%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW237+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n003.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 12:25:48 EDT 2023

% Result   : Theorem 61.55s 59.43s
% Output   : Proof 61.55s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWW237+1 : TPTP v8.1.2. Released v5.2.0.
% 0.03/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.34  % Computer : n003.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Thu May 18 22:30:15 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 61.55/59.43  
% 61.55/59.43  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 61.55/59.43  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 61.55/59.43  %-----------------------------------------------------
% 61.55/59.43  ncf(matrix, plain, [(13044 ^ _788666) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_da____, v_mazh)], !, (8134 ^ _319074) ^ [_598106, _598108, _598110] : [class_Rings_Oidom(_598106), 8137 ^ _319074 : [(8144 ^ _319074) ^ [] : [hAPP(c_Polynomial_Opoly(_598106, _598110), c_Groups_Ouminus__class_Ouminus(_598106, _598108)) = c_Groups_Ozero__class_Ozero(_598106), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_598106), c_Polynomial_OpCons(_598106, _598108, c_Polynomial_OpCons(_598106, c_Groups_Oone__class_Oone(_598106), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_598106)))), _598110))], (8138 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_598106), c_Polynomial_OpCons(_598106, _598108, c_Polynomial_OpCons(_598106, c_Groups_Oone__class_Oone(_598106), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_598106)))), _598110), -(hAPP(c_Polynomial_Opoly(_598106, _598110), c_Groups_Ouminus__class_Ouminus(_598106, _598108)) = c_Groups_Ozero__class_Ozero(_598106))]]], (5441 ^ _319074) ^ [_503202, _503204, _503206, _503208] : [class_Fields_Olinordered__field(_503202), c_Orderings_Oord__class_Oless(_503202, _503204, _503206), c_Orderings_Oord__class_Oless(_503202, _503208, c_Groups_Ozero__class_Ozero(_503202)), c_Orderings_Oord__class_Oless(_503202, c_Groups_Ozero__class_Ozero(_503202), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_503202), _503204), _503206)), -(c_Orderings_Oord__class_Oless(_503202, c_Rings_Oinverse__class_Odivide(_503202, _503208, _503204), c_Rings_Oinverse__class_Odivide(_503202, _503208, _503206)))], (12170 ^ _319074) ^ [_742637, _742639, _742641] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_742637), _742639), c_Nat_OSuc(_742641)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _742637, _742639), _742641))], (2202 ^ _319074) ^ [_391633, _391635, _391637, _391639] : [class_Orderings_Oord(_391633), _391635 = _391637, c_Orderings_Oord__class_Oless(_391633, _391637, _391639), -(c_Orderings_Oord__class_Oless(_391633, _391635, _391639))], (3368 ^ _319074) ^ [_429471, _429473, _429475] : [class_Groups_Oordered__ab__group__add__abs(_429471), c_Orderings_Oord__class_Oless__eq(_429471, c_Groups_Oabs__class_Oabs(_429471, _429473), _429475), -(c_Orderings_Oord__class_Oless__eq(_429471, c_Groups_Ouminus__class_Ouminus(_429471, _429473), _429475))], (290 ^ _319074) ^ [_327974, _327976] : [-(class_Groups_Oordered__comm__monoid__add(_327974)), _327976 = _327974, class_Groups_Oordered__comm__monoid__add(_327976)], (12262 ^ _319074) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (1956 ^ _319074) ^ [_383658, _383660, _383662] : [class_Groups_Oordered__comm__monoid__add(_383658), c_Orderings_Oord__class_Oless(_383658, c_Groups_Ozero__class_Ozero(_383658), _383660), c_Orderings_Oord__class_Oless__eq(_383658, c_Groups_Ozero__class_Ozero(_383658), _383662), -(c_Orderings_Oord__class_Oless(_383658, c_Groups_Ozero__class_Ozero(_383658), c_Groups_Oplus__class_Oplus(_383658, _383660, _383662)))], (8690 ^ _319074) ^ [_617918, _617920] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _617918, _617920), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _617920), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _617918, _617920))], (1882 ^ _319074) ^ [_380586, _380588] : [class_Groups_Ocomm__monoid__add(_380586), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_380586), _380588, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_380586))) = _380588)], (12564 ^ _319074) ^ [] : [-(class_Rings_Oring__1(tc_RealDef_Oreal))], (8484 ^ _319074) ^ [_610256, _610258] : [class_Rings_Ocomm__semiring__1(_610256), -(hAPP(hAPP(c_Power_Opower__class_Opower(_610256), _610258), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _610258)], (12782 ^ _319074) ^ [_760243] : [class_Rings_Olinordered__idom(_760243), -(class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(_760243)))], (10790 ^ _319074) ^ [_689376, _689378] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_689376)), _689378) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _689378, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _689376), _689378)))], (2076 ^ _319074) ^ [_387651, _387653] : [class_Groups_Oordered__ab__group__add(_387651), 2079 ^ _319074 : [(2086 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_387651, c_Groups_Ozero__class_Ozero(_387651), _387653), -(c_Orderings_Oord__class_Oless(_387651, c_Groups_Ouminus__class_Ouminus(_387651, _387653), c_Groups_Ozero__class_Ozero(_387651)))], (2080 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_387651, c_Groups_Ouminus__class_Ouminus(_387651, _387653), c_Groups_Ozero__class_Ozero(_387651)), -(c_Orderings_Oord__class_Oless(_387651, c_Groups_Ozero__class_Ozero(_387651), _387653))]]], (11380 ^ _319074) ^ [_710250, _710252, _710254] : [class_RealVector_Oreal__normed__vector(_710250), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_710250, c_Groups_Ominus__class_Ominus(_710250, _710252, _710254)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_710250, _710252), c_RealVector_Onorm__class_Onorm(_710250, _710254))))], (2504 ^ _319074) ^ [_401215, _401217] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _401215), _401217), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _401215, _401217)))], (360 ^ _319074) ^ [_330039, _330041] : [-(class_Rings_Oordered__comm__semiring(_330039)), _330041 = _330039, class_Rings_Oordered__comm__semiring(_330041)], (1048 ^ _319074) ^ [_352424, _352426, _352428, _352430, _352432, _352434] : [-(c_Rings_Oinverse__class_Odivide(_352434, _352430, _352426) = c_Rings_Oinverse__class_Odivide(_352432, _352428, _352424)), _352434 = _352432, _352430 = _352428, _352426 = _352424], (12290 ^ _319074) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (9312 ^ _319074) ^ [_637612] : [-(c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, _637612) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, _637612, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _637612)))], (12360 ^ _319074) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (450 ^ _319074) ^ [_332694, _332696] : [-(class_Groups_Oab__semigroup__add(_332694)), _332696 = _332694, class_Groups_Oab__semigroup__add(_332696)], (10117 ^ _319074) ^ [_665613, _665615] : [10118 ^ _319074 : [(10121 ^ _319074) ^ [] : [_665613 = _665615], (10119 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _665613, _665615)]], -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _665613, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _665615, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (510 ^ _319074) ^ [_334464, _334466] : [-(class_Rings_Ozero__neq__one(_334464)), _334466 = _334464, class_Rings_Ozero__neq__one(_334466)], (10383 ^ _319074) ^ [_674683] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_674683), _674683)], (7264 ^ _319074) ^ [_565311, _565313, _565315, _565317] : [class_Rings_Ocomm__semiring__0(_565311), -(hAPP(c_Polynomial_Opoly(_565311, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_565311), _565313, _565315)), _565317) = c_Groups_Oplus__class_Oplus(_565311, hAPP(c_Polynomial_Opoly(_565311, _565313), _565317), hAPP(c_Polynomial_Opoly(_565311, _565315), _565317)))], (3124 ^ _319074) ^ [_421337, _421339, _421341, _421343] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_421337), 3127 ^ _319074 : [(3134 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_421337, _421339, _421343), -(c_Orderings_Oord__class_Oless(_421337, c_Groups_Oplus__class_Oplus(_421337, _421339, _421341), c_Groups_Oplus__class_Oplus(_421337, _421343, _421341)))], (3128 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_421337, c_Groups_Oplus__class_Oplus(_421337, _421339, _421341), c_Groups_Oplus__class_Oplus(_421337, _421343, _421341)), -(c_Orderings_Oord__class_Oless(_421337, _421339, _421343))]]], (560 ^ _319074) ^ [_335939, _335941] : [-(class_Groups_Ocomm__monoid__add(_335939)), _335941 = _335939, class_Groups_Ocomm__monoid__add(_335941)], (12508 ^ _319074) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_RealDef_Oreal))], (1062 ^ _319074) ^ [_352940, _352942, _352944, _352946, _352948, _352950] : [-(c_Groups_Ominus__class_Ominus(_352950, _352946, _352942) = c_Groups_Ominus__class_Ominus(_352948, _352944, _352940)), _352950 = _352948, _352946 = _352944, _352942 = _352940], (11060 ^ _319074) ^ [_698840, _698842] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _698840, _698842) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _698842, _698840))], (8063 ^ _319074) ^ [_595308] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _595308), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _595308)], (1439 ^ _319074) ^ [_365875, _365877] : [class_Groups_Olinordered__ab__group__add(_365875), 1442 ^ _319074 : [(1449 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_365875, c_Groups_Ozero__class_Ozero(_365875), _365877), -(c_Orderings_Oord__class_Oless__eq(_365875, c_Groups_Ozero__class_Ozero(_365875), c_Groups_Oplus__class_Oplus(_365875, _365877, _365877)))], (1443 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_365875, c_Groups_Ozero__class_Ozero(_365875), c_Groups_Oplus__class_Oplus(_365875, _365877, _365877)), -(c_Orderings_Oord__class_Oless__eq(_365875, c_Groups_Ozero__class_Ozero(_365875), _365877))]]], (10828 ^ _319074) ^ [_690903, _690905, _690907, _690909] : [class_Rings_Olinordered__semidom(_690903), c_Orderings_Oord__class_Oless__eq(_690903, hAPP(hAPP(c_Power_Opower__class_Opower(_690903), _690905), c_Nat_OSuc(_690907)), hAPP(hAPP(c_Power_Opower__class_Opower(_690903), _690909), c_Nat_OSuc(_690907))), c_Orderings_Oord__class_Oless__eq(_690903, c_Groups_Ozero__class_Ozero(_690903), _690909), -(c_Orderings_Oord__class_Oless__eq(_690903, _690905, _690909))], (7423 ^ _319074) ^ [_571282, _571284] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _571282, _571284), -(_571284 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _571282, 7426 ^ [_571282, _571284]))], (7088 ^ _319074) ^ [_559152, _559154, _559156, _559158] : [class_Rings_Ocomm__semiring__0(_559152), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_559152)), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_559152), _559154, _559156)), _559158) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_559152), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_559152)), _559154), _559158), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_559152)), _559156), _559158)))], (3012 ^ _319074) ^ [_417505, _417507, _417509] : [class_Orderings_Olinorder(_417505), -(c_Orderings_Oord__class_Oless__eq(_417505, _417507, _417509)), -(c_Orderings_Oord__class_Oless(_417505, _417509, _417507))], (4755 ^ _319074) ^ [_480384, _480386, _480388] : [class_Rings_Oring(_480384), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_480384), c_Groups_Ouminus__class_Ouminus(_480384, _480386)), c_Groups_Ouminus__class_Ouminus(_480384, _480388)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_480384), _480386), _480388))], (8768 ^ _319074) ^ [_620388, _620390] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _620388), 8771 ^ _319074 : [(8778 ^ _319074) ^ [] : [_620390 = 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), _620388), _620390), _620388))], (8772 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _620388), _620390), _620388), -(_620390 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (10550 ^ _319074) ^ [_681209] : [10551 ^ _319074 : [(10552 ^ _319074) ^ [_681280] : [_681209 = c_Nat_OSuc(_681280)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _681209))], (1507 ^ _319074) ^ [_368121, _368123, _368125, _368127] : [class_Orderings_Oorder(_368121), c_Orderings_Oord__class_Oless__eq(_368121, _368123, _368125), c_Orderings_Oord__class_Oless__eq(_368121, _368127, _368123), -(c_Orderings_Oord__class_Oless__eq(_368121, _368127, _368125))], (12932 ^ _319074) ^ [_764993] : [class_Rings_Ocomm__ring(_764993), -(class_Rings_Ocomm__ring(tc_Polynomial_Opoly(_764993)))], (11054 ^ _319074) ^ [_698619, _698621, _698623] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _698619, _698621), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _698623, _698619), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _698623, _698621)))], (90 ^ _319074) ^ [_322074, _322076] : [-(class_Fields_Olinordered__field__inverse__zero(_322074)), _322076 = _322074, class_Fields_Olinordered__field__inverse__zero(_322076)], (7799 ^ _319074) ^ [_586478, _586480] : [class_Groups_Omonoid__mult(_586478), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_586478), c_Groups_Oone__class_Oone(_586478)), _586480) = _586480)], (12418 ^ _319074) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (12542 ^ _319074) ^ [] : [-(class_Rings_Osemiring__0(tc_RealDef_Oreal))], (1776 ^ _319074) ^ [_376995, _376997] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _376995, _376997), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _376997, _376995), -(_376995 = _376997)], (5813 ^ _319074) ^ [_515966, _515968, _515970, _515972] : [class_Rings_Odivision__ring(_515966), -(_515968 = c_Groups_Ozero__class_Ozero(_515966)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_515966), _515970), _515968) = _515972, -(_515970 = c_Rings_Oinverse__class_Odivide(_515966, _515972, _515968))], (12484 ^ _319074) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal))], (2336 ^ _319074) ^ [_395868, _395870, _395872] : [class_Groups_Ogroup__add(_395868), 2339 ^ _319074 : [(2346 ^ _319074) ^ [] : [_395870 = _395872, -(c_Groups_Ouminus__class_Ouminus(_395868, _395870) = c_Groups_Ouminus__class_Ouminus(_395868, _395872))], (2340 ^ _319074) ^ [] : [c_Groups_Ouminus__class_Ouminus(_395868, _395870) = c_Groups_Ouminus__class_Ouminus(_395868, _395872), -(_395870 = _395872)]]], (10562 ^ _319074) ^ [_681616] : [_681616 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _681616, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (10912 ^ _319074) ^ [_693664, _693666] : [-(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), _693664), _693666))), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _693664), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _693666)], (230 ^ _319074) ^ [_326204, _326206] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_326204)), _326206 = _326204, class_Groups_Oordered__ab__semigroup__add__imp__le(_326206)], (2604 ^ _319074) ^ [_404556, _404558] : [class_Groups_Ogroup__add(_404556), 2607 ^ _319074 : [(2614 ^ _319074) ^ [] : [_404558 = c_Groups_Ozero__class_Ozero(_404556), -(c_Groups_Ouminus__class_Ouminus(_404556, _404558) = c_Groups_Ozero__class_Ozero(_404556))], (2608 ^ _319074) ^ [] : [c_Groups_Ouminus__class_Ouminus(_404556, _404558) = c_Groups_Ozero__class_Ozero(_404556), -(_404558 = c_Groups_Ozero__class_Ozero(_404556))]]], (12824 ^ _319074) ^ [_761573] : [class_Rings_Oidom(_761573), -(class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(_761573)))], (5699 ^ _319074) ^ [_511680, _511682, _511684, _511686] : [class_Rings_Olinordered__comm__semiring__strict(_511680), c_Orderings_Oord__class_Oless(_511680, _511682, _511684), c_Orderings_Oord__class_Oless(_511680, c_Groups_Ozero__class_Ozero(_511680), _511686), -(c_Orderings_Oord__class_Oless(_511680, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_511680), _511686), _511682), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_511680), _511686), _511684)))], (4407 ^ _319074) ^ [_465216, _465218] : [class_Lattices_Oab__semigroup__idem__mult(_465216), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_465216), _465218), _465218) = _465218)], (3882 ^ _319074) ^ [_446653, _446655] : [3883 ^ _319074 : [(3886 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _446655, _446653)], (3884 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _446653, _446655)]], _446653 = _446655], (750 ^ _319074) ^ [_341544, _341546] : [-(class_Groups_Ozero(_341544)), _341546 = _341544, class_Groups_Ozero(_341546)], (2092 ^ _319074) ^ [_388136, _388138] : [class_Groups_Oordered__ab__group__add(_388136), 2095 ^ _319074 : [(2102 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_388136, _388138, c_Groups_Ozero__class_Ozero(_388136)), -(c_Orderings_Oord__class_Oless(_388136, c_Groups_Ozero__class_Ozero(_388136), c_Groups_Ouminus__class_Ouminus(_388136, _388138)))], (2096 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_388136, c_Groups_Ozero__class_Ozero(_388136), c_Groups_Ouminus__class_Ouminus(_388136, _388138)), -(c_Orderings_Oord__class_Oless(_388136, _388138, c_Groups_Ozero__class_Ozero(_388136)))]]], (10978 ^ _319074) ^ [_695865, _695867, _695869] : [-(_695865 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 10981 ^ _319074 : [(10988 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _695867, _695869), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _695867), _695865), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _695869), _695865)))], (10982 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _695867), _695865), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _695869), _695865)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _695867, _695869))]]], (11244 ^ _319074) ^ [_705181, _705183, _705185] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _705181), _705181 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _705183, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _705181), _705185)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _705183), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _705185, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (1944 ^ _319074) ^ [_383105, _383107, _383109, _383111] : [class_Groups_Ozero(_383105), hAPP(hAPP(hAPP(_383107, c_Groups_Ozero__class_Ozero(_383105)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_383105))), _383109) = _383109, -(c_Polynomial_Opoly__rec(_383111, _383105, _383109, _383107, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_383105))) = _383109)], (8378 ^ _319074) ^ [_606459, _606461, _606463, _606465] : [class_Rings_Oidom(_606459), 8381 ^ _319074 : [(8382 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(_606459, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_606459), _606461), _606463), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_606459), _606465), _606463)), -(_606463 = c_Groups_Ozero__class_Ozero(_606459)), -(c_Rings_Odvd__class_Odvd(_606459, _606461, _606465))], (8392 ^ _319074) ^ [] : [8393 ^ _319074 : [(8396 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(_606459, _606461, _606465)], (8394 ^ _319074) ^ [] : [_606463 = c_Groups_Ozero__class_Ozero(_606459)]], -(c_Rings_Odvd__class_Odvd(_606459, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_606459), _606461), _606463), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_606459), _606465), _606463)))]]], (7076 ^ _319074) ^ [_558560, _558562] : [class_Rings_Ocomm__semiring__0(_558560), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_558560)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_558560))), _558562) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_558560)))], (11948 ^ _319074) ^ [_733784, _733786, _733788, _733790] : [class_Rings_Olinordered__idom(_733784), 11951 ^ _319074 : [(11960 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_733784, c_Groups_Oabs__class_Oabs(_733784, c_Groups_Ominus__class_Ominus(_733784, _733786, _733788)), _733790)), c_Orderings_Oord__class_Oless(_733784, c_Groups_Ominus__class_Ominus(_733784, _733788, _733790), _733786), c_Orderings_Oord__class_Oless(_733784, _733786, c_Groups_Oplus__class_Oplus(_733784, _733788, _733790))], (11952 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_733784, c_Groups_Oabs__class_Oabs(_733784, c_Groups_Ominus__class_Ominus(_733784, _733786, _733788)), _733790), 11955 ^ _319074 : [(11958 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_733784, _733786, c_Groups_Oplus__class_Oplus(_733784, _733788, _733790)))], (11956 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_733784, c_Groups_Ominus__class_Ominus(_733784, _733788, _733790), _733786))]]]]], (10335 ^ _319074) ^ [_673054, _673056] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _673054, _673056), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _673054, c_Nat_OSuc(_673056)))], (9504 ^ _319074) ^ [_644431, _644433, _644435, _644437] : [class_Rings_Olinordered__semidom(_644431), c_Orderings_Oord__class_Oless(_644431, c_Groups_Oone__class_Oone(_644431), _644433), 9511 ^ _319074 : [(9518 ^ _319074) ^ [] : [_644435 = _644437, -(hAPP(hAPP(c_Power_Opower__class_Opower(_644431), _644433), _644435) = hAPP(hAPP(c_Power_Opower__class_Opower(_644431), _644433), _644437))], (9512 ^ _319074) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_644431), _644433), _644435) = hAPP(hAPP(c_Power_Opower__class_Opower(_644431), _644433), _644437), -(_644435 = _644437)]]], (310 ^ _319074) ^ [_328564, _328566] : [-(class_Groups_Ocancel__ab__semigroup__add(_328564)), _328566 = _328564, class_Groups_Ocancel__ab__semigroup__add(_328566)], (12722 ^ _319074) ^ [_758343] : [class_Rings_Olinordered__idom(_758343), -(class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(_758343)))], (10874 ^ _319074) ^ [_692429, _692431] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _692429), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _692431), -(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), _692431), _692429)))], (4197 ^ _319074) ^ [_457802, _457804] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _457802, _457804) = _457802, -(_457804 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10059 ^ _319074) ^ [_663659, _663661] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _663659, _663661), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _663659, c_Groups_Oone__class_Oone(tc_Int_Oint)), _663661))], (2246 ^ _319074) ^ [_393041, _393043, _393045] : [class_Orderings_Oorder(_393041), c_Orderings_Oord__class_Oless(_393041, _393043, _393045), _393043 = _393045], (3524 ^ _319074) ^ [_434497, _434499, _434501, _434503, _434505] : [class_Groups_Ocomm__monoid__add(_434497), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_434497), c_Polynomial_OpCons(_434497, _434499, _434501), c_Polynomial_OpCons(_434497, _434503, _434505)) = c_Polynomial_OpCons(_434497, c_Groups_Oplus__class_Oplus(_434497, _434499, _434503), c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_434497), _434501, _434505)))], (12648 ^ _319074) ^ [] : [-(class_Groups_Ouminus(tc_Complex_Ocomplex))], (12460 ^ _319074) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal))], (6948 ^ _319074) ^ [_553774, _553776, _553778] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _553774), _553776) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _553778), _553776), -(_553774 = _553778), -(_553776 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9302 ^ _319074) ^ [_637302, _637304, _637306] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _637302), _637304), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _637302), _637306)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _637302), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _637304, _637306))], (858 ^ _319074) ^ [_345420, _345422, _345424, _345426, _345428, _345430, _345432, _345434] : [-(c_If(_345434, _345430, _345426, _345422) = c_If(_345432, _345428, _345424, _345420)), _345434 = _345432, _345430 = _345428, _345426 = _345424, _345422 = _345420], (11510 ^ _319074) ^ [_715201, _715203, _715205] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _715201, _715203)), _715205) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _715201), _715205), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _715203), _715205)))], (1351 ^ _319074) ^ [_363175, _363177, _363179, _363181] : [class_Groups_Oordered__comm__monoid__add(_363175), c_Orderings_Oord__class_Oless__eq(_363175, c_Groups_Ozero__class_Ozero(_363175), _363177), c_Orderings_Oord__class_Oless__eq(_363175, _363179, _363181), -(c_Orderings_Oord__class_Oless__eq(_363175, _363179, c_Groups_Oplus__class_Oplus(_363175, _363181, _363177)))], (44 ^ _319074) ^ [_320617, _320619, _320621, _320623, _320625, _320627] : [-(c_Rings_Odvd__class_Odvd(_320625, _320621, _320617)), c_Rings_Odvd__class_Odvd(_320627, _320623, _320619), _320627 = _320625, _320623 = _320621, _320619 = _320617], (7038 ^ _319074) ^ [_556838, _556840, _556842] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _556838), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _556840, _556842)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _556838), _556840), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _556838), _556842)))], (12240 ^ _319074) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (12330 ^ _319074) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (4014 ^ _319074) ^ [_451435, _451437, _451439] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _451437, _451439), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _451435, _451437), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _451435, _451439)))], (9580 ^ _319074) ^ [_647364, _647366, _647368, _647370] : [class_Rings_Ocomm__semiring__1(_647364), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _647366, _647368), -(c_Rings_Odvd__class_Odvd(_647364, hAPP(hAPP(c_Power_Opower__class_Opower(_647364), _647370), _647366), hAPP(hAPP(c_Power_Opower__class_Opower(_647364), _647370), _647368)))], (7524 ^ _319074) ^ [_575134, _575136, _575138] : [class_Rings_Oidom(_575134), 7527 ^ _319074 : [(7528 ^ _319074) ^ [] : [hAPP(c_Polynomial_Opoly(_575134, _575136), _575138) = c_Groups_Ozero__class_Ozero(_575134), -(_575136 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_575134))), c_Polynomial_Oorder(_575134, _575138, _575136) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (7538 ^ _319074) ^ [] : [7539 ^ _319074 : [(7542 ^ _319074) ^ [] : [-(c_Polynomial_Oorder(_575134, _575138, _575136) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7540 ^ _319074) ^ [] : [_575136 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_575134))]], -(hAPP(c_Polynomial_Opoly(_575134, _575136), _575138) = c_Groups_Ozero__class_Ozero(_575134))]]], (4371 ^ _319074) ^ [_463737, _463739, _463741] : [class_Fields_Olinordered__field__inverse__zero(_463737), c_Orderings_Oord__class_Oless(_463737, c_Groups_Ozero__class_Ozero(_463737), _463739), -(c_Rings_Oinverse__class_Odivide(_463737, c_Groups_Oabs__class_Oabs(_463737, _463741), _463739) = c_Groups_Oabs__class_Oabs(_463737, c_Rings_Oinverse__class_Odivide(_463737, _463741, _463739)))], (11402 ^ _319074) ^ [_711026, _711028, _711030] : [class_Groups_Ogroup__add(_711026), 11405 ^ _319074 : [(11412 ^ _319074) ^ [] : [_711028 = _711030, -(c_Groups_Ominus__class_Ominus(_711026, _711028, _711030) = c_Groups_Ozero__class_Ozero(_711026))], (11406 ^ _319074) ^ [] : [c_Groups_Ominus__class_Ominus(_711026, _711028, _711030) = c_Groups_Ozero__class_Ozero(_711026), -(_711028 = _711030)]]], (6883 ^ _319074) ^ [_551472, _551474, _551476] : [class_Rings_Olinordered__ring__strict(_551472), 6886 ^ _319074 : [(6895 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_551472, c_Groups_Oplus__class_Oplus(_551472, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_551472), _551474), _551474), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_551472), _551476), _551476)), c_Groups_Ozero__class_Ozero(_551472))), _551474 = c_Groups_Ozero__class_Ozero(_551472), _551476 = c_Groups_Ozero__class_Ozero(_551472)], (6887 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_551472, c_Groups_Oplus__class_Oplus(_551472, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_551472), _551474), _551474), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_551472), _551476), _551476)), c_Groups_Ozero__class_Ozero(_551472)), 6890 ^ _319074 : [(6893 ^ _319074) ^ [] : [-(_551476 = c_Groups_Ozero__class_Ozero(_551472))], (6891 ^ _319074) ^ [] : [-(_551474 = c_Groups_Ozero__class_Ozero(_551472))]]]]], (8896 ^ _319074) ^ [_624372] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _624372, _624372))], (7004 ^ _319074) ^ [_555671] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _555671) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6205 ^ _319074) ^ [_528936, _528938, _528940, _528942, _528944] : [class_Rings_Olinordered__semiring__strict(_528936), c_Orderings_Oord__class_Oless(_528936, _528938, _528940), c_Orderings_Oord__class_Oless(_528936, _528942, _528944), c_Orderings_Oord__class_Oless__eq(_528936, c_Groups_Ozero__class_Ozero(_528936), _528938), c_Orderings_Oord__class_Oless__eq(_528936, c_Groups_Ozero__class_Ozero(_528936), _528942), -(c_Orderings_Oord__class_Oless(_528936, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_528936), _528938), _528942), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_528936), _528940), _528944)))], (8244 ^ _319074) ^ [_602153, _602155, _602157, _602159] : [class_Rings_Ocomm__semiring__1(_602153), c_Rings_Odvd__class_Odvd(_602153, _602155, _602157), c_Rings_Odvd__class_Odvd(_602153, _602157, _602159), -(c_Rings_Odvd__class_Odvd(_602153, _602155, _602159))], (10317 ^ _319074) ^ [_672401, _672403] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Nat_OSuc(_672401), _672403) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _672401, c_Nat_OSuc(_672403)))], (1497 ^ _319074) ^ [_367744, _367746, _367748, _367750, _367752] : [class_Orderings_Oord(_367744), c_Orderings_Oord__class_Oless__eq(tc_fun(_367746, _367744), _367748, _367750), -(c_Orderings_Oord__class_Oless__eq(_367744, hAPP(_367748, _367752), hAPP(_367750, _367752)))], (8208 ^ _319074) ^ [_600850, _600852, _600854, _600856] : [class_Rings_Odvd(_600850), _600852 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_600850), _600854), _600856), -(c_Rings_Odvd__class_Odvd(_600850, _600854, _600852))], (4473 ^ _319074) ^ [_467954, _467956] : [class_RealVector_Oreal__normed__algebra(_467954), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_467954), c_Groups_Ozero__class_Ozero(_467954)), _467956) = c_Groups_Ozero__class_Ozero(_467954))], (660 ^ _319074) ^ [_338889, _338891] : [-(class_Groups_Ouminus(_338889)), _338891 = _338889, class_Groups_Ouminus(_338891)], (11315 ^ _319074) ^ [_707591, _707593, _707595, _707597] : [-(hAPP(hAPP(c_Power_Opower_Opower(_707591, _707593, _707595), _707597), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _707593)], (1912 ^ _319074) ^ [_381998, _382000, _382002, _382004] : [class_Rings_Ocomm__semiring__1(_381998), -(c_Groups_Oplus__class_Oplus(_381998, _382000, c_Groups_Oplus__class_Oplus(_381998, _382002, _382004)) = c_Groups_Oplus__class_Oplus(_381998, _382002, c_Groups_Oplus__class_Oplus(_381998, _382000, _382004)))], (10806 ^ _319074) ^ [_690087] : [-(c_Nat_OSuc(_690087) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _690087, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (12144 ^ _319074) ^ [_741630] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _741630, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _741630)], (9977 ^ _319074) ^ [_661102, _661104] : [-(_661102 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Rings_Odvd__class_Odvd(tc_Int_Oint, _661104, _661102), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oabs__class_Oabs(tc_Int_Oint, _661104), c_Groups_Oabs__class_Oabs(tc_Int_Oint, _661102)))], (7903 ^ _319074) ^ [_590092, _590094, _590096] : [class_Rings_Ocomm__semiring__1(_590092), -(c_Groups_Oplus__class_Oplus(_590092, _590094, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_590092), _590096), _590094)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_590092), c_Groups_Oplus__class_Oplus(_590092, _590096, c_Groups_Oone__class_Oone(_590092))), _590094))], (3796 ^ _319074) ^ [_443529, _443531, _443533] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _443531, _443533), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _443529, _443531), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _443529, _443533)))], (7068 ^ _319074) ^ [_558179, _558181, _558183] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _558179, _558181)), _558183) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _558179), _558183), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _558181), _558183)))], (5211 ^ _319074) ^ [_495699, _495701, _495703, _495705] : [class_Fields_Olinordered__field__inverse__zero(_495699), 5214 ^ _319074 : [(5215 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_495699, _495701, c_Rings_Oinverse__class_Odivide(_495699, _495703, _495705)), 5218 ^ _319074 : [(5225 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_495699, c_Groups_Ozero__class_Ozero(_495699), _495705)), 5228 ^ _319074 : [(5235 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_495699, _495705, c_Groups_Ozero__class_Ozero(_495699))), -(c_Orderings_Oord__class_Oless(_495699, _495701, c_Groups_Ozero__class_Ozero(_495699)))], (5229 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_495699, _495705, c_Groups_Ozero__class_Ozero(_495699)), -(c_Orderings_Oord__class_Oless(_495699, _495703, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_495699), _495701), _495705)))]]], (5219 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_495699, c_Groups_Ozero__class_Ozero(_495699), _495705), -(c_Orderings_Oord__class_Oless(_495699, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_495699), _495701), _495705), _495703))]]], (5241 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_495699, _495701, c_Rings_Oinverse__class_Odivide(_495699, _495703, _495705))), 5244 ^ _319074 : [(5247 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_495699, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_495699), _495701), _495705), _495703)], (5245 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_495699, c_Groups_Ozero__class_Ozero(_495699), _495705))]], 5248 ^ _319074 : [(5251 ^ _319074) ^ [] : [5252 ^ _319074 : [(5255 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_495699, _495703, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_495699), _495701), _495705))], (5253 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_495699, _495705, c_Groups_Ozero__class_Ozero(_495699)))]], 5256 ^ _319074 : [(5259 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_495699, _495701, c_Groups_Ozero__class_Ozero(_495699))], (5257 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_495699, _495705, c_Groups_Ozero__class_Ozero(_495699))]]], (5249 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_495699, c_Groups_Ozero__class_Ozero(_495699), _495705)]]]]], (10473 ^ _319074) ^ [_677891, _677893, _677895] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _677891), _677893)), _677895) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _677891), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _677893), _677895)))], (3604 ^ _319074) ^ [_437259, _437261] : [-(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _437259, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _437261))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _437261, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _437259))))], (9426 ^ _319074) ^ [_641917, _641919, _641921] : [class_Rings_Olinordered__semidom(_641917), c_Orderings_Oord__class_Oless__eq(_641917, c_Groups_Ozero__class_Ozero(_641917), _641919), -(c_Orderings_Oord__class_Oless__eq(_641917, c_Groups_Ozero__class_Ozero(_641917), hAPP(hAPP(c_Power_Opower__class_Opower(_641917), _641919), _641921)))], (12594 ^ _319074) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex))], (1036 ^ _319074) ^ [_351932, _351934] : [_351934 = _351932, -(c_Groups_Ozero__class_Ozero(_351934) = c_Groups_Ozero__class_Ozero(_351932))], (12764 ^ _319074) ^ [_759673] : [class_Rings_Olinordered__idom(_759673), -(class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(_759673)))], (10 ^ _319074) ^ [_319509, _319511, _319513] : [-(_319513 = _319509), _319513 = _319511, _319511 = _319509], (11556 ^ _319074) ^ [_717223, _717225, _717227, _717229] : [class_RealVector_Oreal__normed__field(_717223), -(c_Rings_Oinverse__class_Odivide(_717223, c_Groups_Ominus__class_Ominus(_717223, _717225, _717227), _717229) = c_Groups_Ominus__class_Ominus(_717223, c_Rings_Oinverse__class_Odivide(_717223, _717225, _717229), c_Rings_Oinverse__class_Odivide(_717223, _717227, _717229)))], (4491 ^ _319074) ^ [_468758, _468760, _468762, _468764] : [class_RealVector_Oreal__normed__algebra(_468758), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_468758), _468760), c_Groups_Oplus__class_Oplus(_468758, _468762, _468764)) = c_Groups_Oplus__class_Oplus(_468758, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_468758), _468760), _468762), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_468758), _468760), _468764)))], (2740 ^ _319074) ^ [_409159, _409161, _409163, _409165] : [class_Orderings_Oorder(_409159), c_Orderings_Oord__class_Oless__eq(_409159, _409161, _409163), c_Orderings_Oord__class_Oless(_409159, _409165, _409161), -(c_Orderings_Oord__class_Oless(_409159, _409165, _409163))], (11806 ^ _319074) ^ [_727513, _727515, _727517] : [class_Groups_Ogroup__add(_727513), -(c_Groups_Oplus__class_Oplus(_727513, c_Groups_Ominus__class_Ominus(_727513, _727515, _727517), _727517) = _727515)], (12350 ^ _319074) ^ [] : [-(class_Rings_Odvd(tc_Int_Oint))], (12758 ^ _319074) ^ [_759483] : [class_Rings_Olinordered__idom(_759483), -(class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(_759483)))], (7094 ^ _319074) ^ [_559456, _559458] : [class_Int_Oring__char__0(_559456), class_Rings_Oidom(_559456), 7101 ^ _319074 : [(7108 ^ _319074) ^ [] : [_559458 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_559456)), -(c_Polynomial_Opoly(_559456, _559458) = c_Polynomial_Opoly(_559456, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_559456))))], (7102 ^ _319074) ^ [] : [c_Polynomial_Opoly(_559456, _559458) = c_Polynomial_Opoly(_559456, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_559456))), -(_559458 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_559456)))]]], (4515 ^ _319074) ^ [_469952, _469954, _469956] : [class_RealVector_Oreal__normed__algebra(_469952), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_469952), c_Groups_Ouminus__class_Ouminus(_469952, _469954)), _469956) = c_Groups_Ouminus__class_Ouminus(_469952, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_469952), _469954), _469956)))], (210 ^ _319074) ^ [_325614, _325616] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_325614)), _325616 = _325614, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_325616)], (12070 ^ _319074) ^ [_738983, _738985, _738987] : [hBOOL(hAPP(_738983, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _738985, _738987))), 12073 ^ _319074 : [(12080 ^ _319074) ^ [_739321] : [_738985 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _738987, _739321), -(hBOOL(hAPP(_738983, _739321)))], (12074 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _738985, _738987), -(hBOOL(hAPP(_738983, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (5149 ^ _319074) ^ [_493733, _493735, _493737, _493739, _493741] : [class_Rings_Oordered__semiring(_493733), c_Orderings_Oord__class_Oless__eq(_493733, _493735, _493737), c_Orderings_Oord__class_Oless__eq(_493733, _493739, _493741), c_Orderings_Oord__class_Oless__eq(_493733, c_Groups_Ozero__class_Ozero(_493733), _493737), c_Orderings_Oord__class_Oless__eq(_493733, c_Groups_Ozero__class_Ozero(_493733), _493739), -(c_Orderings_Oord__class_Oless__eq(_493733, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_493733), _493735), _493739), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_493733), _493737), _493741)))], (12644 ^ _319074) ^ [] : [-(class_Int_Oring__char__0(tc_Complex_Ocomplex))], (4277 ^ _319074) ^ [_460468] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _460468, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7891 ^ _319074) ^ [_589608, _589610] : [class_Rings_Olinordered__semidom(_589608), -(c_Orderings_Oord__class_Oless(_589608, _589610, c_Groups_Oplus__class_Oplus(_589608, _589610, c_Groups_Oone__class_Oone(_589608))))], (7114 ^ _319074) ^ [_560059, _560061, _560063] : [class_Rings_Olinordered__idom(_560059), c_Polynomial_Opos__poly(_560059, _560061), c_Polynomial_Opos__poly(_560059, _560063), -(c_Polynomial_Opos__poly(_560059, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_560059)), _560061), _560063)))], (370 ^ _319074) ^ [_330334, _330336] : [-(class_Rings_Olinordered__semiring__1(_330334)), _330336 = _330334, class_Rings_Olinordered__semiring__1(_330336)], (8406 ^ _319074) ^ [_607439, _607441, _607443, _607445] : [class_Rings_Ocomm__semiring__0(_607439), -(c_Polynomial_Osynthetic__div(_607439, c_Polynomial_OpCons(_607439, _607441, _607443), _607445) = c_Polynomial_OpCons(_607439, hAPP(c_Polynomial_Opoly(_607439, _607443), _607445), c_Polynomial_Osynthetic__div(_607439, _607443, _607445)))], (7753 ^ _319074) ^ [_584868, _584870] : [class_Groups_Oone(_584868), 7756 ^ _319074 : [(7763 ^ _319074) ^ [] : [_584870 = c_Groups_Oone__class_Oone(_584868), -(c_Groups_Oone__class_Oone(_584868) = _584870)], (7757 ^ _319074) ^ [] : [c_Groups_Oone__class_Oone(_584868) = _584870, -(_584870 = c_Groups_Oone__class_Oone(_584868))]]], (7546 ^ _319074) ^ [_575822, _575824] : [class_RealVector_Oreal__normed__field(_575822), 7550 ^ _319074 : [(7553 ^ _319074) ^ [_576113] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_575822, c_Rings_Oinverse__class_Odivide(_575822, _576113, _575824)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_575822, _576113)), 7549 ^ [_575822, _575824])))], (7551 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 7549 ^ [_575822, _575824]))]]], (9138 ^ _319074) ^ [_632001, _632003] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _632001, _632003), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _632003, _632001)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _632003, _632001), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _632001, _632003))], (8218 ^ _319074) ^ [_601213, _601215, _601217, _601219] : [class_Rings_Ocomm__semiring__1(_601213), c_Rings_Odvd__class_Odvd(_601213, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_601213), _601215), _601217), _601219), -(c_Rings_Odvd__class_Odvd(_601213, _601215, _601219))], (12276 ^ _319074) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (12496 ^ _319074) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal))], (2 ^ _319074) ^ [_319198] : [-(_319198 = _319198)], (12492 ^ _319074) ^ [] : [-(class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal))], (12406 ^ _319074) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (4467 ^ _319074) ^ [_467722, _467724] : [class_RealVector_Oreal__normed__algebra(_467722), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_467722), _467724), c_Groups_Ozero__class_Ozero(_467722)) = c_Groups_Ozero__class_Ozero(_467722))], (12504 ^ _319074) ^ [] : [-(class_Rings_Oordered__semiring(tc_RealDef_Oreal))], (9590 ^ _319074) ^ [_647731, _647733, _647735] : [class_Rings_Olinordered__idom(_647731), -(c_Groups_Oabs__class_Oabs(_647731, hAPP(hAPP(c_Power_Opower__class_Opower(_647731), c_Groups_Ouminus__class_Ouminus(_647731, _647733)), _647735)) = c_Groups_Oabs__class_Oabs(_647731, hAPP(hAPP(c_Power_Opower__class_Opower(_647731), _647733), _647735)))], (7843 ^ _319074) ^ [_588053, _588055] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _588053), _588055) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _588053 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _588055 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (3064 ^ _319074) ^ [_419202, _419204, _419206, _419208] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_419202), c_Orderings_Oord__class_Oless(_419202, c_Groups_Oplus__class_Oplus(_419202, _419204, _419206), c_Groups_Oplus__class_Oplus(_419202, _419208, _419206)), -(c_Orderings_Oord__class_Oless(_419202, _419204, _419208))], (800 ^ _319074) ^ [_343019, _343021] : [-(class_Rings_Ocomm__semiring__1(_343019)), _343021 = _343019, class_Rings_Ocomm__semiring__1(_343021)], (350 ^ _319074) ^ [_329744, _329746] : [-(class_Rings_Oring__no__zero__divisors(_329744)), _329746 = _329744, class_Rings_Oring__no__zero__divisors(_329746)], (11768 ^ _319074) ^ [_726078, _726080, _726082] : [class_Groups_Ogroup__add(_726078), -(c_Groups_Ominus__class_Ominus(_726078, _726080, c_Groups_Ouminus__class_Ouminus(_726078, _726082)) = c_Groups_Oplus__class_Oplus(_726078, _726080, _726082))], (12716 ^ _319074) ^ [_758153] : [class_Rings_Olinordered__idom(_758153), -(class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(_758153)))], (7615 ^ _319074) ^ [_578956, _578958, _578960] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _578956), _578958), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, _578960), _578956)), 7611 ^ [_578958, _578960]))], (10696 ^ _319074) ^ [_686005, _686007] : [10697 ^ _319074 : [(10698 ^ _319074) ^ [_686082] : [_686007 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _686005, _686082))]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _686005, _686007))], (430 ^ _319074) ^ [_332104, _332106] : [-(class_Groups_Oab__semigroup__mult(_332104)), _332106 = _332104, class_Groups_Oab__semigroup__mult(_332106)], (9320 ^ _319074) ^ [_637933] : [_637933 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, _637933) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (8156 ^ _319074) ^ [_598878, _598880] : [class_Rings_Ocomm__semiring__1(_598878), -(c_Rings_Odvd__class_Odvd(_598878, c_Groups_Oone__class_Oone(_598878), _598880))], (10443 ^ _319074) ^ [_676868, _676870] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _676868, _676870)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _676868, _676870), -(_676868 = _676870)], (1243 ^ _319074) ^ [_359691, _359693, _359695, _359697, _359699] : [class_Groups_Oordered__ab__semigroup__add(_359691), c_Orderings_Oord__class_Oless__eq(_359691, _359693, _359695), c_Orderings_Oord__class_Oless__eq(_359691, _359697, _359699), -(c_Orderings_Oord__class_Oless__eq(_359691, c_Groups_Oplus__class_Oplus(_359691, _359693, _359697), c_Groups_Oplus__class_Oplus(_359691, _359695, _359699)))], (9566 ^ _319074) ^ [_646870, _646872, _646874, _646876, _646878] : [class_Rings_Ocomm__semiring__1(_646870), c_Rings_Odvd__class_Odvd(_646870, _646872, _646874), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _646876, _646878), -(c_Rings_Odvd__class_Odvd(_646870, hAPP(hAPP(c_Power_Opower__class_Opower(_646870), _646872), _646876), hAPP(hAPP(c_Power_Opower__class_Opower(_646870), _646874), _646878)))], (5423 ^ _319074) ^ [_502615, _502617, _502619, _502621] : [class_Fields_Olinordered__field(_502615), c_Orderings_Oord__class_Oless(_502615, _502617, _502619), c_Orderings_Oord__class_Oless(_502615, c_Groups_Ozero__class_Ozero(_502615), _502621), c_Orderings_Oord__class_Oless(_502615, c_Groups_Ozero__class_Ozero(_502615), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_502615), _502619), _502617)), -(c_Orderings_Oord__class_Oless(_502615, c_Rings_Oinverse__class_Odivide(_502615, _502621, _502619), c_Rings_Oinverse__class_Odivide(_502615, _502621, _502617)))], (1718 ^ _319074) ^ [_374937, _374939, _374941, _374943] : [class_Groups_Ocancel__ab__semigroup__add(_374937), c_Groups_Oplus__class_Oplus(_374937, _374939, _374941) = c_Groups_Oplus__class_Oplus(_374937, _374939, _374943), -(_374941 = _374943)], (12848 ^ _319074) ^ [_762333] : [class_Rings_Ocomm__semiring__1(_762333), -(class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(_762333)))], (4155 ^ _319074) ^ [_456433, _456435] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _456433), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, _456433, _456435)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _456435))))], (9851 ^ _319074) ^ [_656745, _656747, _656749] : [class_Rings_Oidom(_656745), -(_656747 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_656745))), c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_656745), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_656745)), c_Polynomial_OpCons(_656745, c_Groups_Ouminus__class_Ouminus(_656745, _656749), c_Polynomial_OpCons(_656745, c_Groups_Oone__class_Oone(_656745), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_656745))))), c_Nat_OSuc(c_Polynomial_Oorder(_656745, _656749, _656747))), _656747)], (1810 ^ _319074) ^ [_378175, _378177, _378179, _378181] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_378175), c_Orderings_Oord__class_Oless__eq(_378175, c_Groups_Oplus__class_Oplus(_378175, _378177, _378179), c_Groups_Oplus__class_Oplus(_378175, _378177, _378181)), -(c_Orderings_Oord__class_Oless__eq(_378175, _378179, _378181))], (12518 ^ _319074) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal))], (2926 ^ _319074) ^ [_414868, _414870, _414872] : [class_Orderings_Olinorder(_414868), -(c_Orderings_Oord__class_Oless__eq(_414868, _414870, _414872)), -(c_Orderings_Oord__class_Oless(_414868, _414872, _414870))], (260 ^ _319074) ^ [_327089, _327091] : [-(class_Rings_Olinordered__semiring__strict(_327089)), _327091 = _327089, class_Rings_Olinordered__semiring__strict(_327091)], (12282 ^ _319074) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (4503 ^ _319074) ^ [_469382, _469384, _469386, _469388] : [class_RealVector_Oreal__normed__algebra(_469382), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_469382), c_Groups_Oplus__class_Oplus(_469382, _469384, _469386)), _469388) = c_Groups_Oplus__class_Oplus(_469382, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_469382), _469384), _469388), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_469382), _469386), _469388)))], (7897 ^ _319074) ^ [_589830, _589832] : [class_Rings_Ocomm__semiring__1(_589830), -(c_Groups_Oplus__class_Oplus(_589830, _589832, _589832) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_589830), c_Groups_Oplus__class_Oplus(_589830, c_Groups_Oone__class_Oone(_589830), c_Groups_Oone__class_Oone(_589830))), _589832))], (3616 ^ _319074) ^ [_437703, _437705] : [class_Groups_Oordered__ab__group__add__abs(_437703), -(c_Orderings_Oord__class_Oless__eq(_437703, c_Groups_Ouminus__class_Ouminus(_437703, c_Groups_Oabs__class_Oabs(_437703, _437705)), c_Groups_Ozero__class_Ozero(_437703)))], (10007 ^ _319074) ^ [_662031, _662033] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _662031, _662033), c_Rings_Odvd__class_Odvd(tc_Int_Oint, _662033, _662031), -(c_Groups_Oabs__class_Oabs(tc_Int_Oint, _662031) = c_Groups_Oabs__class_Oabs(tc_Int_Oint, _662033))], (10101 ^ _319074) ^ [_665106] : [_665106 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oabs__class_Oabs(tc_Int_Oint, _665106), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (12592 ^ _319074) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex))], (12516 ^ _319074) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal))], (9280 ^ _319074) ^ [_636446, _636448] : [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), _636446), _636448)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _636446)), -(_636448 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9738 ^ _319074) ^ [_653017, _653019, _653021, _653023] : [class_Rings_Olinordered__semidom(_653017), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _653019, _653021), c_Orderings_Oord__class_Oless(_653017, c_Groups_Ozero__class_Ozero(_653017), _653023), c_Orderings_Oord__class_Oless(_653017, _653023, c_Groups_Oone__class_Oone(_653017)), -(c_Orderings_Oord__class_Oless(_653017, hAPP(hAPP(c_Power_Opower__class_Opower(_653017), _653023), _653021), hAPP(hAPP(c_Power_Opower__class_Opower(_653017), _653023), _653019)))], (10319 ^ _319074) ^ [_672522, _672524] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_672522), _672524), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _672522, _672524))], (9650 ^ _319074) ^ [_649836, _649838, _649840] : [class_Rings_Olinordered__idom(_649836), -(c_Orderings_Oord__class_Oless__eq(_649836, c_Groups_Ozero__class_Ozero(_649836), hAPP(hAPP(c_Power_Opower__class_Opower(_649836), c_Groups_Oabs__class_Oabs(_649836, _649838)), _649840)))], (12668 ^ _319074) ^ [_756633] : [class_Rings_Oidom(_756633), -(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(_756633)))], (7184 ^ _319074) ^ [_562532, _562534] : [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), _562532), _562534)), 7187 ^ _319074 : [(7190 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _562534))], (7188 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _562532))]]], (10962 ^ _319074) ^ [_695334, _695336, _695338] : [class_Rings_Olinordered__semidom(_695334), c_Orderings_Oord__class_Oless(_695334, c_Groups_Ozero__class_Ozero(_695334), _695336), c_Orderings_Oord__class_Oless(_695334, _695336, c_Groups_Oone__class_Oone(_695334)), -(c_Orderings_Oord__class_Oless(_695334, hAPP(hAPP(c_Power_Opower__class_Opower(_695334), _695336), c_Nat_OSuc(_695338)), c_Groups_Oone__class_Oone(_695334)))], (5741 ^ _319074) ^ [_513132, _513134, _513136, _513138] : [class_Fields_Ofield__inverse__zero(_513132), -(_513134 = c_Groups_Ozero__class_Ozero(_513132)), -(c_Groups_Oplus__class_Oplus(_513132, _513136, c_Rings_Oinverse__class_Odivide(_513132, _513138, _513134)) = c_Rings_Oinverse__class_Odivide(_513132, c_Groups_Oplus__class_Oplus(_513132, _513138, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_513132), _513136), _513134)), _513134))], (4020 ^ _319074) ^ [_451673, _451675] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _451673, _451675)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _451675, _451673))], (11446 ^ _319074) ^ [_712506, _712508, _712510, _712512, _712514] : [class_Groups_Oordered__ab__group__add(_712506), c_Groups_Ominus__class_Ominus(_712506, _712508, _712510) = c_Groups_Ominus__class_Ominus(_712506, _712512, _712514), 11453 ^ _319074 : [(11460 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_712506, _712512, _712514), -(c_Orderings_Oord__class_Oless(_712506, _712508, _712510))], (11454 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_712506, _712508, _712510), -(c_Orderings_Oord__class_Oless(_712506, _712512, _712514))]]], (12304 ^ _319074) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (5713 ^ _319074) ^ [_512164, _512166, _512168, _512170] : [class_Rings_Olinordered__ring__strict(_512164), c_Orderings_Oord__class_Oless(_512164, _512166, _512168), c_Orderings_Oord__class_Oless(_512164, _512170, c_Groups_Ozero__class_Ozero(_512164)), -(c_Orderings_Oord__class_Oless(_512164, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_512164), _512168), _512170), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_512164), _512166), _512170)))], (9152 ^ _319074) ^ [_632406, _632408] : [_632406 = _632408, c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _632406, _632408), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _632408, _632406))], (4719 ^ _319074) ^ [_478610, _478612, _478614, _478616] : [class_Rings_Ocomm__semiring__1(_478610), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_478610), _478612), c_Groups_Oplus__class_Oplus(_478610, _478614, _478616)) = c_Groups_Oplus__class_Oplus(_478610, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_478610), _478612), _478614), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_478610), _478612), _478616)))], (10055 ^ _319074) ^ [_663488, _663490] : [-(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), c_Groups_Oabs__class_Oabs(tc_Int_Oint, _663488)), _663490)))], (8646 ^ _319074) ^ [_616476, _616478] : [class_Rings_Olinordered__idom(_616476), 8649 ^ _319074 : [(8656 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_616476, c_Groups_Ozero__class_Ozero(_616476), _616478), -(c_Orderings_Oord__class_Oless(_616476, c_Groups_Ozero__class_Ozero(_616476), c_Groups_Osgn__class_Osgn(_616476, _616478)))], (8650 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_616476, c_Groups_Ozero__class_Ozero(_616476), c_Groups_Osgn__class_Osgn(_616476, _616478)), -(c_Orderings_Oord__class_Oless(_616476, c_Groups_Ozero__class_Ozero(_616476), _616478))]]], (3536 ^ _319074) ^ [_435000, _435002] : [class_Groups_Oordered__ab__group__add__abs(_435000), 3539 ^ _319074 : [(3546 ^ _319074) ^ [] : [-(_435002 = c_Groups_Ozero__class_Ozero(_435000)), -(c_Orderings_Oord__class_Oless(_435000, c_Groups_Ozero__class_Ozero(_435000), c_Groups_Oabs__class_Oabs(_435000, _435002)))], (3540 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_435000, c_Groups_Ozero__class_Ozero(_435000), c_Groups_Oabs__class_Oabs(_435000, _435002)), _435002 = c_Groups_Ozero__class_Ozero(_435000)]]], (12596 ^ _319074) ^ [] : [-(class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex))], (12036 ^ _319074) ^ [_737634, _737636, _737638, _737640, _737642] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _737634, _737636), 12039 ^ _319074 : [(12046 ^ _319074) ^ [] : [_737640 = 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, _737636, _737634)), _737638), _737642), -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _737634), _737638), _737640) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _737636), _737638), _737642))], (12040 ^ _319074) ^ [] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _737634), _737638), _737640) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _737636), _737638), _737642), -(_737640 = 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, _737636, _737634)), _737638), _737642))]]], (10157 ^ _319074) ^ [_667026, _667028] : [c_Groups_Oabs__class_Oabs(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _667026), _667028)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(c_Groups_Oabs__class_Oabs(tc_Int_Oint, _667026) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (2236 ^ _319074) ^ [_392717, _392719, _392721] : [class_Orderings_Oorder(_392717), c_Orderings_Oord__class_Oless(_392717, _392719, _392721), _392721 = _392719], (12752 ^ _319074) ^ [_759293] : [class_Rings_Oidom(_759293), -(class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(_759293)))], (6271 ^ _319074) ^ [_531088, _531090, _531092, _531094] : [class_Rings_Olinordered__semiring(_531088), c_Orderings_Oord__class_Oless(_531088, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_531088), _531090), _531092), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_531088), _531094), _531092)), c_Orderings_Oord__class_Oless__eq(_531088, c_Groups_Ozero__class_Ozero(_531088), _531092), -(c_Orderings_Oord__class_Oless(_531088, _531090, _531094))], (12514 ^ _319074) ^ [] : [-(class_Rings_Olinordered__idom(tc_RealDef_Oreal))], (3054 ^ _319074) ^ [_418837, _418839, _418841, _418843] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_418837), c_Orderings_Oord__class_Oless(_418837, c_Groups_Oplus__class_Oplus(_418837, _418839, _418841), c_Groups_Oplus__class_Oplus(_418837, _418839, _418843)), -(c_Orderings_Oord__class_Oless(_418837, _418841, _418843))], (6665 ^ _319074) ^ [_544309, _544311, _544313, _544315] : [class_Fields_Olinordered__field(_544309), c_Orderings_Oord__class_Oless(_544309, _544311, _544313), c_Orderings_Oord__class_Oless(_544309, _544315, c_Groups_Ozero__class_Ozero(_544309)), -(c_Orderings_Oord__class_Oless(_544309, c_Rings_Oinverse__class_Odivide(_544309, _544313, _544315), c_Rings_Oinverse__class_Odivide(_544309, _544311, _544315)))], (12258 ^ _319074) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (3688 ^ _319074) ^ [_439958] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _439958))], (6827 ^ _319074) ^ [_549580, _549582, _549584] : [class_Fields_Olinordered__field(_549580), c_Orderings_Oord__class_Oless__eq(_549580, _549582, c_Groups_Ozero__class_Ozero(_549580)), c_Orderings_Oord__class_Oless(_549580, c_Groups_Ozero__class_Ozero(_549580), _549584), -(c_Orderings_Oord__class_Oless__eq(_549580, c_Rings_Oinverse__class_Odivide(_549580, _549582, _549584), c_Groups_Ozero__class_Ozero(_549580)))], (4002 ^ _319074) ^ [_450992, _450994] : [_450992 = _450994, -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _450992, _450994))], (5781 ^ _319074) ^ [_514746, _514748, _514750, _514752, _514754] : [class_Fields_Ofield(_514746), -(_514748 = c_Groups_Ozero__class_Ozero(_514746)), -(_514750 = c_Groups_Ozero__class_Ozero(_514746)), -(c_Groups_Oplus__class_Oplus(_514746, c_Rings_Oinverse__class_Odivide(_514746, _514752, _514748), c_Rings_Oinverse__class_Odivide(_514746, _514754, _514750)) = c_Rings_Oinverse__class_Odivide(_514746, c_Groups_Oplus__class_Oplus(_514746, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_514746), _514752), _514750), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_514746), _514754), _514748)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_514746), _514748), _514750)))], (2516 ^ _319074) ^ [_401621] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _401621, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), -(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _401621) = _401621)], (3510 ^ _319074) ^ [_434005, _434007, _434009, _434011, _434013] : [class_Groups_Oordered__cancel__ab__semigroup__add(_434005), c_Orderings_Oord__class_Oless(_434005, _434007, _434009), c_Orderings_Oord__class_Oless__eq(_434005, _434011, _434013), -(c_Orderings_Oord__class_Oless(_434005, c_Groups_Oplus__class_Oplus(_434005, _434007, _434011), c_Groups_Oplus__class_Oplus(_434005, _434009, _434013)))], (10519 ^ _319074) ^ [_679873, _679875, _679877] : [class_Rings_Ocomm__semiring__1(_679873), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_679873), _679875), hAPP(hAPP(c_Power_Opower__class_Opower(_679873), _679875), _679877)) = hAPP(hAPP(c_Power_Opower__class_Opower(_679873), _679875), c_Nat_OSuc(_679877)))], (6984 ^ _319074) ^ [_555054, _555056] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _555054), _555056) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_555054 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_555056 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8284 ^ _319074) ^ [_603425, _603427, _603429] : [class_Rings_Olinordered__idom(_603425), 8287 ^ _319074 : [(8294 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(_603425, _603427, _603429), -(c_Rings_Odvd__class_Odvd(_603425, _603427, c_Groups_Oabs__class_Oabs(_603425, _603429)))], (8288 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(_603425, _603427, c_Groups_Oabs__class_Oabs(_603425, _603429)), -(c_Rings_Odvd__class_Odvd(_603425, _603427, _603429))]]], (10137 ^ _319074) ^ [_666353] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _666353), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _666353))], (12606 ^ _319074) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex))], (12770 ^ _319074) ^ [_759863] : [class_Rings_Olinordered__idom(_759863), -(class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(_759863)))], (6623 ^ _319074) ^ [_542947, _542949, _542951] : [class_Fields_Olinordered__field(_542947), c_Orderings_Oord__class_Oless(_542947, _542949, c_Groups_Ozero__class_Ozero(_542947)), c_Orderings_Oord__class_Oless(_542947, c_Groups_Ozero__class_Ozero(_542947), _542951), -(c_Orderings_Oord__class_Oless(_542947, c_Rings_Oinverse__class_Odivide(_542947, _542949, _542951), c_Groups_Ozero__class_Ozero(_542947)))], (6905 ^ _319074) ^ [_552205, _552207, _552209] : [class_Rings_Olinordered__ring(_552205), -(c_Orderings_Oord__class_Oless__eq(_552205, c_Groups_Ozero__class_Ozero(_552205), c_Groups_Oplus__class_Oplus(_552205, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_552205), _552207), _552207), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_552205), _552209), _552209))))], (12382 ^ _319074) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (4663 ^ _319074) ^ [_476306, _476308, _476310, _476312, _476314] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_476306), 4666 ^ _319074 : [(4667 ^ _319074) ^ [] : [c_Groups_Oplus__class_Oplus(_476306, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_476306), _476308), _476310), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_476306), _476312), _476314)) = c_Groups_Oplus__class_Oplus(_476306, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_476306), _476308), _476314), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_476306), _476312), _476310)), -(_476308 = _476312), -(_476310 = _476314)], (4677 ^ _319074) ^ [] : [4678 ^ _319074 : [(4681 ^ _319074) ^ [] : [_476310 = _476314], (4679 ^ _319074) ^ [] : [_476308 = _476312]], -(c_Groups_Oplus__class_Oplus(_476306, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_476306), _476308), _476310), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_476306), _476312), _476314)) = c_Groups_Oplus__class_Oplus(_476306, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_476306), _476308), _476314), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_476306), _476312), _476310)))]]], (3690 ^ _319074) ^ [_440036] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _440036, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (7192 ^ _319074) ^ [_562787, _562789] : [-(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), _562787), _562789))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _562787), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _562789)], (4113 ^ _319074) ^ [_454986] : [class_Groups_Oab__group__add(_454986), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_454986), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_454986))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_454986)))], (2266 ^ _319074) ^ [_393691, _393693, _393695] : [class_Orderings_Opreorder(_393691), c_Orderings_Oord__class_Oless(_393691, _393693, _393695), c_Orderings_Oord__class_Oless(_393691, _393695, _393693)], (11036 ^ _319074) ^ [_697982, _697984, _697986] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _697982), _697982 = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _697984, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _697982), _697986)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _697984, _697982), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _697986))], (1998 ^ _319074) ^ [_385012, _385014, _385016, _385018] : [class_Groups_Oordered__comm__monoid__add(_385012), c_Orderings_Oord__class_Oless__eq(_385012, c_Groups_Ozero__class_Ozero(_385012), _385014), c_Orderings_Oord__class_Oless(_385012, _385016, _385018), -(c_Orderings_Oord__class_Oless(_385012, _385016, c_Groups_Oplus__class_Oplus(_385012, _385014, _385018)))], (5171 ^ _319074) ^ [_494427, _494429, _494431] : [class_Rings_Oordered__ring(_494427), -(c_Orderings_Oord__class_Oless__eq(_494427, c_Groups_Ozero__class_Ozero(_494427), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_494427), _494429), _494431))), 5176 ^ _319074 : [(5183 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_494427, _494429, c_Groups_Ozero__class_Ozero(_494427)), c_Orderings_Oord__class_Oless__eq(_494427, _494431, c_Groups_Ozero__class_Ozero(_494427))], (5177 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_494427, c_Groups_Ozero__class_Ozero(_494427), _494429), c_Orderings_Oord__class_Oless__eq(_494427, c_Groups_Ozero__class_Ozero(_494427), _494431)]]], (4045 ^ _319074) ^ [_452671, _452673] : [class_Rings_Odivision__ring__inverse__zero(_452671), -(c_Rings_Oinverse__class_Odivide(_452671, _452673, c_Groups_Ozero__class_Ozero(_452671)) = c_Groups_Ozero__class_Ozero(_452671))], (9364 ^ _319074) ^ [_639219, _639221, _639223] : [class_Rings_Oring__1__no__zero__divisors(_639219), -(_639221 = c_Groups_Ozero__class_Ozero(_639219)), hAPP(hAPP(c_Power_Opower__class_Opower(_639219), _639221), _639223) = c_Groups_Ozero__class_Ozero(_639219)], (8174 ^ _319074) ^ [_599612, _599614, _599616, _599618] : [class_Rings_Ocomm__semiring__1(_599612), c_Rings_Odvd__class_Odvd(_599612, _599614, _599616), -(c_Rings_Odvd__class_Odvd(_599612, _599614, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_599612), _599616), _599618)))], (10976 ^ _319074) ^ [_695743] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _695743, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (12986 ^ _319074) ^ [_766703] : [class_Groups_Oab__group__add(_766703), -(class_Groups_Ominus(tc_Polynomial_Opoly(_766703)))], (13010 ^ _319074) ^ [_767463] : [class_Rings_Oidom(_767463), -(class_Rings_Oidom(tc_Polynomial_Opoly(_767463)))], (9534 ^ _319074) ^ [_645488, _645490] : [class_Power_Opower(_645488), -(hAPP(hAPP(c_Power_Opower__class_Opower(_645488), _645490), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_645488))], (12086 ^ _319074) ^ [_739522, _739524, _739526] : [-(hBOOL(hAPP(_739522, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _739524, _739526)))), 12089 ^ _319074 : [(12092 ^ _319074) ^ [] : [hBOOL(hAPP(_739522, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (12090 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _739524, _739526))]], 12094 ^ _319074 : [(12097 ^ _319074) ^ [] : [hBOOL(hAPP(_739522, 12093 ^ [_739522, _739524, _739526]))], (12095 ^ _319074) ^ [] : [-(_739524 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _739526, 12093 ^ [_739522, _739524, _739526]))]]], (12344 ^ _319074) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (3466 ^ _319074) ^ [_432557, _432559, _432561] : [class_Groups_Oordered__comm__monoid__add(_432557), c_Orderings_Oord__class_Oless(_432557, _432559, c_Groups_Ozero__class_Ozero(_432557)), c_Orderings_Oord__class_Oless(_432557, _432561, c_Groups_Ozero__class_Ozero(_432557)), -(c_Orderings_Oord__class_Oless(_432557, c_Groups_Oplus__class_Oplus(_432557, _432559, _432561), c_Groups_Ozero__class_Ozero(_432557)))], (1423 ^ _319074) ^ [_365387, _365389] : [class_Groups_Olinordered__ab__group__add(_365387), 1426 ^ _319074 : [(1433 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_365387, _365389, c_Groups_Ozero__class_Ozero(_365387)), -(c_Orderings_Oord__class_Oless__eq(_365387, c_Groups_Oplus__class_Oplus(_365387, _365389, _365389), c_Groups_Ozero__class_Ozero(_365387)))], (1427 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_365387, c_Groups_Oplus__class_Oplus(_365387, _365389, _365389), c_Groups_Ozero__class_Ozero(_365387)), -(c_Orderings_Oord__class_Oless__eq(_365387, _365389, c_Groups_Ozero__class_Ozero(_365387)))]]], (7713 ^ _319074) ^ [_583448, _583450, _583452, _583454] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Complex_Orcis(_583448, _583450)), c_Complex_Orcis(_583452, _583454)) = c_Complex_Orcis(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _583448), _583452), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _583450, _583454)))], (9987 ^ _319074) ^ [_661420, _661422] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _661420), c_Orderings_Oord__class_Oless(tc_Int_Oint, _661420, _661422), c_Rings_Odvd__class_Odvd(tc_Int_Oint, _661422, _661420)], (10810 ^ _319074) ^ [_690312, _690314, _690316, _690318] : [class_Rings_Olinordered__semidom(_690312), hAPP(hAPP(c_Power_Opower__class_Opower(_690312), _690314), c_Nat_OSuc(_690316)) = hAPP(hAPP(c_Power_Opower__class_Opower(_690312), _690318), c_Nat_OSuc(_690316)), c_Orderings_Oord__class_Oless__eq(_690312, c_Groups_Ozero__class_Ozero(_690312), _690314), c_Orderings_Oord__class_Oless__eq(_690312, c_Groups_Ozero__class_Ozero(_690312), _690318), -(_690314 = _690318)], (11156 ^ _319074) ^ [_702189, _702191, _702193, _702195, _702197] : [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), _702189), _702191), _702193), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _702189), _702195), _702197)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _702193), c_Orderings_Oord__class_Oless(tc_Int_Oint, _702193, _702189), c_Orderings_Oord__class_Oless(tc_Int_Oint, _702197, _702189), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _702191, _702195))], (5827 ^ _319074) ^ [_516439, _516441, _516443, _516445] : [class_Rings_Odivision__ring(_516439), -(_516441 = c_Groups_Ozero__class_Ozero(_516439)), _516443 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_516439), _516445), _516441), -(c_Rings_Oinverse__class_Odivide(_516439, _516443, _516441) = _516445)], (1287 ^ _319074) ^ [_361104, _361106] : [class_Groups_Olinordered__ab__group__add(_361104), 1290 ^ _319074 : [(1297 ^ _319074) ^ [] : [_361106 = c_Groups_Ozero__class_Ozero(_361104), -(c_Groups_Ozero__class_Ozero(_361104) = c_Groups_Oplus__class_Oplus(_361104, _361106, _361106))], (1291 ^ _319074) ^ [] : [c_Groups_Ozero__class_Ozero(_361104) = c_Groups_Oplus__class_Oplus(_361104, _361106, _361106), -(_361106 = c_Groups_Ozero__class_Ozero(_361104))]]], (8053 ^ _319074) ^ [_594995, _594997, _594999] : [class_Fields_Olinordered__field(_594995), c_Orderings_Oord__class_Oless(_594995, _594997, _594999), -(c_Orderings_Oord__class_Oless(_594995, c_Rings_Oinverse__class_Odivide(_594995, c_Groups_Oplus__class_Oplus(_594995, _594997, _594999), c_Groups_Oplus__class_Oplus(_594995, c_Groups_Oone__class_Oone(_594995), c_Groups_Oone__class_Oone(_594995))), _594999))], (470 ^ _319074) ^ [_333284, _333286] : [-(class_Rings_Oordered__ring__abs(_333284)), _333286 = _333284, class_Rings_Oordered__ring__abs(_333286)], (2276 ^ _319074) ^ [_394017, _394019, _394021] : [class_Orderings_Oorder(_394017), c_Orderings_Oord__class_Oless(_394017, _394019, _394021), _394019 = _394021], (8976 ^ _319074) ^ [_626937, _626939] : [_626937 = _626939, -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _626937, _626939))], (8228 ^ _319074) ^ [_601578, _601580, _601582, _601584] : [class_Rings_Ocomm__semiring__1(_601578), c_Rings_Odvd__class_Odvd(_601578, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_601578), _601580), _601582), _601584), -(c_Rings_Odvd__class_Odvd(_601578, _601582, _601584))], (8794 ^ _319074) ^ [_621190, _621192] : [class_Rings_Olinordered__idom(_621190), 8797 ^ _319074 : [(8804 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_621190, _621192, c_Groups_Ozero__class_Ozero(_621190)), -(c_Groups_Osgn__class_Osgn(_621190, _621192) = c_Groups_Ouminus__class_Ouminus(_621190, c_Groups_Oone__class_Oone(_621190)))], (8798 ^ _319074) ^ [] : [c_Groups_Osgn__class_Osgn(_621190, _621192) = c_Groups_Ouminus__class_Ouminus(_621190, c_Groups_Oone__class_Oone(_621190)), -(c_Orderings_Oord__class_Oless(_621190, _621192, c_Groups_Ozero__class_Ozero(_621190)))]]], (6355 ^ _319074) ^ [_533978, _533980, _533982] : [class_Rings_Oordered__ring__abs(_533978), -(c_Groups_Oabs__class_Oabs(_533978, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_533978), _533980), _533982)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_533978), c_Groups_Oabs__class_Oabs(_533978, _533980)), c_Groups_Oabs__class_Oabs(_533978, _533982))), 6362 ^ _319074 : [(6365 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_533978, _533980, c_Groups_Ozero__class_Ozero(_533978))], (6363 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_533978, c_Groups_Ozero__class_Ozero(_533978), _533980)]], 6366 ^ _319074 : [(6369 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_533978, _533982, c_Groups_Ozero__class_Ozero(_533978))], (6367 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_533978, c_Groups_Ozero__class_Ozero(_533978), _533982)]]], (10635 ^ _319074) ^ [_684038, _684040] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _684038, _684040) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 10640 ^ _319074 : [(10643 ^ _319074) ^ [] : [-(_684040 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10641 ^ _319074) ^ [] : [-(_684038 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 10644 ^ _319074 : [(10647 ^ _319074) ^ [] : [-(_684040 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10645 ^ _319074) ^ [] : [-(_684038 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (270 ^ _319074) ^ [_327384, _327386] : [-(class_Groups_Oordered__ab__semigroup__add(_327384)), _327386 = _327384, class_Groups_Oordered__ab__semigroup__add(_327386)], (4243 ^ _319074) ^ [_459386, _459388] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _459386, _459388)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _459386)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _459388))], (918 ^ _319074) ^ [_347665, _347667, _347669, _347671] : [-(c_Complex_Orcis(_347671, _347667) = c_Complex_Orcis(_347669, _347665)), _347671 = _347669, _347667 = _347665], (670 ^ _319074) ^ [_339184, _339186] : [-(class_Groups_Osgn__if(_339184)), _339186 = _339184, class_Groups_Osgn__if(_339186)], (876 ^ _319074) ^ [_346137, _346139, _346141, _346143, _346145, _346147, _346149, _346151, _346153, _346155] : [-(c_Polynomial_Opoly__rec(_346155, _346151, _346147, _346143, _346139) = c_Polynomial_Opoly__rec(_346153, _346149, _346145, _346141, _346137)), _346155 = _346153, _346151 = _346149, _346147 = _346145, _346143 = _346141, _346139 = _346137], (7657 ^ _319074) ^ [_580992, _580994] : [-(c_Complex_Oexpi(c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, _580992, _580994)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), c_Complex_Oexpi(_580992)), c_Complex_Oexpi(_580994)))], (12854 ^ _319074) ^ [_762523] : [class_Rings_Ocomm__semiring__0(_762523), -(class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(_762523)))], (5499 ^ _319074) ^ [_505123, _505125, _505127, _505129] : [class_Rings_Olinordered__ring__strict(_505123), 5502 ^ _319074 : [(5517 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_505123, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_505123), _505125), _505127), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_505123), _505125), _505129))), 5518 ^ _319074 : [(5525 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_505123, _505125, c_Groups_Ozero__class_Ozero(_505123)), c_Orderings_Oord__class_Oless(_505123, _505129, _505127)], (5519 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_505123, c_Groups_Ozero__class_Ozero(_505123), _505125), c_Orderings_Oord__class_Oless(_505123, _505127, _505129)]]], (5503 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_505123, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_505123), _505125), _505127), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_505123), _505125), _505129)), 5508 ^ _319074 : [(5511 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_505123, _505127, _505129))], (5509 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_505123, c_Groups_Ozero__class_Ozero(_505123), _505125))]], 5512 ^ _319074 : [(5515 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_505123, _505129, _505127))], (5513 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_505123, _505125, c_Groups_Ozero__class_Ozero(_505123)))]]]]], (170 ^ _319074) ^ [_324434, _324436] : [-(class_Fields_Ofield__inverse__zero(_324434)), _324436 = _324434, class_Fields_Ofield__inverse__zero(_324436)], (160 ^ _319074) ^ [_324139, _324141] : [-(class_RealVector_Oreal__normed__field(_324139)), _324141 = _324139, class_RealVector_Oreal__normed__field(_324141)], (5029 ^ _319074) ^ [_489667, _489669, _489671] : [class_Rings_Oordered__cancel__semiring(_489667), c_Orderings_Oord__class_Oless__eq(_489667, _489669, c_Groups_Ozero__class_Ozero(_489667)), c_Orderings_Oord__class_Oless__eq(_489667, c_Groups_Ozero__class_Ozero(_489667), _489671), -(c_Orderings_Oord__class_Oless__eq(_489667, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_489667), _489669), _489671), c_Groups_Ozero__class_Ozero(_489667)))], (5113 ^ _319074) ^ [_492513, _492515, _492517, _492519] : [class_Rings_Oordered__ring(_492513), c_Orderings_Oord__class_Oless__eq(_492513, _492515, _492517), c_Orderings_Oord__class_Oless__eq(_492513, _492519, c_Groups_Ozero__class_Ozero(_492513)), -(c_Orderings_Oord__class_Oless__eq(_492513, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_492513), _492519), _492517), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_492513), _492519), _492515)))], (4008 ^ _319074) ^ [_451247, _451249, _451251] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _451247, _451249), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _451247, _451251)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _451249, _451251))], (2368 ^ _319074) ^ [_396886, _396888, _396890] : [class_Groups_Ogroup__add(_396886), 2371 ^ _319074 : [(2378 ^ _319074) ^ [] : [c_Groups_Ouminus__class_Ouminus(_396886, _396890) = _396888, -(c_Groups_Ouminus__class_Ouminus(_396886, _396888) = _396890)], (2372 ^ _319074) ^ [] : [c_Groups_Ouminus__class_Ouminus(_396886, _396888) = _396890, -(c_Groups_Ouminus__class_Ouminus(_396886, _396890) = _396888)]]], (10479 ^ _319074) ^ [_678341, _678343, _678345] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_678341)), _678343) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_678341)), _678345), -(_678343 = _678345)], (1086 ^ _319074) ^ [_353759, _353761] : [_353761 = _353759, -(c_Groups_Otimes__class_Otimes(_353761) = c_Groups_Otimes__class_Otimes(_353759))], (3562 ^ _319074) ^ [_435822, _435824] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _435822, _435824), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _435824, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _435822)))], (9696 ^ _319074) ^ [_651573, _651575, _651577, _651579] : [class_Rings_Olinordered__semidom(_651573), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _651575, _651577), c_Orderings_Oord__class_Oless(_651573, c_Groups_Oone__class_Oone(_651573), _651579), -(c_Orderings_Oord__class_Oless(_651573, hAPP(hAPP(c_Power_Opower__class_Opower(_651573), _651579), _651575), hAPP(hAPP(c_Power_Opower__class_Opower(_651573), _651579), _651577)))], (12214 ^ _319074) ^ [_744457, _744459] : [class_Orderings_Oord(_744457), -(class_Orderings_Oord(tc_fun(_744459, _744457)))], (1004 ^ _319074) ^ [_350806, _350808, _350810, _350812] : [-(c_Groups_Ouminus__class_Ouminus(_350812, _350808) = c_Groups_Ouminus__class_Ouminus(_350810, _350806)), _350812 = _350810, _350808 = _350806], (10457 ^ _319074) ^ [_677346] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _677346, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Groups_Oabs__class_Oabs(tc_Int_Oint, _677346) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _677346))], (7573 ^ _319074) ^ [_577168, _577170] : [class_RealVector_Oreal__normed__algebra(_577168), 7577 ^ _319074 : [(7580 ^ _319074) ^ [_577467] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_577168, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_577168), _577467), _577170)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_577168, _577467)), 7576 ^ [_577168, _577170])))], (7578 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 7576 ^ [_577168, _577170]))]]], (9907 ^ _319074) ^ [_658631, _658633] : [-(_658631 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 9910 ^ _319074 : [(9917 ^ _319074) ^ [] : [c_Groups_Oabs__class_Oabs(tc_Int_Oint, _658633) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _658631), _658633), _658631))], (9911 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _658631), _658633), _658631), -(c_Groups_Oabs__class_Oabs(tc_Int_Oint, _658633) = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (12486 ^ _319074) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal))], (10689 ^ _319074) ^ [_685766, _685768] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _685766, _685768), -(_685768 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _685766, 10692 ^ [_685766, _685768])))], (12386 ^ _319074) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (7174 ^ _319074) ^ [_562162, _562164, _562166] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _562162), _562164), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _562162), _562166))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _562162), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _562164, _562166)], (12636 ^ _319074) ^ [] : [-(class_Rings_Osemiring__0(tc_Complex_Ocomplex))], (6313 ^ _319074) ^ [_532540, _532542, _532544, _532546] : [class_Rings_Olinordered__semiring__strict(_532540), c_Orderings_Oord__class_Oless(_532540, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_532540), _532542), _532544), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_532540), _532542), _532546)), c_Orderings_Oord__class_Oless__eq(_532540, c_Groups_Ozero__class_Ozero(_532540), _532542), -(c_Orderings_Oord__class_Oless(_532540, _532544, _532546))], (4479 ^ _319074) ^ [_468186, _468188] : [class_RealVector_Oreal__normed__algebra(_468186), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_468186), c_Groups_Ozero__class_Ozero(_468186)), _468188) = c_Groups_Ozero__class_Ozero(_468186))], (12058 ^ _319074) ^ [_738496] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _738496), -(c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _738496, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _738496)], (8478 ^ _319074) ^ [_610048] : [_610048 = c_Groups_Oone__class_Oone(tc_Nat_Onat), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _610048, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (5191 ^ _319074) ^ [_495056, _495058, _495060] : [class_Rings_Oordered__cancel__semiring(_495056), -(c_Orderings_Oord__class_Oless__eq(_495056, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_495056), _495058), _495060), c_Groups_Ozero__class_Ozero(_495056))), 5196 ^ _319074 : [(5203 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_495056, _495058, c_Groups_Ozero__class_Ozero(_495056)), c_Orderings_Oord__class_Oless__eq(_495056, c_Groups_Ozero__class_Ozero(_495056), _495060)], (5197 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_495056, c_Groups_Ozero__class_Ozero(_495056), _495058), c_Orderings_Oord__class_Oless__eq(_495056, _495060, c_Groups_Ozero__class_Ozero(_495056))]]], (9871 ^ _319074) ^ [_657491] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _657491))], (1175 ^ _319074) ^ [_357276, _357278] : [class_Groups_Oordered__ab__group__add__abs(_357276), -(c_Orderings_Oord__class_Oless__eq(_357276, _357278, c_Groups_Oabs__class_Oabs(_357276, _357278)))], (11278 ^ _319074) ^ [_706258, _706260] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _706258), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _706260), -(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, _706258, _706260)))], (3452 ^ _319074) ^ [_432117, _432119, _432121] : [class_Groups_Oordered__comm__monoid__add(_432117), c_Orderings_Oord__class_Oless(_432117, c_Groups_Ozero__class_Ozero(_432117), _432119), c_Orderings_Oord__class_Oless(_432117, c_Groups_Ozero__class_Ozero(_432117), _432121), -(c_Orderings_Oord__class_Oless(_432117, c_Groups_Ozero__class_Ozero(_432117), c_Groups_Oplus__class_Oplus(_432117, _432119, _432121)))], (9042 ^ _319074) ^ [_629034, _629036] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _629034, _629036), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _629036, _629034), -(_629034 = _629036)], (10758 ^ _319074) ^ [_688198, _688200] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _688198, _688200), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _688198, c_Nat_OSuc(_688200)))], (3574 ^ _319074) ^ [_436261, _436263] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _436261, _436263)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _436261), _436263))], (4497 ^ _319074) ^ [_469070, _469072, _469074, _469076] : [class_RealVector_Oreal__normed__algebra(_469070), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_469070), c_Groups_Oplus__class_Oplus(_469070, _469072, _469074)), _469076) = c_Groups_Oplus__class_Oplus(_469070, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_469070), _469072), _469076), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_469070), _469074), _469076)))], (1259 ^ _319074) ^ [_360194, _360196] : [class_Groups_Ozero(_360194), 1262 ^ _319074 : [(1269 ^ _319074) ^ [] : [_360196 = c_Groups_Ozero__class_Ozero(_360194), -(c_Groups_Ozero__class_Ozero(_360194) = _360196)], (1263 ^ _319074) ^ [] : [c_Groups_Ozero__class_Ozero(_360194) = _360196, -(_360196 = c_Groups_Ozero__class_Ozero(_360194))]]], (2572 ^ _319074) ^ [_403604, _403606] : [class_Groups_Ogroup__add(_403604), 2575 ^ _319074 : [(2582 ^ _319074) ^ [] : [c_Groups_Ozero__class_Ozero(_403604) = _403606, -(c_Groups_Ozero__class_Ozero(_403604) = c_Groups_Ouminus__class_Ouminus(_403604, _403606))], (2576 ^ _319074) ^ [] : [c_Groups_Ozero__class_Ozero(_403604) = c_Groups_Ouminus__class_Ouminus(_403604, _403606), -(c_Groups_Ozero__class_Ozero(_403604) = _403606)]]], (5685 ^ _319074) ^ [_511196, _511198, _511200, _511202] : [class_Rings_Olinordered__semiring__strict(_511196), c_Orderings_Oord__class_Oless(_511196, _511198, _511200), c_Orderings_Oord__class_Oless(_511196, c_Groups_Ozero__class_Ozero(_511196), _511202), -(c_Orderings_Oord__class_Oless(_511196, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_511196), _511202), _511198), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_511196), _511202), _511200)))], (4443 ^ _319074) ^ [_466626, _466628, _466630] : [_466628 = _466630, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _466626, _466628) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _466626, _466630))], (11100 ^ _319074) ^ [_700336, _700338] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _700336), _700338), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _700336, _700338))], (6747 ^ _319074) ^ [_547022, _547024, _547026] : [class_Fields_Olinordered__field(_547022), c_Orderings_Oord__class_Oless__eq(_547022, c_Groups_Ozero__class_Ozero(_547022), _547024), c_Orderings_Oord__class_Oless(_547022, _547026, c_Groups_Ozero__class_Ozero(_547022)), -(c_Orderings_Oord__class_Oless__eq(_547022, c_Rings_Oinverse__class_Odivide(_547022, _547024, _547026), c_Groups_Ozero__class_Ozero(_547022)))], (12052 ^ _319074) ^ [_738260, _738262, _738264] : [class_RealVector_Oreal__normed__vector(_738260), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_738260, _738262), c_RealVector_Onorm__class_Onorm(_738260, _738264)), c_RealVector_Onorm__class_Onorm(_738260, c_Groups_Oplus__class_Oplus(_738260, _738262, _738264))))], (710 ^ _319074) ^ [_340364, _340366] : [-(class_Rings_Oring__1(_340364)), _340366 = _340364, class_Rings_Oring__1(_340366)], (12320 ^ _319074) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (11052 ^ _319074) ^ [_698492] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _698492)) = _698492)], (10752 ^ _319074) ^ [_688028, _688030] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _688028, c_Nat_OSuc(_688030)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _688028, _688030))], (10469 ^ _319074) ^ [] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (5085 ^ _319074) ^ [_491545, _491547, _491549, _491551] : [class_Rings_Oordered__comm__semiring(_491545), c_Orderings_Oord__class_Oless__eq(_491545, _491547, _491549), c_Orderings_Oord__class_Oless__eq(_491545, c_Groups_Ozero__class_Ozero(_491545), _491551), -(c_Orderings_Oord__class_Oless__eq(_491545, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_491545), _491551), _491547), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_491545), _491551), _491549)))], (10377 ^ _319074) ^ [_674492, _674494] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_674494), _674492), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _674492, _674494)], (740 ^ _319074) ^ [_341249, _341251] : [-(class_Power_Opower(_341249)), _341251 = _341249, class_Power_Opower(_341251)], (1900 ^ _319074) ^ [_381438, _381440, _381442, _381444] : [class_Rings_Ocomm__semiring__1(_381438), -(c_Groups_Oplus__class_Oplus(_381438, c_Groups_Oplus__class_Oplus(_381438, _381440, _381442), _381444) = c_Groups_Oplus__class_Oplus(_381438, _381440, c_Groups_Oplus__class_Oplus(_381438, _381442, _381444)))], (12370 ^ _319074) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (3954 ^ _319074) ^ [_449285, _449287, _449289, _449291] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _449285, _449287), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _449289, _449291), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _449285, _449289), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _449287, _449291)))], (7811 ^ _319074) ^ [_586909] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)), _586909) = _586909)], (3594 ^ _319074) ^ [_436955, _436957] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _436955), _436957)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _436957), _436955), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _436955, _436957)], (12624 ^ _319074) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Complex_Ocomplex))], (3308 ^ _319074) ^ [_427410, _427412] : [class_Groups_Ogroup__add(_427410), -(c_Groups_Oplus__class_Oplus(_427410, _427412, c_Groups_Ouminus__class_Ouminus(_427410, _427412)) = c_Groups_Ozero__class_Ozero(_427410))], (6922 ^ _319074) ^ [_552775] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _552775)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _552775)))], (8496 ^ _319074) ^ [_610711, _610713] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _610711, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _610713, _610711)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _610711, _610713))], (4135 ^ _319074) ^ [_455750, _455752, _455754] : [class_Rings_Odivision__ring(_455750), -(_455752 = c_Groups_Ozero__class_Ozero(_455750)), -(c_Rings_Oinverse__class_Odivide(_455750, c_Groups_Ouminus__class_Ouminus(_455750, _455754), c_Groups_Ouminus__class_Ouminus(_455750, _455752)) = c_Rings_Oinverse__class_Odivide(_455750, _455754, _455752))], (9756 ^ _319074) ^ [_653604, _653606, _653608, _653610] : [class_Rings_Olinordered__semidom(_653604), hAPP(hAPP(c_Power_Opower__class_Opower(_653604), _653606), _653608) = hAPP(hAPP(c_Power_Opower__class_Opower(_653604), _653610), _653608), c_Orderings_Oord__class_Oless__eq(_653604, c_Groups_Ozero__class_Ozero(_653604), _653606), c_Orderings_Oord__class_Oless__eq(_653604, c_Groups_Ozero__class_Ozero(_653604), _653610), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _653608), -(_653606 = _653610)], (3358 ^ _319074) ^ [_429132, _429134, _429136] : [class_Groups_Ogroup__add(_429132), c_Groups_Oplus__class_Oplus(_429132, _429134, _429136) = c_Groups_Ozero__class_Ozero(_429132), -(c_Groups_Ouminus__class_Ouminus(_429132, _429134) = _429136)], (3820 ^ _319074) ^ [_444479, _444481, _444483] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _444479, _444481), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _444479, _444483), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _444481, _444483)))], (530 ^ _319074) ^ [_335054, _335056] : [-(class_Orderings_Opreorder(_335054)), _335056 = _335054, class_Orderings_Opreorder(_335056)], (10347 ^ _319074) ^ [_673475, _673477] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _673475, _673477), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_673475), c_Nat_OSuc(_673477)))], (6855 ^ _319074) ^ [_550460, _550462, _550464] : [class_Rings_Olinordered__ring(_550460), c_Orderings_Oord__class_Oless(_550460, c_Groups_Oplus__class_Oplus(_550460, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_550460), _550462), _550462), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_550460), _550464), _550464)), c_Groups_Ozero__class_Ozero(_550460))], (3996 ^ _319074) ^ [_450764, _450766, _450768] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _450764, _450766), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _450764, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _450766, _450768)))], (11902 ^ _319074) ^ [_731919, _731921, _731923] : [class_Groups_Oordered__ab__group__add(_731919), 11905 ^ _319074 : [(11912 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_731919, c_Groups_Ominus__class_Ominus(_731919, _731921, _731923), c_Groups_Ozero__class_Ozero(_731919)), -(c_Orderings_Oord__class_Oless__eq(_731919, _731921, _731923))], (11906 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_731919, _731921, _731923), -(c_Orderings_Oord__class_Oless__eq(_731919, c_Groups_Ominus__class_Ominus(_731919, _731921, _731923), c_Groups_Ozero__class_Ozero(_731919)))]]], (4069 ^ _319074) ^ [_453663, _453665] : [class_Rings_Olinordered__idom(_453663), -(_453665 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_453663))), -(c_Polynomial_Opos__poly(_453663, _453665)), -(c_Polynomial_Opos__poly(_453663, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_453663), _453665)))], (11936 ^ _319074) ^ [_733194, _733196, _733198] : [class_Rings_Ocomm__ring__1(_733194), -(c_Groups_Ominus__class_Ominus(_733194, hAPP(hAPP(c_Power_Opower__class_Opower(_733194), _733196), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(hAPP(c_Power_Opower__class_Opower(_733194), _733198), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_733194), c_Groups_Ominus__class_Ominus(_733194, _733196, _733198)), c_Groups_Oplus__class_Oplus(_733194, _733196, _733198)))], (7128 ^ _319074) ^ [_560493, _560495, _560497] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _560493, _560495), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _560497), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _560497), _560493), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _560497), _560495)))], (7680 ^ _319074) ^ [_582197, _582199] : [class_RealVector_Oreal__normed__algebra(_582197), 7684 ^ _319074 : [(7685 ^ _319074) ^ [_582408] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_582197, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_582197), _582199), _582408)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_582197, _582408)), 7683 ^ [_582197, _582199])))]]], (10792 ^ _319074) ^ [_689488, _689490] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _689488), c_Nat_OSuc(_689490)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _689488, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _689488), _689490)))], (520 ^ _319074) ^ [_334759, _334761] : [-(class_Rings_Oordered__ring(_334759)), _334761 = _334759, class_Rings_Oordered__ring(_334761)], (2174 ^ _319074) ^ [_390741, _390743, _390745, _390747] : [class_Orderings_Oord(_390741), c_Orderings_Oord__class_Oless(_390741, _390743, _390745), _390745 = _390747, -(c_Orderings_Oord__class_Oless(_390741, _390743, _390747))], (5861 ^ _319074) ^ [_517570, _517572, _517574, _517576] : [class_Rings_Odivision__ring(_517570), -(_517572 = c_Groups_Ozero__class_Ozero(_517570)), 5868 ^ _319074 : [(5875 ^ _319074) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_517570), _517574), _517572) = _517576, -(_517574 = c_Rings_Oinverse__class_Odivide(_517570, _517576, _517572))], (5869 ^ _319074) ^ [] : [_517574 = c_Rings_Oinverse__class_Odivide(_517570, _517576, _517572), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_517570), _517574), _517572) = _517576)]]], (10435 ^ _319074) ^ [_676626, _676628] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _676626, _676628), 10438 ^ _319074 : [(10441 ^ _319074) ^ [] : [_676626 = _676628], (10439 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _676626, _676628))]]], (4913 ^ _319074) ^ [_485981, _485983] : [class_Rings_Olinordered__ring(_485981), -(c_Orderings_Oord__class_Oless__eq(_485981, c_Groups_Ozero__class_Ozero(_485981), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_485981), _485983), _485983)))], (8898 ^ _319074) ^ [_624509, _624511] : [_624509 = _624511, 8901 ^ _319074 : [(8904 ^ _319074) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _624511, _624509))], (8902 ^ _319074) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _624509, _624511))]]], (11066 ^ _319074) ^ [_699180] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _699180, _699180))], (12252 ^ _319074) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (10746 ^ _319074) ^ [_687779, _687781] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _687779, _687781), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_687779), _687781))], (13016 ^ _319074) ^ [_767653] : [class_Rings_Ocomm__semiring__1(_767653), -(class_Groups_Oone(tc_Polynomial_Opoly(_767653)))], (4301 ^ _319074) ^ [_461360, _461362] : [class_Lattices_Oboolean__algebra(_461360), -(c_Groups_Ouminus__class_Ouminus(_461360, c_Groups_Ouminus__class_Ouminus(_461360, _461362)) = _461362)], (9861 ^ _319074) ^ [_657107] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _657107, c_Nat_OSuc(_657107)))], (11628 ^ _319074) ^ [_720335, _720337, _720339, _720341] : [class_Fields_Ofield(_720335), -(_720337 = c_Groups_Ozero__class_Ozero(_720335)), -(c_Groups_Ominus__class_Ominus(_720335, _720339, c_Rings_Oinverse__class_Odivide(_720335, _720341, _720337)) = c_Rings_Oinverse__class_Odivide(_720335, c_Groups_Ominus__class_Ominus(_720335, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_720335), _720337), _720339), _720341), _720337))], (1926 ^ _319074) ^ [] : [v_c____ = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)], (12312 ^ _319074) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (770 ^ _319074) ^ [_342134, _342136] : [-(class_Rings_Oring(_342134)), _342136 = _342134, class_Rings_Oring(_342136)], (5553 ^ _319074) ^ [_506887, _506889, _506891] : [class_Rings_Olinordered__semiring__strict(_506887), c_Orderings_Oord__class_Oless(_506887, c_Groups_Ozero__class_Ozero(_506887), _506889), c_Orderings_Oord__class_Oless(_506887, c_Groups_Ozero__class_Ozero(_506887), _506891), -(c_Orderings_Oord__class_Oless(_506887, c_Groups_Ozero__class_Ozero(_506887), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_506887), _506889), _506891)))], (11828 ^ _319074) ^ [_728461, _728463, _728465] : [class_RealVector_Oreal__normed__vector(_728461), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_728461, _728463), c_RealVector_Onorm__class_Onorm(_728461, _728465))), c_RealVector_Onorm__class_Onorm(_728461, c_Groups_Ominus__class_Ominus(_728461, _728463, _728465))))], (4279 ^ _319074) ^ [_460590, _460592, _460594] : [class_Lattices_Oboolean__algebra(_460590), 4282 ^ _319074 : [(4289 ^ _319074) ^ [] : [_460592 = _460594, -(c_Groups_Ouminus__class_Ouminus(_460590, _460592) = c_Groups_Ouminus__class_Ouminus(_460590, _460594))], (4283 ^ _319074) ^ [] : [c_Groups_Ouminus__class_Ouminus(_460590, _460592) = c_Groups_Ouminus__class_Ouminus(_460590, _460594), -(_460592 = _460594)]]], (3392 ^ _319074) ^ [_430240, _430242, _430244] : [class_Groups_Oordered__ab__group__add__abs(_430240), 3395 ^ _319074 : [(3404 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_430240, c_Groups_Oabs__class_Oabs(_430240, _430242), _430244)), c_Orderings_Oord__class_Oless__eq(_430240, _430242, _430244), c_Orderings_Oord__class_Oless__eq(_430240, c_Groups_Ouminus__class_Ouminus(_430240, _430242), _430244)], (3396 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_430240, c_Groups_Oabs__class_Oabs(_430240, _430242), _430244), 3399 ^ _319074 : [(3402 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_430240, c_Groups_Ouminus__class_Ouminus(_430240, _430242), _430244))], (3400 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_430240, _430242, _430244))]]]]], (12442 ^ _319074) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal))], (8916 ^ _319074) ^ [_625084, _625086] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _625084, _625086), 8921 ^ _319074 : [(8924 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _625086, _625084)], (8922 ^ _319074) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _625084, _625086))]], -(_625084 = _625086)], (5643 ^ _319074) ^ [_509802, _509804, _509806] : [class_Rings_Olinordered__semiring__strict(_509802), c_Orderings_Oord__class_Oless(_509802, _509804, c_Groups_Ozero__class_Ozero(_509802)), c_Orderings_Oord__class_Oless(_509802, c_Groups_Ozero__class_Ozero(_509802), _509806), -(c_Orderings_Oord__class_Oless(_509802, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_509802), _509804), _509806), c_Groups_Ozero__class_Ozero(_509802)))], (12920 ^ _319074) ^ [_764613] : [class_Groups_Oab__group__add(_764613), -(class_Groups_Ogroup__add(tc_Polynomial_Opoly(_764613)))], (3140 ^ _319074) ^ [_421857, _421859] : [class_Groups_Oordered__ab__group__add__abs(_421857), -(c_Groups_Oabs__class_Oabs(_421857, c_Groups_Ouminus__class_Ouminus(_421857, _421859)) = c_Groups_Oabs__class_Oabs(_421857, _421859))], (12148 ^ _319074) ^ [_741837, _741839, _741841] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _741837, _741839), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _741837, _741841), _741839))], (400 ^ _319074) ^ [_331219, _331221] : [-(class_Groups_Ocancel__semigroup__add(_331219)), _331221 = _331219, class_Groups_Ocancel__semigroup__add(_331221)], (12326 ^ _319074) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (10764 ^ _319074) ^ [_688447, _688449] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _688447, _688449), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_688447), _688449))], (2416 ^ _319074) ^ [_398410, _398412, _398414] : [class_Orderings_Olinorder(_398410), -(c_Orderings_Oord__class_Oless(_398410, _398412, _398414)), -(_398412 = _398414), -(c_Orderings_Oord__class_Oless(_398410, _398414, _398412))], (10649 ^ _319074) ^ [_684448, _684450] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _684448, _684450) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 10650 ^ _319074 : [(10657 ^ _319074) ^ [] : [_684448 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _684450 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10651 ^ _319074) ^ [] : [_684448 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _684450 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (3188 ^ _319074) ^ [_423549, _423551] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _423549, _423551), 3191 ^ _319074 : [(3194 ^ _319074) ^ [] : [_423549 = _423551], (3192 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _423549, _423551))]]], (7606 ^ _319074) ^ [_578567, _578569, _578571] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _578567, _578569), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _578567, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _578571, _578569)))], (3826 ^ _319074) ^ [_444715, _444717] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _444715, _444717), -(_444715 = _444717), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _444715, _444717))], (12408 ^ _319074) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (2990 ^ _319074) ^ [_416845, _416847, _416849] : [class_Orderings_Oorder(_416845), 2993 ^ _319074 : [(3002 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_416845, _416847, _416849)), c_Orderings_Oord__class_Oless__eq(_416845, _416847, _416849), -(_416847 = _416849)], (2994 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_416845, _416847, _416849), 2997 ^ _319074 : [(3000 ^ _319074) ^ [] : [_416847 = _416849], (2998 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_416845, _416847, _416849))]]]]], (10209 ^ _319074) ^ [_668824, _668826] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _668824, c_Nat_OSuc(_668826)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _668824, _668826)), -(_668824 = _668826)], (7498 ^ _319074) ^ [_574049, _574051, _574053, _574055] : [class_Rings_Ocomm__semiring__0(_574049), -(hAPP(c_Polynomial_Opoly(_574049, c_Polynomial_Opcompose(_574049, _574051, _574053)), _574055) = hAPP(c_Polynomial_Opoly(_574049, _574051), hAPP(c_Polynomial_Opoly(_574049, _574053), _574055)))], (12992 ^ _319074) ^ [_766893] : [class_Rings_Ocomm__semiring__1(_766893), -(class_Power_Opower(tc_Polynomial_Opoly(_766893)))], (4749 ^ _319074) ^ [_480112, _480114, _480116] : [class_Rings_Oring(_480112), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_480112), c_Groups_Ouminus__class_Ouminus(_480112, _480114)), _480116) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_480112), _480114), c_Groups_Ouminus__class_Ouminus(_480112, _480116)))], (3730 ^ _319074) ^ [_441344, _441346, _441348] : [class_Lattices_Oboolean__algebra(_441344), 3733 ^ _319074 : [(3740 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_441344, _441348, _441346), -(c_Orderings_Oord__class_Oless__eq(_441344, c_Groups_Ouminus__class_Ouminus(_441344, _441346), c_Groups_Ouminus__class_Ouminus(_441344, _441348)))], (3734 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_441344, c_Groups_Ouminus__class_Ouminus(_441344, _441346), c_Groups_Ouminus__class_Ouminus(_441344, _441348)), -(c_Orderings_Oord__class_Oless__eq(_441344, _441348, _441346))]]], (13042 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v_da____), v_ma), v_mzh))], (12674 ^ _319074) ^ [_756823] : [class_Rings_Olinordered__idom(_756823), -(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(_756823)))], (10095 ^ _319074) ^ [_664942] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oabs__class_Oabs(tc_Int_Oint, _664942), c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_664942 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (10189 ^ _319074) ^ [_668026] : [c_Nat_OSuc(_668026) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (4309 ^ _319074) ^ [_461675, _461677, _461679, _461681, _461683] : [class_RealVector_Oreal__normed__vector(_461675), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_461675, _461677), _461679), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_461675, _461681), _461683), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_461675, c_Groups_Oplus__class_Oplus(_461675, _461677, _461681)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _461679, _461683)))], (12602 ^ _319074) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex))], (4725 ^ _319074) ^ [_478936, _478938, _478940, _478942, _478944] : [class_Rings_Osemiring(_478936), -(c_Groups_Oplus__class_Oplus(_478936, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_478936), _478938), _478940), c_Groups_Oplus__class_Oplus(_478936, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_478936), _478942), _478940), _478944)) = c_Groups_Oplus__class_Oplus(_478936, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_478936), c_Groups_Oplus__class_Oplus(_478936, _478938, _478942)), _478940), _478944))], (12378 ^ _319074) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (12384 ^ _319074) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (10313 ^ _319074) ^ [_672189, _672191] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _672189, c_Nat_OSuc(_672191)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _672189, _672191)))], (10131 ^ _319074) ^ [_666114, _666116] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _666114, _666116), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _666114, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _666116, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (9420 ^ _319074) ^ [_641679, _641681] : [class_Groups_Omonoid__mult(_641679), -(hAPP(hAPP(c_Power_Opower__class_Opower(_641679), _641681), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _641681)], (6733 ^ _319074) ^ [_546582, _546584, _546586] : [class_Fields_Olinordered__field(_546582), c_Orderings_Oord__class_Oless__eq(_546582, c_Groups_Ozero__class_Ozero(_546582), _546584), c_Orderings_Oord__class_Oless(_546582, c_Groups_Ozero__class_Ozero(_546582), _546586), -(c_Orderings_Oord__class_Oless__eq(_546582, c_Groups_Ozero__class_Ozero(_546582), c_Rings_Oinverse__class_Odivide(_546582, _546584, _546586)))], (3088 ^ _319074) ^ [_420059, _420061, _420063, _420065] : [class_Groups_Oordered__cancel__ab__semigroup__add(_420059), c_Orderings_Oord__class_Oless(_420059, _420061, _420063), -(c_Orderings_Oord__class_Oless(_420059, c_Groups_Oplus__class_Oplus(_420059, _420065, _420061), c_Groups_Oplus__class_Oplus(_420059, _420065, _420063)))], (4737 ^ _319074) ^ [_479568, _479570, _479572] : [class_Rings_Oring(_479568), -(c_Groups_Ouminus__class_Ouminus(_479568, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_479568), _479570), _479572)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_479568), _479570), c_Groups_Ouminus__class_Ouminus(_479568, _479572)))], (30 ^ _319074) ^ [_320145, _320147, _320149, _320151] : [-(c_Polynomial_Opos__poly(_320149, _320145)), c_Polynomial_Opos__poly(_320151, _320147), _320151 = _320149, _320147 = _320145], (12256 ^ _319074) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (12740 ^ _319074) ^ [_758913] : [class_Rings_Olinordered__idom(_758913), -(class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(_758913)))], (3836 ^ _319074) ^ [_445049, _445051, _445053, _445055] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _445049, _445051), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _445053, _445055), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _445049, _445053), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _445051, _445055)))], (1455 ^ _319074) ^ [_366363, _366365] : [class_Groups_Oordered__ab__group__add__abs(_366363), c_Orderings_Oord__class_Oless__eq(_366363, c_Groups_Ozero__class_Ozero(_366363), _366365), -(c_Groups_Oabs__class_Oabs(_366363, _366365) = _366365)], (3152 ^ _319074) ^ [_422288, _422290] : [_422290 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _422288), -(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _422288, _422290) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (10163 ^ _319074) ^ [_667260, _667262] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _667260), 10166 ^ _319074 : [(10175 ^ _319074) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _667260), _667262) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _667260 = c_Groups_Oone__class_Oone(tc_Int_Oint), _667262 = c_Groups_Oone__class_Oone(tc_Int_Oint)], (10167 ^ _319074) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _667260), _667262) = c_Groups_Oone__class_Oone(tc_Int_Oint), 10170 ^ _319074 : [(10173 ^ _319074) ^ [] : [-(_667262 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (10171 ^ _319074) ^ [] : [-(_667260 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]]]], (3948 ^ _319074) ^ [_449029, _449031, _449033] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _449029, _449031), _449033), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _449031, _449033))], (1970 ^ _319074) ^ [_384098, _384100, _384102] : [class_Groups_Oordered__comm__monoid__add(_384098), c_Orderings_Oord__class_Oless__eq(_384098, c_Groups_Ozero__class_Ozero(_384098), _384100), c_Orderings_Oord__class_Oless(_384098, c_Groups_Ozero__class_Ozero(_384098), _384102), -(c_Orderings_Oord__class_Oless(_384098, c_Groups_Ozero__class_Ozero(_384098), c_Groups_Oplus__class_Oplus(_384098, _384100, _384102)))], (9656 ^ _319074) ^ [_650092, _650094, _650096] : [class_Rings_Oring__1(_650092), -(hAPP(hAPP(c_Power_Opower__class_Opower(_650092), c_Groups_Ouminus__class_Ouminus(_650092, _650094)), _650096) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_650092), hAPP(hAPP(c_Power_Opower__class_Opower(_650092), c_Groups_Ouminus__class_Ouminus(_650092, c_Groups_Oone__class_Oone(_650092))), _650096)), hAPP(hAPP(c_Power_Opower__class_Opower(_650092), _650094), _650096)))], (690 ^ _319074) ^ [_339774, _339776] : [-(class_Groups_Oabs__if(_339774)), _339776 = _339774, class_Groups_Oabs__if(_339776)], (6227 ^ _319074) ^ [_529658, _529660, _529662, _529664, _529666] : [class_Rings_Olinordered__semiring__strict(_529658), c_Orderings_Oord__class_Oless(_529658, _529660, _529662), c_Orderings_Oord__class_Oless__eq(_529658, _529664, _529666), c_Orderings_Oord__class_Oless__eq(_529658, c_Groups_Ozero__class_Ozero(_529658), _529660), c_Orderings_Oord__class_Oless(_529658, c_Groups_Ozero__class_Ozero(_529658), _529664), -(c_Orderings_Oord__class_Oless(_529658, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_529658), _529660), _529664), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_529658), _529662), _529666)))], (3342 ^ _319074) ^ [_428617, _428619, _428621] : [class_Groups_Ogroup__add(_428617), 3345 ^ _319074 : [(3352 ^ _319074) ^ [] : [_428621 = c_Groups_Ouminus__class_Ouminus(_428617, _428619), -(c_Groups_Oplus__class_Oplus(_428617, _428619, _428621) = c_Groups_Ozero__class_Ozero(_428617))], (3346 ^ _319074) ^ [] : [c_Groups_Oplus__class_Oplus(_428617, _428619, _428621) = c_Groups_Ozero__class_Ozero(_428617), -(_428621 = c_Groups_Ouminus__class_Ouminus(_428617, _428619))]]], (9252 ^ _319074) ^ [_635482, _635484] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), c_Groups_Oabs__class_Oabs(tc_Int_Oint, _635482)), _635484)), _635482 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_635484 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8150 ^ _319074) ^ [_598664, _598666] : [class_Rings_Ocomm__semiring__1(_598664), -(c_Rings_Odvd__class_Odvd(_598664, _598666, c_Groups_Ozero__class_Ozero(_598664)))], (11294 ^ _319074) ^ [_706793, _706795, _706797] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _706793), 11300 ^ _319074 : [(11303 ^ _319074) ^ [] : [hBOOL(hAPP(_706795, c_Groups_Oplus__class_Oplus(tc_Int_Oint, 11299 ^ [_706793, _706795, _706797], _706793)))], (11301 ^ _319074) ^ [] : [-(hBOOL(hAPP(_706795, 11299 ^ [_706793, _706795, _706797])))]], c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _706797), 11308 ^ _319074 : [(11309 ^ _319074) ^ [_707308] : [hBOOL(hAPP(_706795, _707308)), -(hBOOL(hAPP(_706795, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _707308, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _706797), _706793)))))]]], (5671 ^ _319074) ^ [_510712, _510714, _510716, _510718] : [class_Rings_Olinordered__semiring__strict(_510712), c_Orderings_Oord__class_Oless(_510712, _510714, _510716), c_Orderings_Oord__class_Oless(_510712, c_Groups_Ozero__class_Ozero(_510712), _510718), -(c_Orderings_Oord__class_Oless(_510712, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_510712), _510714), _510718), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_510712), _510716), _510718)))], (2054 ^ _319074) ^ [_386916, _386918, _386920] : [class_Groups_Oab__group__add(_386916), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_386916), c_Polynomial_OpCons(_386916, _386918, _386920)) = c_Polynomial_OpCons(_386916, c_Groups_Ouminus__class_Ouminus(_386916, _386918), c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_386916), _386920)))], (8810 ^ _319074) ^ [_621681, _621683] : [class_Groups_Osgn__if(_621681), 8813 ^ _319074 : [(8820 ^ _319074) ^ [] : [-(_621683 = c_Groups_Ozero__class_Ozero(_621681)), 8823 ^ _319074 : [(8830 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_621681, c_Groups_Ozero__class_Ozero(_621681), _621683)), -(c_Groups_Osgn__class_Osgn(_621681, _621683) = c_Groups_Ouminus__class_Ouminus(_621681, c_Groups_Oone__class_Oone(_621681)))], (8824 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_621681, c_Groups_Ozero__class_Ozero(_621681), _621683), -(c_Groups_Osgn__class_Osgn(_621681, _621683) = c_Groups_Oone__class_Oone(_621681))]]], (8814 ^ _319074) ^ [] : [_621683 = c_Groups_Ozero__class_Ozero(_621681), -(c_Groups_Osgn__class_Osgn(_621681, _621683) = c_Groups_Ozero__class_Ozero(_621681))]]], (110 ^ _319074) ^ [_322664, _322666] : [-(class_RealVector_Oreal__normed__div__algebra(_322664)), _322666 = _322664, class_RealVector_Oreal__normed__div__algebra(_322666)], (2048 ^ _319074) ^ [_386646, _386648, _386650] : [class_Groups_Oab__group__add(_386646), -(c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_386646), c_Polynomial_OpCons(_386646, _386648, _386650)) = c_Polynomial_OpCons(_386646, c_Groups_Ouminus__class_Ouminus(_386646, _386648), c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_386646), _386650)))], (5459 ^ _319074) ^ [_503761, _503763] : [class_Rings_Olinordered__ring(_503761), c_Orderings_Oord__class_Oless(_503761, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_503761), _503763), _503763), c_Groups_Ozero__class_Ozero(_503761))], (6561 ^ _319074) ^ [_541030, _541032, _541034] : [class_Fields_Olinordered__field__inverse__zero(_541030), 6564 ^ _319074 : [(6579 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_541030, c_Rings_Oinverse__class_Odivide(_541030, _541032, _541034), c_Groups_Ozero__class_Ozero(_541030))), 6580 ^ _319074 : [(6587 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_541030, _541032, c_Groups_Ozero__class_Ozero(_541030)), c_Orderings_Oord__class_Oless(_541030, c_Groups_Ozero__class_Ozero(_541030), _541034)], (6581 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_541030, c_Groups_Ozero__class_Ozero(_541030), _541032), c_Orderings_Oord__class_Oless(_541030, _541034, c_Groups_Ozero__class_Ozero(_541030))]]], (6565 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_541030, c_Rings_Oinverse__class_Odivide(_541030, _541032, _541034), c_Groups_Ozero__class_Ozero(_541030)), 6570 ^ _319074 : [(6573 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_541030, _541034, c_Groups_Ozero__class_Ozero(_541030)))], (6571 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_541030, c_Groups_Ozero__class_Ozero(_541030), _541032))]], 6574 ^ _319074 : [(6577 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_541030, c_Groups_Ozero__class_Ozero(_541030), _541034))], (6575 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_541030, _541032, c_Groups_Ozero__class_Ozero(_541030)))]]]]], (7413 ^ _319074) ^ [_570792] : [_570792 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _570792), _570792))], (11834 ^ _319074) ^ [_728731, _728733, _728735] : [class_Groups_Oordered__ab__group__add__abs(_728731), -(c_Orderings_Oord__class_Oless__eq(_728731, c_Groups_Ominus__class_Ominus(_728731, c_Groups_Oabs__class_Oabs(_728731, _728733), c_Groups_Oabs__class_Oabs(_728731, _728735)), c_Groups_Oabs__class_Oabs(_728731, c_Groups_Ominus__class_Ominus(_728731, _728735, _728733))))], (10679 ^ _319074) ^ [_685424, _685426] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _685424), _685426) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _685424 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _685426 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12164 ^ _319074) ^ [_742410, _742412] : [class_Groups_Oab__group__add(_742410), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_742410), _742412, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_742410))) = _742412)], (2662 ^ _319074) ^ [_406371, _406373, _406375] : [class_Groups_Oordered__ab__group__add(_406371), 2665 ^ _319074 : [(2672 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_406371, c_Groups_Ouminus__class_Ouminus(_406371, _406375), _406373), -(c_Orderings_Oord__class_Oless__eq(_406371, c_Groups_Ouminus__class_Ouminus(_406371, _406373), _406375))], (2666 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_406371, c_Groups_Ouminus__class_Ouminus(_406371, _406373), _406375), -(c_Orderings_Oord__class_Oless__eq(_406371, c_Groups_Ouminus__class_Ouminus(_406371, _406375), _406373))]]], (1142 ^ _319074) ^ [_355934, _355936] : [hAPP(_355934, 1143 ^ [_355934, _355936]) = hAPP(_355936, 1143 ^ [_355934, _355936]), -(_355934 = _355936)], (11276 ^ _319074) ^ [] : [-(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)))], (12830 ^ _319074) ^ [_761763] : [class_Groups_Ocomm__monoid__add(_761763), -(class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(_761763)))], (4485 ^ _319074) ^ [_468446, _468448, _468450, _468452] : [class_RealVector_Oreal__normed__algebra(_468446), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_468446), _468448), c_Groups_Oplus__class_Oplus(_468446, _468450, _468452)) = c_Groups_Oplus__class_Oplus(_468446, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_468446), _468448), _468450), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_468446), _468448), _468452)))], (12264 ^ _319074) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (4227 ^ _319074) ^ [_458831] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _458831, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_458831 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2858 ^ _319074) ^ [_412786, _412788, _412790] : [class_Orderings_Opreorder(_412786), c_Orderings_Oord__class_Oless(_412786, _412788, _412790), -(c_Orderings_Oord__class_Oless__eq(_412786, _412788, _412790))], (12376 ^ _319074) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (10800 ^ _319074) ^ [_689862, _689864, _689866] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _689864, _689866), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_689862)), _689864), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_689862)), _689866)))], (5841 ^ _319074) ^ [_516912, _516914, _516916, _516918] : [class_Rings_Odivision__ring(_516912), -(_516914 = c_Groups_Ozero__class_Ozero(_516912)), 5848 ^ _319074 : [(5855 ^ _319074) ^ [] : [_516916 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_516912), _516918), _516914), -(c_Rings_Oinverse__class_Odivide(_516912, _516916, _516914) = _516918)], (5849 ^ _319074) ^ [] : [c_Rings_Oinverse__class_Odivide(_516912, _516916, _516914) = _516918, -(_516916 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_516912), _516918), _516914))]]], (3856 ^ _319074) ^ [_445771, _445773, _445775] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _445771, _445773), _445775), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _445771, _445775))], (5015 ^ _319074) ^ [_489219, _489221, _489223] : [class_Rings_Oordered__cancel__semiring(_489219), c_Orderings_Oord__class_Oless__eq(_489219, c_Groups_Ozero__class_Ozero(_489219), _489221), c_Orderings_Oord__class_Oless__eq(_489219, _489223, c_Groups_Ozero__class_Ozero(_489219)), -(c_Orderings_Oord__class_Oless__eq(_489219, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_489219), _489223), _489221), c_Groups_Ozero__class_Ozero(_489219)))], (12390 ^ _319074) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (11826 ^ _319074) ^ [_728327, _728329] : [-(c_Groups_Ominus__class_Ominus(tc_Int_Oint, _728327, _728329) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _728327, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _728329)))], (3762 ^ _319074) ^ [_442415, _442417] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _442415, _442417)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _442415, _442417), -(_442415 = _442417)], (7064 ^ _319074) ^ [_557975] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _557975, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _557975), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _557975), _557975))))], (10427 ^ _319074) ^ [_676276, _676278, _676280] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _676276, _676278), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _676276, _676280), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _676278, _676280)))], (3750 ^ _319074) ^ [_441932, _441934] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _441932, _441934), _441932)], (7673 ^ _319074) ^ [_581801] : [class_RealVector_Oreal__normed__algebra(_581801), 7677 ^ _319074 : [(7678 ^ _319074) ^ [_582046, _582048] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_581801, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_581801), _582048), _582046)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_581801, _582048)), c_RealVector_Onorm__class_Onorm(_581801, _582046))), 7676 ^ [_581801])))]]], (10556 ^ _319074) ^ [_681458] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _681458, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_681458 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2256 ^ _319074) ^ [_393365, _393367, _393369] : [class_Orderings_Opreorder(_393365), c_Orderings_Oord__class_Oless(_393365, _393367, _393369), c_Orderings_Oord__class_Oless(_393365, _393369, _393367)], (1796 ^ _319074) ^ [_377627, _377629] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _377627, _377629)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _377629, _377627))], (7781 ^ _319074) ^ [_585794, _585796] : [class_Groups_Ocomm__monoid__mult(_585794), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_585794), _585796), c_Groups_Oone__class_Oone(_585794)) = _585796)], (10453 ^ _319074) ^ [_677147] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _677147, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _677147)], (12538 ^ _319074) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_RealDef_Oreal))], (12470 ^ _319074) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal))], (4449 ^ _319074) ^ [_466859, _466861, _466863] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _466859, _466861), _466863) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _466859, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _466861, _466863)))], (4265 ^ _319074) ^ [_460128] : [-(_460128 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _460128))], (5567 ^ _319074) ^ [_507335, _507337, _507339] : [class_Rings_Olinordered__semiring__strict(_507335), c_Orderings_Oord__class_Oless(_507335, c_Groups_Ozero__class_Ozero(_507335), _507337), c_Orderings_Oord__class_Oless(_507335, _507339, c_Groups_Ozero__class_Ozero(_507335)), -(c_Orderings_Oord__class_Oless(_507335, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_507335), _507337), _507339), c_Groups_Ozero__class_Ozero(_507335)))], (4043 ^ _319074) ^ [_452563] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _452563, _452563))], (7666 ^ _319074) ^ [_581460, _581462] : [class_RealVector_Oreal__normed__algebra(_581460), 7670 ^ _319074 : [(7671 ^ _319074) ^ [_581671] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_581460, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_581460), _581671), _581462)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_581460, _581671)), 7669 ^ [_581460, _581462])))]]], (11068 ^ _319074) ^ [_699288, _699290] : [-(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _699288, _699290)), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _699290, _699288))], (580 ^ _319074) ^ [_336529, _336531] : [-(class_Rings_Osemiring__0(_336529)), _336531 = _336529, class_Rings_Osemiring__0(_336531)], (8662 ^ _319074) ^ [_616961, _616963] : [class_Rings_Olinordered__idom(_616961), 8665 ^ _319074 : [(8672 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_616961, _616963, c_Groups_Ozero__class_Ozero(_616961)), -(c_Orderings_Oord__class_Oless(_616961, c_Groups_Osgn__class_Osgn(_616961, _616963), c_Groups_Ozero__class_Ozero(_616961)))], (8666 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_616961, c_Groups_Osgn__class_Osgn(_616961, _616963), c_Groups_Ozero__class_Ozero(_616961)), -(c_Orderings_Oord__class_Oless(_616961, _616963, c_Groups_Ozero__class_Ozero(_616961)))]]], (3772 ^ _319074) ^ [_442752, _442754] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _442752, _442754), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _442752, _442754)), -(_442752 = _442754)], (11684 ^ _319074) ^ [_722715, _722717, _722719, _722721, _722723, _722725] : [class_Rings_Oordered__ring(_722715), 11687 ^ _319074 : [(11694 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_722715, c_Groups_Oplus__class_Oplus(_722715, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_722715), c_Groups_Ominus__class_Ominus(_722715, _722717, _722723)), _722719), _722721), _722725), -(c_Orderings_Oord__class_Oless(_722715, c_Groups_Oplus__class_Oplus(_722715, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_722715), _722717), _722719), _722721), c_Groups_Oplus__class_Oplus(_722715, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_722715), _722723), _722719), _722725)))], (11688 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_722715, c_Groups_Oplus__class_Oplus(_722715, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_722715), _722717), _722719), _722721), c_Groups_Oplus__class_Oplus(_722715, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_722715), _722723), _722719), _722725)), -(c_Orderings_Oord__class_Oless(_722715, c_Groups_Oplus__class_Oplus(_722715, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_722715), c_Groups_Ominus__class_Ominus(_722715, _722717, _722723)), _722719), _722721), _722725))]]], (1169 ^ _319074) ^ [_357016, _357018, _357020] : [class_Groups_Oordered__ab__group__add__abs(_357016), -(c_Groups_Oabs__class_Oabs(_357016, c_Groups_Oplus__class_Oplus(_357016, c_Groups_Oabs__class_Oabs(_357016, _357018), c_Groups_Oabs__class_Oabs(_357016, _357020))) = c_Groups_Oplus__class_Oplus(_357016, c_Groups_Oabs__class_Oabs(_357016, _357018), c_Groups_Oabs__class_Oabs(_357016, _357020)))], (7344 ^ _319074) ^ [_568269, _568271, _568273, _568275] : [class_Rings_Ocomm__semiring__0(_568269), -(hAPP(c_Polynomial_Opoly(_568269, c_Polynomial_OpCons(_568269, _568271, _568273)), _568275) = c_Groups_Oplus__class_Oplus(_568269, _568271, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_568269), _568275), hAPP(c_Polynomial_Opoly(_568269, _568273), _568275))))], (12394 ^ _319074) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (3872 ^ _319074) ^ [_446394, _446396] : [-(_446394 = _446396), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _446394, _446396)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _446396, _446394))], (11716 ^ _319074) ^ [_724123, _724125, _724127, _724129, _724131, _724133] : [class_Rings_Oordered__ring(_724123), 