ozero(_686877), _686883), -(c_Orderings_Oord__class_Oless(_686877, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_686877), _686879), _686883), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_686877), _686881), _686885)))], (6464 ^ _356604) ^ [_587133, _587135] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _587133, _587135), _587135)], (1273 ^ _356604) ^ [_397917, _397919] : [class_Rings_Ocomm__semiring__0(_397917), -(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_397917, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_397917)), _397919) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_397917)))], (12296 ^ _356604) ^ [_787222] : [class_Rings_Oidom(_787222), -(class_Groups_Ocancel__semigroup__add(_787222))], (12290 ^ _356604) ^ [_787036] : [class_Rings_Oidom(_787036), -(class_Rings_Oring__no__zero__divisors(_787036))], (10599 ^ _356604) ^ [_729342, _729344] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _729342), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _729344), -(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), _729342), _729344)))], (9047 ^ _356604) ^ [_676446, _676448] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _676446, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _676448, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _676446, _676448))], (4790 ^ _356604) ^ [_527584, _527586] : [class_Groups_Omonoid__mult(_527584), -(hAPP(hAPP(c_Power_Opower__class_Opower(_527584), c_Groups_Oone__class_Oone(_527584)), _527586) = c_Groups_Oone__class_Oone(_527584))], (8828 ^ _356604) ^ [_668625, _668627] : [8829 ^ _356604 : [(8832 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _668627)], (8830 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _668625)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _668625, _668627)))], (2579 ^ _356604) ^ [_445809, _445811, _445813] : [class_Rings_Ocomm__semiring__1(_445809), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_445809), _445811), _445813) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_445809), _445813), _445811))], (4836 ^ _356604) ^ [_529294, _529296, _529298] : [class_Rings_Olinordered__semidom(_529294), c_Orderings_Oord__class_Oless__eq(_529294, c_Groups_Ozero__class_Ozero(_529294), _529296), -(c_Orderings_Oord__class_Oless__eq(_529294, c_Groups_Ozero__class_Ozero(_529294), hAPP(hAPP(c_Power_Opower__class_Opower(_529294), _529296), _529298)))], (2929 ^ _356604) ^ [_459183, _459185, _459187] : [class_Orderings_Oorder(_459183), c_Orderings_Oord__class_Oless__eq(_459183, _459185, _459187), 2936 ^ _356604 : [(2943 ^ _356604) ^ [] : [_459187 = _459185, -(c_Orderings_Oord__class_Oless__eq(_459183, _459187, _459185))], (2937 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_459183, _459187, _459185), -(_459187 = _459185)]]], (8802 ^ _356604) ^ [_667668, _667670] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _667668, c_Nat_OSuc(_667670))), 8803 ^ _356604 : [(8806 ^ _356604) ^ [_667837] : [_667668 = c_Nat_OSuc(_667837), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _667837, _667670)], (8804 ^ _356604) ^ [] : [_667668 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (7078 ^ _356604) ^ [_608570, _608572, _608574] : [class_Orderings_Oorder(_608570), c_Orderings_Oord__class_Oless(_608570, _608572, _608574), _608574 = _608572], (10351 ^ _356604) ^ [_720964, _720966] : [-(_720964 = _720966), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _720964, _720966), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _720966, _720964)], (6298 ^ _356604) ^ [_581524, _581526, _581528] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _581524), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _581526, _581528)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _581524), _581526), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _581524), _581528)))], (2182 ^ _356604) ^ [_430465] : [_430465 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _430465, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (2442 ^ _356604) ^ [_439817, _439819, _439821, _439823] : [class_Rings_Ocomm__semiring__0(_439817), -(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_439817, c_Polynomial_OpCons(_439817, _439819, _439821), _439823) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_439817), c_Polynomial_Osmult(_439817, _439823, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_439817, _439821, _439823)), c_Polynomial_OpCons(_439817, _439819, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_439817, _439821, _439823))))], (5836 ^ _356604) ^ [_565083, _565085, _565087] : [-(hBOOL(hAPP(_565083, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _565085, _565087)))), 5839 ^ _356604 : [(5842 ^ _356604) ^ [] : [hBOOL(hAPP(_565083, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (5840 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _565085, _565087))]], 5844 ^ _356604 : [(5847 ^ _356604) ^ [] : [hBOOL(hAPP(_565083, 5843 ^ [_565083, _565085, _565087]))], (5845 ^ _356604) ^ [] : [-(_565085 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _565087, 5843 ^ [_565083, _565085, _565087]))]]], (10409 ^ _356604) ^ [_723044, _723046, _723048, _723050, _723052] : [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), _723044), _723046), _723048), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _723044), _723050), _723052)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _723052, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _723044, _723052), c_Orderings_Oord__class_Oless(tc_Int_Oint, _723044, _723048), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _723050, _723046))], (2454 ^ _356604) ^ [_440278] : [-(c_Nat_Osize__class_Osize(tc_Nat_Onat, c_Nat_OSuc(_440278)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Nat_Osize__class_Osize(tc_Nat_Onat, _440278), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (4722 ^ _356604) ^ [_524707, _524709, _524711] : [class_Rings_Oring__1(_524707), -(hAPP(hAPP(c_Power_Opower__class_Opower(_524707), c_Groups_Ouminus__class_Ouminus(_524707, _524709)), _524711) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_524707), hAPP(hAPP(c_Power_Opower__class_Opower(_524707), c_Groups_Ouminus__class_Ouminus(_524707, c_Groups_Oone__class_Oone(_524707))), _524711)), hAPP(hAPP(c_Power_Opower__class_Opower(_524707), _524709), _524711)))], (11370 ^ _356604) ^ [_756605, _756607, _756609] : [class_Fields_Olinordered__field__inverse__zero(_756605), 11373 ^ _356604 : [(11388 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_756605, c_Groups_Ozero__class_Ozero(_756605), c_Rings_Oinverse__class_Odivide(_756605, _756607, _756609))), 11389 ^ _356604 : [(11396 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_756605, _756607, c_Groups_Ozero__class_Ozero(_756605)), c_Orderings_Oord__class_Oless(_756605, _756609, c_Groups_Ozero__class_Ozero(_756605))], (11390 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_756605, c_Groups_Ozero__class_Ozero(_756605), _756607), c_Orderings_Oord__class_Oless(_756605, c_Groups_Ozero__class_Ozero(_756605), _756609)]]], (11374 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_756605, c_Groups_Ozero__class_Ozero(_756605), c_Rings_Oinverse__class_Odivide(_756605, _756607, _756609)), 11379 ^ _356604 : [(11382 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_756605, c_Groups_Ozero__class_Ozero(_756605), _756609))], (11380 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_756605, c_Groups_Ozero__class_Ozero(_756605), _756607))]], 11383 ^ _356604 : [(11386 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_756605, _756609, c_Groups_Ozero__class_Ozero(_756605)))], (11384 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_756605, _756607, c_Groups_Ozero__class_Ozero(_756605)))]]]]], (4224 ^ _356604) ^ [_506589, _506591, _506593] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _506589), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _506591, _506593)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _506589), _506591)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _506589), _506593)))], (2991 ^ _356604) ^ [_461141, _461143, _461145] : [class_Orderings_Olinorder(_461141), -(c_Orderings_Oord__class_Oless__eq(_461141, _461143, _461145)), -(c_Orderings_Oord__class_Oless__eq(_461141, _461145, _461143))], (10904 ^ _356604) ^ [_740818, _740820, _740822, _740824] : [class_Fields_Ofield__inverse__zero(_740818), -(hAPP(hAPP(c_Power_Opower__class_Opower(_740818), c_Rings_Oinverse__class_Odivide(_740818, _740820, _740822)), _740824) = c_Rings_Oinverse__class_Odivide(_740818, hAPP(hAPP(c_Power_Opower__class_Opower(_740818), _740820), _740824), hAPP(hAPP(c_Power_Opower__class_Opower(_740818), _740822), _740824)))], (8252 ^ _356604) ^ [_648863, _648865, _648867, _648869] : [class_Rings_Olinordered__ring__strict(_648863), 8255 ^ _356604 : [(8270 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_648863, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_648863), _648865), _648867), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_648863), _648865), _648869))), 8271 ^ _356604 : [(8278 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_648863, _648865, c_Groups_Ozero__class_Ozero(_648863)), c_Orderings_Oord__class_Oless(_648863, _648869, _648867)], (8272 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_648863, c_Groups_Ozero__class_Ozero(_648863), _648865), c_Orderings_Oord__class_Oless(_648863, _648867, _648869)]]], (8256 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_648863, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_648863), _648865), _648867), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_648863), _648865), _648869)), 8261 ^ _356604 : [(8264 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_648863, _648867, _648869))], (8262 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_648863, c_Groups_Ozero__class_Ozero(_648863), _648865))]], 8265 ^ _356604 : [(8268 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_648863, _648869, _648867))], (8266 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_648863, _648865, c_Groups_Ozero__class_Ozero(_648863)))]]]]], (3086 ^ _356604) ^ [_465206, _465208, _465210, _465212] : [class_Rings_Ocomm__semiring__0(_465206), -(c_Polynomial_Opcompose(_465206, c_Polynomial_OpCons(_465206, _465208, _465210), _465212) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_465206), c_Polynomial_OpCons(_465206, _465208, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_465206))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_465206)), _465212), c_Polynomial_Opcompose(_465206, _465210, _465212))))], (9173 ^ _356604) ^ [_680702, _680704, _680706] : [class_Groups_Ocomm__monoid__add(_680702), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Polynomial_Odegree(_680702, _680704), c_Polynomial_Odegree(_680702, _680706)), -(c_Polynomial_Odegree(_680702, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_680702), _680704, _680706)) = c_Polynomial_Odegree(_680702, _680706))], (2531 ^ _356604) ^ [_443171, _443173, _443175, _443177] : [class_Groups_Oab__semigroup__mult(_443171), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_443171), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_443171), _443173), _443175)), _443177) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_443171), _443173), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_443171), _443175), _443177)))], (8840 ^ _356604) ^ [_669156, _669158] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _669156, _669158), -(_669158 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _669156, 8843 ^ [_669156, _669158])))], (5460 ^ _356604) ^ [_551338, _551340] : [class_Lattices_Oab__semigroup__idem__mult(_551338), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_551338), _551340), _551340) = _551340)], (6450 ^ _356604) ^ [_586685] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _586685, c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_586685 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (11782 ^ _356604) ^ [_769976, _769978, _769980, _769982] : [class_Fields_Olinordered__field(_769976), c_Orderings_Oord__class_Oless(_769976, c_Groups_Ozero__class_Ozero(_769976), _769978), c_Orderings_Oord__class_Oless(_769976, _769980, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_769976), _769982), _769978)), -(c_Orderings_Oord__class_Oless(_769976, c_Rings_Oinverse__class_Odivide(_769976, _769980, _769978), _769982))], (8654 ^ _356604) ^ [_662193, _662195, _662197] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _662193, _662195), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _662195, _662197), _662193) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _662195, _662193), _662197))], (6814 ^ _356604) ^ [_599464, _599466, _599468, _599470] : [class_Fields_Ofield(_599464), -(c_Polynomial_Opoly__gcd(_599464, _599466, c_Polynomial_Opoly__gcd(_599464, _599468, _599470)) = c_Polynomial_Opoly__gcd(_599464, _599468, c_Polynomial_Opoly__gcd(_599464, _599466, _599470)))], (6792 ^ _356604) ^ [_598694, _598696, _598698] : [class_Groups_Oordered__ab__group__add(_598694), 6795 ^ _356604 : [(6802 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_598694, c_Groups_Ominus__class_Ominus(_598694, _598696, _598698), c_Groups_Ozero__class_Ozero(_598694)), -(c_Orderings_Oord__class_Oless(_598694, _598696, _598698))], (6796 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_598694, _598696, _598698), -(c_Orderings_Oord__class_Oless(_598694, c_Groups_Ominus__class_Ominus(_598694, _598696, _598698), c_Groups_Ozero__class_Ozero(_598694)))]]], (12582 ^ _356604) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (3018 ^ _356604) ^ [_462122, _462124, _462126] : [class_Rings_Ocomm__semiring__0(_462122), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_462122, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_462122)), _462124), _462126)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Polynomial_Odegree(_462122, _462124), c_Polynomial_Odegree(_462122, _462126))))], (12580 ^ _356604) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (6438 ^ _356604) ^ [_586230, _586232] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_586230), _586232), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _586230, _586232))], (1894 ^ _356604) ^ [_420633, _420635, _420637, _420639, _420641] : [class_Groups_Oordered__ab__semigroup__add(_420633), c_Orderings_Oord__class_Oless__eq(_420633, _420635, _420637), c_Orderings_Oord__class_Oless__eq(_420633, _420639, _420641), -(c_Orderings_Oord__class_Oless__eq(_420633, c_Groups_Oplus__class_Oplus(_420633, _420635, _420639), c_Groups_Oplus__class_Oplus(_420633, _420637, _420641)))], (3402 ^ _356604) ^ [_476704, _476706, _476708] : [class_Rings_Ono__zero__divisors(_476704), -(_476706 = c_Groups_Ozero__class_Ozero(_476704)), -(_476708 = c_Groups_Ozero__class_Ozero(_476704)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_476704), _476706), _476708) = c_Groups_Ozero__class_Ozero(_476704)], (6712 ^ _356604) ^ [_595902] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _595902, _595902)], (8728 ^ _356604) ^ [_665022, _665024, _665026] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _665022, _665024), _665026), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _665022, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _665026, _665024)))], (3646 ^ _356604) ^ [_485145, _485147, _485149, _485151] : [class_RealVector_Oreal__normed__algebra(_485145), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_485145), c_Groups_Oplus__class_Oplus(_485145, _485147, _485149)), _485151) = c_Groups_Oplus__class_Oplus(_485145, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_485145), _485147), _485151), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_485145), _485149), _485151)))], (4 ^ _356604) ^ [_356835, _356837] : [_356837 = _356835, -(_356835 = _356837)], (6312 ^ _356604) ^ [_582039] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _582039, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2190 ^ _356604) ^ [_430737, _430739] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _430737, c_Nat_OSuc(_430739)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _430737, _430739)))], (12646 ^ _356604) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (10177 ^ _356604) ^ [_715457, _715459, _715461] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _715457, _715459), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _715457, _715461), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _715457, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _715459, _715461)))], (1689 ^ _356604) ^ [_412735] : [-(c_Nat_Onat_Onat__size(c_Nat_OSuc(_412735)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Nat_Onat_Onat__size(_412735), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (3282 ^ _356604) ^ [_471945, _471947, _471949] : [_471947 = _471949, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_471945)), _471947) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_471945)), _471949))], (6630 ^ _356604) ^ [_593364, _593366] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _593364, _593366), 6633 ^ _356604 : [(6636 ^ _356604) ^ [] : [_593364 = _593366], (6634 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _593364, _593366))]]], (4638 ^ _356604) ^ [_521962, _521964] : [class_Groups_Ozero(_521962), 4641 ^ _356604 : [(4648 ^ _356604) ^ [] : [_521964 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_521962)), -(hAPP(c_Polynomial_Ocoeff(_521962, _521964), c_Polynomial_Odegree(_521962, _521964)) = c_Groups_Ozero__class_Ozero(_521962))], (4642 ^ _356604) ^ [] : [hAPP(c_Polynomial_Ocoeff(_521962, _521964), c_Polynomial_Odegree(_521962, _521964)) = c_Groups_Ozero__class_Ozero(_521962), -(_521964 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_521962)))]]], (2727 ^ _356604) ^ [_452278, _452280, _452282] : [class_Rings_Olinordered__ring__strict(_452278), 2730 ^ _356604 : [(2739 ^ _356604) ^ [] : [-(c_Groups_Oplus__class_Oplus(_452278, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_452278), _452280), _452280), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_452278), _452282), _452282)) = c_Groups_Ozero__class_Ozero(_452278)), _452280 = c_Groups_Ozero__class_Ozero(_452278), _452282 = c_Groups_Ozero__class_Ozero(_452278)], (2731 ^ _356604) ^ [] : [c_Groups_Oplus__class_Oplus(_452278, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_452278), _452280), _452280), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_452278), _452282), _452282)) = c_Groups_Ozero__class_Ozero(_452278), 2734 ^ _356604 : [(2737 ^ _356604) ^ [] : [-(_452282 = c_Groups_Ozero__class_Ozero(_452278))], (2735 ^ _356604) ^ [] : [-(_452280 = c_Groups_Ozero__class_Ozero(_452278))]]]]], (5820 ^ _356604) ^ [_564552, _564554, _564556] : [hBOOL(hAPP(_564552, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _564554, _564556))), 5823 ^ _356604 : [(5830 ^ _356604) ^ [_564884] : [_564554 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _564556, _564884), -(hBOOL(hAPP(_564552, _564884)))], (5824 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _564554, _564556), -(hBOOL(hAPP(_564552, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (12606 ^ _356604) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (828 ^ _356604) ^ [_382484, _382486, _382488, _382490, _382492, _382494, _382496, _382498, _382500, _382502] : [-(c_Polynomial_Opoly__rec(_382502, _382498, _382494, _382490, _382486) = c_Polynomial_Opoly__rec(_382500, _382496, _382492, _382488, _382484)), _382502 = _382500, _382498 = _382496, _382494 = _382492, _382490 = _382488, _382486 = _382484], (1730 ^ _356604) ^ [_414378, _414380, _414382] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _414378, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _414380, _414382)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _414380, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _414378, _414382)))], (1691 ^ _356604) ^ [_412866, _412868, _412870] : [class_Rings_Oidom(_412866), -(_412868 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_412866))), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Oorder(_412866, _412870, _412868), c_Polynomial_Odegree(_412866, _412868)))], (11762 ^ _356604) ^ [_769313, _769315, _769317, _769319] : [class_Fields_Olinordered__field(_769313), c_Orderings_Oord__class_Oless(_769313, c_Groups_Ozero__class_Ozero(_769313), _769315), 11769 ^ _356604 : [(11776 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_769313, _769317, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_769313), _769319), _769315)), -(c_Orderings_Oord__class_Oless(_769313, c_Rings_Oinverse__class_Odivide(_769313, _769317, _769315), _769319))], (11770 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_769313, c_Rings_Oinverse__class_Odivide(_769313, _769317, _769315), _769319), -(c_Orderings_Oord__class_Oless(_769313, _769317, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_769313), _769319), _769315)))]]], (258 ^ _356604) ^ [_364905, _364907] : [-(class_Rings_Olinordered__semiring__1__strict(_364905)), _364907 = _364905, class_Rings_Olinordered__semiring__1__strict(_364907)], (4520 ^ _356604) ^ [_517764, _517766, _517768, _517770] : [class_Rings_Ocomm__semiring__0(_517764), -(hAPP(c_Polynomial_Ocoeff(_517764, c_Polynomial_Osmult(_517764, _517766, _517768)), _517770) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_517764), _517766), hAPP(c_Polynomial_Ocoeff(_517764, _517768), _517770)))], (1874 ^ _356604) ^ [_419897, _419899, _419901, _419903] : [class_Groups_Ocancel__ab__semigroup__add(_419897), c_Groups_Oplus__class_Oplus(_419897, _419899, _419901) = c_Groups_Oplus__class_Oplus(_419897, _419899, _419903), -(_419901 = _419903)], (538 ^ _356604) ^ [_373165, _373167] : [-(class_Groups_Omonoid__mult(_373165)), _373167 = _373165, class_Groups_Omonoid__mult(_373167)], (8967 ^ _356604) ^ [_673605, _673607, _673609] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _673605), _673607), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _673609), _673607))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _673607), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _673605, _673609)], (8472 ^ _356604) ^ [_655936, _655938] : [class_Groups_Oordered__ab__group__add(_655936), 8475 ^ _356604 : [(8482 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_655936, _655938, c_Groups_Ozero__class_Ozero(_655936)), -(c_Orderings_Oord__class_Oless(_655936, c_Groups_Ozero__class_Ozero(_655936), c_Groups_Ouminus__class_Ouminus(_655936, _655938)))], (8476 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_655936, c_Groups_Ozero__class_Ozero(_655936), c_Groups_Ouminus__class_Ouminus(_655936, _655938)), -(c_Orderings_Oord__class_Oless(_655936, _655938, c_Groups_Ozero__class_Ozero(_655936)))]]], (12524 ^ _356604) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (3686 ^ _356604) ^ [_486922, _486924, _486926, _486928] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _486922), _486924), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _486926), _486924), _486928)) = 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, _486922, _486926)), _486924), _486928))], (122 ^ _356604) ^ [_360737, _360739] : [-(class_Rings_Odivision__ring(_360737)), _360739 = _360737, class_Rings_Odivision__ring(_360739)], (9915 ^ _356604) ^ [_707212, _707214] : [_707212 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _707214), _707212) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (2074 ^ _356604) ^ [_426597, _426599, _426601, _426603] : [class_Groups_Oordered__comm__monoid__add(_426597), c_Orderings_Oord__class_Oless__eq(_426597, c_Groups_Ozero__class_Ozero(_426597), _426599), c_Orderings_Oord__class_Oless__eq(_426597, _426601, _426603), -(c_Orderings_Oord__class_Oless__eq(_426597, _426601, c_Groups_Oplus__class_Oplus(_426597, _426599, _426603)))], (3272 ^ _356604) ^ [_471508] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _471508), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (678 ^ _356604) ^ [_377295, _377297] : [-(class_Groups_Oab__group__add(_377295)), _377297 = _377295, class_Groups_Oab__group__add(_377297)], (3364 ^ _356604) ^ [_475380, _475382, _475384, _475386] : [class_Rings_Ocomm__semiring__0(_475380), -(hAPP(c_Polynomial_Opoly(_475380, c_Polynomial_Opcompose(_475380, _475382, _475384)), _475386) = hAPP(c_Polynomial_Opoly(_475380, _475382), hAPP(c_Polynomial_Opoly(_475380, _475384), _475386)))], (4728 ^ _356604) ^ [_525001, _525003] : [class_Power_Opower(_525001), class_Rings_Osemiring__0(_525001), 4735 ^ _356604 : [(4742 ^ _356604) ^ [] : [-(_525003 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_525001), c_Groups_Ozero__class_Ozero(_525001)), _525003) = c_Groups_Ozero__class_Ozero(_525001))], (4736 ^ _356604) ^ [] : [_525003 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_525001), c_Groups_Ozero__class_Ozero(_525001)), _525003) = c_Groups_Oone__class_Oone(_525001))]]], (6408 ^ _356604) ^ [_585273, _585275] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _585273, _585275), -(c_Nat_OSuc(_585273) = _585275), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_585273), _585275))], (8917 ^ _356604) ^ [_671807, _671809] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_671807), _671809), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _671807, _671809))], (8590 ^ _356604) ^ [_659902, _659904, _659906, _659908] : [class_Rings_Olinordered__semidom(_659902), c_Orderings_Oord__class_Oless(_659902, c_Groups_Oone__class_Oone(_659902), _659904), 8597 ^ _356604 : [(8604 ^ _356604) ^ [] : [_659906 = _659908, -(hAPP(hAPP(c_Power_Opower__class_Opower(_659902), _659904), _659906) = hAPP(hAPP(c_Power_Opower__class_Opower(_659902), _659904), _659908))], (8598 ^ _356604) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_659902), _659904), _659906) = hAPP(hAPP(c_Power_Opower__class_Opower(_659902), _659904), _659908), -(_659906 = _659908)]]], (4484 ^ _356604) ^ [_516126, _516128, _516130] : [class_Rings_Ocomm__semiring__1(_516126), -(c_Groups_Oplus__class_Oplus(_516126, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_516126), _516128), _516130), _516130) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_516126), c_Groups_Oplus__class_Oplus(_516126, _516128, c_Groups_Oone__class_Oone(_516126))), _516130))], (12738 ^ _356604) ^ [_800195] : [class_Rings_Olinordered__idom(_800195), -(class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(_800195)))], (6292 ^ _356604) ^ [_581116, _581118, _581120] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _581116, _581118)), _581120) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _581116), _581120), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _581118), _581120)))], (5050 ^ _356604) ^ [_536926, _536928, _536930, _536932] : [class_Rings_Ocomm__semiring__1(_536926), c_Rings_Odvd__class_Odvd(_536926, _536928, _536930), -(c_Rings_Odvd__class_Odvd(_536926, hAPP(hAPP(c_Power_Opower__class_Opower(_536926), _536928), _536932), hAPP(hAPP(c_Power_Opower__class_Opower(_536926), _536930), _536932)))], (12118 ^ _356604) ^ [_781661, _781663, _781665, _781667] : [class_Fields_Olinordered__field(_781661), c_Orderings_Oord__class_Oless(_781661, c_Groups_Ozero__class_Ozero(_781661), _781663), 12125 ^ _356604 : [(12132 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_781661, _781665, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_781661), _781667), _781663)), -(c_Orderings_Oord__class_Oless__eq(_781661, c_Rings_Oinverse__class_Odivide(_781661, _781665, _781663), _781667))], (12126 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_781661, c_Rings_Oinverse__class_Odivide(_781661, _781665, _781663), _781667), -(c_Orderings_Oord__class_Oless__eq(_781661, _781665, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_781661), _781667), _781663)))]]], (4372 ^ _356604) ^ [_512059, _512061] : [class_Groups_Oordered__ab__group__add(_512059), 4375 ^ _356604 : [(4382 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_512059, c_Groups_Ozero__class_Ozero(_512059), _512061), -(c_Orderings_Oord__class_Oless__eq(_512059, c_Groups_Ouminus__class_Ouminus(_512059, _512061), c_Groups_Ozero__class_Ozero(_512059)))], (4376 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_512059, c_Groups_Ouminus__class_Ouminus(_512059, _512061), c_Groups_Ozero__class_Ozero(_512059)), -(c_Orderings_Oord__class_Oless__eq(_512059, c_Groups_Ozero__class_Ozero(_512059), _512061))]]], (6472 ^ _356604) ^ [_587478, _587480, _587482] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _587480, _587482), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _587478, _587480), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _587478, _587482)))], (7578 ^ _356604) ^ [_624503, _624505, _624507, _624509] : [class_RealVector_Oreal__normed__algebra(_624503), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_624503), _624505), c_Groups_Ominus__class_Ominus(_624503, _624507, _624509)) = c_Groups_Ominus__class_Ominus(_624503, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_624503), _624505), _624507), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_624503), _624505), _624509)))], (8734 ^ _356604) ^ [_665210, _665212, _665214] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _665210, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _665214, _665212)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _665210, _665212), _665214))], (1705 ^ _356604) ^ [_413343, _413345] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _413343, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _413345, _413343)))], (9489 ^ _356604) ^ [_691719, _691721, _691723, _691725] : [class_Groups_Oordered__comm__monoid__add(_691719), c_Orderings_Oord__class_Oless(_691719, c_Groups_Ozero__class_Ozero(_691719), _691721), c_Orderings_Oord__class_Oless__eq(_691719, _691723, _691725), -(c_Orderings_Oord__class_Oless(_691719, _691723, c_Groups_Oplus__class_Oplus(_691719, _691721, _691725)))], (8630 ^ _356604) ^ [_661288, _661290] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _661288, _661290), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_661290), _661288) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _661290, _661288)))], (1253 ^ _356604) ^ [] : [-(c_Polynomial_Opoly(t_a, v_p) = c_Polynomial_Opoly(t_a, c_Polynomial_OpCons(t_a, hAPP(c_Polynomial_Opoly(t_a, v_p), c_Groups_Ozero__class_Ozero(t_a)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))), class_Int_Oring__char__0(t_a), class_Rings_Oidom(t_a)], (12608 ^ _356604) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (4250 ^ _356604) ^ [_507640, _507642] : [class_Groups_Ocomm__monoid__mult(_507640), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_507640), c_Groups_Oone__class_Oone(_507640)), _507642) = _507642)], (2386 ^ _356604) ^ [_437583, _437585, _437587] : [class_Rings_Ocomm__semiring__0(_437583), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_437583, c_Polynomial_Osmult(_437583, _437585, _437587)), c_Polynomial_Odegree(_437583, _437587)))], (4622 ^ _356604) ^ [_521371, _521373, _521375] : [class_Rings_Ocomm__semiring__1(_521371), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Polynomial_Odegree(_521371, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_521371)), _521373), _521375)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Polynomial_Odegree(_521371, _521373)), _521375)))], (5732 ^ _356604) ^ [_561178, _561180] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _561178), _561180), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _561178, _561180))], (5606 ^ _356604) ^ [_556706, _556708, _556710, _556712, _556714, _556716] : [class_Rings_Olinordered__semiring__1__strict(_556706), c_Orderings_Oord__class_Oless(_556706, _556708, _556710), c_Orderings_Oord__class_Oless(_556706, _556712, _556710), c_Orderings_Oord__class_Oless__eq(_556706, c_Groups_Ozero__class_Ozero(_556706), _556714), c_Orderings_Oord__class_Oless__eq(_556706, c_Groups_Ozero__class_Ozero(_556706), _556716), c_Groups_Oplus__class_Oplus(_556706, _556714, _556716) = c_Groups_Oone__class_Oone(_556706), -(c_Orderings_Oord__class_Oless(_556706, c_Groups_Oplus__class_Oplus(_556706, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_556706), _556714), _556708), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_556706), _556716), _556712)), _556710))], (5918 ^ _356604) ^ [_568037, _568039, _568041] : [class_Groups_Ogroup__add(_568037), -(c_Groups_Oplus__class_Oplus(_568037, c_Groups_Ominus__class_Ominus(_568037, _568039, _568041), _568041) = _568039)], (4808 ^ _356604) ^ [_528190, _528192] : [4809 ^ _356604 : [(4812 ^ _356604) ^ [] : [_528190 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4810 ^ _356604) ^ [] : [_528192 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _528190), _528192) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (2102 ^ _356604) ^ [_427503, _427505, _427507] : [class_Groups_Oordered__comm__monoid__add(_427503), c_Orderings_Oord__class_Oless__eq(_427503, _427505, c_Groups_Ozero__class_Ozero(_427503)), c_Orderings_Oord__class_Oless__eq(_427503, _427507, c_Groups_Ozero__class_Ozero(_427503)), -(c_Orderings_Oord__class_Oless__eq(_427503, c_Groups_Oplus__class_Oplus(_427503, _427505, _427507), c_Groups_Ozero__class_Ozero(_427503)))], (7584 ^ _356604) ^ [_624815, _624817, _624819, _624821] : [class_RealVector_Oreal__normed__algebra(_624815), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_624815), c_Groups_Ominus__class_Ominus(_624815, _624817, _624819)), _624821) = c_Groups_Ominus__class_Ominus(_624815, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_624815), _624817), _624821), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_624815), _624819), _624821)))], (3847 ^ _356604) ^ [_493353, _493355] : [class_Rings_Ocomm__semiring__1(_493353), 3850 ^ _356604 : [(3857 ^ _356604) ^ [] : [-(_493355 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_Polynomial_Ocoeff(_493353, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_493353))), _493355) = c_Groups_Ozero__class_Ozero(_493353))], (3851 ^ _356604) ^ [] : [_493355 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Polynomial_Ocoeff(_493353, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_493353))), _493355) = c_Groups_Oone__class_Oone(_493353))]]], (5666 ^ _356604) ^ [_558939, _558941, _558943, _558945] : [class_Rings_Olinordered__semidom(_558939), c_Orderings_Oord__class_Oless(_558939, c_Groups_Oone__class_Oone(_558939), _558941), 5673 ^ _356604 : [(5680 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _558943, _558945), -(c_Orderings_Oord__class_Oless(_558939, hAPP(hAPP(c_Power_Opower__class_Opower(_558939), _558941), _558943), hAPP(hAPP(c_Power_Opower__class_Opower(_558939), _558941), _558945)))], (5674 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_558939, hAPP(hAPP(c_Power_Opower__class_Opower(_558939), _558941), _558943), hAPP(hAPP(c_Power_Opower__class_Opower(_558939), _558941), _558945)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _558943, _558945))]]], (6444 ^ _356604) ^ [_586448, _586450] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_586448), c_Nat_OSuc(_586450)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _586448, _586450))], (588 ^ _356604) ^ [_374640, _374642] : [-(class_Rings_Omult__zero(_374640)), _374642 = _374640, class_Rings_Omult__zero(_374642)], (11886 ^ _356604) ^ [_773428, _773430, _773432, _773434] : [class_Fields_Ofield__inverse__zero(_773428), -(_773430 = c_Groups_Ozero__class_Ozero(_773428)), -(c_Groups_Oplus__class_Oplus(_773428, _773432, c_Rings_Oinverse__class_Odivide(_773428, _773434, _773430)) = c_Rings_Oinverse__class_Odivide(_773428, c_Groups_Oplus__class_Oplus(_773428, _773434, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_773428), _773432), _773430)), _773430))], (11102 ^ _356604) ^ [_747850, _747852, _747854, _747856] : [class_Fields_Olinordered__field__inverse__zero(_747850), c_Orderings_Oord__class_Oless__eq(_747850, _747852, _747854), c_Orderings_Oord__class_Oless__eq(_747850, _747856, c_Groups_Ozero__class_Ozero(_747850)), c_Orderings_Oord__class_Oless(_747850, c_Groups_Ozero__class_Ozero(_747850), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_747850), _747852), _747854)), -(c_Orderings_Oord__class_Oless__eq(_747850, c_Rings_Oinverse__class_Odivide(_747850, _747856, _747852), c_Rings_Oinverse__class_Odivide(_747850, _747856, _747854)))], (2154 ^ _356604) ^ [_429574, _429576] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _429574, _429576) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 2157 ^ _356604 : [(2160 ^ _356604) ^ [] : [-(_429576 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2158 ^ _356604) ^ [] : [-(_429574 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (6070 ^ _356604) ^ [_573374, _573376] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _573374, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _573376, _573374)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _573374, _573376))], (11516 ^ _356604) ^ [_761446, _761448, _761450] : [class_Fields_Olinordered__field(_761446), c_Orderings_Oord__class_Oless__eq(_761446, c_Groups_Ozero__class_Ozero(_761446), _761448), c_Orderings_Oord__class_Oless(_761446, c_Groups_Ozero__class_Ozero(_761446), _761450), -(c_Orderings_Oord__class_Oless__eq(_761446, c_Groups_Ozero__class_Ozero(_761446), c_Rings_Oinverse__class_Odivide(_761446, _761448, _761450)))], (388 ^ _356604) ^ [_368740, _368742] : [-(class_Groups_Ocancel__comm__monoid__add(_368740)), _368742 = _368740, class_Groups_Ocancel__comm__monoid__add(_368742)], (578 ^ _356604) ^ [_374345, _374347] : [-(class_Groups_Ogroup__add(_374345)), _374347 = _374345, class_Groups_Ogroup__add(_374347)], (10776 ^ _356604) ^ [_735624, _735626, _735628, _735630, _735632, _735634, _735636] : [class_Fields_Ofield(_735624), c_Polynomial_Opdivmod__rel(_735624, _735626, _735628, _735630, _735632), c_Polynomial_Opdivmod__rel(_735624, _735626, _735628, _735634, _735636), -(_735632 = _735636)], (2162 ^ _356604) ^ [_429819, _429821] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _429819, _429821) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _429819 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _429821 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3658 ^ _356604) ^ [_485741, _485743] : [class_RealVector_Oreal__normed__algebra(_485741), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_485741), _485743), c_Groups_Ozero__class_Ozero(_485741)) = c_Groups_Ozero__class_Ozero(_485741))], (3388 ^ _356604) ^ [_476261, _476263, _476265] : [class_Rings_Ono__zero__divisors(_476261), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_476261), _476263), _476265) = c_Groups_Ozero__class_Ozero(_476261), -(_476263 = c_Groups_Ozero__class_Ozero(_476261)), -(_476265 = c_Groups_Ozero__class_Ozero(_476261))], (9921 ^ _356604) ^ [_707386, _707388] : [-(_707386 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _707388), _707386) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _707388), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _707388), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _707386, c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (7136 ^ _356604) ^ [_610452, _610454, _610456, _610458] : [class_Orderings_Oord(_610452), c_Orderings_Oord__class_Oless(_610452, _610454, _610456), _610456 = _610458, -(c_Orderings_Oord__class_Oless(_610452, _610454, _610458))], (6320 ^ _356604) ^ [_582323] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _582323), _582323 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (12410 ^ _356604) ^ [_790756] : [class_Rings_Oidom(_790756), -(class_Groups_Ouminus(_790756))], (6940 ^ _356604) ^ [_604290, _604292] : [class_Orderings_Opreorder(_604290), c_Orderings_Oord__class_Oless(_604290, _604292, _604292)], (8660 ^ _356604) ^ [_662457, _662459, _662461] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _662457, _662459), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _662459, _662457), _662461) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _662459, _662461), _662457))], (850 ^ _356604) ^ [_383278, _383280, _383282, _383284] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_383284, _383280) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_383282, _383278)), _383284 = _383282, _383280 = _383278], (12546 ^ _356604) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (10145 ^ _356604) ^ [_714445, _714447, _714449] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _714445, _714447), 10156 ^ _356604 : [(10159 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _714449, _714445)], (10157 ^ _356604) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _714445, _714449))]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _714447, _714449), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _714449, _714447))], (3154 ^ _356604) ^ [_467520, _467522, _467524, _467526, _467528] : [class_Rings_Oordered__semiring(_467520), c_Orderings_Oord__class_Oless__eq(_467520, _467522, _467524), c_Orderings_Oord__class_Oless__eq(_467520, _467526, _467528), c_Orderings_Oord__class_Oless__eq(_467520, c_Groups_Ozero__class_Ozero(_467520), _467522), c_Orderings_Oord__class_Oless__eq(_467520, c_Groups_Ozero__class_Ozero(_467520), _467526), -(c_Orderings_Oord__class_Oless__eq(_467520, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_467520), _467522), _467526), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_467520), _467524), _467528)))], (11868 ^ _356604) ^ [_772841, _772843, _772845, _772847] : [class_Fields_Olinordered__field(_772841), c_Orderings_Oord__class_Oless(_772841, _772843, _772845), c_Orderings_Oord__class_Oless(_772841, _772847, c_Groups_Ozero__class_Ozero(_772841)), c_Orderings_Oord__class_Oless(_772841, c_Groups_Ozero__class_Ozero(_772841), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_772841), _772843), _772845)), -(c_Orderings_Oord__class_Oless(_772841, c_Rings_Oinverse__class_Odivide(_772841, _772847, _772843), c_Rings_Oinverse__class_Odivide(_772841, _772847, _772845)))], (12616 ^ _356604) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (4496 ^ _356604) ^ [_516672, _516674] : [class_Rings_Ocomm__semiring__1(_516672), -(c_Groups_Oplus__class_Oplus(_516672, _516674, _516674) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_516672), c_Groups_Oplus__class_Oplus(_516672, c_Groups_Oone__class_Oone(_516672), c_Groups_Oone__class_Oone(_516672))), _516674))], (4570 ^ _356604) ^ [_519647, _519649, _519651, _519653] : [class_Groups_Ocomm__monoid__add(_519647), -(hAPP(c_Polynomial_Ocoeff(_519647, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_519647), _519649, _519651)), _519653) = c_Groups_Oplus__class_Oplus(_519647, hAPP(c_Polynomial_Ocoeff(_519647, _519649), _519653), hAPP(c_Polynomial_Ocoeff(_519647, _519651), _519653)))], (4226 ^ _356604) ^ [_506728, _506730] : [class_Rings_Ocomm__semiring__1(_506728), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_506728), c_Groups_Oone__class_Oone(_506728)), _506730) = _506730)], (12590 ^ _356604) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (12610 ^ _356604) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (5924 ^ _356604) ^ [_568281, _568283, _568285] : [class_Groups_Ogroup__add(_568281), -(c_Groups_Ominus__class_Ominus(_568281, c_Groups_Oplus__class_Oplus(_568281, _568283, _568285), _568285) = _568283)], (6118 ^ _356604) ^ [_575216, _575218] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _575216, _575218)), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _575218, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _575216, _575218)) = _575216)], (5166 ^ _356604) ^ [_541093, _541095, _541097] : [class_Rings_Ocomm__ring__1(_541093), 5169 ^ _356604 : [(5176 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(_541093, _541095, _541097), -(c_Rings_Odvd__class_Odvd(_541093, _541095, c_Groups_Ouminus__class_Ouminus(_541093, _541097)))], (5170 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(_541093, _541095, c_Groups_Ouminus__class_Ouminus(_541093, _541097)), -(c_Rings_Odvd__class_Odvd(_541093, _541095, _541097))]]], (648 ^ _356604) ^ [_376410, _376412] : [-(class_Groups_Ouminus(_376410)), _376412 = _376410, class_Groups_Ouminus(_376412)], (4984 ^ _356604) ^ [_534424, _534426, _534428] : [class_Rings_Oidom(_534424), -(_534426 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_534424))), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_534424), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_534424)), c_Polynomial_OpCons(_534424, c_Groups_Ouminus__class_Ouminus(_534424, _534428), c_Polynomial_OpCons(_534424, c_Groups_Oone__class_Oone(_534424), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_534424))))), c_Nat_OSuc(c_Polynomial_Oorder(_534424, _534428, _534426))), _534426)], (8877 ^ _356604) ^ [_670510, _670512] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_670510), _670512), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _670510, _670512))], (708 ^ _356604) ^ [_378180, _378182] : [-(class_Groups_Ozero(_378180)), _378182 = _378180, class_Groups_Ozero(_378182)], (8020 ^ _356604) ^ [_640943, _640945, _640947] : [class_Groups_Ogroup__add(_640943), -(c_Groups_Ominus__class_Ominus(_640943, _640945, _640947) = c_Groups_Oplus__class_Oplus(_640943, _640945, c_Groups_Ouminus__class_Ouminus(_640943, _640947)))], (4872 ^ _356604) ^ [_530507, _530509, _530511] : [class_Power_Opower(_530507), class_Rings_Omult__zero(_530507), class_Rings_Ono__zero__divisors(_530507), class_Rings_Ozero__neq__one(_530507), 4887 ^ _356604 : [(4896 ^ _356604) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_530507), _530509), _530511) = c_Groups_Ozero__class_Ozero(_530507)), _530509 = c_Groups_Ozero__class_Ozero(_530507), -(_530511 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4888 ^ _356604) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_530507), _530509), _530511) = c_Groups_Ozero__class_Ozero(_530507), 4891 ^ _356604 : [(4894 ^ _356604) ^ [] : [_530511 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (4892 ^ _356604) ^ [] : [-(_530509 = c_Groups_Ozero__class_Ozero(_530507))]]]]], (10862 ^ _356604) ^ [_739026, _739028] : [class_Rings_Odivision__ring(_739026), -(c_Rings_Oinverse__class_Odivide(_739026, c_Groups_Ozero__class_Ozero(_739026), _739028) = c_Groups_Ozero__class_Ozero(_739026))], (2014 ^ _356604) ^ [_424761, _424763] : [class_Groups_Olinordered__ab__group__add(_424761), 2017 ^ _356604 : [(2024 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_424761, _424763, c_Groups_Ozero__class_Ozero(_424761)), -(c_Orderings_Oord__class_Oless__eq(_424761, c_Groups_Oplus__class_Oplus(_424761, _424763, _424763), c_Groups_Ozero__class_Ozero(_424761)))], (2018 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_424761, c_Groups_Oplus__class_Oplus(_424761, _424763, _424763), c_Groups_Ozero__class_Ozero(_424761)), -(c_Orderings_Oord__class_Oless__eq(_424761, _424763, c_Groups_Ozero__class_Ozero(_424761)))]]], (932 ^ _356604) ^ [_386306, _386308, _386310, _386312, _386314, _386316] : [-(c_Polynomial_Omonom(_386316, _386312, _386308) = c_Polynomial_Omonom(_386314, _386310, _386306)), _386316 = _386314, _386312 = _386310, _386308 = _386306], (10087 ^ _356604) ^ [_712699, _712701] : [_712699 = _712701, c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _712699, _712701), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _712701, _712699))], (12434 ^ _356604) ^ [_791500] : [class_Rings_Oidom(_791500), -(class_Groups_Ozero(_791500))], (7466 ^ _356604) ^ [_620817, _620819, _620821] : [class_Orderings_Oorder(_620817), c_Orderings_Oord__class_Oless__eq(_620817, _620819, _620821), -(_620819 = _620821), -(c_Orderings_Oord__class_Oless(_620817, _620819, _620821))], (6622 ^ _356604) ^ [_593012] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _593012, _593012))], (4134 ^ _356604) ^ [_502682, _502684, _502686] : [class_Rings_Oring(_502682), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_502682), c_Groups_Ouminus__class_Ouminus(_502682, _502684)), c_Groups_Ouminus__class_Ouminus(_502682, _502686)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_502682), _502684), _502686))], (866 ^ _356604) ^ [_383883, _383885, _383887, _383889, _383891, _383893] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_383893, _383889, _383885) = c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_383891, _383887, _383883)), _383893 = _383891, _383889 = _383887, _383885 = _383883], (10427 ^ _356604) ^ [_723681, _723683, _723685, _723687, _723689, _723691] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _723681), _723683), _723685) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _723687), _723689), _723691), 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), _723687), _723689), _723691)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _723691, _723687), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _723685), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _723687), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _723687, _723681), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _723683, _723689))], (1764 ^ _356604) ^ [_415784, _415786, _415788] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _415786, _415788), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _415784, _415786), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _415784, _415788)))], (5060 ^ _356604) ^ [_537279, _537281] : [class_Rings_Ocomm__semiring__1(_537279), c_Rings_Odvd__class_Odvd(_537279, c_Groups_Ozero__class_Ozero(_537279), _537281), -(_537281 = c_Groups_Ozero__class_Ozero(_537279))], (9277 ^ _356604) ^ [_684689, _684691, _684693, _684695] : [class_Rings_Olinordered__semiring(_684689), c_Orderings_Oord__class_Oless(_684689, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_684689), _684691), _684693), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_684689), _684691), _684695)), c_Orderings_Oord__class_Oless__eq(_684689, c_Groups_Ozero__class_Ozero(_684689), _684691), -(c_Orderings_Oord__class_Oless(_684689, _684693, _684695))], (1068 ^ _356604) ^ [_391274, _391276, _391278, _391280, _391282, _391284] : [-(c_Groups_Oplus__class_Oplus(_391284, _391280, _391276) = c_Groups_Oplus__class_Oplus(_391282, _391278, _391274)), _391284 = _391282, _391280 = _391278, _391276 = _391274], (3042 ^ _356604) ^ [_463288, _463290, _463292, _463294] : [class_Rings_Ocomm__semiring__1(_463288), -(c_Groups_Oplus__class_Oplus(_463288, _463290, c_Groups_Oplus__class_Oplus(_463288, _463292, _463294)) = c_Groups_Oplus__class_Oplus(_463288, c_Groups_Oplus__class_Oplus(_463288, _463290, _463292), _463294))], (12440 ^ _356604) ^ [_791686] : [class_Rings_Oidom(_791686), -(class_Rings_Oring(_791686))], (12666 ^ _356604) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (12658 ^ _356604) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (12520 ^ _356604) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (2767 ^ _356604) ^ [] : [-(c_Nat_Osize__class_Osize(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (3680 ^ _356604) ^ [_486677, _486679] : [class_RealVector_Oreal__normed__algebra(_486677), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_486677), c_Groups_Ozero__class_Ozero(_486677)), _486679) = c_Groups_Ozero__class_Ozero(_486677))], (12510 ^ _356604) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (8026 ^ _356604) ^ [_641193, _641195, _641197] : [class_Groups_Oab__group__add(_641193), -(c_Groups_Ominus__class_Ominus(_641193, _641195, _641197) = c_Groups_Oplus__class_Oplus(_641193, _641195, c_Groups_Ouminus__class_Ouminus(_641193, _641197)))], (7412 ^ _356604) ^ [_619159, _619161, _619163] : [class_Orderings_Olinorder(_619159), c_Orderings_Oord__class_Oless__eq(_619159, _619161, _619163), c_Orderings_Oord__class_Oless(_619159, _619163, _619161)], (8816 ^ _356604) ^ [_668210, _668212] : [-(c_Groups_Ominus__class_Ominus(tc_Int_Oint, _668210, _668212) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _668210, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _668212)))], (4200 ^ _356604) ^ [_505686, _505688, _505690] : [class_Groups_Ogroup__add(_505686), -(c_Groups_Ouminus__class_Ouminus(_505686, c_Groups_Oplus__class_Oplus(_505686, _505688, _505690)) = c_Groups_Oplus__class_Oplus(_505686, c_Groups_Ouminus__class_Ouminus(_505686, _505690), c_Groups_Ouminus__class_Ouminus(_505686, _505688)))], (288 ^ _356604) ^ [_365790, _365792] : [-(class_Groups_Oordered__comm__monoid__add(_365790)), _365792 = _365790, class_Groups_Oordered__comm__monoid__add(_365792)], (9461 ^ _356604) ^ [_690805, _690807, _690809] : [class_Groups_Oordered__comm__monoid__add(_690805), c_Orderings_Oord__class_Oless(_690805, _690807, c_Groups_Ozero__class_Ozero(_690805)), c_Orderings_Oord__class_Oless__eq(_690805, _690809, c_Groups_Ozero__class_Ozero(_690805)), -(c_Orderings_Oord__class_Oless(_690805, c_Groups_Oplus__class_Oplus(_690805, _690807, _690809), c_Groups_Ozero__class_Ozero(_690805)))], (5788 ^ _356604) ^ [_563157, _563159, _563161, _563163, _563165, _563167] : [class_Rings_Oordered__ring(_563157), 5791 ^ _356604 : [(5798 