11719 ^ _319074 : [(11726 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_724123, _724129, c_Groups_Oplus__class_Oplus(_724123, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_724123), c_Groups_Ominus__class_Ominus(_724123, _724131, _724125)), _724127), _724133)), -(c_Orderings_Oord__class_Oless__eq(_724123, c_Groups_Oplus__class_Oplus(_724123, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_724123), _724125), _724127), _724129), c_Groups_Oplus__class_Oplus(_724123, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_724123), _724131), _724127), _724133)))], (11720 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_724123, c_Groups_Oplus__class_Oplus(_724123, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_724123), _724125), _724127), _724129), c_Groups_Oplus__class_Oplus(_724123, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_724123), _724131), _724127), _724133)), -(c_Orderings_Oord__class_Oless__eq(_724123, _724129, c_Groups_Oplus__class_Oplus(_724123, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_724123), c_Groups_Ominus__class_Ominus(_724123, _724131, _724125)), _724127), _724133)))]]], (2678 ^ _319074) ^ [_406883, _406885, _406887] : [class_Groups_Oordered__ab__group__add(_406883), 2681 ^ _319074 : [(2688 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_406883, _406887, c_Groups_Ouminus__class_Ouminus(_406883, _406885)), -(c_Orderings_Oord__class_Oless__eq(_406883, _406885, c_Groups_Ouminus__class_Ouminus(_406883, _406887)))], (2682 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_406883, _406885, c_Groups_Ouminus__class_Ouminus(_406883, _406887)), -(c_Orderings_Oord__class_Oless__eq(_406883, _406887, c_Groups_Ouminus__class_Ouminus(_406883, _406885)))]]], (12328 ^ _319074) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (2796 ^ _319074) ^ [_410937, _410939, _410941] : [class_Orderings_Oorder(_410937), c_Orderings_Oord__class_Oless__eq(_410937, _410939, _410941), -(_410941 = _410939), -(c_Orderings_Oord__class_Oless(_410937, _410939, _410941))], (6783 ^ _319074) ^ [_548196, _548198, _548200, _548202, _548204] : [class_Fields_Olinordered__field(_548196), c_Orderings_Oord__class_Oless__eq(_548196, c_Groups_Ozero__class_Ozero(_548196), _548198), c_Orderings_Oord__class_Oless(_548196, _548198, _548200), c_Orderings_Oord__class_Oless(_548196, c_Groups_Ozero__class_Ozero(_548196), _548202), c_Orderings_Oord__class_Oless__eq(_548196, _548202, _548204), -(c_Orderings_Oord__class_Oless(_548196, c_Rings_Oinverse__class_Odivide(_548196, _548198, _548204), c_Rings_Oinverse__class_Odivide(_548196, _548200, _548202)))], (12374 ^ _319074) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (5895 ^ _319074) ^ [_518760, _518762, _518764, _518766] : [class_Fields_Olinordered__field__inverse__zero(_518760), 5898 ^ _319074 : [(5899 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_518760, _518762, c_Rings_Oinverse__class_Odivide(_518760, _518764, _518766)), 5902 ^ _319074 : [(5909 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_518760, c_Groups_Ozero__class_Ozero(_518760), _518766)), 5912 ^ _319074 : [(5919 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_518760, _518766, c_Groups_Ozero__class_Ozero(_518760))), -(c_Orderings_Oord__class_Oless__eq(_518760, _518762, c_Groups_Ozero__class_Ozero(_518760)))], (5913 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_518760, _518766, c_Groups_Ozero__class_Ozero(_518760)), -(c_Orderings_Oord__class_Oless__eq(_518760, _518764, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_518760), _518762), _518766)))]]], (5903 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_518760, c_Groups_Ozero__class_Ozero(_518760), _518766), -(c_Orderings_Oord__class_Oless__eq(_518760, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_518760), _518762), _518766), _518764))]]], (5925 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_518760, _518762, c_Rings_Oinverse__class_Odivide(_518760, _518764, _518766))), 5928 ^ _319074 : [(5931 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_518760, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_518760), _518762), _518766), _518764)], (5929 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_518760, c_Groups_Ozero__class_Ozero(_518760), _518766))]], 5932 ^ _319074 : [(5935 ^ _319074) ^ [] : [5936 ^ _319074 : [(5939 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_518760, _518764, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_518760), _518762), _518766))], (5937 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_518760, _518766, c_Groups_Ozero__class_Ozero(_518760)))]], 5940 ^ _319074 : [(5943 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_518760, _518762, c_Groups_Ozero__class_Ozero(_518760))], (5941 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_518760, _518766, c_Groups_Ozero__class_Ozero(_518760))]]], (5933 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_518760, c_Groups_Ozero__class_Ozero(_518760), _518766)]]]]], (4295 ^ _319074) ^ [_461110, _461112, _461114, _461116] : [class_Groups_Ouminus(_461110), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_461112, _461110), _461114), _461116) = c_Groups_Ouminus__class_Ouminus(_461110, hAPP(_461114, _461116)))], (12794 ^ _319074) ^ [_760623] : [class_Rings_Ocomm__semiring__0(_760623), -(class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(_760623)))], (9218 ^ _319074) ^ [_634455, _634457, _634459] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _634455, _634457), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _634457, _634455)), 9233 ^ _319074 : [(9236 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _634459, _634455)], (9234 ^ _319074) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _634455, _634459))]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _634457, _634459), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _634459, _634457))], (11890 ^ _319074) ^ [_731179, _731181, _731183, _731185, _731187] : [class_RealVector_Oreal__normed__algebra(_731179), -(c_Groups_Ominus__class_Ominus(_731179, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_731179), _731181), _731183), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_731179), _731185), _731187)) = c_Groups_Oplus__class_Oplus(_731179, c_Groups_Oplus__class_Oplus(_731179, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_731179), c_Groups_Ominus__class_Ominus(_731179, _731181, _731185)), c_Groups_Ominus__class_Ominus(_731179, _731183, _731187)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_731179), c_Groups_Ominus__class_Ominus(_731179, _731181, _731185)), _731187)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_731179), _731185), c_Groups_Ominus__class_Ominus(_731179, _731183, _731187))))], (10363 ^ _319074) ^ [_673992, _673994] : [10364 ^ _319074 : [(10367 ^ _319074) ^ [] : [_673992 = c_Nat_OSuc(_673994)], (10365 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _673992, _673994)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _673992, c_Nat_OSuc(_673994)))], (12842 ^ _319074) ^ [_762143] : [class_Rings_Olinordered__idom(_762143), -(class_Rings_Olinordered__idom(tc_Polynomial_Opoly(_762143)))], (10485 ^ _319074) ^ [_678541, _678543, _678545] : [_678543 = _678545, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_678541)), _678543) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_678541)), _678545))], (10593 ^ _319074) ^ [_682732] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _682732, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_682732 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (1465 ^ _319074) ^ [_366672, _366674] : [class_Groups_Oordered__ab__group__add__abs(_366672), 1468 ^ _319074 : [(1475 ^ _319074) ^ [] : [_366674 = c_Groups_Ozero__class_Ozero(_366672), -(c_Orderings_Oord__class_Oless__eq(_366672, c_Groups_Oabs__class_Oabs(_366672, _366674), c_Groups_Ozero__class_Ozero(_366672)))], (1469 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_366672, c_Groups_Oabs__class_Oabs(_366672, _366674), c_Groups_Ozero__class_Ozero(_366672)), -(_366674 = c_Groups_Ozero__class_Ozero(_366672))]]], (9524 ^ _319074) ^ [_645100, _645102, _645104, _645106] : [class_Fields_Ofield(_645100), -(_645102 = c_Groups_Ozero__class_Ozero(_645100)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_645100), c_Rings_Oinverse__class_Odivide(_645100, _645104, _645102)), _645106) = c_Rings_Oinverse__class_Odivide(_645100, hAPP(hAPP(c_Power_Opower__class_Opower(_645100), _645104), _645106), hAPP(hAPP(c_Power_Opower__class_Opower(_645100), _645102), _645106)))], (10491 ^ _319074) ^ [_678776, _678778] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _678776)), _678778) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _678776), _678778)))], (11006 ^ _319074) ^ [_696833, _696835, _696837] : [class_Rings_Oidom(_696833), -(_696835 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_696833))), 11013 ^ _319074 : [(11016 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_696833), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_696833)), c_Polynomial_OpCons(_696833, c_Groups_Ouminus__class_Ouminus(_696833, _696837), c_Polynomial_OpCons(_696833, c_Groups_Oone__class_Oone(_696833), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_696833))))), c_Nat_OSuc(c_Polynomial_Oorder(_696833, _696837, _696835))), _696835)], (11014 ^ _319074) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_696833), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_696833)), c_Polynomial_OpCons(_696833, c_Groups_Ouminus__class_Ouminus(_696833, _696837), c_Polynomial_OpCons(_696833, c_Groups_Oone__class_Oone(_696833), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_696833))))), c_Polynomial_Oorder(_696833, _696837, _696835)), _696835))]]], (12616 ^ _319074) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex))], (11142 ^ _319074) ^ [_701717, _701719, _701721] : [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), _701717), _701719), _701721), 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), _701721), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _701717), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _701719, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (12546 ^ _319074) ^ [] : [-(class_Rings_Omult__zero(tc_RealDef_Oreal))], (7915 ^ _319074) ^ [_590638, _590640] : [class_Rings_Ocomm__ring__1(_590638), -(c_Groups_Ouminus__class_Ouminus(_590638, _590640) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_590638), c_Groups_Ouminus__class_Ouminus(_590638, c_Groups_Oone__class_Oone(_590638))), _590640))], (7859 ^ _319074) ^ [_588551] : [class_Rings_Olinordered__semidom(_588551), -(c_Orderings_Oord__class_Oless__eq(_588551, c_Groups_Ozero__class_Ozero(_588551), c_Groups_Oone__class_Oone(_588551)))], (650 ^ _319074) ^ [_338594, _338596] : [-(class_Orderings_Oord(_338594)), _338596 = _338594, class_Orderings_Oord(_338596)], (12248 ^ _319074) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (10740 ^ _319074) ^ [_687609, _687611] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_687609), _687611), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _687609, _687611))], (1639 ^ _319074) ^ [_372237, _372239, _372241, _372243, _372245] : [class_Orderings_Oord(_372237), c_Orderings_Oord__class_Oless__eq(tc_fun(_372239, _372237), _372241, _372243), -(c_Orderings_Oord__class_Oless__eq(_372237, hAPP(_372241, _372245), hAPP(_372243, _372245)))], (11742 ^ _319074) ^ [_725136, _725138, _725140, _725142] : [class_Rings_Ocomm__ring__1(_725136), c_Rings_Odvd__class_Odvd(_725136, _725138, _725140), c_Rings_Odvd__class_Odvd(_725136, _725138, _725142), -(c_Rings_Odvd__class_Odvd(_725136, _725138, c_Groups_Ominus__class_Ominus(_725136, _725140, _725142)))], (3658 ^ _319074) ^ [_439048, _439050] : [class_Rings_Olinordered__idom(_439048), 3661 ^ _319074 : [(3668 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_439048, _439050, c_Groups_Ozero__class_Ozero(_439048)), -(c_Orderings_Oord__class_Oless(_439048, _439050, c_Groups_Ouminus__class_Ouminus(_439048, _439050)))], (3662 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_439048, _439050, c_Groups_Ouminus__class_Ouminus(_439048, _439050)), -(c_Orderings_Oord__class_Oless(_439048, _439050, c_Groups_Ozero__class_Ozero(_439048)))]]], (6595 ^ _319074) ^ [_542067, _542069, _542071] : [class_Fields_Olinordered__field(_542067), c_Orderings_Oord__class_Oless(_542067, c_Groups_Ozero__class_Ozero(_542067), _542069), c_Orderings_Oord__class_Oless(_542067, c_Groups_Ozero__class_Ozero(_542067), _542071), -(c_Orderings_Oord__class_Oless(_542067, c_Groups_Ozero__class_Ozero(_542067), c_Rings_Oinverse__class_Odivide(_542067, _542069, _542071)))], (11418 ^ _319074) ^ [_711532, _711534, _711536] : [class_Groups_Oab__group__add(_711532), 11421 ^ _319074 : [(11428 ^ _319074) ^ [] : [c_Groups_Ominus__class_Ominus(_711532, _711534, _711536) = c_Groups_Ozero__class_Ozero(_711532), -(_711534 = _711536)], (11422 ^ _319074) ^ [] : [_711534 = _711536, -(c_Groups_Ominus__class_Ominus(_711532, _711534, _711536) = c_Groups_Ozero__class_Ozero(_711532))]]], (12388 ^ _319074) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (11544 ^ _319074) ^ [_716657, _716659, _716661, _716663, _716665] : [class_Groups_Oab__group__add(_716657), -(c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_716657), c_Polynomial_OpCons(_716657, _716659, _716661), c_Polynomial_OpCons(_716657, _716663, _716665)) = c_Polynomial_OpCons(_716657, c_Groups_Ominus__class_Ominus(_716657, _716659, _716663), c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_716657), _716661, _716665)))], (12588 ^ _319074) ^ [] : [-(class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex))], (6067 ^ _319074) ^ [_524350, _524352, _524354, _524356] : [class_Fields_Olinordered__field(_524350), c_Orderings_Oord__class_Oless(_524350, _524352, c_Groups_Ozero__class_Ozero(_524350)), 6074 ^ _319074 : [(6081 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_524350, _524356, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_524350), _524354), _524352)), -(c_Orderings_Oord__class_Oless__eq(_524350, _524354, c_Rings_Oinverse__class_Odivide(_524350, _524356, _524352)))], (6075 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_524350, _524354, c_Rings_Oinverse__class_Odivide(_524350, _524356, _524352)), -(c_Orderings_Oord__class_Oless__eq(_524350, _524356, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_524350), _524354), _524352)))]]], (12612 ^ _319074) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex))], (10894 ^ _319074) ^ [_693063, _693065] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _693063), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _693065), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _693063, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _693065), _693063)))], (6513 ^ _319074) ^ [_539539, _539541, _539543, _539545] : [class_Fields_Olinordered__field__inverse__zero(_539539), c_Orderings_Oord__class_Oless__eq(_539539, _539541, _539543), c_Orderings_Oord__class_Oless__eq(_539539, _539545, c_Groups_Ozero__class_Ozero(_539539)), -(c_Orderings_Oord__class_Oless__eq(_539539, c_Rings_Oinverse__class_Odivide(_539539, _539543, _539545), c_Rings_Oinverse__class_Odivide(_539539, _539541, _539545)))], (8882 ^ _319074) ^ [_623971, _623973, _623975] : [class_Rings_Olinordered__semidom(_623971), c_Orderings_Oord__class_Oless(_623971, c_Groups_Oone__class_Oone(_623971), _623973), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _623975), -(c_Orderings_Oord__class_Oless(_623971, c_Groups_Oone__class_Oone(_623971), hAPP(hAPP(c_Power_Opower__class_Opower(_623971), _623973), _623975)))], (4743 ^ _319074) ^ [_479840, _479842, _479844] : [class_Rings_Oring(_479840), -(c_Groups_Ouminus__class_Ouminus(_479840, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_479840), _479842), _479844)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_479840), c_Groups_Ouminus__class_Ouminus(_479840, _479842)), _479844))], (12176 ^ _319074) ^ [_742974, _742976, _742978] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _742974), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _742976, _742978)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _742974), _742976), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _742974), _742978)))], (5465 ^ _319074) ^ [_504020, _504022, _504024, _504026] : [class_Rings_Olinordered__ring__strict(_504020), 5468 ^ _319074 : [(5483 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_504020, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_504020), _504022), _504024), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_504020), _504026), _504024))), 5484 ^ _319074 : [(5491 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_504020, _504024, c_Groups_Ozero__class_Ozero(_504020)), c_Orderings_Oord__class_Oless(_504020, _504026, _504022)], (5485 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_504020, c_Groups_Ozero__class_Ozero(_504020), _504024), c_Orderings_Oord__class_Oless(_504020, _504022, _504026)]]], (5469 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_504020, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_504020), _504022), _504024), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_504020), _504026), _504024)), 5474 ^ _319074 : [(5477 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_504020, _504022, _504026))], (5475 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_504020, c_Groups_Ozero__class_Ozero(_504020), _504024))]], 5478 ^ _319074 : [(5481 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_504020, _504026, _504022))], (5479 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_504020, _504024, c_Groups_Ozero__class_Ozero(_504020)))]]]]], (5623 ^ _319074) ^ [_509141, _509143, _509145, _509147] : [class_Rings_Olinordered__ring__strict(_509141), c_Orderings_Oord__class_Oless(_509141, _509143, c_Groups_Ozero__class_Ozero(_509141)), 5630 ^ _319074 : [(5637 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_509141, _509147, _509145), -(c_Orderings_Oord__class_Oless(_509141, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_509141), _509143), _509145), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_509141), _509143), _509147)))], (5631 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_509141, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_509141), _509143), _509145), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_509141), _509143), _509147)), -(c_Orderings_Oord__class_Oless(_509141, _509147, _509145))]]], (1832 ^ _319074) ^ [_378930, _378932] : [class_Groups_Olinordered__ab__group__add(_378930), 1835 ^ _319074 : [(1842 ^ _319074) ^ [] : [_378932 = c_Groups_Ozero__class_Ozero(_378930), -(c_Groups_Oplus__class_Oplus(_378930, _378932, _378932) = c_Groups_Ozero__class_Ozero(_378930))], (1836 ^ _319074) ^ [] : [c_Groups_Oplus__class_Oplus(_378930, _378932, _378932) = c_Groups_Ozero__class_Ozero(_378930), -(_378932 = c_Groups_Ozero__class_Ozero(_378930))]]], (11924 ^ _319074) ^ [_732620, _732622] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _732620, _732622), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _732620, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _732622, c_Groups_Oone__class_Oone(tc_Int_Oint))))], (7555 ^ _319074) ^ [_576241] : [class_RealVector_Oreal__normed__algebra(_576241), 7559 ^ _319074 : [(7562 ^ _319074) ^ [_576570, _576572] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_576241, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_576241), _576572), _576570)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_576241, _576572)), c_RealVector_Onorm__class_Onorm(_576241, _576570))), 7558 ^ [_576241])))], (7560 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 7558 ^ [_576241]))]]], (4987 ^ _319074) ^ [_488323, _488325, _488327] : [class_Rings_Oordered__cancel__semiring(_488323), c_Orderings_Oord__class_Oless__eq(_488323, c_Groups_Ozero__class_Ozero(_488323), _488325), c_Orderings_Oord__class_Oless__eq(_488323, c_Groups_Ozero__class_Ozero(_488323), _488327), -(c_Orderings_Oord__class_Oless__eq(_488323, c_Groups_Ozero__class_Ozero(_488323), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_488323), _488325), _488327)))], (9408 ^ _319074) ^ [_641113, _641115, _641117] : [class_Rings_Olinordered__idom(_641113), -(c_Groups_Oabs__class_Oabs(_641113, hAPP(hAPP(c_Power_Opower__class_Opower(_641113), _641115), _641117)) = hAPP(hAPP(c_Power_Opower__class_Opower(_641113), c_Groups_Oabs__class_Oabs(_641113, _641115)), _641117))], (8194 ^ _319074) ^ [_600356, _600358, _600360, _600362, _600364] : [class_Rings_Ocomm__semiring__1(_600356), c_Rings_Odvd__class_Odvd(_600356, _600358, _600360), c_Rings_Odvd__class_Odvd(_600356, _600362, _600364), -(c_Rings_Odvd__class_Odvd(_600356, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_600356), _600358), _600362), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_600356), _600360), _600364)))], (10089 ^ _319074) ^ [_664703, _664705] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _664703, _664705), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _664703, c_Groups_Oone__class_Oone(tc_Int_Oint)), _664705))], (3552 ^ _319074) ^ [_435484, _435486] : [class_Groups_Oordered__ab__group__add__abs(_435484), c_Orderings_Oord__class_Oless(_435484, c_Groups_Ozero__class_Ozero(_435484), _435486), -(c_Groups_Oabs__class_Oabs(_435484, _435486) = _435486)], (7721 ^ _319074) ^ [_583770] : [class_Rings_Ocomm__semiring__1(_583770), -(c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_583770)) = c_Polynomial_OpCons(_583770, c_Groups_Oone__class_Oone(_583770), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_583770))))], (8582 ^ _319074) ^ [_613759, _613761, _613763] : [class_RealVector_Oreal__normed__div__algebra(_613759), -(c_Groups_Osgn__class_Osgn(_613759, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_613759), _613761), _613763)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_613759), c_Groups_Osgn__class_Osgn(_613759, _613761)), c_Groups_Osgn__class_Osgn(_613759, _613763)))], (10599 ^ _319074) ^ [_682890] : [_682890 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _682890, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (9682 ^ _319074) ^ [_651089, _651091, _651093, _651095] : [class_Rings_Olinordered__semidom(_651089), c_Orderings_Oord__class_Oless(_651089, c_Groups_Oone__class_Oone(_651089), _651091), c_Orderings_Oord__class_Oless(_651089, hAPP(hAPP(c_Power_Opower__class_Opower(_651089), _651091), _651093), hAPP(hAPP(c_Power_Opower__class_Opower(_651089), _651091), _651095)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _651093, _651095))], (12404 ^ _319074) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (7419 ^ _319074) ^ [_571012, _571014, _571016] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _571012), _571014)), _571016) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _571012), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _571014), _571016)))], (11930 ^ _319074) ^ [_732886, _732888, _732890, _732892, _732894] : [class_RealVector_Oreal__normed__vector(_732886), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_732886, c_Groups_Ominus__class_Ominus(_732886, c_Groups_Oplus__class_Oplus(_732886, _732888, _732890), c_Groups_Oplus__class_Oplus(_732886, _732892, _732894))), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_732886, c_Groups_Ominus__class_Ominus(_732886, _732888, _732892)), c_RealVector_Onorm__class_Onorm(_732886, c_Groups_Ominus__class_Ominus(_732886, _732890, _732894)))))], (8710 ^ _319074) ^ [_618590, _618592, _618594] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _618590), 8713 ^ _319074 : [(8720 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _618592, _618594), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _618590), _618592), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _618590), _618594)))], (8714 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _618590), _618592), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _618590), _618594)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _618592, _618594))]]], (4381 ^ _319074) ^ [_464120, _464122, _464124, _464126, _464128] : [class_RealVector_Oreal__normed__algebra(_464120), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_464120, _464122), _464124), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_464120, _464126), _464128), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_464120, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_464120), _464122), _464126)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _464124), _464128)))], (7276 ^ _319074) ^ [_565869, _565871, _565873] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _565869), 7279 ^ _319074 : [(7286 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _565871, _565873), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _565871), _565869), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _565873), _565869)))], (7280 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _565871), _565869), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _565873), _565869)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _565871, _565873))]]], (4217 ^ _319074) ^ [_458507, _458509] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _458507, _458509) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _458507 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _458509 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (11700 ^ _319074) ^ [_723419, _723421, _723423, _723425, _723427, _723429] : [class_Rings_Oordered__ring(_723419), 11703 ^ _319074 : [(11710 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_723419, c_Groups_Oplus__class_Oplus(_723419, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_723419), c_Groups_Ominus__class_Ominus(_723419, _723421, _723427)), _723423), _723425), _723429), -(c_Orderings_Oord__class_Oless__eq(_723419, c_Groups_Oplus__class_Oplus(_723419, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_723419), _723421), _723423), _723425), c_Groups_Oplus__class_Oplus(_723419, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_723419), _723427), _723423), _723429)))], (11704 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_723419, c_Groups_Oplus__class_Oplus(_723419, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_723419), _723421), _723423), _723425), c_Groups_Oplus__class_Oplus(_723419, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_723419), _723427), _723423), _723429)), -(c_Orderings_Oord__class_Oless__eq(_723419, c_Groups_Oplus__class_Oplus(_723419, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_723419), c_Groups_Ominus__class_Ominus(_723419, _723421, _723427)), _723423), _723425), _723429))]]], (12274 ^ _319074) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (120 ^ _319074) ^ [_322959, _322961] : [-(class_Rings_Odivision__ring__inverse__zero(_322959)), _322961 = _322959, class_Rings_Odivision__ring__inverse__zero(_322961)], (6527 ^ _319074) ^ [_539993, _539995, _539997] : [class_Fields_Olinordered__field__inverse__zero(_539993), 6530 ^ _319074 : [(6545 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_539993, c_Groups_Ozero__class_Ozero(_539993), c_Rings_Oinverse__class_Odivide(_539993, _539995, _539997))), 6546 ^ _319074 : [(6553 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_539993, _539995, c_Groups_Ozero__class_Ozero(_539993)), c_Orderings_Oord__class_Oless(_539993, _539997, c_Groups_Ozero__class_Ozero(_539993))], (6547 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_539993, c_Groups_Ozero__class_Ozero(_539993), _539995), c_Orderings_Oord__class_Oless(_539993, c_Groups_Ozero__class_Ozero(_539993), _539997)]]], (6531 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_539993, c_Groups_Ozero__class_Ozero(_539993), c_Rings_Oinverse__class_Odivide(_539993, _539995, _539997)), 6536 ^ _319074 : [(6539 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_539993, c_Groups_Ozero__class_Ozero(_539993), _539997))], (6537 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_539993, c_Groups_Ozero__class_Ozero(_539993), _539995))]], 6540 ^ _319074 : [(6543 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_539993, _539997, c_Groups_Ozero__class_Ozero(_539993)))], (6541 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_539993, _539995, c_Groups_Ozero__class_Ozero(_539993)))]]]]], (9955 ^ _319074) ^ [_660248, _660250, _660252] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _660248, _660250), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _660248, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _660250, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _660248), _660252))))], (490 ^ _319074) ^ [_333874, _333876] : [-(class_Rings_Olinordered__ring(_333874)), _333876 = _333874, class_Rings_Olinordered__ring(_333876)], (9863 ^ _319074) ^ [_657217, _657219] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _657217, _657219), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_657217), c_Nat_OSuc(_657219)))], (4419 ^ _319074) ^ [_465678, _465680, _465682] : [class_RealVector_Oreal__normed__div__algebra(_465678), -(c_RealVector_Onorm__class_Onorm(_465678, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_465678), _465680), _465682)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_465678, _465680)), c_RealVector_Onorm__class_Onorm(_465678, _465682)))], (9022 ^ _319074) ^ [_628394, _628396, _628398] : [_628394 = _628396, c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _628396, _628398), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _628394, _628398))], (9436 ^ _319074) ^ [_642280, _642282, _642284, _642286] : [class_Rings_Olinordered__semidom(_642280), c_Orderings_Oord__class_Oless__eq(_642280, _642282, _642284), c_Orderings_Oord__class_Oless__eq(_642280, c_Groups_Ozero__class_Ozero(_642280), _642282), -(c_Orderings_Oord__class_Oless__eq(_642280, hAPP(hAPP(c_Power_Opower__class_Opower(_642280), _642282), _642286), hAPP(hAPP(c_Power_Opower__class_Opower(_642280), _642284), _642286)))], (7058 ^ _319074) ^ [_557760, _557762, _557764] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _557760, _557762), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _557760), _557764), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _557762), _557764)))], (12422 ^ _319074) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (6911 ^ _319074) ^ [] : [-(v_cs____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), 6915 ^ _319074 : [(6916 ^ _319074) ^ [_552573] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, 6914 ^ [], c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _552573)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_da____, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_aa____, c_Polynomial_OpCons(tc_Complex_Ocomplex, v_c____, v_cs____))), _552573))))]]], (2122 ^ _319074) ^ [_389059, _389061, _389063] : [class_Orderings_Opreorder(_389059), c_Orderings_Oord__class_Oless(_389059, _389061, _389063), c_Orderings_Oord__class_Oless(_389059, _389063, _389061)], (6327 ^ _319074) ^ [_533024, _533026, _533028, _533030] : [class_Rings_Olinordered__semiring__strict(_533024), c_Orderings_Oord__class_Oless__eq(_533024, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_533024), _533026), _533028), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_533024), _533030), _533028)), c_Orderings_Oord__class_Oless(_533024, c_Groups_Ozero__class_Ozero(_533024), _533028), -(c_Orderings_Oord__class_Oless__eq(_533024, _533026, _533030))], (8332 ^ _319074) ^ [_604948, _604950, _604952, _604954] : [class_Rings_Ocomm__semiring__1(_604948), c_Rings_Odvd__class_Odvd(_604948, _604950, _604952), c_Rings_Odvd__class_Odvd(_604948, _604950, _604954), -(c_Rings_Odvd__class_Odvd(_604948, _604950, c_Groups_Oplus__class_Oplus(_604948, _604952, _604954)))], (1026 ^ _319074) ^ [_351601, _351603, _351605, _351607] : [-(c_RealVector_Onorm__class_Onorm(_351607, _351603) = c_RealVector_Onorm__class_Onorm(_351605, _351601)), _351607 = _351605, _351603 = _351601], (10155 ^ _319074) ^ [_666913] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _666913), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _666913)], (3900 ^ _319074) ^ [_447223] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _447223, _447223)], (4547 ^ _319074) ^ [_471608, _471610, _471612, _471614, _471616] : [class_Rings_Ocomm__semiring__1(_471608), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_471608), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_471608), _471610), _471612)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_471608), _471614), _471616)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_471608), _471610), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_471608), _471612), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_471608), _471614), _471616))))], (2188 ^ _319074) ^ [_391187, _391189, _391191, _391193] : [class_Orderings_Oorder(_391187), _391189 = _391191, c_Orderings_Oord__class_Oless(_391187, _391193, _391191), -(c_Orderings_Oord__class_Oless(_391187, _391193, _391189))], (6976 ^ _319074) ^ [_554707, _554709, _554711] : [6977 ^ _319074 : [(6980 ^ _319074) ^ [] : [_554707 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (6978 ^ _319074) ^ [] : [_554709 = _554711]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _554707), _554709) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _554707), _554711))], (952 ^ _319074) ^ [_348927, _348929, _348931, _348933, _348935, _348937] : [-(c_Polynomial_Oorder(_348937, _348933, _348929) = c_Polynomial_Oorder(_348935, _348931, _348927)), _348937 = _348935, _348933 = _348931, _348929 = _348927], (6373 ^ _319074) ^ [_534618, _534620, _534622] : [class_Rings_Olinordered__idom(_534618), c_Orderings_Oord__class_Oless__eq(_534618, c_Groups_Ozero__class_Ozero(_534618), _534620), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_534618), c_Groups_Oabs__class_Oabs(_534618, _534622)), _534620) = c_Groups_Oabs__class_Oabs(_534618, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_534618), _534622), _534620)))], (7022 ^ _319074) ^ [_556324, _556326, _556328] : [-(_556324 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 7025 ^ _319074 : [(7032 ^ _319074) ^ [] : [_556326 = _556328, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _556324), _556326) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _556324), _556328))], (7026 ^ _319074) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _556324), _556326) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _556324), _556328), -(_556326 = _556328)]]], (4761 ^ _319074) ^ [_480656, _480658, _480660] : [class_Rings_Oidom(_480656), 4764 ^ _319074 : [(4765 ^ _319074) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_480656), _480658), _480658) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_480656), _480660), _480660), -(_480658 = _480660), -(_480658 = c_Groups_Ouminus__class_Ouminus(_480656, _480660))], (4775 ^ _319074) ^ [] : [4776 ^ _319074 : [(4779 ^ _319074) ^ [] : [_480658 = c_Groups_Ouminus__class_Ouminus(_480656, _480660)], (4777 ^ _319074) ^ [] : [_480658 = _480660]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_480656), _480658), _480658) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_480656), _480660), _480660))]]], (8536 ^ _319074) ^ [_612112] : [class_Groups_Osgn__if(_612112), -(c_Groups_Osgn__class_Osgn(_612112, c_Groups_Ozero__class_Ozero(_612112)) = c_Groups_Ozero__class_Ozero(_612112))], (12632 ^ _319074) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex))], (11484 ^ _319074) ^ [_713846, _713848, _713850, _713852] : [class_RealVector_Oreal__normed__algebra(_713846), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_713846), _713848), c_Groups_Ominus__class_Ominus(_713846, _713850, _713852)) = c_Groups_Ominus__class_Ominus(_713846, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_713846), _713848), _713850), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_713846), _713848), _713852)))], (7514 ^ _319074) ^ [_574642, _574644, _574646] : [7515 ^ _319074 : [(7518 ^ _319074) ^ [] : [_574644 = _574646], (7516 ^ _319074) ^ [] : [_574642 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _574642), _574644) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _574642), _574646))], (7082 ^ _319074) ^ [_558832, _558834, _558836, _558838] : [class_Rings_Ocomm__semiring__0(_558832), -(hAPP(c_Polynomial_Opoly(_558832, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_558832)), _558834), _558836)), _558838) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_558832), hAPP(c_Polynomial_Opoly(_558832, _558834), _558838)), hAPP(c_Polynomial_Opoly(_558832, _558836), _558838)))], (6924 ^ _319074) ^ [_552891, _552893, _552895] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _552891), _552893)), _552895) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _552891), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _552893), _552895)))], (12642 ^ _319074) ^ [] : [-(class_Rings_Ocomm__ring(tc_Complex_Ocomplex))], (12584 ^ _319074) ^ [] : [-(class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex))], (11258 ^ _319074) ^ [_705609, _705611] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _705609), -(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), _705609), _705611)))], (2946 ^ _319074) ^ [_415524, _415526, _415528] : [class_Orderings_Oorder(_415524), 2949 ^ _319074 : [(2950 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_415524, _415526, _415528), -(c_Orderings_Oord__class_Oless(_415524, _415526, _415528)), -(_415526 = _415528)], (2960 ^ _319074) ^ [] : [2961 ^ _319074 : [(2964 ^ _319074) ^ [] : [_415526 = _415528], (2962 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_415524, _415526, _415528)]], -(c_Orderings_Oord__class_Oless__eq(_415524, _415526, _415528))]]], (4 ^ _319074) ^ [_319305, _319307] : [_319307 = _319305, -(_319305 = _319307)], (12436 ^ _319074) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (7648 ^ _319074) ^ [_580562, _580564] : [class_RealVector_Oreal__normed__algebra(_580562), 7652 ^ _319074 : [(7655 ^ _319074) ^ [_580861] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_580562, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_580562), _580861), _580564)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_580562, _580861)), 7651 ^ [_580562, _580564])))], (7653 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 7651 ^ [_580562, _580564]))]]], (12420 ^ _319074) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (7588 ^ _319074) ^ [_577869, _577871, _577873] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _577869, _577871), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _577869, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _577873, _577871)))], (8928 ^ _319074) ^ [_625418, _625420] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _625418, _625420)), 8929 ^ _319074 : [(8930 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _625418, _625420), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _625420, _625418))], (8936 ^ _319074) ^ [] : [_625418 = _625420]]], (12172 ^ _319074) ^ [_742753, _742755] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Nat_OSuc(_742753), c_Nat_OSuc(_742755)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _742753, _742755))], (320 ^ _319074) ^ [_328859, _328861] : [-(class_Rings_Oring__1__no__zero__divisors(_328859)), _328861 = _328859, class_Rings_Oring__1__no__zero__divisors(_328861)], (4026 ^ _319074) ^ [_451917, _451919] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _451917, _451919), -(_451919 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _451917, 4029 ^ [_451917, _451919]))], (1906 ^ _319074) ^ [_381718, _381720, _381722, _381724] : [class_Rings_Ocomm__semiring__1(_381718), -(c_Groups_Oplus__class_Oplus(_381718, _381720, c_Groups_Oplus__class_Oplus(_381718, _381722, _381724)) = c_Groups_Oplus__class_Oplus(_381718, c_Groups_Oplus__class_Oplus(_381718, _381720, _381722), _381724))], (912 ^ _319074) ^ [_347419, _347421] : [_347421 = _347419, -(c_Complex_Oexpi(_347421) = c_Complex_Oexpi(_347419))], (12524 ^ _319074) ^ [] : [-(class_Rings_Ocomm__semiring(tc_RealDef_Oreal))], (12294 ^ _319074) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Int_Oint))], (1257 ^ _319074) ^ [] : [-(v_cs____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))], (2936 ^ _319074) ^ [_415196, _415198, _415200] : [class_Orderings_Olinorder(_415196), -(c_Orderings_Oord__class_Oless(_415196, _415198, _415200)), -(c_Orderings_Oord__class_Oless__eq(_415196, _415200, _415198))], (1118 ^ _319074) ^ [_354969, _354971, _354973, _354975, _354977, _354979] : [-(c_Groups_Oplus__class_Oplus(_354979, _354975, _354971) = c_Groups_Oplus__class_Oplus(_354977, _354973, _354969)), _354979 = _354977, _354975 = _354973, _354971 = _354969], (3164 ^ _319074) ^ [_422719, _422721] : [_422719 = _422721, -(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _422719, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _422721)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (7336 ^ _319074) ^ [_567916, _567918, _567920] : [7337 ^ _319074 : [(7340 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _567918, _567920)], (7338 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _567916))]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _567916), _567918), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _567916), _567920)))], (7492 ^ _319074) ^ [_573789, _573791] : [class_Rings_Ocomm__semiring__0(_573789), -(c_Polynomial_Opcompose(_573789, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_573789)), _573791) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_573789)))], (6717 ^ _319074) ^ [_545998, _546000] : [class_RealVector_Oreal__normed__vector(_545998), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_545998, _546000), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (300 ^ _319074) ^ [_328269, _328271] : [-(class_Groups_Olinordered__ab__group__add(_328269)), _328271 = _328269, class_Groups_Olinordered__ab__group__add(_328271)], (11440 ^ _319074) ^ [_712244, _712246] : [class_Groups_Ogroup__add(_712244), -(c_Groups_Ominus__class_Ominus(_712244, _712246, c_Groups_Ozero__class_Ozero(_712244)) = _712246)], (12412 ^ _319074) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (4607 ^ _319074) ^ [_474446, _474448] : [class_Rings_Omult__zero(_474446), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_474446), _474448), c_Groups_Ozero__class_Ozero(_474446)) = c_Groups_Ozero__class_Ozero(_474446))], (11852 ^ _319074) ^ [_729515, _729517] : [class_Groups_Ogroup__add(_729515), -(c_Groups_Ominus__class_Ominus(_729515, c_Groups_Ozero__class_Ozero(_729515), _729517) = c_Groups_Ouminus__class_Ouminus(_729515, _729517))], (12472 ^ _319074) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal))], (8069 ^ _319074) ^ [_595663, _595665, _595667, _595669, _595671, _595673] : [class_Rings_Olinordered__semiring__1(_595663), c_Orderings_Oord__class_Oless__eq(_595663, _595665, _595667), c_Orderings_Oord__class_Oless__eq(_595663, _595669, _595667), c_Orderings_Oord__class_Oless__eq(_595663, c_Groups_Ozero__class_Ozero(_595663), _595671), c_Orderings_Oord__class_Oless__eq(_595663, c_Groups_Ozero__class_Ozero(_595663), _595673), c_Groups_Oplus__class_Oplus(_595663, _595671, _595673) = c_Groups_Oone__class_Oone(_595663), -(c_Orderings_Oord__class_Oless__eq(_595663, c_Groups_Oplus__class_Oplus(_595663, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_595663), _595671), _595665), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_595663), _595673), _595669)), _595667))], (1108 ^ _319074) ^ [_354582, _354584, _354586, _354588] : [-(c_fequal(_354588, _354584) = c_fequal(_354586, _354582)), _354588 = _354586, _354584 = _354582], (6019 ^ _319074) ^ [_522735, _522737, _522739, _522741] : [class_Fields_Olinordered__field(_522735), c_Orderings_Oord__class_Oless(_522735, c_Groups_Ozero__class_Ozero(_522735), _522737), 6026 ^ _319074 : [(6033 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_522735, _522739, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_522735), _522741), _522737)), -(c_Orderings_Oord__class_Oless__eq(_522735, c_Rings_Oinverse__class_Odivide(_522735, _522739, _522737), _522741))], (6027 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_522735, c_Rings_Oinverse__class_Odivide(_522735, _522739, _522737), _522741), -(c_Orderings_Oord__class_Oless__eq(_522735, _522739, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_522735), _522741), _522737)))]]], (10315 ^ _319074) ^ [_672295, _672297] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Nat_OSuc(_672295), _672297) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _672295, _672297)))], (11780 ^ _319074) ^ [_726578, _726580, _726582] : [class_RealVector_Oreal__normed__vector(_726578), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_726578, _726580), c_RealVector_Onorm__class_Onorm(_726578, _726582)), c_RealVector_Onorm__class_Onorm(_726578, c_Groups_Ominus__class_Ominus(_726578, _726580, _726582))))], (12432 ^ _319074) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (7326 ^ _319074) ^ [_567625, _567627, _567629] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _567625), _567627), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _567625), _567629)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _567625), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _567627, _567629))], (12872 ^ _319074) ^ [_763093] : [class_Rings_Ocomm__semiring__1(_763093), -(class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(_763093)))], (2486 ^ _319074) ^ [_400596, _400598] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _400596, _400598), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _400598, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _400596)))], (6039 ^ _319074) ^ [_523398, _523400, _523402, _523404] : [class_Fields_Olinordered__field(_523398), c_Orderings_Oord__class_Oless(_523398, c_Groups_Ozero__class_Ozero(_523398), _523400), c_Orderings_Oord__class_Oless__eq(_523398, _523402, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_523398), _523404), _523400)), -(c_Orderings_Oord__class_Oless__eq(_523398, c_Rings_Oinverse__class_Odivide(_523398, _523402, _523400), _523404))], (11824 ^ _319074) ^ [_728222, _728224] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _728222, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _728224)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, _728222, _728224))], (7256 ^ _319074) ^ [_564926, _564928] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _564926), _564926)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _564928), _564928)))], (10477 ^ _319074) ^ [_678161, _678163, _678165] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _678161), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _678163, _678165)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _678161), _678163), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _678161), _678165)))], (7751 ^ _319074) ^ [] : [c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)], (7745 ^ _319074) ^ [_584600] : [class_Rings_Olinordered__idom(_584600), -(c_Groups_Oabs__class_Oabs(_584600, c_Groups_Oone__class_Oone(_584600)) = c_Groups_Oone__class_Oone(_584600))], (5771 ^ _319074) ^ [_514332, _514334, _514336, _514338] : [class_Fields_Ofield(_514332), -(_514334 = c_Groups_Ozero__class_Ozero(_514332)), -(c_Groups_Oplus__class_Oplus(_514332, c_Rings_Oinverse__class_Odivide(_514332, _514336, _514334), _514338) = c_Rings_Oinverse__class_Odivide(_514332, c_Groups_Oplus__class_Oplus(_514332, _514336, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_514332), _514334), _514338)), _514334))], (7687 ^ _319074) ^ [_582608, _582610, _582612, _582614, _582616, _582618] : [class_Rings_Olinordered__semiring__1__strict(_582608), c_Orderings_Oord__class_Oless(_582608, _582610, _582612), c_Orderings_Oord__class_Oless(_582608, _582614, _582612), c_Orderings_Oord__class_Oless__eq(_582608, c_Groups_Ozero__class_Ozero(_582608), _582616), c_Orderings_Oord__class_Oless__eq(_582608, c_Groups_Ozero__class_Ozero(_582608), _582618), c_Groups_Oplus__class_Oplus(_582608, _582616, _582618) = c_Groups_Oone__class_Oone(_582608), -(c_Orderings_Oord__class_Oless(_582608, c_Groups_Oplus__class_Oplus(_582608, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_582608), _582616), _582610), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_582608), _582618), _582614)), _582612))], (6805 ^ _319074) ^ [_548902, _548904, _548906, _548908, _548910] : [class_Fields_Olinordered__field(_548902), c_Orderings_Oord__class_Oless__eq(_548902, c_Groups_Ozero__class_Ozero(_548902), _548904), c_Orderings_Oord__class_Oless__eq(_548902, _548904, _548906), c_Orderings_Oord__class_Oless(_548902, c_Groups_Ozero__class_Ozero(_548902), _548908), c_Orderings_Oord__class_Oless__eq(_548902, _548908, _548910), -(c_Orderings_Oord__class_Oless__eq(_548902, c_Rings_Oinverse__class_Odivide(_548902, _548904, _548910), c_Rings_Oinverse__class_Odivide(_548902, _548906, _548908)))], (1830 ^ _319074) ^ [] : [-(v_cs____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)))], (62 ^ _319074) ^ [_321226, _321228, _321230, _321232, _321234, _321236] : [-(c_Orderings_Oord__class_Oless(_321234, _321230, _321226)), c_Orderings_Oord__class_Oless(_321236, _321232, _321228), _321236 = _321234, _321232 = _321230, _321228 = _321226], (10794 ^ _319074) ^ [_689658, _689660, _689662] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_689658)), _689660), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_689658)), _689662)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _689660, _689662))], (12392 ^ _319074) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Nat_Onat))], (3636 ^ _319074) ^ [_438383, _438385, _438387] : [class_Rings_Olinordered__idom(_438383), 3639 ^ _319074 : [(3648 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_438383, c_Groups_Oabs__class_Oabs(_438383, _438385), _438387)), c_Orderings_Oord__class_Oless(_438383, _438385, _438387), c_Orderings_Oord__class_Oless(_438383, c_Groups_Ouminus__class_Ouminus(_438383, _438385), _438387)], (3640 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_438383, c_Groups_Oabs__class_Oabs(_438383, _438385), _438387), 3643 ^ _319074 : [(3646 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_438383, c_Groups_Ouminus__class_Ouminus(_438383, _438385), _438387))], (3644 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_438383, _438385, _438387))]]]]], (12500 ^ _319074) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_RealDef_Oreal))], (3814 ^ _319074) ^ [_444237, _444239, _444241] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _444237, _444239), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _444237, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _444241, _444239)))], (4835 ^ _319074) ^ [_483441, _483443, _483445, _483447] : [class_Fields_Ofield__inverse__zero(_483441), -(_483443 = c_Groups_Ozero__class_Ozero(_483441)), -(c_Rings_Oinverse__class_Odivide(_483441, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_483441), _483445), _483443), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_483441), _483447), _483443)) = c_Rings_Oinverse__class_Odivide(_483441, _483445, _483447))], (760 ^ _319074) ^ [_341839, _341841] : [-(class_Rings_Ocomm__ring(_341839)), _341841 = _341839, class_Rings_Ocomm__ring(_341841)], (7258 ^ _319074) ^ [_565051, _565053] : [class_Rings_Ocomm__semiring__0(_565051), -(hAPP(c_Polynomial_Opoly(_565051, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_565051))), _565053) = c_Groups_Ozero__class_Ozero(_565051))], (12548 ^ _319074) ^ [] : [-(class_Rings_Ocomm__ring(tc_RealDef_Oreal))], (3180 ^ _319074) ^ [_423230, _423232] : [3181 ^ _319074 : [(3184 ^ _319074) ^ [] : [_423230 = _423232], (3182 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _423230, _423232)]], -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _423230, _423232))], (5071 ^ _319074) ^ [_491061, _491063, _491065, _491067] : [class_Rings_Oordered__semiring(_491061), c_Orderings_Oord__class_Oless__eq(_491061, _491063, _491065), c_Orderings_Oord__class_Oless__eq(_491061, c_Groups_Ozero__class_Ozero(_491061), _491067), -(c_Orderings_Oord__class_Oless__eq(_491061, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_491061), _491067), _491063), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_491061), _491067), _491065)))], (5533 ^ _319074) ^ [_506226, _506228, _506230, _506232] : [class_Rings_Olinordered__ring__strict(_506226), c_Orderings_Oord__class_Oless(_506226, c_Groups_Ozero__class_Ozero(_506226), _506228), 5540 ^ _319074 : [(5547 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_506226, _506230, _506232), -(c_Orderings_Oord__class_Oless(_506226, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_506226), _506228), _506230), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_506226), _506228), _506232)))], (5541 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_506226, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_506226), _506228), _506230), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_506226), _506228), _506232)), -(c_Orderings_Oord__class_Oless(_506226, _506230, _506232))]]], (3870 ^ _319074) ^ [_446257] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _446257, _446257)], (4801 ^ _319074) ^ [_482219, _482221, _482223, _482225, _482227] : [class_Fields_Ofield(_482219), -(_482221 = c_Groups_Ozero__class_Ozero(_482219)), -(_482223 = c_Groups_Ozero__class_Ozero(_482219)), 4812 ^ _319074 : [(4819 ^ _319074) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_482219), _482225), _482223) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_482219), _482227), _482221), -(c_Rings_Oinverse__class_Odivide(_482219, _482225, _482221) = c_Rings_Oinverse__class_Odivide(_482219, _482227, _482223))], (4813 ^ _319074) ^ [] : [c_Rings_Oinverse__class_Odivide(_482219, _482225, _482221) = c_Rings_Oinverse__class_Odivide(_482219, _482227, _482223), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_482219), _482225), _482223) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_482219), _482227), _482221))]]], (13022 ^ _319074) ^ [_767843] : [class_Rings_Ocomm__semiring__1(_767843), -(class_Rings_Odvd(tc_Polynomial_Opoly(_767843)))], (966 ^ _319074) ^ [_349443, _349445, _349447, _349449, _349451, _349453] : [-(c_Power_Opower_Opower(_349453, _349449, _349445) = c_Power_Opower_Opower(_349451, _349447, _349443)), _349453 = _349451, _349449 = _349447, _349445 = _349443], (5881 ^ _319074) ^ [_518242, _518244, _518246, _518248, _518250] : [class_Rings_Olinordered__idom(_518242), c_Orderings_Oord__class_Oless(_518242, c_Groups_Oabs__class_Oabs(_518242, _518244), _518246), c_Orderings_Oord__class_Oless(_518242, c_Groups_Oabs__class_Oabs(_518242, _518248), _518250), -(c_Orderings_Oord__class_Oless(_518242, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_518242), c_Groups_Oabs__class_Oabs(_518242, _518244)), c_Groups_Oabs__class_Oabs(_518242, _518248)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_518242), _518246), _518250)))], (810 ^ _319074) ^ [_343314, _343316] : [-(class_Rings_Odvd(_343314)), _343316 = _343314, class_Rings_Odvd(_343316)], (7430 ^ _319074) ^ [_571515, _571517] : [7431 ^ _319074 : [(7432 ^ _319074) ^ [_571590] : [_571517 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _571515, _571590)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _571515, _571517))], (10884 ^ _319074) ^ [_692746, _692748] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _692746), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _692748), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _692746, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _692746), _692748)))], (410 ^ _319074) ^ [_331514, _331516] : [-(class_Rings_Olinordered__semiring(_331514)), _331516 = _331514, class_Rings_Olinordered__semiring(_331516)], (3990 ^ _319074) ^ [_450522, _450524, _450526] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _450522, _450524), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _450522, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _450526, _450524)))], (7659 ^ _319074) ^ [_581117, _581119] : [class_RealVector_Oreal__normed__field(_581117), 7663 ^ _319074 : [(7664 ^ _319074) ^ [_581320] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_581117, c_Rings_Oinverse__class_Odivide(_581117, _581320, _581119)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_581117, _581320)), 7662 ^ [_581117, _581119])))]]], (9392 ^ _319074) ^ [_640434, _640436, _640438, _640440] : [class_Rings_Ocomm__semiring__1(_640434), c_Rings_Odvd__class_Odvd(_640434, _640436, _640438), -(c_Rings_Odvd__class_Odvd(_640434, hAPP(hAPP(c_Power_Opower__class_Opower(_640434), _640436), _640440), hAPP(hAPP(c_Power_Opower__class_Opower(_640434), _640438), _640440)))], (12656 ^ _319074) ^ [] : [-(class_Power_Opower(tc_Complex_Ocomplex))], (12800 ^ _319074) ^ [_760813] : [class_Rings_Ocomm__semiring__1(_760813), -(class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(_760813)))], (12324 ^ _319074) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (10065 ^ _319074) ^ [_663867] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _663867), -(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), _663867)))], (5355 ^ _319074) ^ [_500337, _500339, _500341, _500343] : [class_Fields_Olinordered__field(_500337), c_Orderings_Oord__class_Oless(_500337, c_Groups_Ozero__class_Ozero(_500337), _500339), c_Orderings_Oord__class_Oless(_500337, _500341, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_500337), _500343), _500339)), -(c_Orderings_Oord__class_Oless(_500337, c_Rings_Oinverse__class_Odivide(_500337, _500341, _500339), _500343))], (7397 ^ _319074) ^ [_570267, _570269, _570271] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _570267, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _570269), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _570267), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _570271))), -(_570269 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (3170 ^ _319074) ^ [_422974, _422976] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _422974, _422976), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _422974, _422976)), -(_422974 = _422976)], (8700 ^ _319074) ^ [_618237, _618239, _618241] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _618237), _618239), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _618237), _618241)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _618237), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _618239, _618241))], (7805 ^ _319074) ^ [_586706, _586708] : [class_Rings_Ocomm__semiring__1(_586706), -(hAPP(c_Polynomial_Opoly(_586706, c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_586706))), _586708) = c_Groups_Oone__class_Oone(_586706))], (9238 ^ _319074) ^ [_635048, _635050] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _635048, _635050), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _635050, _635048)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _635050, _635048), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _635048, _635050))], (11874 ^ _319074) ^ [_730495, _730497, _730499, _730501, _730503, _730505] : [class_Rings_Oring(_730495), 11877 ^ _319074 : [(11884 ^ _319074) ^ [] : [_730501 = c_Groups_Oplus__class_Oplus(_730495, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_730495), c_Groups_Ominus__class_Ominus(_730495, _730503, _730497)), _730499), _730505), -(c_Groups_Oplus__class_Oplus(_730495, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_730495), _730497), _730499), _730501) = c_Groups_Oplus__class_Oplus(_730495, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_730495), _730503), _730499), _730505))], (11878 ^ _319074) ^ [] : [c_Groups_Oplus__class_Oplus(_730495, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_730495), _730497), _730499), _730501) = c_Groups_Oplus__class_Oplus(_730495, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_730495), _730503), _730499), _730505), -(_730501 = c_Groups_Oplus__class_Oplus(_730495, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_730495), c_Groups_Ominus__class_Ominus(_730495, _730503, _730497)), _730499), _730505))]]], (7350 ^ _319074) ^ [_568559, _568561, _568563] : [class_Rings_Olinordered__ring__strict(_568559), 7353 ^ _319074 : [(7362 ^ _319074) ^ [] : [-(c_Groups_Oplus__class_Oplus(_568559, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_568559), _568561), _568561), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_568559), _568563), _568563)) = c_Groups_Ozero__class_Ozero(_568559)), _568561 = c_Groups_Ozero__class_Ozero(_568559), _568563 = c_Groups_Ozero__class_Ozero(_568559)], (7354 ^ _319074) ^ [] : [c_Groups_Oplus__class_Oplus(_568559, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_568559), _568561), _568561), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_568559), _568563), _568563)) = c_Groups_Ozero__class_Ozero(_568559), 7357 ^ _319074 : [(7360 ^ _319074) ^ [] : [-(_568563 = c_Groups_Ozero__class_Ozero(_568559))], (7358 ^ _319074) ^ [] : [-(_568561 = c_Groups_Ozero__class_Ozero(_568559))]]]]], (12576 ^ _319074) ^ [] : [-(class_Rings_Oidom(tc_RealDef_Oreal))], (11992 ^ _319074) ^ [_735608, _735610, _735612, _735614, _735616] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _735608, _735610), -(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), _735610), _735612), _735614), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _735608), _735612), _735616)) = 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, _735610, _735608)), _735612), _735614), _735616))], (1754 ^ _319074) ^ [_376201, _376203, _376205, _376207] : [class_Groups_Ocancel__semigroup__add(_376201), 1757 ^ _319074 : [(1764 ^ _319074) ^ [] : [_376205 = _376207, -(c_Groups_Oplus__class_Oplus(_376201, _376203, _376205) = c_Groups_Oplus__class_Oplus(_376201, _376203, _376207))], (1758 ^ _319074) ^ [] : [c_Groups_Oplus__class_Oplus(_376201, _376203, _376205) = c_Groups_Oplus__class_Oplus(_376201, _376203, _376207), -(_376205 = _376207)]]], (9052 ^ _319074) ^ [_629337, _629339] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _629337, _629339), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _629339, _629337), -(_629337 = _629339)], (4795 ^ _319074) ^ [_481913, _481915, _481917] : [class_Rings_Olinordered__idom(_481913), -(c_Groups_Oabs__class_Oabs(_481913, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_481913), _481915), _481917)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_481913), c_Groups_Oabs__class_Oabs(_481913, _481915)), c_Groups_Oabs__class_Oabs(_481913, _481917)))], (12586 ^ _319074) ^ [] : [-(class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex))], (8300 ^ _319074) ^ [_603928, _603930, _603932] : [class_Rings_Ocomm__ring__1(_603928), 8303 ^ _319074 : [(8310 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(_603928, _603930, _603932), -(c_Rings_Odvd__class_Odvd(_603928, _603930, c_Groups_Ouminus__class_Ouminus(_603928, _603932)))], (8304 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(_603928, _603930, c_Groups_Ouminus__class_Ouminus(_603928, _603932)), -(c_Rings_Odvd__class_Odvd(_603928, _603930, _603932))]]], (10568 ^ _319074) ^ [_681853, _681855] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _681853, c_Nat_OSuc(_681855)), -(_681853 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 10576 ^ _319074 : [(10579 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 10575 ^ [_681853, _681855], _681855))], (10577 ^ _319074) ^ [] : [-(_681853 = c_Nat_OSuc(10575 ^ [_681853, _681855]))]]], (5403 ^ _319074) ^ [_501952, _501954, _501956, _501958] : [class_Fields_Olinordered__field(_501952), c_Orderings_Oord__class_Oless(_501952, _501954, c_Groups_Ozero__class_Ozero(_501952)), 5410 ^ _319074 : [(5417 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_501952, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_501952), _501958), _501954), _501956), -(c_Orderings_Oord__class_Oless(_501952, c_Rings_Oinverse__class_Odivide(_501952, _501956, _501954), _501958))], (5411 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_501952, c_Rings_Oinverse__class_Odivide(_501952, _501956, _501954), _501958), -(c_Orderings_Oord__class_Oless(_501952, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_501952), _501958), _501954), _501956))]]], (12522 ^ _319074) ^ [] : [-(class_Rings_Odivision__ring(tc_RealDef_Oreal))], (13004 ^ _319074) ^ [_767273] : [class_Rings_Ocomm__ring(_767273), -(class_Rings_Oring(tc_Polynomial_Opoly(_767273)))], (4533 ^ _319074) ^ [_470725] : [-(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal, _470725) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _470725))], (9374 ^ _319074) ^ [_639568, _639570, _639572] : [class_Groups_Omonoid__mult(_639568), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_639568), hAPP(hAPP(c_Power_Opower__class_Opower(_639568), _639570), _639572)), _639570) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_639568), _639570), hAPP(hAPP(c_Power_Opower__class_Opower(_639568), _639570), _639572)))], (7436 ^ _319074) ^ [_571744, _571746] : [-(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _571744), _571746), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _571744), _571744)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, _571746, _571744))], (9460 ^ _319074) ^ [_643099, _643101, _643103] : [class_Rings_Olinordered__semidom(_643099), c_Orderings_Oord__class_Oless__eq(_643099, c_Groups_Oone__class_Oone(_643099), _643101), -(c_Orderings_Oord__class_Oless__eq(_643099, c_Groups_Oone__class_Oone(_643099), hAPP(hAPP(c_Power_Opower__class_Opower(_643099), _643101), _643103)))], (7943 ^ _319074) ^ [_591559, _591561, _591563] : [class_Rings_Odivision__ring(_591559), -(_591561 = c_Groups_Ozero__class_Ozero(_591559)), 7950 ^ _319074 : [(7957 ^ _319074) ^ [] : [_591563 = _591561, -(c_Rings_Oinverse__class_Odivide(_591559, _591563, _591561) = c_Groups_Oone__class_Oone(_591559))], (7951 ^ _319074) ^ [] : [c_Rings_Oinverse__class_Odivide(_591559, _591563, _591561) = c_Groups_Oone__class_Oone(_591559), -(_591563 = _591561)]]], (10712 ^ _319074) ^ [_686673, _686675] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _686673, _686675), 10715 ^ _319074 : [(10722 ^ _319074) ^ [] : [_686675 = _686673, -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _686675, c_Nat_OSuc(_686673)))], (10716 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _686675, c_Nat_OSuc(_686673)), -(_686675 = _686673)]]], (12208 ^ _319074) ^ [_744245, _744247] : [class_Orderings_Oorder(_744245), -(class_Orderings_Oorder(tc_fun(_744247, _744245)))], (10503 ^ _319074) ^ [_679256, _679258] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_679256), c_Groups_Ozero__class_Ozero(_679256)), c_Nat_OSuc(_679258)) = c_Groups_Ozero__class_Ozero(_679256)), class_Power_Opower(_679256), class_Rings_Osemiring__0(_679256)], (12338 ^ _319074) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (4879 ^ _319074) ^ [_484925, _484927, _484929, _484931] : [class_Fields_Ofield__inverse__zero(_484925), 4882 ^ _319074 : [(4883 ^ _319074) ^ [] : [_484927 = c_Rings_Oinverse__class_Odivide(_484925, _484929, _484931), 4886 ^ _319074 : [(4893 ^ _319074) ^ [] : [_484931 = c_Groups_Ozero__class_Ozero(_484925), -(_484927 = c_Groups_Ozero__class_Ozero(_484925))], (4887 ^ _319074) ^ [] : [-(_484931 = c_Groups_Ozero__class_Ozero(_484925)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_484925), _484927), _484931) = _484929)]]], (4899 ^ _319074) ^ [] : [-(_484927 = c_Rings_Oinverse__class_Odivide(_484925, _484929, _484931)), 4902 ^ _319074 : [(4905 ^ _319074) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_484925), _484927), _484931) = _484929], (4903 ^ _319074) ^ [] : [_484931 = c_Groups_Ozero__class_Ozero(_484925)]], 4906 ^ _319074 : [(4909 ^ _319074) ^ [] : [_484927 = c_Groups_Ozero__class_Ozero(_484925)], (4907 ^ _319074) ^ [] : [-(_484931 = c_Groups_Ozero__class_Ozero(_484925))]]]]], (9891 ^ _319074) ^ [_658160] : [-(_658160 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 9894 ^ _319074 : [(9901 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _658160)), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _658160) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (9895 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _658160), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _658160) = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (8502 ^ _319074) ^ [_610885, _610887] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _610885, _610887), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _610885, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _610887, _610885)))], (2694 ^ _319074) ^ [_407395, _407397, _407399] : [class_Groups_Ogroup__add(_407395), -(c_Groups_Oplus__class_Oplus(_407395, c_Groups_Ouminus__class_Ouminus(_407395, _407397), c_Groups_Oplus__class_Oplus(_407395, _407397, _407399)) = _407399)], (8906 ^ _319074) ^ [_624750, _624752] : [-(_624750 = _624752), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _624750, _624752), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _624752, _624750)], (10994 ^ _319074) ^ [_696400, _696402, _696404] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _696400), _696402), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _696404), _696402)), -(_696402 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _696400, _696404))], (820 ^ _319074) ^ [_343609, _343611] : [-(hBOOL(_343609)), _343611 = _343609, hBOOL(_343611)], (1954 ^ _319074) ^ [_383485, _383487, _383489, _383491] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _383485, _383487), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _383489), c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _383491)))), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _383485, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _383489))), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _383487, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _383491))))))], (12306 ^ _319074) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (11976 ^ _319074) ^ [_734948, _734950, _734952, _734954, _734956] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _734948, _734950), 11979 ^ _319074 : [(11986 ^ _319074) ^ [] : [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, _734950, _734948)), _734952), _734954), _734956), -(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), _734950), _734952), _734954), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _734948), _734952), _734956)))], (11980 ^ _319074) ^ [] : [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), _734950), _734952), _734954), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _734948), _734952), _734956)), -(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, _734950, _734948)), _734952), _734954), _734956))]]], (1728 ^ _319074) ^ [_375298, _375300, _375302, _375304] : [class_Groups_Ocancel__semigroup__add(_375298), c_Groups_Oplus__class_Oplus(_375298, _375300, _375302) = c_Groups_Oplus__class_Oplus(_375298, _375300, _375304), -(_375302 = _375304)], (10463 ^ _319074) ^ [_677516] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _677516, c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Groups_Oabs__class_Oabs(tc_Int_Oint, _677516) = _677516)], (7421 ^ _319074) ^ [_571132, _571134] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _571132), _571134) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _571134), _571132))], (10581 ^ _319074) ^ [_682265, _682267] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _682265, c_Nat_OSuc(_682267))), 10582 ^ _319074 : [(10585 ^ _319074) ^ [_682434] : [_682265 = c_Nat_OSuc(_682434), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _682434, _682267)], (10583 ^ _319074) ^ [] : [_682265 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (9348 ^ _319074) ^ [_638734] : [-(_638734 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 9351 ^ _319074 : [(9358 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _638734)), -(c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, _638734) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (9352 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _638734), -(c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, _638734) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))]]], (3196 ^ _319074) ^ [_423791, _423793] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _423791, _423793)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _423791, _423793), -(_423791 = _423793)], (12268 ^ _319074) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (12746 ^ _319074) ^ [_759103] : [class_Rings_Olinordered__idom(_759103), -(class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(_759103)))], (3260 ^ _319074) ^ [_425967, _425969] : [class_Groups_Olinordered__ab__group__add(_425967), 3263 ^ _319074 : [(3270 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_425967, _425969, c_Groups_Ozero__class_Ozero(_425967)), -(c_Orderings_Oord__class_Oless__eq(_425967, _425969, c_Groups_Ouminus__class_Ouminus(_425967, _425969)))], (3264 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_425967, _425969, c_Groups_Ouminus__class_Ouminus(_425967, _425969)), -(c_Orderings_Oord__class_Oless__eq(_425967, _425969, c_Groups_Ozero__class_Ozero(_425967)))]]], (12298 ^ _319074) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (5335 ^ _319074) ^ [_499674, _499676, _499678, _499680] : [class_Fields_Olinordered__field(_499674), c_Orderings_Oord__class_Oless(_499674, c_Groups_Ozero__class_Ozero(_499674), _499676), 5342 ^ _319074 : [(5349 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_499674, _499678, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_499674), _499680), _499676)), -(c_Orderings_Oord__class_Oless(_499674, c_Rings_Oinverse__class_Odivide(_499674, _499678, _499676), _499680))], (5343 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_499674, c_Rings_Oinverse__class_Odivide(_499674, _499678, _499676), _499680), -(c_Orderings_Oord__class_Oless(_499674, _499678, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_499674), _499680), _499676)))]]], (7238 ^ _319074) ^ [_564339, _564341] : [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _564339), _564339), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _564341), _564341)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 7241 ^ _319074 : [(7244 ^ _319074) ^ [] : [-(_564341 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (7242 ^ _319074) ^ [] : [-(_564339 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (12506 ^ _319074) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_RealDef_Oreal))], (12478 ^ _319074) ^ [] : [-(class_RealVector_Oreal__normed__field(tc_RealDef_Oreal))], (10233 ^ _319074) ^ [_669581, _669583] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _669581, _669583), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_669581), c_Nat_OSuc(_669583)))], (7639 ^ _319074) ^ [_580117, _580119] : [class_RealVector_Oreal__normed__algebra(_580117), 7643 ^ _319074 : [(7646 ^ _319074) ^ [_580416] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_580117, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_580117), _580119), _580416)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_580117, _580416)), 7642 ^ [_580117, _580119])))], (7644 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 7642 ^ [_580117, _580119]))]]], (10605 ^ _319074) ^ [_683127, _683129] : [c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _683127, _683129), 10610 ^ _319074 : [(10613 ^ _319074) ^ [] : [-(_683129 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10611 ^ _319074) ^ [] : [-(_683127 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 10614 ^ _319074 : [(10617 ^ _319074) ^ [] : [-(_683129 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10615 ^ _319074) ^ [] : [-(_683127 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (12628 ^ _319074) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Complex_Ocomplex))], (9032 ^ _319074) ^ [_628721, _628723, _628725] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _628721, _628723), _628723 = _628725, -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _628721, _628725))], (7166 ^ _319074) ^ [_561887, _561889, _561891] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _561887), _561889), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _561887), _561891)), 7169 ^ _319074 : [(7172 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _561889, _561891))], (7170 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _561887))]]], (7823 ^ _319074) ^ [_587378, _587380] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _587378), _587380)), _587378 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _587380 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (11317 ^ _319074) ^ [_707741, _707743, _707745, _707747, _707749] : [-(hAPP(hAPP(c_Power_Opower_Opower(_707741, _707743, _707745), _707747), c_Nat_OSuc(_707749)) = hAPP(hAPP(_707745, _707747), hAPP(hAPP(c_Power_Opower_Opower(_707741, _707743, _707745), _707747), _707749)))], (5795 ^ _319074) ^ [_515332, _515334, _515336, _515338, _515340, _515342] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_515332), -(_515334 = c_Groups_Ozero__class_Ozero(_515332)), c_Groups_Oplus__class_Oplus(_515332, _515336, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_515332), _515334), _515340)) = c_Groups_Oplus__class_Oplus(_515332, _515338, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_515332), _515334), _515342)), _515336 = _515338, -(_515340 = _515342)], (12278 ^ _319074) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (10077 ^ _319074) ^ [_664274] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _664274, 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), _664274), _664274), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (4241 ^ _319074) ^ [_459249] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _459249, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (12117 ^ _319074) ^ [_740683, _740685, _740687] : [-(hBOOL(hAPP(_740683, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _740685, _740687)))), 12120 ^ _319074 : [(12123 ^ _319074) ^ [] : [hBOOL(hAPP(_740683, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (12121 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _740685, _740687))]], 12125 ^ _319074 : [(12128 ^ _319074) ^ [] : [hBOOL(hAPP(_740683, 12124 ^ [_740683, _740685, _740687]))], (12126 ^ _319074) ^ [] : [-(_740685 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _740687, 12124 ^ [_740683, _740685, _740687]))]]], (8019 ^ _319074) ^ [_593885, _593887, _593889] : [class_Rings_Olinordered__idom(_593885), c_Orderings_Oord__class_Oless__eq(_593885, c_Groups_Ozero__class_Ozero(_593885), _593887), c_Orderings_Oord__class_Oless__eq(_593885, c_Groups_Ozero__class_Ozero(_593885), _593889), c_Orderings_Oord__class_Oless__eq(_593885, _593889, c_Groups_Oone__class_Oone(_593885)), -(c_Orderings_Oord__class_Oless__eq(_593885, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_593885), _593889), _593887), _593887))], (6407 ^ _319074) ^ [_536013, _536015, _536017] : [class_Fields_Ofield__inverse__zero(_536013), -(c_Rings_Oinverse__class_Odivide(_536013, c_Groups_Ouminus__class_Ouminus(_536013, _536015), c_Groups_Ouminus__class_Ouminus(_536013, _536017)) = c_Rings_Oinverse__class_Odivide(_536013, _536015, _536017))], (3414 ^ _319074) ^ [_430905, _430907] : [class_Groups_Oordered__ab__group__add__abs(_430905), -(c_Orderings_Oord__class_Oless__eq(_430905, c_Groups_Ouminus__class_Ouminus(_430905, _430907), c_Groups_Oabs__class_Oabs(_430905, _430907)))], (12896 ^ _319074) ^ [_763853] : [class_Rings_Ocomm__semiring__1(_763853), -(class_Groups_Omonoid__mult(tc_Polynomial_Opoly(_763853)))], (942 ^ _319074) ^ [_348540, _348542, _348544, _348546] : [-(c_Groups_Osgn__class_Osgn(_348546, _348542) = c_Groups_Osgn__class_Osgn(_348544, _348540)), _348546 = _348544, _348542 = _348540], (11668 ^ _319074) ^ [_722011, _722013, _722015, _722017, _722019, _722021] : [class_Rings_Oordered__ring(_722011), 11671 ^ _319074 : [(11678 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_722011, _722017, c_Groups_Oplus__class_Oplus(_722011, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_722011), c_Groups_Ominus__class_Ominus(_722011, _722019, _722013)), _722015), _722021)), -(c_Orderings_Oord__class_Oless(_722011, c_Groups_Oplus__class_Oplus(_722011, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_722011), _722013), _722015), _722017), c_Groups_Oplus__class_Oplus(_722011, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_722011), _722019), _722015), _722021)))], (11672 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_722011, c_Groups_Oplus__class_Oplus(_722011, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_722011), _722013), _722015), _722017), c_Groups_Oplus__class_Oplus(_722011, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_722011), _722019), _722015), _722021)), -(c_Orderings_Oord__class_Oless(_722011, _722017, c_Groups_Oplus__class_Oplus(_722011, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_722011), c_Groups_Ominus__class_Ominus(_722011, _722019, _722013)), _722015), _722021)))]]], (10704 ^ _319074) ^ [_686339, _686341] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _686339, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _686339, _686341))))], (9188 ^ _319074) ^ [_633541, _633543, _633545] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _633541, _633543), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _633543, _633541)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _633543, _633545), 9199 ^ _319074 : [(9202 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _633545, _633541)], (9200 ^ _319074) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _633541, _633545))]]], (4613 ^ _319074) ^ [_474692, _474694, _474696] : [class_Rings_Oring__no__zero__divisors(_474692), 4616 ^ _319074 : [(4617 ^ _319074) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_474692), _474694), _474696) = c_Groups_Ozero__class_Ozero(_474692), -(_474694 = c_Groups_Ozero__class_Ozero(_474692)), -(_474696 = c_Groups_Ozero__class_Ozero(_474692))], (4627 ^ _319074) ^ [] : [4628 ^ _319074 : [(4631 ^ _319074) ^ [] : [_474696 = c_Groups_Ozero__class_Ozero(_474692)], (4629 ^ _319074) ^ [] : [_474694 = c_Groups_Ozero__class_Ozero(_474692)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_474692), _474694), _474696) = c_Groups_Ozero__class_Ozero(_474692))]]], (10776 ^ _319074) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (11580 ^ _319074) ^ [_718399, _718401, _718403, _718405] : [class_Rings_Ocomm__ring(_718399), class_Rings_Odvd(_718399), c_Rings_Odvd__class_Odvd(_718399, _718401, _718403), 11591 ^ _319074 : [(11598 ^ _319074) ^ [_719040, _719042] : [c_Rings_Odvd__class_Odvd(_718399, _718401, c_Groups_Oplus__class_Oplus(_718399, c_Groups_Ominus__class_Ominus(_718399, _719042, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_718399), _719040), _718403)), _718405)), -(c_Rings_Odvd__class_Odvd(_718399, _718401, c_Groups_Oplus__class_Oplus(_718399, _719042, _718405)))], (11592 ^ _319074) ^ [_718802, _718804] : [c_Rings_Odvd__class_Odvd(_718399, _718401, c_Groups_Oplus__class_Oplus(_718399, _718804, _718405)), -(c_Rings_Odvd__class_Odvd(_718399, _718401, c_Groups_Oplus__class_Oplus(_718399, c_Groups_Ominus__class_Ominus(_718399, _718804, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_718399), _718802), _718403)), _718405)))]]], (6926 ^ _319074) ^ [_553011, _553013] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _553011), _553013) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _553013), _553011))], (10271 ^ _319074) ^ [_670807, _670809] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _670807, _670809), -(c_Nat_OSuc(_670807) = _670809), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_670807), _670809))], (4697 ^ _319074) ^ [_477774, _477776, _477778, _477780, _477782] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_477774), 4700 ^ _319074 : [(4701 ^ _319074) ^ [] : [c_Groups_Oplus__class_Oplus(_477774, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_477774), _477776), _477780), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_477774), _477778), _477782)) = c_Groups_Oplus__class_Oplus(_477774, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_477774), _477776), _477782), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_477774), _477778), _477780)), -(_477776 = _477778), -(_477780 = _477782)], (4711 ^ _319074) ^ [] : [-(c_Groups_Oplus__class_Oplus(_477774, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_477774), _477776), _477780), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_477774), _477778), _477782)) = c_Groups_Oplus__class_Oplus(_477774, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_477774), _477776), _477782), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_477774), _477778), _477780))), 4714 ^ _319074 : [(4717 ^ _319074) ^ [] : [_477780 = _477782], (4715 ^ _319074) ^ [] : [_477776 = _477778]]]]], (12728 ^ _319074) ^ [_758533] : [class_Groups_Ocancel__comm__monoid__add(_758533), -(class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(_758533)))], (4461 ^ _319074) ^ [_467490, _467492] : [class_RealVector_Oreal__normed__algebra(_467490), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_467490), _467492), c_Groups_Ozero__class_Ozero(_467490)) = c_Groups_Ozero__class_Ozero(_467490))], (13034 ^ _319074) ^ [_768263, _768265] : [_768263 = _768265, -(hBOOL(c_fequal(_768263, _768265)))], (5369 ^ _319074) ^ [_500813, _500815, _500817, _500819] : [class_Fields_Olinordered__field(_500813), c_Orderings_Oord__class_Oless(_500813, c_Groups_Ozero__class_Ozero(_500813), _500815), c_Orderings_Oord__class_Oless(_500813, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_500813), _500817), _500815), _500819), -(c_Orderings_Oord__class_Oless(_500813, _500817, c_Rings_Oinverse__class_Odivide(_500813, _500819, _500815)))], (11174 ^ _319074) ^ [_702826, _702828, _702830, _702832, _702834, _702836] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _702826), _702828), _702830) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _702832), _702834), _702836), 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), _702832), _702834), _702836)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _702836, _702832), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _702830), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _702832), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _702832, _702826), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _702828, _702834))], (12284 ^ _319074) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (8440 ^ _319074) ^ [_608751, _608753] : [class_Rings_Olinordered__idom(_608751), 8443 ^ _319074 : [(8450 ^ _319074) ^ [] : [-(_608753 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_608751))), 8453 ^ _319074 : [(8460 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_608751), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_608751)), _608753)), -(c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(_608751), _608753) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_608751), c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_608751))))], (8454 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_608751), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_608751)), _608753), -(c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(_608751), _608753) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(_608751)))]]], (8444 ^ _319074) ^ [] : [_608753 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_608751)), -(c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(_608751), _608753) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_608751)))]]], (11466 ^ _319074) ^ [_713149, _713151, _713153] : [class_Groups_Oordered__ab__group__add__abs(_713149), -(c_Groups_Oabs__class_Oabs(_713149, c_Groups_Ominus__class_Ominus(_713149, _713151, _713153)) = c_Groups_Oabs__class_Oabs(_713149, c_Groups_Ominus__class_Ominus(_713149, _713153, _713151)))], (9540 ^ _319074) ^ [_645744, _645746, _645748, _645750] : [class_Groups_Omonoid__mult(_645744), -(hAPP(hAPP(c_Power_Opower__class_Opower(_645744), _645746), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _645748, _645750)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_645744), hAPP(hAPP(c_Power_Opower__class_Opower(_645744), _645746), _645748)), hAPP(hAPP(c_Power_Opower__class_Opower(_645744), _645746), _645750)))], (8784 ^ _319074) ^ [_620871, _620873] : [class_Rings_Olinordered__idom(_620871), c_Orderings_Oord__class_Oless(_620871, _620873, c_Groups_Ozero__class_Ozero(_620871)), -(c_Groups_Osgn__class_Osgn(_620871, _620873) = c_Groups_Ouminus__class_Ouminus(_620871, c_Groups_Oone__class_Oone(_620871)))], (12372 ^ _319074) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (4451 ^ _319074) ^ [_466985, _466987, _466989] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _466985, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _466987, _466989)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _466987, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _466985, _466989)))], (12512 ^ _319074) ^ [] : [-(class_Rings_Olinordered__ring(tc_RealDef_Oreal))], (8466 ^ _319074) ^ [_609593, _609595, _609597] : [class_Rings_Oidom(_609593), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_609593), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_609593)), c_Polynomial_OpCons(_609593, c_Groups_Ouminus__class_Ouminus(_609593, _609595), c_Polynomial_OpCons(_609593, c_Groups_Oone__class_Oone(_609593), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_609593))))), c_Polynomial_Oorder(_609593, _609595, _609597)), _609597))], (9830 ^ _319074) ^ [_656004, _656006] : [-(_656004 = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)), -(_656006 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex, c_Groups_Oone__class_Oone(tc_Complex_Ocomplex), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), _656004), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex), 9837 ^ [_656004, _656006]), _656006)))), c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (10191 ^ _319074) ^ [_668105] : [c_Nat_OSuc(_668105) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (3038 ^ _319074) ^ [_418327, _418329, _418331] : [class_Orderings_Olinorder(_418327), 3041 ^ _319074 : [(3048 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_418327, _418331, _418329), c_Orderings_Oord__class_Oless(_418327, _418329, _418331)], (3042 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_418327, _418329, _418331)), -(c_Orderings_Oord__class_Oless__eq(_418327, _418331, _418329))]]], (12142 ^ _319074) ^ [_741548] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _741548, _741548) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (2286 ^ _319074) ^ [_394341, _394343, _394345] : [class_Orderings_Olinorder(_394341), -(_394343 = _394345), -(c_Orderings_Oord__class_Oless(_394341, _394343, _394345)), -(c_Orderings_Oord__class_Oless(_394341, _394345, _394343))], (5657 ^ _319074) ^ [_510250, _510252, _510254] : [class_Rings_Olinordered__ring__strict(_510250), c_Orderings_Oord__class_Oless(_510250, _510252, c_Groups_Ozero__class_Ozero(_510250)), c_Orderings_Oord__class_Oless(_510250, _510254, c_Groups_Ozero__class_Ozero(_510250)), -(c_Orderings_Oord__class_Oless(_510250, c_Groups_Ozero__class_Ozero(_510250), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_510250), _510252), _510254)))], (3790 ^ _319074) ^ [_443341, _443343, _443345] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _443341, _443343), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _443341, _443345)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _443343, _443345))], (11732 ^ _319074) ^ [_724785, _724787, _724789] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _724785, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _724787, _724789)), c_Rings_Odvd__class_Odvd(tc_Int_Oint, _724785, _724789), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _724785, _724787))], (12544 ^ _319074) ^ [] : [-(class_Groups_Ogroup__add(tc_RealDef_Oreal))], (3022 ^ _319074) ^ [_417831, _417833, _417835] : [class_Orderings_Olinorder(_417831), 3025 ^ _319074 : [(3032 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_417831, _417835, _417833), c_Orderings_Oord__class_Oless__eq(_417831, _417833, _417835)], (3026 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_417831, _417833, _417835)), -(c_Orderings_Oord__class_Oless(_417831, _417835, _417833))]]], (700 ^ _319074) ^ [_340069, _340071] : [-(class_Rings_Ocomm__ring__1(_340069)), _340071 = _340069, class_Rings_Ocomm__ring__1(_340071)], (12270 ^ _319074) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (10778 ^ _319074) ^ [_688933, _688935, _688937] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_688933)), _688935), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_688933)), _688937)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _688935, _688937))], (11050 ^ _319074) ^ [_698395, _698397] : [-(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _698395, _698397)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _698395), c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _698397)))], (9298 ^ _319074) ^ [_637015, _637017, _637019] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _637015), _637017)), _637019) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _637015), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _637017), _637019)))], (7006 ^ _319074) ^ [_555795, _555797, _555799] : [-(_555795 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 7009 ^ _319074 : [(7016 ^ _319074) ^ [] : [_555797 = _555799, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _555797), _555795) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _555799), _555795))], (7010 ^ _319074) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _555797), _555795) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _555799), _555795), -(_555797 = _555799)]]], (1928 ^ _319074) ^ [_382598, _382600] : [class_Groups_Ozero(_382598), 1931 ^ _319074 : [(1938 ^ _319074) ^ [] : [_382600 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_382598)), -(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_382598, _382600) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (1932 ^ _319074) ^ [] : [c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_382598, _382600) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_382600 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_382598)))]]], (3890 ^ _319074) ^ [_446944, _446946] : [-(_446944 = _446946), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _446944, _446946)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _446946, _446944))], (12488 ^ _319074) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal))], (1888 ^ _319074) ^ [_380856, _380858, _380860, _380862, _380864] : [class_Rings_Ocomm__semiring__1(_380856), -(c_Groups_Oplus__class_Oplus(_380856, c_Groups_Oplus__class_Oplus(_380856, _380858, _380860), c_Groups_Oplus__class_Oplus(_380856, _380862, _380864)) = c_Groups_Oplus__class_Oplus(_380856, c_Groups_Oplus__class_Oplus(_380856, _380858, _380862), c_Groups_Oplus__class_Oplus(_380856, _380860, _380864)))], (12710 ^ _319074) ^ [_757963] : [class_Rings_Olinordered__idom(_757963), -(class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(_757963)))], (10665 ^ _319074) ^ [_684920, _684922] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _684920), -(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), _684920), _684922)))], (8097 ^ _319074) ^ [_596590, _596592, _596594] : [class_Rings_Ocomm__ring__1(_596590), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_596590), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_596590)), c_Polynomial_OpCons(_596590, c_Groups_Ouminus__class_Ouminus(_596590, _596592), c_Polynomial_OpCons(_596590, c_Groups_Oone__class_Oone(_596590), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_596590))))), c_Polynomial_Osynthetic__div(_596590, _596594, _596592)), c_Polynomial_OpCons(_596590, hAPP(c_Polynomial_Opoly(_596590, _596594), _596592), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_596590)))) = _596594)], (3146 ^ _319074) ^ [_422112, _422114] : [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _422112, _422114) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_422114 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _422112))], (2754 ^ _319074) ^ [_409607, _409609, _409611, _409613] : [class_Orderings_Opreorder(_409607), c_Orderings_Oord__class_Oless__eq(_409607, _409609, _409611), c_Orderings_Oord__class_Oless(_409607, _409611, _409613), -(c_Orderings_Oord__class_Oless(_409607, _409609, _409613))], (6053 ^ _319074) ^ [_523874, _523876, _523878, _523880] : [class_Fields_Olinordered__field(_523874), c_Orderings_Oord__class_Oless(_523874, c_Groups_Ozero__class_Ozero(_523874), _523876), c_Orderings_Oord__class_Oless__eq(_523874, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_523874), _523878), _523876), _523880), -(c_Orderings_Oord__class_Oless__eq(_523874, _523878, c_Rings_Oinverse__class_Odivide(_523874, _523880, _523876)))], (8726 ^ _319074) ^ [_619110, _619112] : [class_Rings_Olinordered__idom(_619110), c_Orderings_Oord__class_Oless(_619110, c_Groups_Ozero__class_Ozero(_619110), _619112), -(c_Groups_Osgn__class_Osgn(_619110, _619112) = c_Groups_Oone__class_Oone(_619110))], (12482 ^ _319074) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal))], (9270 ^ _319074) ^ [_636078, _636080, _636082] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _636078), c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _636078), _636080), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _636078), _636082)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _636080, _636082))], (8684 ^ _319074) ^ [_617682, _617684] : [class_Rings_Olinordered__idom(_617682), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_617682), c_Groups_Osgn__class_Osgn(_617682, _617684)), c_Groups_Oabs__class_Oabs(_617682, _617684)) = _617684)], (4521 ^ _319074) ^ [_470224, _470226, _470228] : [class_RealVector_Oreal__normed__algebra(_470224), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_470224), _470226), c_Groups_Ouminus__class_Ouminus(_470224, _470228)) = c_Groups_Ouminus__class_Ouminus(_470224, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_470224), _470226), _470228)))], (10417 ^ _319074) ^ [_675921, _675923, _675925, _675927] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _675921, _675923), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _675925, _675927), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _675921, _675925), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _675923, _675927)))], (10493 ^ _319074) ^ [_678917, _678919, _678921] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _678917, _678919), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _678921), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _678921), _678917), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _678921), _678919)))], (12662 ^ _319074) ^ [] : [-(class_Rings_Oidom(tc_Complex_Ocomplex))], (2810 ^ _319074) ^ [_411358, _411360, _411362] : [class_Orderings_Oorder(_411358), c_Orderings_Oord__class_Oless__eq(_411358, _411360, _411362), -(_411360 = _411362), -(c_Orderings_Oord__class_Oless(_411358, _411360, _411362))], (11434 ^ _319074) ^ [_712024, _712026] : [class_Groups_Ogroup__add(_712024), -(c_Groups_Ominus__class_Ominus(_712024, _712026, _712026) = c_Groups_Ozero__class_Ozero(_712024))], (12956 ^ _319074) ^ [_765753] : [class_Rings_Olinordered__idom(_765753), -(class_Orderings_Oord(tc_Polynomial_Opoly(_765753)))], (6679 ^ _319074) ^ [_544735] : [class_RealVector_Oreal__normed__vector(_544735), -(c_RealVector_Onorm__class_Onorm(_544735, c_Groups_Ozero__class_Ozero(_544735)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (4239 ^ _319074) ^ [_459168] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _459168, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _459168)], (4455 ^ _319074) ^ [_467228, _467230, _467232] : [class_RealVector_Oreal__normed__algebra(_467228), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_467228, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_467228), _467230), _467232)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_467228, _467230)), c_RealVector_Onorm__class_Onorm(_467228, _467232))))], (10143 ^ _319074) ^ [_666513] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _666513), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _666513))], (7715 ^ _319074) ^ [_583572] : [class_RealVector_Oreal__normed__algebra__1(_583572), -(c_RealVector_Onorm__class_Onorm(_583572, c_Groups_Oone__class_Oone(_583572)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (12806 ^ _319074) ^ [_761003] : [class_Groups_Ocomm__monoid__add(_761003), -(class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(_761003)))], (7909 ^ _319074) ^ [_590372, _590374, _590376] : [class_Rings_Ocomm__semiring__1(_590372), -(c_Groups_Oplus__class_Oplus(_590372, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_590372), _590374), _590376), _590376) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_590372), c_Groups_Oplus__class_Oplus(_590372, _590374, c_Groups_Oone__class_Oone(_590372))), _590376))], (1984 ^ _319074) ^ [_384552, _384554, _384556, _384558] : [class_Groups_Oordered__comm__monoid__add(_384552), c_Orderings_Oord__class_Oless(_384552, c_Groups_Ozero__class_Ozero(_384552), _384554), c_Orderings_Oord__class_Oless__eq(_384552, _384556, _384558), -(c_Orderings_Oord__class_Oless(_384552, _384556, c_Groups_Oplus__class_Oplus(_384552, _384554, _384558)))], (3108 ^ _319074) ^ [_420789, _420791, _420793, _420795] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_420789), 3111 ^ _319074 : [(3118 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_420789, _420793, _420795), -(c_Orderings_Oord__class_Oless(_420789, c_Groups_Oplus__class_Oplus(_420789, _420791, _420793), c_Groups_Oplus__class_Oplus(_420789, _420791, _420795)))], (3112 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_420789, c_Groups_Oplus__class_Oplus(_420789, _420791, _420793), c_Groups_Oplus__class_Oplus(_420789, _420791, _420795)), -(c_Orderings_Oord__class_Oless(_420789, _420793, _420795))]]], (12180 ^ _319074) ^ [_743282, _743284, _743286] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _743282, _743284)), _743286) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _743282), _743286), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _743284), _743286)))], (12238 ^ _319074) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (11774 ^ _319074) ^ [_726328, _726330, _726332] : [class_Rings_Ocomm__ring__1(_726328), -(c_Groups_Ominus__class_Ominus(_726328, _726330, _726332) = c_Groups_Oplus__class_Oplus(_726328, _726330, c_Groups_Ouminus__class_Ouminus(_726328, _726332)))], (12316 ^ _319074) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (3244 ^ _319074) ^ [_425482, _425484] : [class_Groups_Oordered__ab__group__add(_425482), 3247 ^ _319074 : [(3254 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_425482, _425484, c_Groups_Ozero__class_Ozero(_425482)), -(c_Orderings_Oord__class_Oless__eq(_425482, c_Groups_Ozero__class_Ozero(_425482), c_Groups_Ouminus__class_Ouminus(_425482, _425484)))], (3248 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_425482, c_Groups_Ozero__class_Ozero(_425482), c_Groups_Ouminus__class_Ouminus(_425482, _425484)), -(c_Orderings_Oord__class_Oless__eq(_425482, _425484, c_Groups_Ozero__class_Ozero(_425482)))]]], (1649 ^ _319074) ^ [_372600, _372602, _372604] : [class_Orderings_Opreorder(_372600), _372602 = _372604, -(c_Orderings_Oord__class_Oless__eq(_372600, _372602, _372604))], (9450 ^ _319074) ^ [_642750, _642752, _642754] : [class_Rings_Olinordered__semidom(_642750), c_Orderings_Oord__class_Oless(_642750, c_Groups_Ozero__class_Ozero(_642750), _642752), -(c_Orderings_Oord__class_Oless(_642750, c_Groups_Ozero__class_Ozero(_642750), hAPP(hAPP(c_Power_Opower__class_Opower(_642750), _642752), _642754)))], (8940 ^ _319074) ^ [_625831, _625833] : [8947 ^ _319074 : [(8950 ^ _319074) ^ [] : [_625831 = _625833], (8948 ^ _319074) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _625831, _625833))]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _625831, _625833), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _625833, _625831))], (12464 ^ _319074) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal))], (12580 ^ _319074) ^ [] : [-(class_Rings_Odvd(tc_RealDef_Oreal))], (12414 ^ _319074) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (3862 ^ _319074) ^ [_445999, _446001] : [3863 ^ _319074 : [(3866 ^ _319074) ^ [] : [_445999 = _446001], (3864 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _445999, _446001)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _445999, _446001))], (3568 ^ _319074) ^ [_436002, _436004] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _436004, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _436002)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _436002, _436004), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (12944 ^ _319074) ^ [_765373] : [class_Rings_Olinordered__idom(_765373), -(class_Int_Oring__char__0(tc_Polynomial_Opoly(_765373)))], (10057 ^ _319074) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (80 ^ _319074) ^ [_321779, _321781] : [-(class_Lattices_Oboolean__algebra(_321779)), _321781 = _321779, class_Lattices_Oboolean__algebra(_321781)], (8508 ^ _319074) ^ [_611123, _611125, _611127] : [class_RealVector_Oreal__normed__div__algebra(_611123), -(c_RealVector_Onorm__class_Onorm(_611123, hAPP(hAPP(c_Power_Opower__class_Opower(_611123), _611125), _611127)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_611123, _611125)), _611127))], (8412 ^ _319074) ^ [_607717, _607719, _607721] : [class_Rings_Odvd(_607717), class_Rings_Osemiring__0(_607717), 8419 ^ _319074 : [(8429 ^ _319074) ^ [] : [-(hBOOL(hAPP(_607719, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_607717), _607721), 8436 ^ [_607717, _607719, _607721])))), 8430 ^ _319074 : [(8431 ^ _319074) ^ [_608366] : [c_Rings_Odvd__class_Odvd(_607717, _607721, c_Groups_Oplus__class_Oplus(_607717, _608366, c_Groups_Ozero__class_Ozero(_607717))), hBOOL(hAPP(_607719, _608366))]]], (8420 ^ _319074) ^ [] : [8421 ^ _319074 : [(8422 ^ _319074) ^ [_608026] : [hBOOL(hAPP(_607719, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_607717), _607721), _608026)))]], 8424 ^ _319074 : [(8427 ^ _319074) ^ [] : [-(hBOOL(hAPP(_607719, 8423 ^ [_607717, _607719, _607721])))], (8425 ^ _319074) ^ [] : [-(c_Rings_Odvd__class_Odvd(_607717, _607721, c_Groups_Oplus__class_Oplus(_607717, 8423 ^ [_607717, _607719, _607721], c_Groups_Ozero__class_Ozero(_607717))))]]]]], (9796 ^ _319074) ^ [_654873, _654875, _654877, _654879] : [class_Rings_Olinordered__semidom(_654873), c_Orderings_Oord__class_Oless(_654873, c_Groups_Oone__class_Oone(_654873), _654875), 9803 ^ _319074 : [(9810 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _654877, _654879), -(c_Orderings_Oord__class_Oless__eq(_654873, hAPP(hAPP(c_Power_Opower__class_Opower(_654873), _654875), _654877), hAPP(hAPP(c_Power_Opower__class_Opower(_654873), _654875), _654879)))], (9804 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_654873, hAPP(hAPP(c_Power_Opower__class_Opower(_654873), _654875), _654877), hAPP(hAPP(c_Power_Opower__class_Opower(_654873), _654875), _654879)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _654877, _654879))]]], (7835 ^ _319074) ^ [_587804, _587806] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _587804), _587806) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 7838 ^ _319074 : [(7841 ^ _319074) ^ [] : [-(_587806 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (7839 ^ _319074) ^ [] : [-(_587804 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (11538 ^ _319074) ^ [_716349, _716351, _716353, _716355, _716357] : [class_Groups_Ominus(_716349), -(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_716351, _716349), _716353, _716355), _716357) = c_Groups_Ominus__class_Ominus(_716349, hAPP(_716353, _716357), hAPP(_716355, _716357)))], (130 ^ _319074) ^ [_323254, _323256] : [-(class_RealVector_Oreal__normed__algebra__1(_323254)), _323256 = _323254, class_RealVector_Oreal__normed__algebra__1(_323256)], (9662 ^ _319074) ^ [_650414, _650416, _650418, _650420] : [class_Rings_Olinordered__semidom(_650414), c_Orderings_Oord__class_Oless(_650414, c_Groups_Oone__class_Oone(_650414), _650416), 9669 ^ _319074 : [(9676 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _650418, _650420), -(c_Orderings_Oord__class_Oless(_650414, hAPP(hAPP(c_Power_Opower__class_Opower(_650414), _650416), _650418), hAPP(hAPP(c_Power_Opower__class_Opower(_650414), _650416), _650420)))], (9670 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_650414, hAPP(hAPP(c_Power_Opower__class_Opower(_650414), _650416), _650418), hAPP(hAPP(c_Power_Opower__class_Opower(_650414), _650416), _650420)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _650418, _650420))]]], (12446 ^ _319074) ^ [] : [-(class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal))], (3158 ^ _319074) ^ [_422543, _422545] : [c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _422543, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _422545)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_422543 = _422545)], (540 ^ _319074) ^ [_335349, _335351] : [-(class_Orderings_Olinorder(_335349)), _335351 = _335349, class_Orderings_Olinorder(_335351)], (12598 ^ _319074) ^ [] : [-(class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex))], (1151 ^ _319074) ^ [_356292, _356294, _356296] : [class_Groups_Oordered__ab__group__add__abs(_356292), -(c_Orderings_Oord__class_Oless__eq(_356292, c_Groups_Oabs__class_Oabs(_356292, c_Groups_Oplus__class_Oplus(_356292, _356294, _356296)), c_Groups_Oplus__class_Oplus(_356292, c_Groups_Oabs__class_Oabs(_356292, _356294), c_Groups_Oabs__class_Oabs(_356292, _356296))))], (10904 ^ _319074) ^ [_693409, _693411] : [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), _693409), _693411)), 10907 ^ _319074 : [(10910 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _693411))], (10908 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _693409))]]], (12968 ^ _319074) ^ [_766133] : [class_Rings_Olinordered__idom(_766133), -(class_Groups_Osgn__if(tc_Polynomial_Opoly(_766133)))], (12558 ^ _319074) ^ [] : [-(class_Groups_Ouminus(tc_RealDef_Oreal))], (11338 ^ _319074) ^ [_708633, _708635] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _708633), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _708635), 11346 ^ _319074 : [(11349 ^ _319074) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), 11345 ^ [_708633, _708635]), _708633) = _708635)], (11347 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 11345 ^ [_708633, _708635]))]]], (10187 ^ _319074) ^ [_667947] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_667947)], (10391 ^ _319074) ^ [_675040, _675042] : [c_Nat_OSuc(_675040) = c_Nat_OSuc(_675042), -(_675040 = _675042)], (898 ^ _319074) ^ [_346959, _346961, _346963, _346965, _346967, _346969] : [-(c_Polynomial_Opcompose(_346969, _346965, _346961) = c_Polynomial_Opcompose(_346967, _346963, _346959)), _346969 = _346967, _346965 = _346963, _346961 = _346959], (1786 ^ _319074) ^ [_377312, _377314, _377316] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _377312, _377314), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _377314, _377316), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _377312, _377316))], (11112 ^ _319074) ^ [_700759, _700761] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _700759, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _700761)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _700759, _700761))], (330 ^ _319074) ^ [_329154, _329156] : [-(class_Rings_Oordered__cancel__semiring(_329154)), _329156 = _329154, class_Rings_Oordered__cancel__semiring(_329156)], (1233 ^ _319074) ^ [_359312, _359314, _359316, _359318] : [class_Groups_Oordered__ab__semigroup__add(_359312), c_Orderings_Oord__class_Oless__eq(_359312, _359314, _359316), -(c_Orderings_Oord__class_Oless__eq(_359312, c_Groups_Oplus__class_Oplus(_359312, _359318, _359314), c_Groups_Oplus__class_Oplus(_359312, _359318, _359316)))], (2498 ^ _319074) ^ [_401035, _401037] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _401035, _401037)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _401035), _401037))], (190 ^ _319074) ^ [_325024, _325026] : [-(class_Rings_Odivision__ring(_325024)), _325026 = _325024, class_Rings_Odivision__ring(_325026)], (2430 ^ _319074) ^ [_398830, _398832, _398834] : [class_Orderings_Olinorder(_398830), 2433 ^ _319074 : [(2434 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_398830, _398832, _398834)), -(c_Orderings_Oord__class_Oless(_398830, _398834, _398832)), -(_398832 = _398834)], (2444 ^ _319074) ^ [] : [2445 ^ _319074 : [(2448 ^ _319074) ^ [] : [_398832 = _398834], (2446 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_398830, _398834, _398832)]], c_Orderings_Oord__class_Oless(_398830, _398832, _398834)]]], (3206 ^ _319074) ^ [_424155, _424157, _424159, _424161, _424163, _424165] : [class_Groups_Ozero(_424155), hAPP(hAPP(hAPP(_424157, c_Groups_Ozero__class_Ozero(_424155)), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_424155))), _424159) = _424159, -(c_Polynomial_Opoly__rec(_424161, _424155, _424159, _424157, c_Polynomial_OpCons(_424155, _424163, _424165)) = hAPP(hAPP(hAPP(_424157, _424163), _424165), c_Polynomial_Opoly__rec(_424161, _424155, _424159, _424157, _424165)))], (8638 ^ _319074) ^ [_616154, _616156, _616158] : [8639 ^ _319074 : [(8642 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _616156, _616158)], (8640 ^ _319074) ^ [] : [_616154 = 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), _616154), _616156), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _616154), _616158)))], (2510 ^ _319074) ^ [_401451] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _401451, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _401451) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _401451))], (10702 ^ _319074) ^ [_686238, _686240] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _686238, c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _686240, _686238))))], (550 ^ _319074) ^ [_335644, _335646] : [-(class_Groups_Omonoid__mult(_335644)), _335646 = _335644, class_Groups_Omonoid__mult(_335646)], (12430 ^ _319074) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (11064 ^ _319074) ^ [_699082, _699084, _699086] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _699082, _699084), _699086) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _699082, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _699084, _699086)))], (11288 ^ _319074) ^ [_706557] : [class_Power_Opower(_706557), -(c_Power_Opower__class_Opower(_706557) = c_Power_Opower_Opower(_706557, c_Groups_Oone__class_Oone(_706557), c_Groups_Otimes__class_Otimes(_706557)))], (12604 ^ _319074) ^ [] : [-(class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex))], (12286 ^ _319074) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (11472 ^ _319074) ^ [_713420, _713422] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _713420, _713422), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _713420, _713422), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (10513 ^ _319074) ^ [_679593, _679595, _679597] : [class_Rings_Ocomm__semiring__1(_679593), -(hAPP(hAPP(c_Power_Opower__class_Opower(_679593), _679595), c_Nat_OSuc(_679597)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_679593), _679595), hAPP(hAPP(c_Power_Opower__class_Opower(_679593), _679595), _679597)))], (11094 ^ _319074) ^ [_700164, _700166] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _700164, _700166), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _700164), _700166))], (11128 ^ _319074) ^ [_701273, _701275, _701277] : [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), _701273), _701275), _701277)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _701277, _701273), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _701273), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _701275))], (9949 ^ _319074) ^ [_660056, _660058, _660060] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _660056, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _660058, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _660056), _660060))), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _660056, _660058))], (2528 ^ _319074) ^ [_402014] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _402014, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), -(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _402014) = _402014)], (10325 ^ _319074) ^ [_672740, _672742] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _672740, c_Nat_OSuc(_672742)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _672740, _672742)), -(_672740 = c_Nat_OSuc(_672742))], (12926 ^ _319074) ^ [_764803] : [class_Rings_Ocomm__semiring__0(_764803), -(class_Rings_Omult__zero(tc_Polynomial_Opoly(_764803)))], (1076 ^ _319074) ^ [_353428, _353430, _353432, _353434] : [-(hAPP(_353434, _353430) = hAPP(_353432, _353428)), _353434 = _353432, _353430 = _353428], (8472 ^ _319074) ^ [_609890] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _609890, c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_609890 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (1770 ^ _319074) ^ [_376743, _376745, _376747, _376749] : [class_Groups_Oab__semigroup__add(_376743), -(c_Groups_Oplus__class_Oplus(_376743, c_Groups_Oplus__class_Oplus(_376743, _376745, _376747), _376749) = c_Groups_Oplus__class_Oplus(_376743, _376745, c_Groups_Oplus__class_Oplus(_376743, _376747, _376749)))], (12366 ^ _319074) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (8118 ^ _319074) ^ [_597534, _597536, _597538] : [class_Rings_Oidom(_597534), 8121 ^ _319074 : [(8128 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_597534), c_Polynomial_OpCons(_597534, c_Groups_Ouminus__class_Ouminus(_597534, _597538), c_Polynomial_OpCons(_597534, c_Groups_Oone__class_Oone(_597534), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_597534)))), _597536), -(hAPP(c_Polynomial_Opoly(_597534, _597536), _597538) = c_Groups_Ozero__class_Ozero(_597534))], (8122 ^ _319074) ^ [] : [hAPP(c_Polynomial_Opoly(_597534, _597536), _597538) = c_Groups_Ozero__class_Ozero(_597534), -(c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(_597534), c_Polynomial_OpCons(_597534, c_Groups_Ouminus__class_Ouminus(_597534, _597538), c_Polynomial_OpCons(_597534, c_Groups_Oone__class_Oone(_597534), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_597534)))), _597536))]]], (12638 ^ _319074) ^ [] : [-(class_Groups_Ogroup__add(tc_Complex_Ocomplex))], (7308 ^ _319074) ^ [_566966, _566968, _566970] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _566966), _566968), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _566970), _566968)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _566968), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _566966, _566970))], (10475 ^ _319074) ^ [_678025, _678027, _678029] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, _678025, _678027)), _678029) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _678025), _678029), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _678027), _678029)))], (4509 ^ _319074) ^ [_469680, _469682, _469684] : [class_RealVector_Oreal__normed__algebra(_469680), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_469680), c_Groups_Ouminus__class_Ouminus(_469680, _469682)), _469684) = c_Groups_Ouminus__class_Ouminus(_469680, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_469680), _469682), _469684)))], (7921 ^ _319074) ^ [_590878, _590880] : [class_Rings_Oring__1__no__zero__divisors(_590878), 7924 ^ _319074 : [(7925 ^ _319074) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_590878), _590880), _590880) = c_Groups_Oone__class_Oone(_590878), -(_590880 = c_Groups_Oone__class_Oone(_590878)), -(_590880 = c_Groups_Ouminus__class_Ouminus(_590878, c_Groups_Oone__class_Oone(_590878)))], (7935 ^ _319074) ^ [] : [7936 ^ _319074 : [(7939 ^ _319074) ^ [] : [_590880 = c_Groups_Ouminus__class_Ouminus(_590878, c_Groups_Oone__class_Oone(_590878))], (7937 ^ _319074) ^ [] : [_590880 = c_Groups_Oone__class_Oone(_590878)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_590878), _590880), _590880) = c_Groups_Oone__class_Oone(_590878))]]], (10035 ^ _319074) ^ [_662802] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _662802) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (9470 ^ _319074) ^ [_643448, _643450, _643452] : [class_Power_Opower(_643448), class_Rings_Omult__zero(_643448), class_Rings_Ono__zero__divisors(_643448), class_Rings_Ozero__neq__one(_643448), 9485 ^ _319074 : [(9494 ^ _319074) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_643448), _643450), _643452) = c_Groups_Ozero__class_Ozero(_643448)), _643450 = c_Groups_Ozero__class_Ozero(_643448), -(_643452 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9486 ^ _319074) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_643448), _643450), _643452) = c_Groups_Ozero__class_Ozero(_643448), 9489 ^ _319074 : [(9492 ^ _319074) ^ [] : [_643452 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (9490 ^ _319074) ^ [] : [-(_643450 = c_Groups_Ozero__class_Ozero(_643448))]]]]], (9710 ^ _319074) ^ [_652057, _652059, _652061, _652063] : [class_Rings_Olinordered__semidom(_652057), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _652059, _652061), c_Orderings_Oord__class_Oless__eq(_652057, c_Groups_Oone__class_Oone(_652057), _652063), -(c_Orderings_Oord__class_Oless__eq(_652057, hAPP(hAPP(c_Power_Opower__class_Opower(_652057), _652063), _652059), hAPP(hAPP(c_Power_Opower__class_Opower(_652057), _652063), _652061)))], (11550 ^ _319074) ^ [_716953, _716955, _716957] : [class_RealVector_Oreal__normed__vector(_716953), -(c_RealVector_Onorm__class_Onorm(_716953, c_Groups_Ominus__class_Ominus(_716953, _716955, _716957)) = c_RealVector_Onorm__class_Onorm(_716953, c_Groups_Ominus__class_Ominus(_716953, _716957, _716955)))], (6413 ^ _319074) ^ [_536255, _536257] : [class_RealVector_Oreal__normed__vector(_536255), -(c_RealVector_Onorm__class_Onorm(_536255, c_Groups_Ouminus__class_Ouminus(_536255, _536257)) = c_RealVector_Onorm__class_Onorm(_536255, _536257))], (6928 ^ _319074) ^ [_553146, _553148, _553150] : [class_Int_Oring__char__0(_553146), class_Rings_Oidom(_553146), 6935 ^ _319074 : [(6942 ^ _319074) ^ [] : [_553148 = _553150, -(c_Polynomial_Opoly(_553146, _553148) = c_Polynomial_Opoly(_553146, _553150))], (6936 ^ _319074) ^ [] : [c_Polynomial_Opoly(_553146, _553148) = c_Polynomial_Opoly(_553146, _553150), -(_553148 = _553150)]]], (12734 ^ _319074) ^ [_758723] : [class_Rings_Oidom(_758723), -(class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(_758723)))], (11756 ^ _319074) ^ [_725578, _725580, _725582] : [class_Groups_Ogroup__add(_725578), -(c_Groups_Ominus__class_Ominus(_725578, _725580, _725582) = c_Groups_Oplus__class_Oplus(_725578, _725580, c_Groups_Ouminus__class_Ouminus(_725578, _725582)))], (440 ^ _319074) ^ [_332399, _332401] : [-(class_Groups_Ocomm__monoid__mult(_332399)), _332401 = _332399, class_Groups_Ocomm__monoid__mult(_332401)], (12680 ^ _319074) ^ [_757013] : [class_Rings_Olinordered__idom(_757013), -(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(_757013)))], (12608 ^ _319074) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex))], (7066 ^ _319074) ^ [_558066] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _558066, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _558066), _558066)))], (3974 ^ _319074) ^ [_449943, _449945, _449947] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _449943, _449945), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _449945, _449947), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _449943, _449947))], (180 ^ _319074) ^ [_324729, _324731] : [-(class_RealVector_Oreal__field(_324729)), _324731 = _324729, class_RealVector_Oreal__field(_324731)], (2534 ^ _319074) ^ [_402287, _402289, _402291, _402293, _402295, _402297] : [class_Groups_Ozero(_402287), -(c_Polynomial_Opoly__rec(_402289, _402287, _402291, _402293, c_Polynomial_OpCons(_402287, _402295, _402297)) = hAPP(hAPP(hAPP(_402293, _402295), _402297), c_If(_402289, c_fequal(_402297, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_402287))), _402291, c_Polynomial_Opoly__rec(_402289, _402287, _402291, _402293, _402297))))], (8095 ^ _319074) ^ [_596461] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal), c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _596461))))], (12590 ^ _319074) ^ [] : [-(class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex))], (12578 ^ _319074) ^ [] : [-(class_Groups_Oone(tc_RealDef_Oreal))], (5609 ^ _319074) ^ [_508679, _508681, _508683] : [class_Rings_Olinordered__semiring__strict(_508679), c_Orderings_Oord__class_Oless(_508679, c_Groups_Ozero__class_Ozero(_508679), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_508679), _508681), _508683)), c_Orderings_Oord__class_Oless(_508679, c_Groups_Ozero__class_Ozero(_508679), _508683), -(c_Orderings_Oord__class_Oless(_508679, c_Groups_Ozero__class_Ozero(_508679), _508681))], (4083 ^ _319074) ^ [_454098, _454100] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, _454098, _454100)), 4086 ^ _319074 : [(4093 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _454098)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _454100, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (4087 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _454098, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _454100))]]], (12064 ^ _319074) ^ [_738714, _738716] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _738714), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _738714, c_Nat_OSuc(_738716)), _738714))], (6341 ^ _319074) ^ [_533508, _533510, _533512, _533514] : [class_Rings_Olinordered__semiring__strict(_533508), c_Orderings_Oord__class_Oless__eq(_533508, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_533508), _533510), _533512), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_533508), _533510), _533514)), c_Orderings_Oord__class_Oless(_533508, c_Groups_Ozero__class_Ozero(_533508), _533510), -(c_Orderings_Oord__class_Oless__eq(_533508, _533512, _533514))], (2452 ^ _319074) ^ [_399490, _399492, _399494] : [class_Orderings_Olinorder(_399490), 2455 ^ _319074 : [(2456 ^ _319074) ^ [] : [-(_399492 = _399494), -(c_Orderings_Oord__class_Oless(_399490, _399492, _399494)), -(c_Orderings_Oord__class_Oless(_399490, _399494, _399492))], (2466 ^ _319074) ^ [] : [2467 ^ _319074 : [(2470 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_399490, _399494, _399492)], (2468 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_399490, _399492, _399494)]], _399492 = _399494]]], (7769 ^ _319074) ^ [_585338, _585340] : [class_Rings_Ocomm__semiring__1(_585338), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_585338), _585340), c_Groups_Oone__class_Oone(_585338)) = _585340)], (10017 ^ _319074) ^ [_662346, _662348] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _662346), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _662348), c_Rings_Odvd__class_Odvd(tc_Int_Oint, _662346, _662348), c_Rings_Odvd__class_Odvd(tc_Int_Oint, _662348, _662346), -(_662346 = _662348)], (6499 ^ _319074) ^ [_539071, _539073, _539075, _539077] : [class_Fields_Olinordered__field__inverse__zero(_539071), c_Orderings_Oord__class_Oless__eq(_539071, _539073, _539075), c_Orderings_Oord__class_Oless__eq(_539071, c_Groups_Ozero__class_Ozero(_539071), _539077), -(c_Orderings_Oord__class_Oless__eq(_539071, c_Rings_Oinverse__class_Odivide(_539071, _539073, _539077), c_Rings_Oinverse__class_Odivide(_539071, _539075, _539077)))], (12660 ^ _319074) ^ [] : [-(class_Rings_Oring(tc_Complex_Ocomplex))], (8852 ^ _319074) ^ [_622981, _622983, _622985, _622987] : [class_Rings_Olinordered__semidom(_622981), c_Orderings_Oord__class_Oless(_622981, _622983, _622985), c_Orderings_Oord__class_Oless__eq(_622981, c_Groups_Ozero__class_Ozero(_622981), _622983), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _622987), -(c_Orderings_Oord__class_Oless(_622981, hAPP(hAPP(c_Power_Opower__class_Opower(_622981), _622983), _622987), hAPP(hAPP(c_Power_Opower__class_Opower(_622981), _622985), _622987)))], (9869 ^ _319074) ^ [_657410] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Nat_OSuc(_657410)))], (11264 ^ _319074) ^ [_705835, _705837] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _705835), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _705837), -(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), _705835), _705837)))], (12220 ^ _319074) ^ [_744669, _744671] : [class_Groups_Ouminus(_744669), -(class_Groups_Ouminus(tc_fun(_744671, _744669)))], (10219 ^ _319074) ^ [_669084, _669086] : [10220 ^ _319074 : [(10223 ^ _319074) ^ [] : [_669084 = _669086], (10221 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _669084, _669086)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _669084, c_Nat_OSuc(_669086)))], (12618 ^ _319074) ^ [] : [-(class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex))], (12640 ^ _319074) ^ [] : [-(class_Rings_Omult__zero(tc_Complex_Ocomplex))], (4307 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v_da____), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex), v_z____), v_c____))))], (6701 ^ _319074) ^ [_545434, _545436, _545438] : [class_Fields_Olinordered__field(_545434), -(_545436 = c_Groups_Ozero__class_Ozero(_545434)), -(c_Groups_Oabs__class_Oabs(_545434, c_Rings_Oinverse__class_Odivide(_545434, _545438, _545436)) = c_Rings_Oinverse__class_Odivide(_545434, c_Groups_Oabs__class_Oabs(_545434, _545438), c_Groups_Oabs__class_Oabs(_545434, _545436)))], (4401 ^ _319074) ^ [_464954, _464956, _464958] : [class_Lattices_Oab__semigroup__idem__mult(_464954), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_464954), _464956), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_464954), _464956), _464958)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_464954), _464956), _464958))], (12574 ^ _319074) ^ [] : [-(class_Rings_Oring(tc_RealDef_Oreal))], (7594 ^ _319074) ^ [_578097, _578099] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _578097, _578099), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _578097, _578099))], (7793 ^ _319074) ^ [_586250, _586252] : [class_Groups_Ocomm__monoid__mult(_586250), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_586250), c_Groups_Oone__class_Oone(_586250)), _586252) = _586252)], (1157 ^ _319074) ^ [_356542, _356544] : [class_Orderings_Opreorder(_356542), -(c_Orderings_Oord__class_Oless__eq(_356542, _356544, _356544))], (11562 ^ _319074) ^ [_717511, _717513, _717515, _717517] : [class_Rings_Odivision__ring(_717511), -(c_Rings_Oinverse__class_Odivide(_717511, c_Groups_Ominus__class_Ominus(_717511, _717513, _717515), _717517) = c_Groups_Ominus__class_Ominus(_717511, c_Rings_Oinverse__class_Odivide(_717511, _717513, _717517), c_Rings_Oinverse__class_Odivide(_717511, _717515, _717517)))], (10239 ^ _319074) ^ [_669805, _669807] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _669805, _669807)), 10242 ^ _319074 : [(10249 ^ _319074) ^ [] : [_669805 = _669807, -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _669805, c_Nat_OSuc(_669807)))], (10243 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _669805, c_Nat_OSuc(_669807)), -(_669805 = _669807)]]], (7042 ^ _319074) ^ [_557139, _557141, _557143, _557145] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _557139, _557141), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _557143, _557145), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _557139), _557143), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _557141), _557145)))], (12520 ^ _319074) ^ [] : [-(class_RealVector_Oreal__field(tc_RealDef_Oreal))], (10706 ^ _319074) ^ [_686455, _686457] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_686455), _686457), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _686455, _686457))], (9873 ^ _319074) ^ [_657614] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _657614, c_Groups_Oone__class_Oone(tc_Int_Oint)), -(c_Groups_Oabs__class_Oabs(tc_Int_Oint, _657614) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (2566 ^ _319074) ^ [_403388] : [class_Groups_Ogroup__add(_403388), -(c_Groups_Ouminus__class_Ouminus(_403388, c_Groups_Ozero__class_Ozero(_403388)) = c_Groups_Ozero__class_Ozero(_403388))], (380 ^ _319074) ^ [_330629, _330631] : [-(class_Groups_Oordered__ab__group__add(_330629)), _330631 = _330629, class_Groups_Oordered__ab__group__add(_330631)], (12698 ^ _319074) ^ [_757583] : [class_Rings_Olinordered__idom(_757583), -(class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(_757583)))], (10770 ^ _319074) ^ [_688617, _688619] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_688617), _688619), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _688617, _688619))], (11502 ^ _319074) ^ [_714782, _714784, _714786, _714788] : [class_RealVector_Oreal__normed__algebra(_714782), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_714782), c_Groups_Ominus__class_Ominus(_714782, _714784, _714786)), _714788) = c_Groups_Ominus__class_Ominus(_714782, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_714782), _714784), _714788), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_714782), _714786), _714788)))], (4589 ^ _319074) ^ [_473750, _473752] : [class_Rings_Ocomm__semiring__1(_473750), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_473750), c_Groups_Ozero__class_Ozero(_473750)), _473752) = c_Groups_Ozero__class_Ozero(_473750))], (980 ^ _319074) ^ [_349931, _349933, _349935, _349937] : [-(c_Polynomial_Opoly(_349937, _349933) = c_Polynomial_Opoly(_349935, _349931)), _349937 = _349935, _349933 = _349931], (12498 ^ _319074) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal))], (9724 ^ _319074) ^ [_652527, _652529, _652531] : [class_Rings_Olinordered__semidom(_652527), c_Orderings_Oord__class_Oless(_652527, c_Groups_Ozero__class_Ozero(_652527), _652529), c_Orderings_Oord__class_Oless(_652527, _652529, c_Groups_Oone__class_Oone(_652527)), -(c_Orderings_Oord__class_Oless(_652527, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_652527), _652529), hAPP(hAPP(c_Power_Opower__class_Opower(_652527), _652529), _652531)), hAPP(hAPP(c_Power_Opower__class_Opower(_652527), _652529), _652531)))], (7963 ^ _319074) ^ [_592151, _592153] : [class_Rings_Odivision__ring(_592151), -(_592153 = c_Groups_Ozero__class_Ozero(_592151)), -(c_Rings_Oinverse__class_Odivide(_592151, _592153, _592153) = c_Groups_Oone__class_Oone(_592151))], (10842 ^ _319074) ^ [_691381, _691383, _691385] : [class_Rings_Olinordered__semidom(_691381), c_Orderings_Oord__class_Oless(_691381, c_Groups_Oone__class_Oone(_691381), _691383), -(c_Orderings_Oord__class_Oless(_691381, c_Groups_Oone__class_Oone(_691381), hAPP(hAPP(c_Power_Opower__class_Opower(_691381), _691383), c_Nat_OSuc(_691385))))], (1820 ^ _319074) ^ [_378540, _378542, _378544, _378546] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_378540), c_Orderings_Oord__class_Oless__eq(_378540, c_Groups_Oplus__class_Oplus(_378540, _378542, _378544), c_Groups_Oplus__class_Oplus(_378540, _378546, _378544)), -(c_Orderings_Oord__class_Oless__eq(_378540, _378542, _378546))], (1591 ^ _319074) ^ [_370745, _370747, _370749, _370751] : [class_Orderings_Oorder(_370745), _370747 = _370749, c_Orderings_Oord__class_Oless__eq(_370745, _370751, _370749), -(c_Orderings_Oord__class_Oless__eq(_370745, _370751, _370747))], (6299 ^ _319074) ^ [_532056, _532058, _532060, _532062] : [class_Rings_Olinordered__semiring(_532056), c_Orderings_Oord__class_Oless(_532056, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_532056), _532058), _532060), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_532056), _532058), _532062)), c_Orderings_Oord__class_Oless__eq(_532056, c_Groups_Ozero__class_Ozero(_532056), _532058), -(c_Orderings_Oord__class_Oless(_532056, _532060, _532062))], (9620 ^ _319074) ^ [_648858, _648860, _648862] : [class_Rings_Olinordered__semidom(_648858), c_Orderings_Oord__class_Oless(_648858, c_Groups_Oone__class_Oone(_648858), _648860), -(c_Orderings_Oord__class_Oless(_648858, hAPP(hAPP(c_Power_Opower__class_Opower(_648858), _648860), _648862), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_648858), _648860), hAPP(hAPP(c_Power_Opower__class_Opower(_648858), _648860), _648862))))], (12410 ^ _319074) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (12526 ^ _319074) ^ [] : [-(class_Groups_Oab__group__add(tc_RealDef_Oreal))], (7833 ^ _319074) ^ [_587662] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _587662), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _587662)], (12426 ^ _319074) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (4099 ^ _319074) ^ [_454533, _454535] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, _454533, _454535))), 4102 ^ _319074 : [(4105 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _454535)], (4103 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _454533, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]], 4106 ^ _319074 : [(4109 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _454535, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (4107 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _454533)]]], (6425 ^ _319074) ^ [_536743, _536745] : [class_RealVector_Oreal__normed__vector(_536743), -(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_536743, _536745)) = c_RealVector_Onorm__class_Onorm(_536743, _536745))], (12692 ^ _319074) ^ [_757393] : [class_Rings_Olinordered__idom(_757393), -(class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(_757393)))], (4157 ^ _319074) ^ [_456546] : [class_Rings_Olinordered__idom(_456546), c_Polynomial_Opos__poly(_456546, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_456546)))], (1020 ^ _319074) ^ [_351355, _351357] : [_351357 = _351355, -(c_Groups_Oone__class_Oone(_351357) = c_Groups_Oone__class_Oone(_351355))], (12434 ^ _319074) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (1487 ^ _319074) ^ [_367388, _367390, _367392] : [class_Orderings_Olinorder(_367388), -(c_Orderings_Oord__class_Oless__eq(_367388, _367390, _367392)), -(c_Orderings_Oord__class_Oless__eq(_367388, _367392, _367390))], (640 ^ _319074) ^ [_338299, _338301] : [-(class_Rings_Osemiring(_338299)), _338301 = _338299, class_Rings_Osemiring(_338301)], (12254 ^ _319074) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (12494 ^ _319074) ^ [] : [-(class_Rings_Olinordered__semidom(tc_RealDef_Oreal))], (5057 ^ _319074) ^ [_490577, _490579, _490581, _490583] : [class_Rings_Oordered__semiring(_490577), c_Orderings_Oord__class_Oless__eq(_490577, _490579, _490581), c_Orderings_Oord__class_Oless__eq(_490577, c_Groups_Ozero__class_Ozero(_490577), _490583), -(c_Orderings_Oord__class_Oless__eq(_490577, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_490577), _490579), _490583), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_490577), _490581), _490583)))], (1577 ^ _319074) ^ [_370299, _370301, _370303, _370305] : [class_Orderings_Oord(_370299), c_Orderings_Oord__class_Oless__eq(_370299, _370301, _370303), _370303 = _370305, -(c_Orderings_Oord__class_Oless__eq(_370299, _370301, _370305))], (2108 ^ _319074) ^ [_388635, _388637, _388639] : [class_Orderings_Olinorder(_388635), -(c_Orderings_Oord__class_Oless(_388635, _388637, _388639)), -(_388637 = _388639), -(c_Orderings_Oord__class_Oless(_388635, _388639, _388637))], (9778 ^ _319074) ^ [_654286, _654288, _654290, _654292] : [class_Rings_Olinordered__semidom(_654286), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _654288, _654290), c_Orderings_Oord__class_Oless__eq(_654286, c_Groups_Ozero__class_Ozero(_654286), _654292), c_Orderings_Oord__class_Oless__eq(_654286, _654292, c_Groups_Oone__class_Oone(_654286)), -(c_Orderings_Oord__class_Oless__eq(_654286, hAPP(hAPP(c_Power_Opower__class_Opower(_654286), _654292), _654290), hAPP(hAPP(c_Power_Opower__class_Opower(_654286), _654292), _654288)))], (12352 ^ _319074) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (7454 ^ _319074) ^ [_572421, _572423, _572425] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _572421), 7457 ^ _319074 : [(7464 ^ _319074) ^ [] : [_572423 = _572425, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _572421), _572423) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _572421), _572425))], (7458 ^ _319074) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _572421), _572423) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _572421), _572425), -(_572423 = _572425)]]], (630 ^ _319074) ^ [_338004, _338006] : [-(class_Rings_Ocomm__semiring__0(_338004)), _338006 = _338004, class_Rings_Ocomm__semiring__0(_338006)], (7470 ^ _319074) ^ [_572949, _572951, _572953] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _572949), 7473 ^ _319074 : [(7480 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _572951, _572953), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _572949), _572951), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _572949), _572953)))], (7474 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _572949), _572951), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _572949), _572953)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _572951, _572953))]]], (2146 ^ _319074) ^ [_389847, _389849, _389851, _389853] : [class_Orderings_Opreorder(_389847), c_Orderings_Oord__class_Oless(_389847, _389849, _389851), c_Orderings_Oord__class_Oless(_389847, _389851, _389853), -(c_Orderings_Oord__class_Oless(_389847, _389849, _389853))], (9596 ^ _319074) ^ [_648023, _648025, _648027, _648029] : [class_Rings_Olinordered__semidom(_648023), c_Orderings_Oord__class_Oless(_648023, hAPP(hAPP(c_Power_Opower__class_Opower(_648023), _648025), _648027), hAPP(hAPP(c_Power_Opower__class_Opower(_648023), _648029), _648027)), c_Orderings_Oord__class_Oless__eq(_648023, c_Groups_Ozero__class_Ozero(_648023), _648029), -(c_Orderings_Oord__class_Oless(_648023, _648025, _648029))], (10083 ^ _319074) ^ [_664529, _664531] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _664529, c_Groups_Oone__class_Oone(tc_Int_Oint)), _664531), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _664529, _664531))], (720 ^ _319074) ^ [_340659, _340661] : [-(class_Groups_Oab__group__add(_340659)), _340661 = _340659, class_Groups_Oab__group__add(_340661)], (460 ^ _319074) ^ [_332989, _332991] : [-(class_Rings_Oordered__semiring(_332989)), _332991 = _332989, class_Rings_Oordered__semiring(_332991)], (4051 ^ _319074) ^ [_452895, _452897] : [class_Rings_Odivision__ring(_452895), -(c_Rings_Oinverse__class_Odivide(_452895, c_Groups_Ozero__class_Ozero(_452895), _452897) = c_Groups_Ozero__class_Ozero(_452895))], (5099 ^ _319074) ^ [_492029, _492031, _492033, _492035] : [class_Rings_Oordered__ring(_492029), c_Orderings_Oord__class_Oless__eq(_492029, _492031, _492033), c_Orderings_Oord__class_Oless__eq(_492029, _492035, c_Groups_Ozero__class_Ozero(_492029)), -(c_Orderings_Oord__class_Oless__eq(_492029, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_492029), _492033), _492035), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_492029), _492031), _492035)))], (11512 ^ _319074) ^ [_715366, _715368, _715370, _715372] : [class_Rings_Ocomm__ring(_715366), -(hAPP(c_Polynomial_Opoly(_715366, c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(_715366), _715368, _715370)), _715372) = c_Groups_Ominus__class_Ominus(_715366, hAPP(c_Polynomial_Opoly(_715366, _715368), _715372), hAPP(c_Polynomial_Opoly(_715366, _715370), _715372)))], (5727 ^ _319074) ^ [_512648, _512650, _512652, _512654] : [class_Rings_Olinordered__ring__strict(_512648), c_Orderings_Oord__class_Oless(_512648, _512650, _512652), c_Orderings_Oord__class_Oless(_512648, _512654, c_Groups_Ozero__class_Ozero(_512648)), -(c_Orderings_Oord__class_Oless(_512648, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_512648), _512654), _512652), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_512648), _512654), _512650)))], (12866 ^ _319074) ^ [_762903] : [class_Groups_Oab__group__add(_762903), -(class_Groups_Oab__group__add(tc_Polynomial_Opoly(_762903)))], (11970 ^ _319074) ^ [_734554, _734556, _734558, _734560, _734562, _734564] : [class_RealVector_Oreal__field(_734554), -(c_Rings_Oinverse__class_Odivide(_734554, c_Groups_Ominus__class_Ominus(_734554, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_734554), _734556), _734558), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_734554), _734560), _734562)), _734564) = c_Groups_Oplus__class_Oplus(_734554, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_734554), _734556), c_Rings_Oinverse__class_Odivide(_734554, c_Groups_Ominus__class_Ominus(_734554, _734558, _734562), _734564)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_734554), c_Rings_Oinverse__class_Odivide(_734554, c_Groups_Ominus__class_Ominus(_734554, _734556, _734560), _734564)), _734562)))], (5383 ^ _319074) ^ [_501289, _501291, _501293, _501295] : [class_Fields_Olinordered__field(_501289), c_Orderings_Oord__class_Oless(_501289, _501291, c_Groups_Ozero__class_Ozero(_501289)), 5390 ^ _319074 : [(5397 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_501289, _501295, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_501289), _501293), _501291)), -(c_Orderings_Oord__class_Oless(_501289, _501293, c_Rings_Oinverse__class_Odivide(_501289, _501295, _501291)))], (5391 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_501289, _501293, c_Rings_Oinverse__class_Odivide(_501289, _501295, _501291)), -(c_Orderings_Oord__class_Oless(_501289, _501295, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_501289), _501293), _501291)))]]], (8588 ^ _319074) ^ [_614051, _614053, _614055, _614057] : [class_Rings_Ocomm__semiring__1(_614051), -(hAPP(hAPP(c_Power_Opower__class_Opower(_614051), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_614051), _614053), _614055)), _614057) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_614051), hAPP(hAPP(c_Power_Opower__class_Opower(_614051), _614053), _614057)), hAPP(hAPP(c_Power_Opower__class_Opower(_614051), _614055), _614057)))], (12440 ^ _319074) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal))], (12296 ^ _319074) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (10852 ^ _319074) ^ [_691734, _691736, _691738] : [class_Rings_Oidom(_691734), 10855 ^ _319074 : [(10856 ^ _319074) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_691734), _691736), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(_691734), _691738), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_691736 = _691738), -(_691736 = c_Groups_Ouminus__class_Ouminus(_691734, _691738))], (10866 ^ _319074) ^ [] : [10867 ^ _319074 : [(10870 ^ _319074) ^ [] : [_691736 = c_Groups_Ouminus__class_Ouminus(_691734, _691738)], (10868 ^ _319074) ^ [] : [_691736 = _691738]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_691734), _691736), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(_691734), _691738), c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))]]], (12400 ^ _319074) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (1605 ^ _319074) ^ [_371191, _371193, _371195, _371197] : [class_Orderings_Oord(_371191), _371193 = _371195, c_Orderings_Oord__class_Oless__eq(_371191, _371195, _371197), -(c_Orderings_Oord__class_Oless__eq(_371191, _371193, _371197))], (6841 ^ _319074) ^ [_550020, _550022, _550024] : [class_Fields_Olinordered__field(_550020), c_Orderings_Oord__class_Oless__eq(_550020, _550022, c_Groups_Ozero__class_Ozero(_550020)), c_Orderings_Oord__class_Oless(_550020, _550024, c_Groups_Ozero__class_Ozero(_550020)), -(c_Orderings_Oord__class_Oless__eq(_550020, c_Groups_Ozero__class_Ozero(_550020), c_Rings_Oinverse__class_Odivide(_550020, _550022, _550024)))], (12416 ^ _319074) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (9128 ^ _319074) ^ [_631693, _631695] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _631693, _631695)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _631693, _631695), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _631695, _631693))], (6419 ^ _319074) ^ [_536495, _536497, _536499] : [class_Fields_Olinordered__field__inverse__zero(_536495), -(c_Groups_Oabs__class_Oabs(_536495, c_Rings_Oinverse__class_Odivide(_536495, _536497, _536499)) = c_Rings_Oinverse__class_Odivide(_536495, c_Groups_Oabs__class_Oabs(_536495, _536497), c_Groups_Oabs__class_Oabs(_536495, _536499)))], (12622 ^ _319074) ^ [] : [-(class_Rings_Odivision__ring(tc_Complex_Ocomplex))], (6163 ^ _319074) ^ [_527525, _527527, _527529, _527531] : [class_Rings_Olinordered__ring__strict(_527525), c_Orderings_Oord__class_Oless(_527525, _527527, c_Groups_Ozero__class_Ozero(_527525)), 6170 ^ _319074 : [(6177 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_527525, _527531, _527529), -(c_Orderings_Oord__class_Oless__eq(_527525, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_527525), _527527), _527529), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_527525), _527527), _527531)))], (6171 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_527525, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_527525), _527527), _527529), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_527525), _527527), _527531)), -(c_Orderings_Oord__class_Oless__eq(_527525, _527531, _527529))]]], (8400 ^ _319074) ^ [_607179, _607181] : [class_Rings_Ocomm__semiring__0(_607179), -(c_Polynomial_Osynthetic__div(_607179, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_607179)), _607181) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_607179)))], (1303 ^ _319074) ^ [_361586, _361588] : [class_Groups_Ocomm__monoid__add(_361586), -(c_Groups_Oplus__class_Oplus(_361586, c_Groups_Ozero__class_Ozero(_361586), _361588) = _361588)], (10071 ^ _319074) ^ [_664098] : [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), _664098), _664098), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _664098, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (1181 ^ _319074) ^ [_357506, _357508, _357510] : [class_Groups_Oordered__ab__group__add__abs(_357506), c_Orderings_Oord__class_Oless__eq(_357506, c_Groups_Oabs__class_Oabs(_357506, _357508), _357510), -(c_Orderings_Oord__class_Oless__eq(_357506, _357508, _357510))], (11812 ^ _319074) ^ [_727757, _727759, _727761] : [class_Groups_Ogroup__add(_727757), -(c_Groups_Ominus__class_Ominus(_727757, c_Groups_Oplus__class_Oplus(_727757, _727759, _727761), _727761) = _727759)], (8870 ^ _319074) ^ [_623550, _623552, _623554] : [class_Rings_Ocomm__semiring__1(_623550), 8875 ^ _319074 : [(8878 ^ _319074) ^ [] : [_623554 = c_Groups_Oone__class_Oone(_623550)], (8876 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _623552)]], -(c_Rings_Odvd__class_Odvd(_623550, _623554, hAPP(hAPP(c_Power_Opower__class_Opower(_623550), _623554), _623552)))], (12664 ^ _319074) ^ [] : [-(class_Groups_Oone(tc_Complex_Ocomplex))], (12568 ^ _319074) ^ [] : [-(class_Fields_Ofield(tc_RealDef_Oreal))], (12474 ^ _319074) ^ [] : [-(class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal))], (11478 ^ _319074) ^ [_713594, _713596] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _713594, _713596), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _713594, _713596))], (2320 ^ _319074) ^ [_395356, _395358, _395360] : [class_Groups_Oordered__ab__group__add(_395356), 2323 ^ _319074 : [(2330 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_395356, _395360, _395358), -(c_Orderings_Oord__class_Oless(_395356, c_Groups_Ouminus__class_Ouminus(_395356, _395358), c_Groups_Ouminus__class_Ouminus(_395356, _395360)))], (2324 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_395356, c_Groups_Ouminus__class_Ouminus(_395356, _395358), c_Groups_Ouminus__class_Ouminus(_395356, _395360)), -(c_Orderings_Oord__class_Oless(_395356, _395360, _395358))]]], (10525 ^ _319074) ^ [_680153, _680155, _680157] : [class_Rings_Ocomm__semiring__1(_680153), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_680153), hAPP(hAPP(c_Power_Opower__class_Opower(_680153), _680155), _680157)), _680155) = hAPP(hAPP(c_Power_Opower__class_Opower(_680153), _680155), c_Nat_OSuc(_680157)))], (7202 ^ _319074) ^ [_563120, _563122, _563124] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _563120), 7205 ^ _319074 : [(7212 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _563122, _563124), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _563122), _563120), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _563124), _563120)))], (7206 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _563122), _563120), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _563124), _563120)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _563122, _563124))]]], (13028 ^ _319074) ^ [_768047, _768049] : [hBOOL(c_fequal(_768047, _768049)), -(_768047 = _768049)], (10734 ^ _319074) ^ [_687362, _687364] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _687362, _687364), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _687362, c_Nat_OSuc(_687364)))], (6685 ^ _319074) ^ [_544947, _544949] : [class_RealVector_Oreal__normed__vector(_544947), 6688 ^ _319074 : [(6695 ^ _319074) ^ [] : [_544949 = c_Groups_Ozero__class_Ozero(_544947), -(c_RealVector_Onorm__class_Onorm(_544947, _544949) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (6689 ^ _319074) ^ [] : [c_RealVector_Onorm__class_Onorm(_544947, _544949) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(_544949 = c_Groups_Ozero__class_Ozero(_544947))]]], (2522 ^ _319074) ^ [_401844] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _401844, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _401844) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _401844))], (200 ^ _319074) ^ [_325319, _325321] : [-(class_Fields_Ofield(_325319)), _325321 = _325319, class_Fields_Ofield(_325321)], (12194 ^ _319074) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint))], (12788 ^ _319074) ^ [_760433] : [class_Rings_Olinordered__idom(_760433), -(class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(_760433)))], (10151 ^ _319074) ^ [_666746] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _666746), _666746) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (12380 ^ _319074) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (8490 ^ _319074) ^ [_610466] : [class_RealVector_Oreal__normed__algebra__1(_610466), -(c_Groups_Osgn__class_Osgn(_610466, c_Groups_Oone__class_Oone(_610466)) = c_Groups_Oone__class_Oone(_610466))], (10471 ^ _319074) ^ [_677771, _677773] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _677771), _677773) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _677773), _677771))], (7228 ^ _319074) ^ [_563971, _563973, _563975] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _563971), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _563973, _563975), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _563971), _563973), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _563971), _563975)))], (4825 ^ _319074) ^ [_483041, _483043, _483045, _483047] : [class_Fields_Ofield__inverse__zero(_483041), -(_483043 = c_Groups_Ozero__class_Ozero(_483041)), -(c_Rings_Oinverse__class_Odivide(_483041, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_483041), _483043), _483045), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_483041), _483043), _483047)) = c_Rings_Oinverse__class_Odivide(_483041, _483045, _483047))], (10227 ^ _319074) ^ [_669407, _669409] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_669407), c_Nat_OSuc(_669409)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _669407, _669409))], (4527 ^ _319074) ^ [_470496, _470498, _470500] : [class_RealVector_Oreal__normed__algebra(_470496), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_470496), _470498), c_Groups_Ouminus__class_Ouminus(_470496, _470500)) = c_Groups_Ouminus__class_Ouminus(_470496, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_470496), _470498), _470500)))], (11004 ^ _319074) ^ [_696711] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _696711))], (5315 ^ _319074) ^ [_499011, _499013, _499015, _499017] : [class_Fields_Olinordered__field(_499011), c_Orderings_Oord__class_Oless(_499011, c_Groups_Ozero__class_Ozero(_499011), _499013), 5322 ^ _319074 : [(5329 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_499011, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_499011), _499015), _499013), _499017), -(c_Orderings_Oord__class_Oless(_499011, _499015, c_Rings_Oinverse__class_Odivide(_499011, _499017, _499013)))], (5323 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_499011, _499015, c_Rings_Oinverse__class_Odivide(_499011, _499017, _499013)), -(c_Orderings_Oord__class_Oless(_499011, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_499011), _499015), _499013), _499017))]]], (1876 ^ _319074) ^ [_380358, _380360] : [class_Groups_Ocomm__monoid__add(_380358), -(c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_380358), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_380358)), _380360) = _380360)], (7630 ^ _319074) ^ [_579635] : [class_RealVector_Oreal__normed__algebra(_579635), 7634 ^ _319074 : [(7637 ^ _319074) ^ [_579964, _579966] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_579635, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_579635), _579966), _579964)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_579635, _579966)), c_RealVector_Onorm__class_Onorm(_579635, _579964))), 7633 ^ [_579635])))], (7635 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 7633 ^ [_579635]))]]], (9402 ^ _319074) ^ [_640815, _640817, _640819, _640821] : [class_Fields_Ofield__inverse__zero(_640815), -(hAPP(hAPP(c_Power_Opower__class_Opower(_640815), c_Rings_Oinverse__class_Odivide(_640815, _640817, _640819)), _640821) = c_Rings_Oinverse__class_Odivide(_640815, hAPP(hAPP(c_Power_Opower__class_Opower(_640815), _640817), _640821), hAPP(hAPP(c_Power_Opower__class_Opower(_640815), _640819), _640821)))], (10301 ^ _319074) ^ [_671764, _671766] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_671764), _671766), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _671764, _671766))], (2968 ^ _319074) ^ [_416182, _416184, _416186] : [class_Orderings_Opreorder(_416182), 2971 ^ _319074 : [(2980 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_416182, _416184, _416186)), c_Orderings_Oord__class_Oless__eq(_416182, _416184, _416186), -(c_Orderings_Oord__class_Oless__eq(_416182, _416186, _416184))], (2972 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_416182, _416184, _416186), 2975 ^ _319074 : [(2978 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_416182, _416186, _416184)], (2976 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_416182, _416184, _416186))]]]]], (2474 ^ _319074) ^ [_400136, _400138] : [class_Groups_Ogroup__add(_400136), -(c_Groups_Ouminus__class_Ouminus(_400136, c_Groups_Ouminus__class_Ouminus(_400136, _400138)) = _400138)], (4177 ^ _319074) ^ [_457197, _457199, _457201] : [class_Rings_Olinordered__idom(_457197), -(_457199 = _457201), -(c_Orderings_Oord__class_Oless(_457197, _457199, _457201)), -(c_Orderings_Oord__class_Oless(_457197, _457201, _457199))], (6711 ^ _319074) ^ [_545782, _545784] : [class_RealVector_Oreal__normed__vector(_545782), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_545782, _545784)))], (6389 ^ _319074) ^ [_535227, _535229, _535231, _535233] : [class_RealVector_Oreal__normed__field(_535227), -(c_Rings_Oinverse__class_Odivide(_535227, c_Groups_Oplus__class_Oplus(_535227, _535229, _535231), _535233) = c_Groups_Oplus__class_Oplus(_535227, c_Rings_Oinverse__class_Odivide(_535227, _535229, _535233), c_Rings_Oinverse__class_Odivide(_535227, _535231, _535233)))], (2300 ^ _319074) ^ [_394765, _394767, _394769] : [class_Orderings_Olinorder(_394765), -(c_Orderings_Oord__class_Oless(_394765, _394767, _394769)), 2307 ^ _319074 : [(2314 ^ _319074) ^ [] : [_394769 = _394767, c_Orderings_Oord__class_Oless(_394765, _394769, _394767)], (2308 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_394765, _394769, _394767)), -(_394769 = _394767)]]], (9204 ^ _319074) ^ [_634036, _634038] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _634036, _634038), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _634038, _634036)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _634038, _634036), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _634036, _634038))], (9072 ^ _319074) ^ [_629983, _629985, _629987] : [_629983 = _629985, 9083 ^ _319074 : [(9086 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _629987, _629983)], (9084 ^ _319074) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _629983, _629987))]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _629985, _629987), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _629987, _629985))], (8564 ^ _319074) ^ [_613009, _613011] : [class_Rings_Olinordered__idom(_613009), -(c_Groups_Osgn__class_Osgn(_613009, c_Groups_Osgn__class_Osgn(_613009, _613011)) = c_Groups_Osgn__class_Osgn(_613009, _613011))], (11662 ^ _319074) ^ [_721679, _721681] : [class_Rings_Oring__1(_721679), -(c_Groups_Ominus__class_Ominus(_721679, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_721679), _721681), _721681), c_Groups_Oone__class_Oone(_721679)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_721679), c_Groups_Oplus__class_Oplus(_721679, _721681, c_Groups_Oone__class_Oone(_721679))), c_Groups_Ominus__class_Ominus(_721679, _721681, c_Groups_Oone__class_Oone(_721679))))], (340 ^ _319074) ^ [_329449, _329451] : [-(class_Rings_Olinordered__ring__strict(_329449)), _329451 = _329449, class_Rings_Olinordered__ring__strict(_329451)], (9114 ^ _319074) ^ [_631288, _631290] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _631288, _631290), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _631290, _631288)), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _631290, _631288), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _631288, _631290))], (250 ^ _319074) ^ [_326794, _326796] : [-(class_Rings_Olinordered__semiring__1__strict(_326794)), _326796 = _326794, class_Rings_Olinordered__semiring__1__strict(_326796)], (12554 ^ _319074) ^ [] : [-(class_Rings_Osemiring(tc_RealDef_Oreal))], (9841 ^ _319074) ^ [_656426, _656428] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _656426), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _656428, _656426), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _656428))], (6285 ^ _319074) ^ [_531572, _531574, _531576, _531578] : [class_Rings_Olinordered__semiring__strict(_531572), c_Orderings_Oord__class_Oless(_531572, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_531572), _531574), _531576), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_531572), _531578), _531576)), c_Orderings_Oord__class_Oless__eq(_531572, c_Groups_Ozero__class_Ozero(_531572), _531576), -(c_Orderings_Oord__class_Oless(_531572, _531574, _531578))], (12438 ^ _319074) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal))], (1864 ^ _319074) ^ [_379918, _379920] : [class_Rings_Ocomm__semiring__1(_379918), -(c_Groups_Oplus__class_Oplus(_379918, _379920, c_Groups_Ozero__class_Ozero(_379918)) = _379920)], (12600 ^ _319074) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex))], (570 ^ _319074) ^ [_336234, _336236] : [-(class_Groups_Omonoid__add(_336234)), _336236 = _336234, class_Groups_Omonoid__add(_336236)], (480 ^ _319074) ^ [_333579, _333581] : [-(class_Rings_Ono__zero__divisors(_333579)), _333581 = _333579, class_Rings_Ono__zero__divisors(_333581)], (11074 ^ _319074) ^ [_699517, _699519, _699521] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _699517, _699519), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _699519, _699521), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _699517, _699521))], (780 ^ _319074) ^ [_342429, _342431] : [-(class_Rings_Oidom(_342429)), _342431 = _342429, class_Rings_Oidom(_342431)], (7999 ^ _319074) ^ [] : [-(c_Complex_Oexpi(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))], (2540 ^ _319074) ^ [_402593, _402595] : [class_Groups_Oabs__if(_402593), 2543 ^ _319074 : [(2550 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_402593, _402595, c_Groups_Ozero__class_Ozero(_402593))), -(c_Groups_Oabs__class_Oabs(_402593, _402595) = _402595)], (2544 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_402593, _402595, c_Groups_Ozero__class_Ozero(_402593)), -(c_Groups_Oabs__class_Oabs(_402593, _402595) = c_Groups_Ouminus__class_Ouminus(_402593, _402595))]]], (4535 ^ _319074) ^ [_470880, _470882, _470884, _470886, _470888] : [class_Rings_Ocomm__semiring__1(_470880), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_470880), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_470880), _470882), _470884)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_470880), _470886), _470888)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_470880), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_470880), _470882), _470886)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_470880), _470884), _470888)))], (6431 ^ _319074) ^ [_536983, _536985, _536987] : [class_Fields_Olinordered__field__inverse__zero(_536983), 6434 ^ _319074 : [(6449 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_536983, c_Groups_Ozero__class_Ozero(_536983), c_Rings_Oinverse__class_Odivide(_536983, _536985, _536987))), 6450 ^ _319074 : [(6457 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_536983, _536985, c_Groups_Ozero__class_Ozero(_536983)), c_Orderings_Oord__class_Oless__eq(_536983, _536987, c_Groups_Ozero__class_Ozero(_536983))], (6451 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_536983, c_Groups_Ozero__class_Ozero(_536983), _536985), c_Orderings_Oord__class_Oless__eq(_536983, c_Groups_Ozero__class_Ozero(_536983), _536987)]]], (6435 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_536983, c_Groups_Ozero__class_Ozero(_536983), c_Rings_Oinverse__class_Odivide(_536983, _536985, _536987)), 6440 ^ _319074 : [(6443 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_536983, c_Groups_Ozero__class_Ozero(_536983), _536987))], (6441 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_536983, c_Groups_Ozero__class_Ozero(_536983), _536985))]], 6444 ^ _319074 : [(6447 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_536983, _536987, c_Groups_Ozero__class_Ozero(_536983)))], (6445 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_536983, _536985, c_Groups_Ozero__class_Ozero(_536983)))]]]]], (1331 ^ _319074) ^ [_362491] : [class_Groups_Oordered__ab__group__add__abs(_362491), -(c_Groups_Oabs__class_Oabs(_362491, c_Groups_Ozero__class_Ozero(_362491)) = c_Groups_Ozero__class_Ozero(_362491))], (4431 ^ _319074) ^ [_466165, _466167, _466169] : [_466165 = _466169, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _466165, _466167) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _466169, _466167))], (1738 ^ _319074) ^ [_375659, _375661, _375663, _375665] : [class_Groups_Ocancel__semigroup__add(_375659), 1741 ^ _319074 : [(1748 ^ _319074) ^ [] : [_375661 = _375665, -(c_Groups_Oplus__class_Oplus(_375659, _375661, _375663) = c_Groups_Oplus__class_Oplus(_375659, _375665, _375663))], (1742 ^ _319074) ^ [] : [c_Groups_Oplus__class_Oplus(_375659, _375661, _375663) = c_Groups_Oplus__class_Oplus(_375659, _375665, _375663), -(_375661 = _375665)]]], (12654 ^ _319074) ^ [] : [-(class_Fields_Ofield(tc_Complex_Ocomplex))], (12818 ^ _319074) ^ [_761383] : [class_Rings_Olinordered__idom(_761383), -(class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(_761383)))], (4425 ^ _319074) ^ [_465981, _465983, _465985] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _465981, _465983) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _465985, _465983), -(_465981 = _465985)], (990 ^ _319074) ^ [_350318, _350320, _350322, _350324, _350326, _350328] : [-(c_Polynomial_OpCons(_350328, _350324, _350320) = c_Polynomial_OpCons(_350326, _350322, _350318)), _350328 = _350326, _350324 = _350322, _350320 = _350318], (12562 ^ _319074) ^ [] : [-(class_Groups_Oabs__if(tc_RealDef_Oreal))], (12314 ^ _319074) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (7727 ^ _319074) ^ [_583986] : [class_Rings_Ozero__neq__one(_583986), c_Groups_Ozero__class_Ozero(_583986) = c_Groups_Oone__class_Oone(_583986)], (3914 ^ _319074) ^ [_447771, _447773, _447775] : [3915 ^ _319074 : [(3918 ^ _319074) ^ [] : [hBOOL(hAPP(hAPP(_447775, _447773), _447771))], (3916 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _447771, _447773))]], 3921 ^ _319074 : [(3924 ^ _319074) ^ [] : [hBOOL(hAPP(hAPP(_447775, _447773), _447771))], (3922 ^ _319074) ^ [] : [-(_447771 = _447773)]], 3927 ^ _319074 : [(3930 ^ _319074) ^ [] : [hBOOL(hAPP(hAPP(_447775, _447773), _447771))], (3928 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _447773, _447771))]], -(hBOOL(hAPP(hAPP(_447775, _447773), _447771)))], (12980 ^ _319074) ^ [_766513] : [class_Rings_Ocomm__ring__1(_766513), -(class_Rings_Oring__1(tc_Polynomial_Opoly(_766513)))], (6761 ^ _319074) ^ [_547490, _547492, _547494, _547496, _547498] : [class_Fields_Olinordered__field(_547490), c_Orderings_Oord__class_Oless(_547490, c_Groups_Ozero__class_Ozero(_547490), _547492), c_Orderings_Oord__class_Oless__eq(_547490, _547492, _547494), c_Orderings_Oord__class_Oless(_547490, c_Groups_Ozero__class_Ozero(_547490), _547496), c_Orderings_Oord__class_Oless(_547490, _547496, _547498), -(c_Orderings_Oord__class_Oless(_547490, c_Rings_Oinverse__class_Odivide(_547490, _547492, _547498), c_Rings_Oinverse__class_Odivide(_547490, _547494, _547496)))], (12560 ^ _319074) ^ [] : [-(class_Groups_Osgn__if(tc_RealDef_Oreal))], (12704 ^ _319074) ^ [_757773] : [class_Rings_Olinordered__idom(_757773), -(class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(_757773)))], (7871 ^ _319074) ^ [_588948] : [class_Rings_Olinordered__semidom(_588948), -(c_Orderings_Oord__class_Oless(_588948, c_Groups_Ozero__class_Ozero(_588948), c_Groups_Oone__class_Oone(_588948)))], (8168 ^ _319074) ^ [_599352, _599354, _599356] : [class_Rings_Ocomm__semiring__1(_599352), -(c_Rings_Odvd__class_Odvd(_599352, _599354, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_599352), _599356), _599354)))], (11568 ^ _319074) ^ [_717813, _717815, _717817, _717819, _717821] : [class_Groups_Oordered__ab__group__add__abs(_717813), -(c_Orderings_Oord__class_Oless__eq(_717813, c_Groups_Oabs__class_Oabs(_717813, c_Groups_Ominus__class_Ominus(_717813, c_Groups_Oplus__class_Oplus(_717813, _717815, _717817), c_Groups_Oplus__class_Oplus(_717813, _717819, _717821))), c_Groups_Oplus__class_Oplus(_717813, c_Groups_Oabs__class_Oabs(_717813, c_Groups_Ominus__class_Ominus(_717813, _717815, _717819)), c_Groups_Oabs__class_Oabs(_717813, c_Groups_Ominus__class_Ominus(_717813, _717817, _717821)))))], (1409 ^ _319074) ^ [_364961, _364963, _364965] : [class_Groups_Oordered__comm__monoid__add(_364961), c_Orderings_Oord__class_Oless__eq(_364961, c_Groups_Ozero__class_Ozero(_364961), _364963), c_Orderings_Oord__class_Oless__eq(_364961, c_Groups_Ozero__class_Ozero(_364961), _364965), -(c_Orderings_Oord__class_Oless__eq(_364961, c_Groups_Ozero__class_Ozero(_364961), c_Groups_Oplus__class_Oplus(_364961, _364963, _364965)))], (3098 ^ _319074) ^ [_420424, _420426, _420428, _420430] : [class_Groups_Oordered__cancel__ab__semigroup__add(_420424), c_Orderings_Oord__class_Oless(_420424, _420426, _420428), -(c_Orderings_Oord__class_Oless(_420424, c_Groups_Oplus__class_Oplus(_420424, _420426, _420430), c_Groups_Oplus__class_Oplus(_420424, _420428, _420430)))], (11518 ^ _319074) ^ [_715684, _715686, _715688, _715690, _715692] : [class_Groups_Oab__group__add(_715684), c_Groups_Ominus__class_Ominus(_715684, _715686, _715688) = c_Groups_Ominus__class_Ominus(_715684, _715690, _715692), 11525 ^ _319074 : [(11532 ^ _319074) ^ [] : [_715690 = _715692, -(_715686 = _715688)], (11526 ^ _319074) ^ [] : [_715686 = _715688, -(_715690 = _715692)]]], (600 ^ _319074) ^ [_337119, _337121] : [-(class_Rings_Omult__zero(_337119)), _337121 = _337119, class_Rings_Omult__zero(_337121)], (8752 ^ _319074) ^ [_619905, _619907] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _619905), 8755 ^ _319074 : [(8762 ^ _319074) ^ [] : [_619907 = 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), _619907), _619905), _619905))], (8756 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _619907), _619905), _619905), -(_619907 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (1521 ^ _319074) ^ [_368555, _368557, _368559] : [class_Orderings_Oorder(_368555), c_Orderings_Oord__class_Oless__eq(_368555, _368557, _368559), c_Orderings_Oord__class_Oless__eq(_368555, _368559, _368557), -(_368559 = _368557)], (2700 ^ _319074) ^ [_407645, _407647, _407649] : [class_Groups_Ogroup__add(_407645), -(c_Groups_Oplus__class_Oplus(_407645, _407647, c_Groups_Oplus__class_Oplus(_407645, c_Groups_Ouminus__class_Ouminus(_407645, _407647), _407649)) = _407649)], (6966 ^ _319074) ^ [_554421, _554423, _554425] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _554421), _554423) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _554421), _554425), -(_554423 = _554425), -(_554421 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (6465 ^ _319074) ^ [_538020, _538022, _538024] : [class_Fields_Olinordered__field__inverse__zero(_538020), 6468 ^ _319074 : [(6483 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_538020, c_Rings_Oinverse__class_Odivide(_538020, _538022, _538024), c_Groups_Ozero__class_Ozero(_538020))), 6484 ^ _319074 : [(6491 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_538020, _538022, c_Groups_Ozero__class_Ozero(_538020)), c_Orderings_Oord__class_Oless__eq(_538020, c_Groups_Ozero__class_Ozero(_538020), _538024)], (6485 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_538020, c_Groups_Ozero__class_Ozero(_538020), _538022), c_Orderings_Oord__class_Oless__eq(_538020, _538024, c_Groups_Ozero__class_Ozero(_538020))]]], (6469 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_538020, c_Rings_Oinverse__class_Odivide(_538020, _538022, _538024), c_Groups_Ozero__class_Ozero(_538020)), 6474 ^ _319074 : [(6477 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_538020, _538024, c_Groups_Ozero__class_Ozero(_538020)))], (6475 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_538020, c_Groups_Ozero__class_Ozero(_538020), _538022))]], 6478 ^ _319074 : [(6481 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_538020, c_Groups_Ozero__class_Ozero(_538020), _538024))], (6479 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_538020, _538022, c_Groups_Ozero__class_Ozero(_538020)))]]]]], (12476 ^ _319074) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal))], (9414 ^ _319074) ^ [_641399, _641401, _641403, _641405] : [class_Groups_Omonoid__mult(_641399), -(hAPP(hAPP(c_Power_Opower__class_Opower(_641399), _641401), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _641403), _641405)) = hAPP(hAPP(c_Power_Opower__class_Opower(_641399), hAPP(hAPP(c_Power_Opower__class_Opower(_641399), _641401), _641403)), _641405))], (3802 ^ _319074) ^ [_443767, _443769] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _443767, _443769), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _443767, _443769))], (12532 ^ _319074) ^ [] : [-(class_Orderings_Opreorder(tc_RealDef_Oreal))], (12454 ^ _319074) ^ [] : [-(class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal))], (8356 ^ _319074) ^ [_605711, _605713, _605715, _605717] : [class_Rings_Oidom(_605711), 8359 ^ _319074 : [(8360 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(_605711, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_605711), _605713), _605715), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_605711), _605713), _605717)), -(_605713 = c_Groups_Ozero__class_Ozero(_605711)), -(c_Rings_Odvd__class_Odvd(_605711, _605715, _605717))], (8370 ^ _319074) ^ [] : [8371 ^ _319074 : [(8374 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(_605711, _605715, _605717)], (8372 ^ _319074) ^ [] : [_605713 = c_Groups_Ozero__class_Ozero(_605711)]], -(c_Rings_Odvd__class_Odvd(_605711, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_605711), _605713), _605715), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_605711), _605713), _605717)))]]], (4033 ^ _319074) ^ [_452150, _452152] : [4034 ^ _319074 : [(4035 ^ _319074) ^ [_452225] : [_452152 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _452150, _452225)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _452150, _452152))], (1132 ^ _319074) ^ [_355437, _355439, _355441, _355443] : [-(c_Groups_Oabs__class_Oabs(_355443, _355439) = c_Groups_Oabs__class_Oabs(_355441, _355437)), _355443 = _355441, _355439 = _355437], (8037 ^ _319074) ^ [_594400] : [class_Rings_Olinordered__semidom(_594400), -(c_Orderings_Oord__class_Oless(_594400, c_Groups_Ozero__class_Ozero(_594400), c_Groups_Oplus__class_Oplus(_594400, c_Groups_Oone__class_Oone(_594400), c_Groups_Oone__class_Oone(_594400))))], (4145 ^ _319074) ^ [_456106, _456108, _456110] : [class_Rings_Odivision__ring(_456106), -(_456108 = c_Groups_Ozero__class_Ozero(_456106)), -(c_Groups_Ouminus__class_Ouminus(_456106, c_Rings_Oinverse__class_Odivide(_456106, _456110, _456108)) = c_Rings_Oinverse__class_Odivide(_456106, _456110, c_Groups_Ouminus__class_Ouminus(_456106, _456108)))], (13040 