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_563157, c_Groups_Oplus__class_Oplus(_563157, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_563157), c_Groups_Ominus__class_Ominus(_563157, _563159, _563165)), _563161), _563163), _563167), -(c_Orderings_Oord__class_Oless(_563157, c_Groups_Oplus__class_Oplus(_563157, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_563157), _563159), _563161), _563163), c_Groups_Oplus__class_Oplus(_563157, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_563157), _563165), _563161), _563167)))], (5792 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_563157, c_Groups_Oplus__class_Oplus(_563157, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_563157), _563159), _563161), _563163), c_Groups_Oplus__class_Oplus(_563157, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_563157), _563165), _563161), _563167)), -(c_Orderings_Oord__class_Oless(_563157, c_Groups_Oplus__class_Oplus(_563157, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_563157), c_Groups_Ominus__class_Ominus(_563157, _563159, _563165)), _563161), _563163), _563167))]]], (1928 ^ _356604) ^ [_421841, _421843, _421845, _421847] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_421841), 1931 ^ _356604 : [(1938 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_421841, _421845, _421847), -(c_Orderings_Oord__class_Oless__eq(_421841, c_Groups_Oplus__class_Oplus(_421841, _421843, _421845), c_Groups_Oplus__class_Oplus(_421841, _421843, _421847)))], (1932 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_421841, c_Groups_Oplus__class_Oplus(_421841, _421843, _421845), c_Groups_Oplus__class_Oplus(_421841, _421843, _421847)), -(c_Orderings_Oord__class_Oless__eq(_421841, _421845, _421847))]]], (4388 ^ _356604) ^ [_512544, _512546] : [class_Groups_Olinordered__ab__group__add(_512544), 4391 ^ _356604 : [(4398 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_512544, c_Groups_Ozero__class_Ozero(_512544), _512546), -(c_Orderings_Oord__class_Oless__eq(_512544, c_Groups_Ouminus__class_Ouminus(_512544, _512546), _512546))], (4392 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(_512544, c_Groups_Ouminus__class_Ouminus(_512544, _512546), _512546), -(c_Orderings_Oord__class_Oless__eq(_512544, c_Groups_Ozero__class_Ozero(_512544), _512546))]]], (12578 ^ _356604) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (5762 ^ _356604) ^ [_562226, _562228, _562230] : [-(_562226 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 5765 ^ _356604 : [(5772 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _562226), _562228), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _562226), _562230)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _562228, _562230))], (5766 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _562228, _562230), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _562226), _562228), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _562226), _562230)))]]], (13008 ^ _356604) ^ [_808745] : [class_Rings_Ocomm__semiring__1(_808745), -(class_Power_Opower(tc_Polynomial_Opoly(_808745)))], (4594 ^ _356604) ^ [_520480, _520482, _520484] : [class_Rings_Olinordered__idom(_520480), c_Orderings_Oord__class_Oless__eq(_520480, c_Groups_Ozero__class_Ozero(_520480), _520482), c_Orderings_Oord__class_Oless__eq(_520480, c_Groups_Ozero__class_Ozero(_520480), _520484), c_Orderings_Oord__class_Oless__eq(_520480, _520484, c_Groups_Oone__class_Oone(_520480)), -(c_Orderings_Oord__class_Oless__eq(_520480, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_520480), _520484), _520482), _520482))], (9763 ^ _356604) ^ [_701999, _702001, _702003] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _701999), 9766 ^ _356604 : [(9773 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _702001, _702003), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _701999), _702001), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _701999), _702003)))], (9767 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _701999), _702001), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _701999), _702003)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _702001, _702003))]]], (5454 ^ _356604) ^ [_551114, _551116] : [class_Lattices_Oab__semigroup__idem__mult(_551114), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_551114), _551116), _551116) = _551116)], (3370 ^ _356604) ^ [_475673, _475675] : [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), _475673), _475675)), 3373 ^ _356604 : [(3376 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _475675))], (3374 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _475673))]]], (1451 ^ _356604) ^ [_403856, _403858] : [class_Rings_Ocomm__semiring__0(_403856), -(c_Polynomial_Osmult(_403856, c_Groups_Ozero__class_Ozero(_403856), _403858) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_403856)))], (8814 ^ _356604) ^ [_668105, _668107] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _668105, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _668107)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _668105, _668107))], (10972 ^ _356604) ^ [_743340, _743342, _743344] : [class_Rings_Odivision__ring(_743340), -(_743342 = c_Groups_Ozero__class_Ozero(_743340)), 10979 ^ _356604 : [(10986 ^ _356604) ^ [] : [_743344 = _743342, -(c_Rings_Oinverse__class_Odivide(_743340, _743344, _743342) = c_Groups_Oone__class_Oone(_743340))], (10980 ^ _356604) ^ [] : [c_Rings_Oinverse__class_Odivide(_743340, _743344, _743342) = c_Groups_Oone__class_Oone(_743340), -(_743344 = _743342)]]], (9517 ^ _356604) ^ [_692605, _692607, _692609] : [class_Groups_Oordered__comm__monoid__add(_692605), c_Orderings_Oord__class_Oless(_692605, c_Groups_Ozero__class_Ozero(_692605), _692607), c_Orderings_Oord__class_Oless__eq(_692605, c_Groups_Ozero__class_Ozero(_692605), _692609), -(c_Orderings_Oord__class_Oless(_692605, c_Groups_Ozero__class_Ozero(_692605), c_Groups_Oplus__class_Oplus(_692605, _692607, _692609)))], (10237 ^ _356604) ^ [_717369, _717371] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _717369, _717371), -(_717369 = _717371), 10244 ^ _356604 : [(10247 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _717371, _717369)], (10245 ^ _356604) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _717369, _717371))]]], (9095 ^ _356604) ^ [_678099] : [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), _678099), _678099), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _678099, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (10609 ^ _356604) ^ [_729687, _729689, _729691, _729693] : [class_Fields_Ofield(_729687), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_729687), _729689, _729691), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_729687), _729689, _729693), 10623 ^ _356604 : [(10628 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_729687), 10622 ^ [_729687, _729689, _729691, _729693], _729689)], (10626 ^ _356604) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_729687), 10622 ^ [_729687, _729689, _729691, _729693], _729693))], (10624 ^ _356604) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_729687), 10622 ^ [_729687, _729689, _729691, _729693], _729691))]], -(c_Polynomial_Opoly__gcd(_729687, _729691, _729693) = _729689), 10633 ^ _356604 : [(10638 ^ _356604) ^ [] : [hAPP(c_Polynomial_Ocoeff(_729687, _729689), c_Polynomial_Odegree(_729687, _729689)) = c_Groups_Ozero__class_Ozero(_729687)], (10636 ^ _356604) ^ [] : [-(_729693 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_729687)))], (10634 ^ _356604) ^ [] : [-(_729691 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_729687)))]], 10639 ^ _356604 : [(10640 ^ _356604) ^ [] : [_729691 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_729687)), _729693 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_729687))], (10646 ^ _356604) ^ [] : [hAPP(c_Polynomial_Ocoeff(_729687, _729689), c_Polynomial_Odegree(_729687, _729689)) = c_Groups_Oone__class_Oone(_729687)]]], (11742 ^ _356604) ^ [_768650, _768652, _768654, _768656] : [class_Fields_Olinordered__field(_768650), c_Orderings_Oord__class_Oless(_768650, c_Groups_Ozero__class_Ozero(_768650), _768652), 11749 ^ _356604 : [(11756 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_768650, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_768650), _768654), _768652), _768656), -(c_Orderings_Oord__class_Oless(_768650, _768654, c_Rings_Oinverse__class_Odivide(_768650, _768656, _768652)))], (11750 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_768650, _768654, c_Rings_Oinverse__class_Odivide(_768650, _768656, _768652)), -(c_Orderings_Oord__class_Oless(_768650, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_768650), _768654), _768652), _768656))]]], (12700 ^ _356604) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (5664 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (11796 ^ _356604) ^ [_770452, _770454, _770456, _770458] : [class_Fields_Olinordered__field(_770452), c_Orderings_Oord__class_Oless(_770452, c_Groups_Ozero__class_Ozero(_770452), _770454), c_Orderings_Oord__class_Oless(_770452, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_770452), _770456), _770454), _770458), -(c_Orderings_Oord__class_Oless(_770452, _770456, c_Rings_Oinverse__class_Odivide(_770452, _770458, _770454)))], (1615 ^ _356604) ^ [] : [-(c_Nat_Osize__class_Osize(tc_HOL_Obool, c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8430 ^ _356604) ^ [_654610, _654612, _654614, _654616, _654618] : [class_Groups_Oordered__cancel__ab__semigroup__add(_654610), c_Orderings_Oord__class_Oless__eq(_654610, _654612, _654614), c_Orderings_Oord__class_Oless(_654610, _654616, _654618), -(c_Orderings_Oord__class_Oless(_654610, c_Groups_Oplus__class_Oplus(_654610, _654612, _654616), c_Groups_Oplus__class_Oplus(_654610, _654614, _654618)))], (10575 ^ _356604) ^ [] : [-(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)))], (5930 ^ _356604) ^ [_568525, _568527, _568529] : [class_Groups_Oab__group__add(_568525), -(c_Groups_Ouminus__class_Ouminus(_568525, c_Groups_Ominus__class_Ominus(_568525, _568527, _568529)) = c_Groups_Ominus__class_Ominus(_568525, _568529, _568527))], (8534 ^ _356604) ^ [_657847, _657849, _657851] : [class_Rings_Olinordered__semidom(_657847), c_Orderings_Oord__class_Oless(_657847, c_Groups_Ozero__class_Ozero(_657847), _657849), -(c_Orderings_Oord__class_Oless(_657847, c_Groups_Ozero__class_Ozero(_657847), hAPP(hAPP(c_Power_Opower__class_Opower(_657847), _657849), _657851)))], (418 ^ _356604) ^ [_369625, _369627] : [-(class_Rings_Olinordered__semidom(_369625)), _369627 = _369625, class_Rings_Olinordered__semidom(_369627)], (6946 ^ _356604) ^ [_604515, _604517, _604519] : [class_Orderings_Olinorder(_604515), 6949 ^ _356604 : [(6950 ^ _356604) ^ [] : [-(_604517 = _604519), -(c_Orderings_Oord__class_Oless(_604515, _604517, _604519)), -(c_Orderings_Oord__class_Oless(_604515, _604519, _604517))], (6960 ^ _356604) ^ [] : [6961 ^ _356604 : [(6964 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_604515, _604519, _604517)], (6962 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_604515, _604517, _604519)]], _604517 = _604519]]], (6912 ^ _356604) ^ [_603326, _603328] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _603328, _603326), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _603326, _603328)))], (11144 ^ _356604) ^ [_749350, _749352, _749354] : [class_Fields_Ofield__inverse__zero(_749350), -(c_Rings_Oinverse__class_Odivide(_749350, c_Groups_Ouminus__class_Ouminus(_749350, _749352), c_Groups_Ouminus__class_Ouminus(_749350, _749354)) = c_Rings_Oinverse__class_Odivide(_749350, _749352, _749354))], (7654 ^ _356604) ^ [_627314, _627316] : [class_Groups_Ogroup__add(_627314), -(c_Groups_Ominus__class_Ominus(_627314, _627316, c_Groups_Ozero__class_Ozero(_627314)) = _627316)], (12422 ^ _356604) ^ [_791128] : [class_Rings_Oidom(_791128), -(class_Groups_Ominus(_791128))], (2172 ^ _356604) ^ [_430099] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _430099, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _430099)], (308 ^ _356604) ^ [_366380, _366382] : [-(class_Groups_Ocancel__ab__semigroup__add(_366380)), _366382 = _366380, class_Groups_Ocancel__ab__semigroup__add(_366382)], (10762 ^ _356604) ^ [_735086, _735088, _735090, _735092, _735094, _735096, _735098] : [class_Fields_Ofield(_735086), c_Polynomial_Opdivmod__rel(_735086, _735088, _735090, _735092, _735094), c_Polynomial_Opdivmod__rel(_735086, _735088, _735090, _735096, _735098), -(_735092 = _735096)], (9599 ^ _356604) ^ [_695493, _695495, _695497] : [class_Rings_Olinordered__semidom(_695493), c_Orderings_Oord__class_Oless(_695493, c_Groups_Oone__class_Oone(_695493), _695495), -(c_Orderings_Oord__class_Oless(_695493, c_Groups_Oone__class_Oone(_695493), hAPP(hAPP(c_Power_Opower__class_Opower(_695493), _695495), c_Nat_OSuc(_695497))))], (10892 ^ _356604) ^ [_740242, _740244, _740246, _740248] : [class_Rings_Odivision__ring(_740242), -(c_Rings_Oinverse__class_Odivide(_740242, c_Groups_Oplus__class_Oplus(_740242, _740244, _740246), _740248) = c_Groups_Oplus__class_Oplus(_740242, c_Rings_Oinverse__class_Odivide(_740242, _740244, _740248), c_Rings_Oinverse__class_Odivide(_740242, _740246, _740248)))], (2142 ^ _356604) ^ [_429063, _429065, _429067, _429069] : [class_Rings_Ocomm__semiring__0(_429063), -(c_Polynomial_Osmult(_429063, c_Groups_Oplus__class_Oplus(_429063, _429065, _429067), _429069) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_429063), c_Polynomial_Osmult(_429063, _429065, _429069), c_Polynomial_Osmult(_429063, _429067, _429069)))], (970 ^ _356604) ^ [_387641, _387643] : [_387643 = _387641, -(c_Nat_OSuc(_387643) = c_Nat_OSuc(_387641))], (8722 ^ _356604) ^ [_664743, _664745, _664747] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _664743, _664745), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _664747, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _664745, _664747), _664743)))], (6328 ^ _356604) ^ [_582610, _582612] : [class_Groups_Oab__group__add(_582610), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_582610), _582612, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_582610))) = _582612)], (7088 ^ _356604) ^ [_608894, _608896, _608898] : [class_Orderings_Opreorder(_608894), c_Orderings_Oord__class_Oless(_608894, _608896, _608898), c_Orderings_Oord__class_Oless(_608894, _608898, _608896)], (6002 ^ _356604) ^ [_571107, _571109, _571111, _571113] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_571107), c_Orderings_Oord__class_Oless(_571107, c_Groups_Oplus__class_Oplus(_571107, _571109, _571111), c_Groups_Oplus__class_Oplus(_571107, _571113, _571111)), -(c_Orderings_Oord__class_Oless(_571107, _571109, _571113))], (12696 ^ _356604) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (7252 ^ _356604) ^ [_614269, _614271, _614273] : [class_Orderings_Olinorder(_614269), 7255 ^ _356604 : [(7262 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_614269, _614273, _614271), c_Orderings_Oord__class_Oless__eq(_614269, _614271, _614273)], (7256 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_614269, _614271, _614273)), -(c_Orderings_Oord__class_Oless(_614269, _614273, _614271))]]], (12338 ^ _356604) ^ [_788524] : [class_Rings_Oidom(_788524), -(class_Rings_Ocomm__semiring__0(_788524))], (13038 ^ _356604) ^ [_809695] : [class_Rings_Ocomm__semiring__1(_809695), -(class_Rings_Odvd(tc_Polynomial_Opoly(_809695)))], (2204 ^ _356604) ^ [_431471, _431473] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _431471, _431473)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_431473), _431471))], (3274 ^ _356604) ^ [_471592] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _471592) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10790 ^ _356604) ^ [_736162, _736164, _736166, _736168, _736170, _736172, _736174] : [class_Fields_Ofield(_736162), c_Polynomial_Opdivmod__rel(_736162, _736164, _736166, _736168, _736170), c_Polynomial_Opdivmod__rel(_736162, _736164, _736166, _736172, _736174), 10801 ^ _356604 : [(10804 ^ _356604) ^ [] : [-(_736170 = _736174)], (10802 ^ _356604) ^ [] : [-(_736168 = _736172)]]], (10485 ^ _356604) ^ [_725593, _725595, _725597] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _725593), _725595), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _725597), _725595)), -(_725595 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _725593, _725597))], (12518 ^ _356604) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (2370 ^ _356604) ^ [_437097, _437099] : [-(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _437097, _437099)), 2371 ^ _356604 : [(2378 ^ _356604) ^ [] : [_437097 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _437099 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2372 ^ _356604) ^ [] : [_437097 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _437099 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (2537 ^ _356604) ^ [_443497, _443499, _443501, _443503, _443505] : [class_Rings_Ocomm__semiring__1(_443497), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_443497), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_443497), _443499), _443501)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_443497), _443503), _443505)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_443497), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_443497), _443499), _443503)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_443497), _443501), _443505)))], (11066 ^ _356604) ^ [_746510, _746512, _746514, _746516] : [class_Rings_Odivision__ring(_746510), -(c_Rings_Oinverse__class_Odivide(_746510, c_Groups_Ominus__class_Ominus(_746510, _746512, _746514), _746516) = c_Groups_Ominus__class_Ominus(_746510, c_Rings_Oinverse__class_Odivide(_746510, _746512, _746516), c_Rings_Oinverse__class_Odivide(_746510, _746514, _746516)))], (7232 ^ _356604) ^ [_613566] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _613566, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _613566)], (6668 ^ _356604) ^ [_594560, _594562, _594564] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _594560, _594562), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _594560, _594564), 6675 ^ _356604 : [(6682 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _594562, _594564), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _594562, _594560), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _594564, _594560)))], (6676 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _594562, _594560), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _594564, _594560)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _594562, _594564))]]], (2326 ^ _356604) ^ [_435776, _435778] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _435776, _435778) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 2331 ^ _356604 : [(2334 ^ _356604) ^ [] : [-(_435778 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2332 ^ _356604) ^ [] : [-(_435776 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 2335 ^ _356604 : [(2338 ^ _356604) ^ [] : [-(_435778 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (2336 ^ _356604) ^ [] : [-(_435776 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (2591 ^ _356604) ^ [_446287, _446289] : [class_Rings_Ocomm__semiring__1(_446287), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_446287), _446289), c_Groups_Ozero__class_Ozero(_446287)) = c_Groups_Ozero__class_Ozero(_446287))], (7230 ^ _356604) ^ [_613484] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _613484, _613484) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (5484 ^ _356604) ^ [_552350, _552352, _552354] : [class_Lattices_Oboolean__algebra(_552350), 5487 ^ _356604 : [(5494 ^ _356604) ^ [] : [_552352 = _552354, -(c_Groups_Ouminus__class_Ouminus(_552350, _552352) = c_Groups_Ouminus__class_Ouminus(_552350, _552354))], (5488 ^ _356604) ^ [] : [c_Groups_Ouminus__class_Ouminus(_552350, _552352) = c_Groups_Ouminus__class_Ouminus(_552350, _552354), -(_552352 = _552354)]]], (4784 ^ _356604) ^ [_527284, _527286, _527288, _527290] : [class_Groups_Ocomm__monoid__mult(_527284), -(hAPP(hAPP(c_Power_Opower__class_Opower(_527284), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_527284), _527286), _527288)), _527290) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_527284), hAPP(hAPP(c_Power_Opower__class_Opower(_527284), _527286), _527290)), hAPP(hAPP(c_Power_Opower__class_Opower(_527284), _527288), _527290)))], (7178 ^ _356604) ^ [_611792, _611794, _611796, _611798] : [class_Orderings_Oorder(_611792), c_Orderings_Oord__class_Oless(_611792, _611794, _611796), c_Orderings_Oord__class_Oless(_611792, _611798, _611794), -(c_Orderings_Oord__class_Oless(_611792, _611798, _611796))], (4778 ^ _356604) ^ [_526978, _526980, _526982] : [class_Groups_Omonoid__mult(_526978), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_526978), hAPP(hAPP(c_Power_Opower__class_Opower(_526978), _526980), _526982)), _526980) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_526978), _526980), hAPP(hAPP(c_Power_Opower__class_Opower(_526978), _526980), _526982)))], (7550 ^ _356604) ^ [_623465, _623467, _623469, _623471] : [class_Orderings_Oord(_623465), 7553 ^ _356604 : [(7562 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_fun(_623467, _623465), _623469, _623471)), c_Orderings_Oord__class_Oless__eq(tc_fun(_623467, _623465), _623469, _623471), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_623467, _623465), _623471, _623469))], (7554 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(tc_fun(_623467, _623465), _623469, _623471), 7557 ^ _356604 : [(7560 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_623467, _623465), _623471, _623469)], (7558 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_fun(_623467, _623465), _623469, _623471))]]]]], (2314 ^ _356604) ^ [_435223, _435225] : [class_Groups_Ocomm__monoid__add(_435223), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_435223), _435225, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_435223))) = _435225)], (11252 ^ _356604) ^ [_752886, _752888, _752890, _752892] : [class_Fields_Olinordered__field(_752886), c_Orderings_Oord__class_Oless(_752886, _752888, _752890), c_Orderings_Oord__class_Oless(_752886, _752892, c_Groups_Ozero__class_Ozero(_752886)), -(c_Orderings_Oord__class_Oless(_752886, c_Rings_Oinverse__class_Odivide(_752886, _752890, _752892), c_Rings_Oinverse__class_Odivide(_752886, _752888, _752892)))], (4170 ^ _356604) ^ [_504314, _504316, _504318] : [class_RealVector_Oreal__normed__algebra(_504314), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_504314), c_Groups_Ouminus__class_Ouminus(_504314, _504316)), _504318) = c_Groups_Ouminus__class_Ouminus(_504314, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_504314), _504316), _504318)))], (6756 ^ _356604) ^ [_597416, _597418, _597420] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _597416, _597418), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _597416, _597420), _597418))], (668 ^ _356604) ^ [_377000, _377002] : [-(class_Rings_Oring__1(_377000)), _377002 = _377000, class_Rings_Oring__1(_377002)], (3176 ^ _356604) ^ [_468228, _468230, _468232, _468234] : [class_Rings_Oordered__ring(_468228), c_Orderings_Oord__class_Oless__eq(_468228, _468230, _468232), c_Orderings_Oord__class_Oless__eq(_468228, _468234, c_Groups_Ozero__class_Ozero(_468228)), -(c_Orderings_Oord__class_Oless__eq(_468228, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_468228), _468234), _468232), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_468228), _468234), _468230)))], (12516 ^ _356604) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (2673 ^ _356604) ^ [_449886, _449888] : [class_Rings_Ocomm__semiring__0(_449886), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_449886)), _449888), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_449886))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_449886)))], (1391 ^ _356604) ^ [_401911, _401913, _401915, _401917] : [class_Rings_Ocomm__semiring__0(_401911), c_Polynomial_Osmult(_401911, _401913, _401915) = c_Polynomial_OpCons(_401911, _401917, _401915), -(_401915 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_401911)))], (4238 ^ _356604) ^ [_507184, _507186] : [class_Groups_Ocomm__monoid__mult(_507184), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_507184), _507186), c_Groups_Oone__class_Oone(_507184)) = _507186)], (4612 ^ _356604) ^ [_521023, _521025, _521027] : [class_Groups_Ozero(_521023), -(hAPP(c_Polynomial_Ocoeff(_521023, _521025), _521027) = c_Groups_Ozero__class_Ozero(_521023)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _521027, c_Polynomial_Odegree(_521023, _521025)))], (6184 ^ _356604) ^ [_577572, _577574, _577576, _577578] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _577572, _577574), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _577576, _577578), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _577572, _577576), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _577574, _577578)))], (12744 ^ _356604) ^ [_800385] : [class_Rings_Olinordered__idom(_800385), -(class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(_800385)))], (4538 ^ _356604) ^ [_518537, _518539] : [_518537 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _518537), _518539), -(_518539 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_518537 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4010 ^ _356604) ^ [_498716, _498718] : [class_Groups_Olinordered__ab__group__add(_498716), 4013 ^ _356604 : [(4020 ^ _356604) ^ [] : [_498718 = c_Groups_Ozero__class_Ozero(_498716), -(_498718 = c_Groups_Ouminus__class_Ouminus(_498716, _498718))], (4014 ^ _356604) ^ [] : [_498718 = c_Groups_Ouminus__class_Ouminus(_498716, _498718), -(_498718 = c_Groups_Ozero__class_Ozero(_498716))]]], (12852 ^ _356604) ^ [_803805] : [class_Rings_Oidom(_803805), -(class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(_803805)))], (1732 ^ _356604) ^ [_414504, _414506, _414508] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _414504, _414506), _414508) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _414504, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _414506, _414508)))], (6762 ^ _356604) ^ [_597658, _597660, _597662] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _597658, _597660), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _597658, _597662), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _597662, _597660), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _597662, _597658)))], (7672 ^ _356604) ^ [_627992, _627994, _627996, _627998] : [class_Rings_Olinordered__semidom(_627992), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _627994, _627996), c_Orderings_Oord__class_Oless(_627992, c_Groups_Ozero__class_Ozero(_627992), _627998), c_Orderings_Oord__class_Oless(_627992, _627998, c_Groups_Oone__class_Oone(_627992)), -(c_Orderings_Oord__class_Oless(_627992, hAPP(hAPP(c_Power_Opower__class_Opower(_627992), _627998), _627996), hAPP(hAPP(c_Power_Opower__class_Opower(_627992), _627998), _627994)))], (8386 ^ _356604) ^ [_653128, _653130] : [class_Groups_Olinordered__ab__group__add(_653128), 8389 ^ _356604 : [(8396 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_653128, c_Groups_Ozero__class_Ozero(_653128), _653130), -(c_Orderings_Oord__class_Oless(_653128, c_Groups_Ozero__class_Ozero(_653128), c_Groups_Oplus__class_Oplus(_653128, _653130, _653130)))], (8390 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_653128, c_Groups_Ozero__class_Ozero(_653128), c_Groups_Oplus__class_Oplus(_653128, _653130, _653130)), -(c_Orderings_Oord__class_Oless(_653128, c_Groups_Ozero__class_Ozero(_653128), _653130))]]], (6600 ^ _356604) ^ [_592102, _592104, _592106] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _592102, _592104), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _592106), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _592106), _592102), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _592106), _592104)))], (12562 ^ _356604) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (4708 ^ _356604) ^ [_524237, _524239, _524241, _524243] : [class_Rings_Olinordered__semidom(_524237), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _524239, _524241), c_Orderings_Oord__class_Oless__eq(_524237, c_Groups_Oone__class_Oone(_524237), _524243), -(c_Orderings_Oord__class_Oless__eq(_524237, hAPP(hAPP(c_Power_Opower__class_Opower(_524237), _524243), _524239), hAPP(hAPP(c_Power_Opower__class_Opower(_524237), _524243), _524241)))], (1758 ^ _356604) ^ [_415596, _415598, _415600] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _415596, _415598), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _415596, _415600)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _415598, _415600))], (4146 ^ _356604) ^ [_503226, _503228, _503230] : [class_Rings_Oring(_503226), -(c_Groups_Ouminus__class_Ouminus(_503226, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_503226), _503228), _503230)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_503226), c_Groups_Ouminus__class_Ouminus(_503226, _503228)), _503230))], (12708 ^ _356604) ^ [_799245] : [class_Rings_Oidom(_799245), -(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(_799245)))], (12858 ^ _356604) ^ [_803995] : [class_Groups_Ocomm__monoid__add(_803995), -(class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(_803995)))], (2573 ^ _356604) ^ [_445511, _445513, _445515, _445517] : [class_Rings_Ocomm__semiring__1(_445511), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_445511), _445513), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_445511), _445515), _445517)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_445511), _445515), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_445511), _445513), _445517)))], (4232 ^ _356604) ^ [_506956, _506958] : [class_Rings_Ocomm__semiring__1(_506956), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_506956), _506958), c_Groups_Oone__class_Oone(_506956)) = _506958)], (8666 ^ _356604) ^ [_662721, _662723, _662725] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _662721, _662723), -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _662725, _662723), _662721) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _662725, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _662723, _662721)))], (12626 ^ _356604) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (12786 ^ _356604) ^ [_801715] : [class_Rings_Oidom(_801715), -(class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(_801715)))], (8162 ^ _356604) ^ [_645934, _645936, _645938] : [class_Rings_Olinordered__semiring__strict(_645934), c_Orderings_Oord__class_Oless(_645934, c_Groups_Ozero__class_Ozero(_645934), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_645934), _645936), _645938)), c_Orderings_Oord__class_Oless(_645934, c_Groups_Ozero__class_Ozero(_645934), _645938), -(c_Orderings_Oord__class_Oless(_645934, c_Groups_Ozero__class_Ozero(_645934), _645936))], (12532 ^ _356604) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (12680 ^ _356604) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (738 ^ _356604) ^ [_379065, _379067] : [-(class_Groups_Oone(_379065)), _379067 = _379065, class_Groups_Oone(_379067)], (1098 ^ _356604) ^ [_392311, _392313] : [_392313 = _392311, -(c_Groups_Otimes__class_Otimes(_392313) = c_Groups_Otimes__class_Otimes(_392311))], (5472 ^ _356604) ^ [_551838, _551840] : [class_Lattices_Oboolean__algebra(_551838), -(c_Groups_Ouminus__class_Ouminus(_551838, c_Groups_Ouminus__class_Ouminus(_551838, _551840)) = _551840)], (2252 ^ _356604) ^ [_433101, _433103] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _433101, c_Nat_OSuc(_433103)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _433101, _433103)), -(_433101 = c_Nat_OSuc(_433103))], (12684 ^ _356604) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (10331 ^ _356604) ^ [_720310, _720312] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _720310, _720312)), 10332 ^ _356604 : [(10333 ^ _356604) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _720310, _720312), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _720312, _720310))], (10339 ^ _356604) ^ [] : [_720310 = _720312]]], (7648 ^ _356604) ^ [_627094, _627096] : [class_Groups_Ogroup__add(_627094), -(c_Groups_Ominus__class_Ominus(_627094, _627096, _627096) = c_Groups_Ozero__class_Ozero(_627094))], (478 ^ _356604) ^ [_371395, _371397] : [-(class_Rings_Olinordered__ring(_371395)), _371397 = _371395, class_Rings_Olinordered__ring(_371397)], (12350 ^ _356604) ^ [_788896] : [class_Rings_Oidom(_788896), -(class_Groups_Oab__group__add(_788896))], (804 ^ _356604) ^ [_381465, _381467] : [_381467 = _381465, -(c_String_Ochar_Ochar__size(_381467) = c_String_Ochar_Ochar__size(_381465))], (3290 ^ _356604) ^ [_472330, _472332, _472334] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _472330, _472332)), _472334) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _472330), _472334), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _472332), _472334)))], (5082 ^ _356604) ^ [_538106, _538108, _538110, _538112] : [class_Rings_Ocomm__semiring__1(_538106), c_Rings_Odvd__class_Odvd(_538106, _538108, _538110), -(c_Rings_Odvd__class_Odvd(_538106, _538108, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_538106), _538110), _538112)))], (238 ^ _356604) ^ [_364315, _364317] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_364315)), _364317 = _364315, class_Groups_Oordered__ab__semigroup__add__imp__le(_364317)], (8544 ^ _356604) ^ [_658225, _658227, _658229] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _658225, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _658227, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _658225), _658229))), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _658225, _658227))], (12804 ^ _356604) ^ [_802285] : [class_Rings_Olinordered__idom(_802285), -(class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(_802285)))], (6204 ^ _356604) ^ [_578218, _578220] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _578218), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _578220), c_Rings_Odvd__class_Odvd(tc_Int_Oint, _578218, _578220), c_Rings_Odvd__class_Odvd(tc_Int_Oint, _578220, _578218), -(_578218 = _578220)], (172 ^ _356604) ^ [_362268, _362270, _362272, _362274, _362276, _362278] : [-(c_Orderings_Oord__class_Oless(_362276, _362272, _362268)), c_Orderings_Oord__class_Oless(_362278, _362274, _362270), _362278 = _362276, _362274 = _362272, _362270 = _362268], (12534 ^ _356604) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (7218 ^ _356604) ^ [_613067, _613069, _613071] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_613067), _613069), c_Nat_OSuc(_613071)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _613067, _613069), _613071))], (5778 ^ _356604) ^ [_562761, _562763, _562765] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _562761), _562763), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _562761), _562765)), -(_562761 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _562763, _562765))], (6506 ^ _356604) ^ [_588847, _588849, _588851, _588853] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _588847, _588849), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _588851, _588849) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _588847, _588853), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _588851, _588853))], (2497 ^ _356604) ^ [_441883, _441885, _441887] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_441883), 2500 ^ _356604 : [(2507 ^ _356604) ^ [] : [_441887 = c_Groups_Ozero__class_Ozero(_441883), -(_441885 = c_Groups_Oplus__class_Oplus(_441883, _441885, _441887))], (2501 ^ _356604) ^ [] : [_441885 = c_Groups_Oplus__class_Oplus(_441883, _441885, _441887), -(_441887 = c_Groups_Ozero__class_Ozero(_441883))]]], (12650 ^ _356604) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (3254 ^ _356604) ^ [_470975, _470977] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _470975), _470977) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_470975 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_470977 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6242 ^ _356604) ^ [_579544, _579546, _579548] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _579544, _579546), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _579544, _579548), 6249 ^ _356604 : [(6256 ^ _356604) ^ [] : [_579546 = _579548, -(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _579546, _579544) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _579548, _579544))], (6250 ^ _356604) ^ [] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _579546, _579544) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _579548, _579544), -(_579546 = _579548)]]], (468 ^ _356604) ^ [_371100, _371102] : [-(class_Rings_Ono__zero__divisors(_371100)), _371102 = _371100, class_Rings_Ono__zero__divisors(_371102)], (2234 ^ _356604) ^ [_432485, _432487] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_432485), c_Nat_OSuc(_432487)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _432485, _432487))], (1193 ^ _356604) ^ [_395717, _395719, _395721] : [class_Rings_Ocomm__semiring__0(_395717), -(c_Polynomial_Odegree(_395717, c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(_395717, _395719, _395721)) = c_Polynomial_Odegree(_395717, _395719))], (9621 ^ _356604) ^ [_696418, _696420, _696422, _696424, _696426] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _696418, _696420), 9624 ^ _356604 : [(9631 ^ _356604) ^ [] : [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, _696420, _696418)), _696422), _696424), _696426), -(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), _696420), _696422), _696424), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _696418), _696422), _696426)))], (9625 ^ _356604) ^ [] : [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), _696420), _696422), _696424), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _696418), _696422), _696426)), -(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, _696420, _696418)), _696422), _696424), _696426))]]], (13062 ^ _356604) ^ [] : [-(class_Rings_Oidom(t_a))], (5450 ^ _356604) ^ [_550821, _550823, _550825, _550827] : [-(hAPP(hAPP(c_Power_Opower_Opower(_550821, _550823, _550825), _550827), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _550823)], (10838 ^ _356604) ^ [_738113, _738115] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _738113, _738115), -(c_Nat__Transfer_Otsub(_738115, _738113) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _738115, _738113))], (12544 ^ _356604) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (6570 ^ _356604) ^ [_591066, _591068] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _591066, _591068), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _591066, _591068))], (12472 ^ _356604) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint))], (6542 ^ _356604) ^ [_590183, _590185] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _590183, _590185)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _590183, _590185), -(_590183 = _590185)], (5867 ^ _356604) ^ [_566244, _566246, _566248] : [-(hBOOL(hAPP(_566244, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _566246, _566248)))), 5870 ^ _356604 : [(5873 ^ _356604) ^ [] : [hBOOL(hAPP(_566244, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (5871 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _566246, _566248))]], 5875 ^ _356604 : [(5878 ^ _356604) ^ [] : [hBOOL(hAPP(_566244, 5874 ^ [_566244, _566246, _566248]))], (5876 ^ _356604) ^ [] : [-(_566246 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _566248, 5874 ^ [_566244, _566246, _566248]))]]], (1128 ^ _356604) ^ [_393404, _393406] : [_393406 = _393404, -(tc_Polynomial_Opoly(_393406) = tc_Polynomial_Opoly(_393404))], (12822 ^ _356604) ^ [_802855] : [class_Rings_Olinordered__idom(_802855), -(class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(_802855)))], (8044 ^ _356604) ^ [_641957, _641959, _641961, _641963] : [class_Rings_Olinordered__ring__strict(_641957), c_Orderings_Oord__class_Oless(_641957, _641959, _641961), c_Orderings_Oord__class_Oless(_641957, _641963, c_Groups_Ozero__class_Ozero(_641957)), -(c_Orderings_Oord__class_Oless(_641957, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_641957), _641963), _641961), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_641957), _641963), _641959)))], (11690 ^ _356604) ^ [_766994, _766996, _766998, _767000] : [class_Fields_Olinordered__field__inverse__zero(_766994), 11693 ^ _356604 : [(11694 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_766994, c_Rings_Oinverse__class_Odivide(_766994, _766996, _766998), _767000), 11697 ^ _356604 : [(11704 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_766994, c_Groups_Ozero__class_Ozero(_766994), _766998)), 11707 ^ _356604 : [(11714 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_766994, _766998, c_Groups_Ozero__class_Ozero(_766994))), -(c_Orderings_Oord__class_Oless(_766994, c_Groups_Ozero__class_Ozero(_766994), _767000))], (11708 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_766994, _766998, c_Groups_Ozero__class_Ozero(_766994)), -(c_Orderings_Oord__class_Oless(_766994, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_766994), _767000), _766998), _766996))]]], (11698 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_766994, c_Groups_Ozero__class_Ozero(_766994), _766998), -(c_Orderings_Oord__class_Oless(_766994, _766996, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_766994), _767000), _766998)))]]], (11720 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_766994, c_Rings_Oinverse__class_Odivide(_766994, _766996, _766998), _767000)), 11723 ^ _356604 : [(11726 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_766994, _766996, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_766994), _767000), _766998))], (11724 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_766994, c_Groups_Ozero__class_Ozero(_766994), _766998))]], 11727 ^ _356604 : [(11730 ^ _356604) ^ [] : [11731 ^ _356604 : [(11734 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_766994, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_766994), _767000), _766998), _766996)], (11732 ^ _356604) ^ [] : [-(c_Orderings_Oord__class_Oless(_766994, _766998, c_Groups_Ozero__class_Ozero(_766994)))]], 11735 ^ _356604 : [(11738 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_766994, c_Groups_Ozero__class_Ozero(_766994), _767000)], (11736 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_766994, _766998, c_Groups_Ozero__class_Ozero(_766994))]]], (11728 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_766994, c_Groups_Ozero__class_Ozero(_766994), _766998)]]]]], (1884 ^ _356604) ^ [_420258, _420260, _420262, _420264] : [class_Groups_Ocancel__semigroup__add(_420258), c_Groups_Oplus__class_Oplus(_420258, _420260, _420262) = c_Groups_Oplus__class_Oplus(_420258, _420260, _420264), -(_420262 = _420264)], (3841 ^ _356604) ^ [_493107, _493109, _493111] : [class_Groups_Oab__group__add(_493107), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_493107), c_Polynomial_Omonom(_493107, _493109, _493111)) = c_Polynomial_Omonom(_493107, c_Groups_Ouminus__class_Ouminus(_493107, _493109), _493111))], (1054 ^ _356604) ^ [_390758, _390760, _390762, _390764, _390766, _390768] : [-(c_Groups_Ominus__class_Ominus(_390768, _390764, _390760) = c_Groups_Ominus__class_Ominus(_390766, _390762, _390758)), _390768 = _390766, _390764 = _390762, _390760 = _390758], (2202 ^ _356604) ^ [_431332] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_431332), _431332)], (5936 ^ _356604) ^ [_568789, _568791, _568793, _568795] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_568789), 5939 ^ _356604 : [(5946 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_568789, _568791, _568795), -(c_Orderings_Oord__class_Oless(_568789, c_Groups_Oplus__class_Oplus(_568789, _568791, _568793), c_Groups_Oplus__class_Oplus(_568789, _568795, _568793)))], (5940 ^ _356604) ^ [] : [c_Orderings_Oord__class_Oless(_568789, c_Groups_Oplus__class_Oplus(_568789, _568791, _568793), c_Groups_Oplus__class_Oplus(_568789, _568795, _568793)), -(c_Orderings_Oord__class_Oless(_568789, _568791, _568795))]]], (12668 ^ _356604) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (12636 ^ _356604) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (8618 ^ _356604) ^ [_660894, _660896] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _660894, _660896) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _660894, _660896))], (11120 ^ _356604) ^ [_748437, _748439, _748441, _748443] : [class_Fields_Olinordered__field(_748437), c_Orderings_Oord__class_Oless__eq(_748437, _748439, _748441), c_Orderings_Oord__class_Oless__eq(_748437, c_Groups_Ozero__class_Ozero(_748437), _748443), c_Orderings_Oord__class_Oless(_748437, c_Groups_Ozero__class_Ozero(_748437), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_748437), _748441), _748439)), -(c_Orderings_Oord__class_Oless__eq(_748437, c_Rings_Oinverse__class_Odivide(_748437, _748443, _748441), c_Rings_Oinverse__class_Odivide(_748437, _748443, _748439)))], (8889 ^ _356604) ^ [_670900, _670902] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _670900, _670902), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _670900, c_Nat_OSuc(_670902)))], (11156 ^ _356604) ^ [_749876, _749878, _749880, _749882] : [class_Fields_Olinordered__field__inverse__zero(_749876), c_Orderings_Oord__class_Oless__eq(_749876, _749878, _749880), c_Orderings_Oord__class_Oless__eq(_749876, _749882, c_Groups_Ozero__class_Ozero(_749876)), -(c_Orderings_Oord__class_Oless__eq(_749876, c_Rings_Oinverse__class_Odivide(_749876, _749880, _749882), c_Rings_Oinverse__class_Odivide(_749876, _749878, _749882)))], (11308 ^ _356604) ^ [_754688, _754690, _754692] : [class_Fields_Olinordered__field(_754688), c_Orderings_Oord__class_Oless(_754688, c_Groups_Ozero__class_Ozero(_754688), _754690), c_Orderings_Oord__class_Oless(_754688, _754692, c_Groups_Ozero__class_Ozero(_754688)), -(c_Orderings_Oord__class_Oless(_754688, c_Rings_Oinverse__class_Odivide(_754688, _754690, _754692), c_Groups_Ozero__class_Ozero(_754688)))], (5968 ^ _356604) ^ [_569885, _569887, _569889, _569891] : [class_Groups_Oordered__cancel__ab__semigroup__add(_569885), c_Orderings_Oord__class_Oless(_569885, _569887, _569889), -(c_Orderings_Oord__class_Oless(_569885, c_Groups_Oplus__class_Oplus(_569885, _569887, _569891), c_Groups_Oplus__class_Oplus(_569885, _569889, _569891)))], (12768 ^ _356604) ^ [_801145] : [class_Rings_Oidom(_801145), -(class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(_801145)))], (1044 ^ _356604) ^ [_390371, _390373, _390375, _390377] : [-(c_Groups_Ouminus__class_Ouminus(_390377, _390373) = c_Groups_Ouminus__class_Ouminus(_390375, _390371)), _390377 = _390375, _390373 = _390371], (1463 ^ _356604) ^ [_404330, _404332, _404334] : [class_Groups_Ozero(_404330), 1466 ^ _356604 : [(1473 ^ _356604) ^ [] : [_404332 = c_Groups_Ozero__class_Ozero(_404330), -(c_Polynomial_Omonom(_404330, _404332, _404334) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_404330)))], (1467 ^ _356604) ^ [] : [c_Polynomial_Omonom(_404330, _404332, _404334) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_404330)), -(_404332 = c_Groups_Ozero__class_Ozero(_404330))]]], (10589 ^ _356604) ^ [_729029, _729031] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _729029), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _729031), -(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, _729029, _729031)))]], input).
% 76.87/74.89 ncf('1',plain,[c_Polynomial_Odegree(t_a, v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)],start(13064 ^ 0)).
% 76.87/74.89 ncf('1.1',plain,[-(c_Polynomial_Odegree(t_a, v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 2641 : c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)), c_Polynomial_Odegree(t_a, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)), c_Polynomial_Odegree(t_a, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))), 2641 : -(c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), 2641 : class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(tc_Int_Oint))],extension(2637 ^ 1,bind([[_448349, _448351, _448353, _448355, _448357], [tc_Polynomial_Opoly(tc_Int_Oint), c_Polynomial_Odegree(t_a, v_p), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))]]))).
% 76.87/74.89 ncf('1.1.1',plain,[-(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)), c_Polynomial_Odegree(t_a, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)), c_Polynomial_Odegree(t_a, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)), c_Polynomial_Odegree(t_a, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)), c_Polynomial_Odegree(t_a, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)), c_Polynomial_Odegree(t_a, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)), c_Polynomial_Odegree(t_a, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))))],extension(10197 ^ 4,bind([[_716109, _716111], [c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)), c_Polynomial_Odegree(t_a, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)), c_Polynomial_Odegree(t_a, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))]]))).
% 76.87/74.89 ncf('1.1.1.1',plain,[-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)), c_Polynomial_Odegree(t_a, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)), c_Polynomial_Odegree(t_a, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))))), class_Rings_Ocomm__semiring__1(tc_Nat_Onat)],extension(5222 ^ 5,bind([[_543051, _543053], [tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)), c_Polynomial_Odegree(t_a, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))]]))).
% 76.87/74.89 ncf('1.1.1.1.1',plain,[-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))],extension(12660 ^ 6)).
% 76.87/74.89 ncf('1.1.1.2',plain,[-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)), c_Polynomial_Odegree(t_a, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)), c_Polynomial_Odegree(t_a, v_p)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(tc_Int_Oint)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))))],lemmata('[1, 1].x')).
% 76.87/74.89 ncf('1.1.2',plain,[c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)), 1595 : -(c_Polynomial_Odegree(t_a, c_Polynomial_OpCons(t_a, hAPP(c_Polynomial_Opoly(t_a, v_p), c_Groups_Ozero__class_Ozero(t_a)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 1595 : class_Groups_Ozero(t_a)],extension(1591 ^ 4,bind([[_409092, _409094, _409096], [t_a, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)), hAPP(c_Polynomial_Opoly(t_a, v_p), c_Groups_Ozero__class_Ozero(t_a))]]))).
% 76.87/74.89 ncf('1.1.2.1',plain,[c_Polynomial_Odegree(t_a, c_Polynomial_OpCons(t_a, hAPP(c_Polynomial_Opoly(t_a, v_p), c_Groups_Ozero__class_Ozero(t_a)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Polynomial_Odegree(t_a, v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), c_Polynomial_Odegree(t_a, v_p) = c_Polynomial_Odegree(t_a, c_Polynomial_OpCons(t_a, hAPP(c_Polynomial_Opoly(t_a, v_p), c_Groups_Ozero__class_Ozero(t_a)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))],extension(10 ^ 7,bind([[_357039, _357041, _357043], [c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Polynomial_Odegree(t_a, c_Polynomial_OpCons(t_a, hAPP(c_Polynomial_Opoly(t_a, v_p), c_Groups_Ozero__class_Ozero(t_a)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)))), c_Polynomial_Odegree(t_a, v_p)]]))).
% 76.87/74.89 ncf('1.1.2.1.1',plain,[c_Polynomial_Odegree(t_a, v_p) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)],reduction('1')).
% 76.87/74.89 ncf('1.1.2.1.2',plain,[-(c_Polynomial_Odegree(t_a, v_p) = c_Polynomial_Odegree(t_a, c_Polynomial_OpCons(t_a, hAPP(c_Polynomial_Opoly(t_a, v_p), c_Groups_Ozero__class_Ozero(t_a)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a))))), class_Int_Oring__char__0(t_a), class_Rings_Oidom(t_a)],extension(1215 ^ 8)).
% 76.87/74.89 ncf('1.1.2.1.2.1',plain,[-(class_Int_Oring__char__0(t_a))],extension(13060 ^ 9)).
% 76.87/74.89 ncf('1.1.2.1.2.2',plain,[-(class_Rings_Oidom(t_a))],extension(13062 ^ 9)).
% 76.87/74.89 ncf('1.1.2.2',plain,[-(class_Groups_Ozero(t_a)), class_Int_Oring__char__0(t_a)],extension(12248 ^ 5,bind([[_785734], [t_a]]))).
% 76.87/74.89 ncf('1.1.2.2.1',plain,[-(class_Int_Oring__char__0(t_a))],extension(13060 ^ 6)).
% 76.87/74.89 ncf('1.1.3',plain,[-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(tc_Int_Oint))), class_Rings_Oidom(tc_Polynomial_Opoly(tc_Int_Oint))],extension(12272 ^ 2,bind([[_786478], [tc_Polynomial_Opoly(tc_Int_Oint)]]))).
% 76.87/74.89 ncf('1.1.3.1',plain,[-(class_Rings_Oidom(tc_Polynomial_Opoly(tc_Int_Oint))), class_Rings_Oidom(tc_Int_Oint)],extension(13026 ^ 3,bind([[_809315], [tc_Int_Oint]]))).
% 76.87/74.89 ncf('1.1.3.1.1',plain,[-(class_Rings_Oidom(tc_Int_Oint))],extension(12616 ^ 4)).
% 76.87/74.89 %-----------------------------------------------------
% 76.87/74.89 End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------