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_mzh, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v_mazh, v_ma)))], (4685 ^ _319074) ^ [_477136, _477138, _477140, _477142] : [class_Rings_Ocomm__semiring__1(_477136), -(c_Groups_Oplus__class_Oplus(_477136, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_477136), _477138), _477140), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_477136), _477142), _477140)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_477136), c_Groups_Oplus__class_Oplus(_477136, _477138, _477142)), _477140))], (6958 ^ _319074) ^ [_554060, _554062, _554064] : [6959 ^ _319074 : [(6962 ^ _319074) ^ [] : [_554062 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (6960 ^ _319074) ^ [] : [_554060 = _554064]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _554060), _554062) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _554064), _554062))], (8952 ^ _319074) ^ [_626167, _626169] : [8959 ^ _319074 : [(8962 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _626169, _626167)], (8960 ^ _319074) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _626167, _626169))]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _626167, _626169), -(_626167 = _626169)], (11106 ^ _319074) ^ [_700587, _700589] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _700587, _700589), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _700587, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _700589)))], (12192 ^ _319074) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat))], (12398 ^ _319074) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (9885 ^ _319074) ^ [_657998] : [_657998 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _657998) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (2906 ^ _319074) ^ [_414279, _414281, _414283] : [class_Orderings_Olinorder(_414279), -(c_Orderings_Oord__class_Oless(_414279, _414281, _414283)), 2913 ^ _319074 : [(2920 ^ _319074) ^ [] : [_414281 = _414283, -(c_Orderings_Oord__class_Oless__eq(_414279, _414281, _414283))], (2914 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_414279, _414281, _414283), -(_414281 = _414283)]]], (12540 ^ _319074) ^ [] : [-(class_Groups_Omonoid__add(tc_RealDef_Oreal))], (12634 ^ _319074) ^ [] : [-(class_Groups_Omonoid__add(tc_Complex_Ocomplex))], (1619 ^ _319074) ^ [_371623, _371625, _371627] : [class_Orderings_Oorder(_371623), c_Orderings_Oord__class_Oless__eq(_371623, _371625, _371627), 1626 ^ _319074 : [(1633 ^ _319074) ^ [] : [_371627 = _371625, -(c_Orderings_Oord__class_Oless__eq(_371623, _371627, _371625))], (1627 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_371623, _371627, _371625), -(_371627 = _371625)]]], (9262 ^ _319074) ^ [_635755, _635757] : [9263 ^ _319074 : [(9266 ^ _319074) ^ [] : [_635757 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (9264 ^ _319074) ^ [] : [-(_635755 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]], -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), c_Groups_Oabs__class_Oabs(tc_Int_Oint, _635755)), _635757)))], (420 ^ _319074) ^ [_331809, _331811] : [-(class_Rings_Olinordered__semidom(_331809)), _331811 = _331809, class_Rings_Olinordered__semidom(_331811)], (1223 ^ _319074) ^ [_358947, _358949, _358951, _358953] : [class_Groups_Oordered__ab__semigroup__add(_358947), c_Orderings_Oord__class_Oless__eq(_358947, _358949, _358951), -(c_Orderings_Oord__class_Oless__eq(_358947, c_Groups_Oplus__class_Oplus(_358947, _358949, _358953), c_Groups_Oplus__class_Oplus(_358947, _358951, _358953)))], (7989 ^ _319074) ^ [_592963, _592965] : [_592963 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _592963), _592965), -(_592965 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_592963 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9162 ^ _319074) ^ [_632713, _632715] : [_632715 = _632713, c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _632713, _632715), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _632715, _632713))], (2718 ^ _319074) ^ [_408433, _408435, _408437, _408439] : [class_Orderings_Oord(_408433), 2721 ^ _319074 : [(2730 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_fun(_408435, _408433), _408437, _408439)), c_Orderings_Oord__class_Oless__eq(tc_fun(_408435, _408433), _408437, _408439), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_408435, _408433), _408439, _408437))], (2722 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(tc_fun(_408435, _408433), _408437, _408439), 2725 ^ _319074 : [(2728 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_408435, _408433), _408439, _408437)], (2726 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_fun(_408435, _408433), _408437, _408439))]]]]], (11918 ^ _319074) ^ [_732446, _732448] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _732446, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _732448, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _732446, _732448))], (390 ^ _319074) ^ [_330924, _330926] : [-(class_Groups_Ocancel__comm__monoid__add(_330924)), _330926 = _330924, class_Groups_Ocancel__comm__monoid__add(_330926)], (12530 ^ _319074) ^ [] : [-(class_Rings_Oordered__ring(tc_RealDef_Oreal))], (12666 ^ _319074) ^ [] : [-(class_Rings_Odvd(tc_Complex_Ocomplex))], (7148 ^ _319074) ^ [_561228, _561230, _561232] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _561228), _561230), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _561232), _561230)), 7151 ^ _319074 : [(7154 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _561228, _561232))], (7152 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _561230))]]], (7002 ^ _319074) ^ [_555587] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _555587), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10407 ^ _319074) ^ [_675588, _675590] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, _675588, _675590)), -(_675588 = _675590), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _675590, _675588))], (12448 ^ _319074) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal))], (2132 ^ _319074) ^ [_389399, _389401, _389403, _389405] : [class_Orderings_Oorder(_389399), c_Orderings_Oord__class_Oless(_389399, _389401, _389403), c_Orderings_Oord__class_Oless(_389399, _389405, _389401), -(c_Orderings_Oord__class_Oless(_389399, _389405, _389403))], (12146 ^ _319074) ^ [_741712] : [-(c_Groups_Ominus__class_Ominus(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _741712) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (9816 ^ _319074) ^ [_655548, _655550, _655552, _655554] : [class_Rings_Olinordered__semidom(_655548), c_Orderings_Oord__class_Oless(_655548, c_Groups_Oone__class_Oone(_655548), _655550), c_Orderings_Oord__class_Oless__eq(_655548, hAPP(hAPP(c_Power_Opower__class_Opower(_655548), _655550), _655552), hAPP(hAPP(c_Power_Opower__class_Opower(_655548), _655550), _655554)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _655552, _655554))], (12466 ^ _319074) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal))], (12260 ^ _319074) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (10397 ^ _319074) ^ [_675210, _675212] : [_675210 = _675212, -(c_Nat_OSuc(_675210) = c_Nat_OSuc(_675212))], (10385 ^ _319074) ^ [_674793, _674795] : [c_Nat_OSuc(_674793) = c_Nat_OSuc(_674795), -(_674793 = _674795)], (8998 ^ _319074) ^ [_627614, _627616] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _627614, _627616), 9003 ^ _319074 : [(9006 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _627616, _627614)], (9004 ^ _319074) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _627614, _627616))]], -(_627614 = _627616)], (8514 ^ _319074) ^ [_611391, _611393, _611395] : [class_RealVector_Oreal__normed__algebra__1(_611391), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_611391, hAPP(hAPP(c_Power_Opower__class_Opower(_611391), _611393), _611395)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_611391, _611393)), _611395)))], (11846 ^ _319074) ^ [_729259, _729261, _729263] : [class_Groups_Oordered__ab__group__add__abs(_729259), -(c_Orderings_Oord__class_Oless__eq(_729259, c_Groups_Oabs__class_Oabs(_729259, c_Groups_Ominus__class_Ominus(_729259, c_Groups_Oabs__class_Oabs(_729259, _729261), c_Groups_Oabs__class_Oabs(_729259, _729263))), c_Groups_Oabs__class_Oabs(_729259, c_Groups_Ominus__class_Ominus(_729259, _729261, _729263))))], (12322 ^ _319074) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (4271 ^ _319074) ^ [_460289] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _460289), _460289 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (680 ^ _319074) ^ [_339479, _339481] : [-(class_Rings_Olinordered__idom(_339479)), _339481 = _339479, class_Rings_Olinordered__idom(_339481)], (12490 ^ _319074) ^ [] : [-(class_Rings_Olinordered__semiring(tc_RealDef_Oreal))], (6994 ^ _319074) ^ [_555318, _555320] : [6995 ^ _319074 : [(6998 ^ _319074) ^ [] : [_555320 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (6996 ^ _319074) ^ [] : [_555318 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _555318), _555320) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (8103 ^ _319074) ^ [_596920, _596922, _596924] : [class_Fields_Olinordered__field__inverse__zero(_596920), 8109 ^ _319074 : [(8114 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_596920, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_596920), 8108 ^ [_596920, _596922, _596924]), _596922), _596924)], (8112 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_596920, 8108 ^ [_596920, _596922, _596924], c_Groups_Oone__class_Oone(_596920)))], (8110 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_596920, c_Groups_Ozero__class_Ozero(_596920), 8108 ^ [_596920, _596922, _596924]))]], -(c_Orderings_Oord__class_Oless__eq(_596920, _596922, _596924))], (12101 ^ _319074) ^ [_740152, _740154, _740156] : [hBOOL(hAPP(_740152, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _740154, _740156))), 12104 ^ _319074 : [(12111 ^ _319074) ^ [_740484] : [_740154 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _740156, _740484), -(hBOOL(hAPP(_740152, _740484)))], (12105 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _740154, _740156), -(hBOOL(hAPP(_740152, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (12902 ^ _319074) ^ [_764043] : [class_Rings_Ocomm__ring__1(_764043), -(class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(_764043)))], (12246 ^ _319074) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (4163 ^ _319074) ^ [_456771, _456773, _456775] : [class_Rings_Olinordered__idom(_456771), c_Polynomial_Opos__poly(_456771, _456773), c_Polynomial_Opos__poly(_456771, _456775), -(c_Polynomial_Opos__poly(_456771, c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_456771), _456773, _456775)))], (4323 ^ _319074) ^ [_462157, _462159, _462161] : [class_RealVector_Oreal__normed__vector(_462157), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_462157, c_Groups_Oplus__class_Oplus(_462157, _462159, _462161)), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_462157, _462159), c_RealVector_Onorm__class_Onorm(_462157, _462161))))], (12652 ^ _319074) ^ [] : [-(class_Groups_Ominus(tc_Complex_Ocomplex))], (790 ^ _319074) ^ [_342724, _342726] : [-(class_Groups_Oone(_342724)), _342726 = _342724, class_Groups_Oone(_342726)], (12626 ^ _319074) ^ [] : [-(class_Groups_Oab__group__add(tc_Complex_Ocomplex))], (7052 ^ _319074) ^ [_557502, _557504, _557506] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _557502, _557504), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _557506), _557502), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _557506), _557504)))], (12480 ^ _319074) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal))], (6395 ^ _319074) ^ [_535501, _535503, _535505] : [class_Fields_Ofield__inverse__zero(_535501), -(c_Groups_Ouminus__class_Ouminus(_535501, c_Rings_Oinverse__class_Odivide(_535501, _535503, _535505)) = c_Rings_Oinverse__class_Odivide(_535501, _535503, c_Groups_Ouminus__class_Ouminus(_535501, _535505)))], (10922 ^ _319074) ^ [_693997, _693999, _694001] : [-(_693997 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 10925 ^ _319074 : [(10932 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _693999, _694001), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _693999), _693997), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _694001), _693997)))], (10926 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _693999), _693997), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _694001), _693997)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _693999, _694001))]]], (1275 ^ _319074) ^ [_360664, _360666] : [class_Groups_Ocomm__monoid__add(_360664), -(c_Groups_Oplus__class_Oplus(_360664, _360666, c_Groups_Ozero__class_Ozero(_360664)) = _360666)], (1207 ^ _319074) ^ [_358399, _358401, _358403, _358405] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_358399), 1210 ^ _319074 : [(1217 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_358399, _358403, _358405), -(c_Orderings_Oord__class_Oless__eq(_358399, c_Groups_Oplus__class_Oplus(_358399, _358401, _358403), c_Groups_Oplus__class_Oplus(_358399, _358401, _358405)))], (1211 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_358399, c_Groups_Oplus__class_Oplus(_358399, _358401, _358403), c_Groups_Oplus__class_Oplus(_358399, _358401, _358405)), -(c_Orderings_Oord__class_Oless__eq(_358399, _358403, _358405))]]], (4041 ^ _319074) ^ [_452478, _452480] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _452478, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _452480, _452478)))], (8258 ^ _319074) ^ [_602587, _602589, _602591] : [class_Rings_Olinordered__idom(_602587), c_Groups_Oabs__class_Oabs(_602587, _602589) = c_Groups_Oabs__class_Oabs(_602587, _602591), -(c_Rings_Odvd__class_Odvd(_602587, _602589, _602591))], (11648 ^ _319074) ^ [_721149, _721151, _721153, _721155, _721157] : [class_Fields_Ofield(_721149), -(_721151 = c_Groups_Ozero__class_Ozero(_721149)), -(_721153 = c_Groups_Ozero__class_Ozero(_721149)), -(c_Groups_Ominus__class_Ominus(_721149, c_Rings_Oinverse__class_Odivide(_721149, _721155, _721151), c_Rings_Oinverse__class_Odivide(_721149, _721157, _721153)) = c_Rings_Oinverse__class_Odivide(_721149, c_Groups_Ominus__class_Ominus(_721149, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_721149), _721155), _721153), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_721149), _721157), _721151)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_721149), _721151), _721153)))], (6651 ^ _319074) ^ [_543841, _543843, _543845, _543847] : [class_Fields_Olinordered__field(_543841), c_Orderings_Oord__class_Oless(_543841, _543843, _543845), c_Orderings_Oord__class_Oless(_543841, c_Groups_Ozero__class_Ozero(_543841), _543847), -(c_Orderings_Oord__class_Oless(_543841, c_Rings_Oinverse__class_Odivide(_543841, _543843, _543847), c_Rings_Oinverse__class_Odivide(_543841, _543845, _543847)))], (12974 ^ _319074) ^ [_766323] : [class_Rings_Olinordered__idom(_766323), -(class_Groups_Oabs__if(tc_Polynomial_Opoly(_766323)))], (7564 ^ _319074) ^ [_576723, _576725] : [class_RealVector_Oreal__normed__algebra(_576723), 7568 ^ _319074 : [(7571 ^ _319074) ^ [_577022] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_576723, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_576723), _576725), _577022)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_576723, _577022)), 7567 ^ [_576723, _576725])))], (7569 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 7567 ^ [_576723, _576725]))]]], (12402 ^ _319074) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (2646 ^ _319074) ^ [_405859, _405861, _405863] : [class_Groups_Oordered__ab__group__add(_405859), 2649 ^ _319074 : [(2656 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_405859, _405863, _405861), -(c_Orderings_Oord__class_Oless__eq(_405859, c_Groups_Ouminus__class_Ouminus(_405859, _405861), c_Groups_Ouminus__class_Ouminus(_405859, _405863)))], (2650 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_405859, c_Groups_Ouminus__class_Ouminus(_405859, _405861), c_Groups_Ouminus__class_Ouminus(_405859, _405863)), -(c_Orderings_Oord__class_Oless__eq(_405859, _405863, _405861))]]], (2556 ^ _319074) ^ [_403087, _403089] : [class_Groups_Oordered__ab__group__add__abs(_403087), c_Orderings_Oord__class_Oless(_403087, _403089, c_Groups_Ozero__class_Ozero(_403087)), -(c_Groups_Oabs__class_Oabs(_403087, _403089) = c_Groups_Ouminus__class_Ouminus(_403087, _403089))], (5947 ^ _319074) ^ [_520416, _520418, _520420, _520422] : [class_Fields_Olinordered__field__inverse__zero(_520416), 5950 ^ _319074 : [(5951 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_520416, c_Rings_Oinverse__class_Odivide(_520416, _520418, _520420), _520422), 5954 ^ _319074 : [(5961 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_520416, c_Groups_Ozero__class_Ozero(_520416), _520420)), 5964 ^ _319074 : [(5971 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_520416, _520420, c_Groups_Ozero__class_Ozero(_520416))), -(c_Orderings_Oord__class_Oless__eq(_520416, c_Groups_Ozero__class_Ozero(_520416), _520422))], (5965 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_520416, _520420, c_Groups_Ozero__class_Ozero(_520416)), -(c_Orderings_Oord__class_Oless__eq(_520416, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_520416), _520422), _520420), _520418))]]], (5955 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_520416, c_Groups_Ozero__class_Ozero(_520416), _520420), -(c_Orderings_Oord__class_Oless__eq(_520416, _520418, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_520416), _520422), _520420)))]]], (5977 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_520416, c_Rings_Oinverse__class_Odivide(_520416, _520418, _520420), _520422)), 5980 ^ _319074 : [(5983 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_520416, _520418, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_520416), _520422), _520420))], (5981 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_520416, c_Groups_Ozero__class_Ozero(_520416), _520420))]], 5984 ^ _319074 : [(5987 ^ _319074) ^ [] : [5988 ^ _319074 : [(5991 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_520416, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_520416), _520422), _520420), _520418)], (5989 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_520416, _520420, c_Groups_Ozero__class_Ozero(_520416)))]], 5992 ^ _319074 : [(5995 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_520416, c_Groups_Ozero__class_Ozero(_520416), _520422)], (5993 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_520416, _520420, c_Groups_Ozero__class_Ozero(_520416))]]], (5985 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_520416, c_Groups_Ozero__class_Ozero(_520416), _520420)]]]]], (8542 ^ _319074) ^ [_612314] : [class_RealVector_Oreal__normed__vector(_612314), -(c_Groups_Osgn__class_Osgn(_612314, c_Groups_Ozero__class_Ozero(_612314)) = c_Groups_Ozero__class_Ozero(_612314))], (10153 ^ _319074) ^ [_666832] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _666832) = _666832)], (4039 ^ _319074) ^ [_452379, _452381] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _452379, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _452379, _452381)))], (12556 ^ _319074) ^ [] : [-(class_Orderings_Oord(tc_RealDef_Oreal))], (8982 ^ _319074) ^ [_627149, _627151] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _627149, _627151), 8985 ^ _319074 : [(8992 ^ _319074) ^ [] : [_627151 = _627149, -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _627151, _627149))], (8986 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _627151, _627149), -(_627151 = _627149)]]], (11942 ^ _319074) ^ [_733494, _733496, _733498] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _733494), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _733496, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oabs__class_Oabs(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _733496, _733498)), c_Groups_Oone__class_Oone(tc_Int_Oint))), _733494)), _733498))], (8184 ^ _319074) ^ [_599977, _599979, _599981, _599983] : [class_Rings_Ocomm__semiring__1(_599977), c_Rings_Odvd__class_Odvd(_599977, _599979, _599981), -(c_Rings_Odvd__class_Odvd(_599977, _599979, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_599977), _599983), _599981)))], (4209 ^ _319074) ^ [_458262, _458264] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _458262, _458264) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 4212 ^ _319074 : [(4215 ^ _319074) ^ [] : [-(_458264 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (4213 ^ _319074) ^ [] : [-(_458262 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (8576 ^ _319074) ^ [_613481, _613483, _613485] : [class_Rings_Olinordered__idom(_613481), -(c_Groups_Osgn__class_Osgn(_613481, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_613481), _613483), _613485)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_613481), c_Groups_Osgn__class_Osgn(_613481, _613483)), c_Groups_Osgn__class_Osgn(_613481, _613485)))], (2868 ^ _319074) ^ [_413111, _413113, _413115] : [class_Orderings_Olinorder(_413111), c_Orderings_Oord__class_Oless__eq(_413111, _413113, _413115), c_Orderings_Oord__class_Oless(_413111, _413115, _413113)], (9552 ^ _319074) ^ [_646362, _646364, _646366, _646368, _646370] : [class_Rings_Ocomm__semiring__1(_646362), c_Rings_Odvd__class_Odvd(_646362, hAPP(hAPP(c_Power_Opower__class_Opower(_646362), _646364), _646366), _646368), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _646370, _646366), -(c_Rings_Odvd__class_Odvd(_646362, hAPP(hAPP(c_Power_Opower__class_Opower(_646362), _646364), _646370), _646368))], (11840 ^ _319074) ^ [_728995, _728997, _728999] : [class_Groups_Oordered__ab__group__add__abs(_728995), -(c_Orderings_Oord__class_Oless__eq(_728995, c_Groups_Ominus__class_Ominus(_728995, c_Groups_Oabs__class_Oabs(_728995, _728997), c_Groups_Oabs__class_Oabs(_728995, _728999)), c_Groups_Oabs__class_Oabs(_728995, c_Groups_Ominus__class_Ominus(_728995, _728997, _728999))))], (9088 ^ _319074) ^ [_630488, _630490, _630492] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _630488, _630490), 9099 ^ _319074 : [(9102 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _630492, _630488)], (9100 ^ _319074) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _630488, _630492))]], c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _630490, _630492), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _630492, _630490))], (6087 ^ _319074) ^ [_525013, _525015, _525017, _525019] : [class_Fields_Olinordered__field(_525013), c_Orderings_Oord__class_Oless(_525013, _525015, c_Groups_Ozero__class_Ozero(_525013)), 6094 ^ _319074 : [(6101 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_525013, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_525013), _525019), _525015), _525017), -(c_Orderings_Oord__class_Oless__eq(_525013, c_Rings_Oinverse__class_Odivide(_525013, _525017, _525015), _525019))], (6095 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_525013, c_Rings_Oinverse__class_Odivide(_525013, _525017, _525015), _525019), -(c_Orderings_Oord__class_Oless__eq(_525013, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_525013), _525019), _525015), _525017))]]], (4953 ^ _319074) ^ [_487274, _487276, _487278] : [class_Rings_Olinordered__ring__strict(_487274), 4956 ^ _319074 : [(4971 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_487274, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_487274), _487276), _487278), c_Groups_Ozero__class_Ozero(_487274))), 4972 ^ _319074 : [(4979 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_487274, _487276, c_Groups_Ozero__class_Ozero(_487274)), c_Orderings_Oord__class_Oless__eq(_487274, c_Groups_Ozero__class_Ozero(_487274), _487278)], (4973 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_487274, c_Groups_Ozero__class_Ozero(_487274), _487276), c_Orderings_Oord__class_Oless__eq(_487274, _487278, c_Groups_Ozero__class_Ozero(_487274))]]], (4957 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_487274, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_487274), _487276), _487278), c_Groups_Ozero__class_Ozero(_487274)), 4962 ^ _319074 : [(4965 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_487274, _487278, c_Groups_Ozero__class_Ozero(_487274)))], (4963 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_487274, c_Groups_Ozero__class_Ozero(_487274), _487276))]], 4966 ^ _319074 : [(4969 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_487274, c_Groups_Ozero__class_Ozero(_487274), _487278))], (4967 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_487274, _487276, c_Groups_Ozero__class_Ozero(_487274)))]]]]], (3216 ^ _319074) ^ [_424558] : [class_Groups_Ozero(_424558), -(c_Polynomial_OpCons(_424558, c_Groups_Ozero__class_Ozero(_424558), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_424558))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_424558)))], (280 ^ _319074) ^ [_327679, _327681] : [-(class_Groups_Oordered__ab__group__add__abs(_327679)), _327681 = _327679, class_Groups_Oordered__ab__group__add__abs(_327681)], (12502 ^ _319074) ^ [] : [-(class_Fields_Olinordered__field(tc_RealDef_Oreal))], (10948 ^ _319074) ^ [_694886, _694888, _694890] : [class_Rings_Olinordered__semidom(_694886), c_Orderings_Oord__class_Oless__eq(_694886, c_Groups_Ozero__class_Ozero(_694886), _694888), c_Orderings_Oord__class_Oless__eq(_694886, _694888, c_Groups_Oone__class_Oone(_694886)), -(c_Orderings_Oord__class_Oless__eq(_694886, hAPP(hAPP(c_Power_Opower__class_Opower(_694886), _694888), c_Nat_OSuc(_694890)), _694888))], (4057 ^ _319074) ^ [_453147, _453149, _453151, _453153] : [class_Rings_Odivision__ring(_453147), -(c_Rings_Oinverse__class_Odivide(_453147, c_Groups_Oplus__class_Oplus(_453147, _453149, _453151), _453153) = c_Groups_Oplus__class_Oplus(_453147, c_Rings_Oinverse__class_Odivide(_453147, _453149, _453153), c_Rings_Oinverse__class_Odivide(_453147, _453151, _453153)))], (150 ^ _319074) ^ [_323844, _323846] : [-(class_RealVector_Oreal__normed__vector(_323844)), _323846 = _323844, class_RealVector_Oreal__normed__vector(_323846)], (1659 ^ _319074) ^ [_372923, _372925, _372927] : [class_Orderings_Oorder(_372923), 1662 ^ _319074 : [(1671 ^ _319074) ^ [] : [-(_372925 = _372927), c_Orderings_Oord__class_Oless__eq(_372923, _372925, _372927), c_Orderings_Oord__class_Oless__eq(_372923, _372927, _372925)], (1663 ^ _319074) ^ [] : [_372925 = _372927, 1666 ^ _319074 : [(1669 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_372923, _372927, _372925))], (1667 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_372923, _372925, _372927))]]]]], (12534 ^ _319074) ^ [] : [-(class_Orderings_Olinorder(tc_RealDef_Oreal))], (12178 ^ _319074) ^ [_743110, _743112, _743114] : [-(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(_743110, _743112), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(_743110, _743114), hAPP(_743110, _743112)), c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _743114, _743112))), _743112)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(_743110, _743114), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, hAPP(_743110, _743114), hAPP(_743110, _743112)), c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal, _743114, _743112))), _743114)))], (2384 ^ _319074) ^ [_397392, _397394, _397396] : [class_Groups_Oordered__ab__group__add(_397392), 2387 ^ _319074 : [(2394 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_397392, _397396, c_Groups_Ouminus__class_Ouminus(_397392, _397394)), -(c_Orderings_Oord__class_Oless(_397392, _397394, c_Groups_Ouminus__class_Ouminus(_397392, _397396)))], (2388 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_397392, _397394, c_Groups_Ouminus__class_Ouminus(_397392, _397396)), -(c_Orderings_Oord__class_Oless(_397392, _397396, c_Groups_Ouminus__class_Ouminus(_397392, _397394)))]]], (20 ^ _319074) ^ [_319822, _319824] : [-(class_Lattices_Oab__semigroup__idem__mult(_319822)), _319824 = _319822, class_Lattices_Oab__semigroup__idem__mult(_319824)], (100 ^ _319074) ^ [_322369, _322371] : [-(class_Fields_Olinordered__field(_322369)), _322371 = _322369, class_Fields_Olinordered__field(_322371)], (12452 ^ _319074) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal))], (7813 ^ _319074) ^ [_586990] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _586990) = _586990)], (12646 ^ _319074) ^ [] : [-(class_Rings_Osemiring(tc_Complex_Ocomplex))], (1691 ^ _319074) ^ [_373921, _373923, _373925, _373927] : [class_Orderings_Oord(_373921), 1694 ^ _319074 : [(1701 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_373921, hAPP(_373925, 1702 ^ [_373921, _373923, _373925, _373927]), hAPP(_373927, 1702 ^ [_373921, _373923, _373925, _373927])), -(c_Orderings_Oord__class_Oless__eq(tc_fun(_373923, _373921), _373925, _373927))], (1695 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_fun(_373923, _373921), _373925, _373927), 1698 ^ _319074 : [(1699 ^ _319074) ^ [_374180] : [-(c_Orderings_Oord__class_Oless__eq(_373921, hAPP(_373925, _374180), hAPP(_373927, _374180)))]]]]], (12182 ^ _319074) ^ [_743405] : [class_Groups_Ocancel__comm__monoid__add(_743405), -(class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(_743405)))], (8570 ^ _319074) ^ [_613235, _613237] : [class_RealVector_Oreal__normed__vector(_613235), -(c_Groups_Osgn__class_Osgn(_613235, c_Groups_Ouminus__class_Ouminus(_613235, _613237)) = c_Groups_Ouminus__class_Ouminus(_613235, c_Groups_Osgn__class_Osgn(_613235, _613237)))], (9923 ^ _319074) ^ [_659138, _659140, _659142] : [-(_659138 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 9926 ^ _319074 : [(9933 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _659138), _659140), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _659138), _659142)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _659140, _659142))], (9927 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _659140, _659142), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _659138), _659140), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _659138), _659142)))]]], (10341 ^ _319074) ^ [_673301, _673303] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_673301), c_Nat_OSuc(_673303)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _673301, _673303))], (4553 ^ _319074) ^ [_471958, _471960, _471962, _471964] : [class_Rings_Ocomm__semiring__1(_471958), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_471958), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_471958), _471960), _471962)), _471964) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_471958), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_471958), _471960), _471964)), _471962))], (1708 ^ _319074) ^ [_374576, _374578, _374580, _374582] : [class_Groups_Ocancel__semigroup__add(_374576), c_Groups_Oplus__class_Oplus(_374576, _374578, _374580) = c_Groups_Oplus__class_Oplus(_374576, _374582, _374580), -(_374578 = _374582)], (12334 ^ _319074) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (9630 ^ _319074) ^ [_649221, _649223] : [class_Power_Opower(_649221), class_Rings_Osemiring__0(_649221), 9637 ^ _319074 : [(9644 ^ _319074) ^ [] : [-(_649223 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_649221), c_Groups_Ozero__class_Ozero(_649221)), _649223) = c_Groups_Ozero__class_Ozero(_649221))], (9638 ^ _319074) ^ [] : [_649223 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_649221), c_Groups_Ozero__class_Ozero(_649221)), _649223) = c_Groups_Oone__class_Oone(_649221))]]], (8612 ^ _319074) ^ [_615223, _615225, _615227, _615229] : [class_Rings_Ocomm__semiring__1(_615223), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_615223), hAPP(hAPP(c_Power_Opower__class_Opower(_615223), _615225), _615227)), hAPP(hAPP(c_Power_Opower__class_Opower(_615223), _615225), _615229)) = hAPP(hAPP(c_Power_Opower__class_Opower(_615223), _615225), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _615227, _615229)))], (1365 ^ _319074) ^ [_363635, _363637, _363639, _363641] : [class_Groups_Oordered__comm__monoid__add(_363635), c_Orderings_Oord__class_Oless__eq(_363635, c_Groups_Ozero__class_Ozero(_363635), _363637), c_Orderings_Oord__class_Oless__eq(_363635, _363639, _363641), -(c_Orderings_Oord__class_Oless__eq(_363635, _363639, c_Groups_Oplus__class_Oplus(_363635, _363637, _363641)))], (3074 ^ _319074) ^ [_419581, _419583, _419585, _419587, _419589] : [class_Groups_Oordered__cancel__ab__semigroup__add(_419581), c_Orderings_Oord__class_Oless(_419581, _419583, _419585), c_Orderings_Oord__class_Oless(_419581, _419587, _419589), -(c_Orderings_Oord__class_Oless(_419581, c_Groups_Oplus__class_Oplus(_419581, _419583, _419587), c_Groups_Oplus__class_Oplus(_419581, _419585, _419589)))], (10047 ^ _319074) ^ [_663205, _663207] : [10048 ^ _319074 : [(10051 ^ _319074) ^ [] : [_663205 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10049 ^ _319074) ^ [] : [_663207 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _663205), _663207) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (8520 ^ _319074) ^ [_611647, _611649] : [class_Rings_Olinordered__idom(_611647), 8523 ^ _319074 : [(8530 ^ _319074) ^ [] : [_611649 = c_Groups_Ozero__class_Ozero(_611647), -(c_Groups_Osgn__class_Osgn(_611647, _611649) = c_Groups_Ozero__class_Ozero(_611647))], (8524 ^ _319074) ^ [] : [c_Groups_Osgn__class_Osgn(_611647, _611649) = c_Groups_Ozero__class_Ozero(_611647), -(_611649 = c_Groups_Ozero__class_Ozero(_611647))]]], (4119 ^ _319074) ^ [_455214, _455216] : [class_Rings_Olinordered__idom(_455214), 4122 ^ _319074 : [(4129 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_455214), _455216, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_455214)))), -(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(_455214), _455216) = _455216)], (4123 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(_455214), _455216, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_455214))), -(c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(_455214), _455216) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_455214), _455216))]]], (12962 ^ _319074) ^ [_765943] : [class_Groups_Oab__group__add(_765943), -(class_Groups_Ouminus(tc_Polynomial_Opoly(_765943)))], (12812 ^ _319074) ^ [_761193] : [class_Rings_Olinordered__idom(_761193), -(class_Rings_Oordered__semiring(tc_Polynomial_Opoly(_761193)))], (12610 ^ _319074) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex))], (6183 ^ _319074) ^ [_528214, _528216, _528218, _528220, _528222] : [class_Rings_Olinordered__semiring__strict(_528214), c_Orderings_Oord__class_Oless(_528214, _528216, _528218), c_Orderings_Oord__class_Oless(_528214, _528220, _528222), c_Orderings_Oord__class_Oless(_528214, c_Groups_Ozero__class_Ozero(_528214), _528218), c_Orderings_Oord__class_Oless__eq(_528214, c_Groups_Ozero__class_Ozero(_528214), _528220), -(c_Orderings_Oord__class_Oless(_528214, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_528214), _528216), _528220), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_528214), _528218), _528222)))], (3942 ^ _319074) ^ [_448787, _448789, _448791] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _448787, _448789), _448791), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _448787, _448791))], (4783 ^ _319074) ^ [_481379, _481381, _481383, _481385] : [class_Rings_Odivision__ring(_481379), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_481379), _481381), c_Rings_Oinverse__class_Odivide(_481379, _481383, _481385)) = c_Rings_Oinverse__class_Odivide(_481379, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_481379), _481381), _481383), _481385))], (1563 ^ _319074) ^ [_369853, _369855, _369857, _369859] : [class_Orderings_Oorder(_369853), c_Orderings_Oord__class_Oless__eq(_369853, _369855, _369857), _369855 = _369859, -(c_Orderings_Oord__class_Oless__eq(_369853, _369859, _369857))], (8678 ^ _319074) ^ [_617446, _617448] : [class_Rings_Olinordered__idom(_617446), -(c_Groups_Oabs__class_Oabs(_617446, _617448) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_617446), _617448), c_Groups_Osgn__class_Osgn(_617446, _617448)))], (2768 ^ _319074) ^ [_410055, _410057, _410059, _410061] : [class_Orderings_Oorder(_410055), c_Orderings_Oord__class_Oless(_410055, _410057, _410059), c_Orderings_Oord__class_Oless__eq(_410055, _410061, _410057), -(c_Orderings_Oord__class_Oless(_410055, _410061, _410059))], (12424 ^ _319074) ^ [] : [-(class_Rings_Odvd(tc_Nat_Onat))], (1337 ^ _319074) ^ [_362721, _362723, _362725] : [class_Groups_Oordered__comm__monoid__add(_362721), c_Orderings_Oord__class_Oless__eq(_362721, _362723, c_Groups_Ozero__class_Ozero(_362721)), c_Orderings_Oord__class_Oless__eq(_362721, _362725, c_Groups_Ozero__class_Ozero(_362721)), -(c_Orderings_Oord__class_Oless__eq(_362721, c_Groups_Oplus__class_Oplus(_362721, _362723, _362725), c_Groups_Ozero__class_Ozero(_362721)))], (5595 ^ _319074) ^ [_508231, _508233, _508235] : [class_Rings_Olinordered__semiring__strict(_508231), c_Orderings_Oord__class_Oless(_508231, c_Groups_Ozero__class_Ozero(_508231), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_508231), _508233), _508235)), c_Orderings_Oord__class_Oless(_508231, c_Groups_Ozero__class_Ozero(_508231), _508233), -(c_Orderings_Oord__class_Oless(_508231, c_Groups_Ozero__class_Ozero(_508231), _508235))], (3292 ^ _319074) ^ [_426931, _426933] : [class_Groups_Olinordered__ab__group__add(_426931), 3295 ^ _319074 : [(3302 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_426931, c_Groups_Ozero__class_Ozero(_426931), _426933), -(c_Orderings_Oord__class_Oless__eq(_426931, c_Groups_Ouminus__class_Ouminus(_426931, _426933), _426933))], (3296 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_426931, c_Groups_Ouminus__class_Ouminus(_426931, _426933), _426933), -(c_Orderings_Oord__class_Oless__eq(_426931, c_Groups_Ozero__class_Ozero(_426931), _426933))]]], (4845 ^ _319074) ^ [_483841, _483843, _483845, _483847] : [class_Fields_Ofield__inverse__zero(_483841), 4848 ^ _319074 : [(4849 ^ _319074) ^ [] : [c_Rings_Oinverse__class_Odivide(_483841, _483843, _483845) = _483847, 4852 ^ _319074 : [(4859 ^ _319074) ^ [] : [_483845 = c_Groups_Ozero__class_Ozero(_483841), -(_483847 = c_Groups_Ozero__class_Ozero(_483841))], (4853 ^ _319074) ^ [] : [-(_483845 = c_Groups_Ozero__class_Ozero(_483841)), -(_483843 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_483841), _483847), _483845))]]], (4865 ^ _319074) ^ [] : [-(c_Rings_Oinverse__class_Odivide(_483841, _483843, _483845) = _483847), 4868 ^ _319074 : [(4871 ^ _319074) ^ [] : [_483843 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_483841), _483847), _483845)], (4869 ^ _319074) ^ [] : [_483845 = c_Groups_Ozero__class_Ozero(_483841)]], 4872 ^ _319074 : [(4875 ^ _319074) ^ [] : [_483847 = c_Groups_Ozero__class_Ozero(_483841)], (4873 ^ _319074) ^ [] : [-(_483845 = c_Groups_Ozero__class_Ozero(_483841))]]]]], (9939 ^ _319074) ^ [_659673, _659675, _659677] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _659673), _659675), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _659673), _659677)), -(_659673 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _659675, _659677))], (1481 ^ _319074) ^ [_367154, _367156] : [class_Groups_Oordered__ab__group__add__abs(_367154), -(c_Orderings_Oord__class_Oless__eq(_367154, c_Groups_Ozero__class_Ozero(_367154), c_Groups_Oabs__class_Oabs(_367154, _367156)))], (3480 ^ _319074) ^ [_432983, _432985] : [class_Rings_Olinordered__idom(_432983), 3483 ^ _319074 : [(3490 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_432983, _432985, c_Groups_Ozero__class_Ozero(_432983)), -(c_Orderings_Oord__class_Oless(_432983, c_Groups_Oplus__class_Oplus(_432983, _432985, _432985), c_Groups_Ozero__class_Ozero(_432983)))], (3484 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_432983, c_Groups_Oplus__class_Oplus(_432983, _432985, _432985), c_Groups_Ozero__class_Ozero(_432983)), -(c_Orderings_Oord__class_Oless(_432983, _432985, c_Groups_Ozero__class_Ozero(_432983)))]]], (4789 ^ _319074) ^ [_481647, _481649] : [class_Rings_Olinordered__idom(_481647), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_481647), c_Groups_Oabs__class_Oabs(_481647, _481649)), c_Groups_Oabs__class_Oabs(_481647, _481649)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_481647), _481649), _481649))], (10728 ^ _319074) ^ [_687144, _687146] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _687144, _687146), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_687144), _687146))], (240 ^ _319074) ^ [_326499, _326501] : [-(class_Rings_Olinordered__comm__semiring__strict(_326499)), _326501 = _326499, class_Rings_Olinordered__comm__semiring__strict(_326501)], (12342 ^ _319074) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (12950 ^ _319074) ^ [_765563] : [class_Rings_Ocomm__semiring__0(_765563), -(class_Rings_Osemiring(tc_Polynomial_Opoly(_765563)))], (12364 ^ _319074) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (8043 ^ _319074) ^ [_594638, _594640, _594642] : [class_Fields_Olinordered__field(_594638), c_Orderings_Oord__class_Oless(_594638, _594640, _594642), -(c_Orderings_Oord__class_Oless(_594638, _594640, c_Rings_Oinverse__class_Odivide(_594638, c_Groups_Oplus__class_Oplus(_594638, _594640, _594642), c_Groups_Oplus__class_Oplus(_594638, c_Groups_Oone__class_Oone(_594638), c_Groups_Oone__class_Oone(_594638)))))], (3530 ^ _319074) ^ [_434779, _434781] : [class_Groups_Oordered__ab__group__add__abs(_434779), c_Orderings_Oord__class_Oless(_434779, c_Groups_Oabs__class_Oabs(_434779, _434781), c_Groups_Ozero__class_Ozero(_434779))], (3908 ^ _319074) ^ [_447544, _447546] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _447544, _447546), _447544 = _447546], (3964 ^ _319074) ^ [_449626, _449628] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _449626, _449628), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _449628, _449626), -(_449626 = _449628)], (7582 ^ _319074) ^ [_577627, _577629, _577631] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _577627, _577629), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _577627, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _577629, _577631)))], (3222 ^ _319074) ^ [_424802, _424804, _424806] : [class_Groups_Ozero(_424802), 3225 ^ _319074 : [(3234 ^ _319074) ^ [] : [-(c_Polynomial_OpCons(_424802, _424804, _424806) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_424802))), _424804 = c_Groups_Ozero__class_Ozero(_424802), _424806 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_424802))], (3226 ^ _319074) ^ [] : [c_Polynomial_OpCons(_424802, _424804, _424806) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_424802)), 3229 ^ _319074 : [(3232 ^ _319074) ^ [] : [-(_424806 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_424802)))], (3230 ^ _319074) ^ [] : [-(_424804 = c_Groups_Ozero__class_Ozero(_424802))]]]]], (5043 ^ _319074) ^ [_490115, _490117, _490119] : [class_Rings_Oordered__ring(_490115), c_Orderings_Oord__class_Oless__eq(_490115, _490117, c_Groups_Ozero__class_Ozero(_490115)), c_Orderings_Oord__class_Oless__eq(_490115, _490119, c_Groups_Ozero__class_Ozero(_490115)), -(c_Orderings_Oord__class_Oless__eq(_490115, c_Groups_Ozero__class_Ozero(_490115), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_490115), _490117), _490119)))], (11084 ^ _319074) ^ [_699832, _699834] : [c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _699832, _699834), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _699834, _699832), -(_699832 = _699834)], (8067 ^ _319074) ^ [_595497] : [-(c_Complex_Orcis(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _595497) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex))], (2824 ^ _319074) ^ [_411779, _411781, _411783] : [class_Orderings_Oorder(_411779), c_Orderings_Oord__class_Oless__eq(_411779, _411781, _411783), -(c_Orderings_Oord__class_Oless(_411779, _411781, _411783)), -(_411781 = _411783)], (3782 ^ _319074) ^ [_443008, _443010] : [3783 ^ _319074 : [(3786 ^ _319074) ^ [] : [_443008 = _443010], (3784 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _443008, _443010)]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _443008, _443010))], (10307 ^ _319074) ^ [_671982, _671984] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_671982), c_Nat_OSuc(_671984)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _671982, _671984))], (12686 ^ _319074) ^ [_757203] : [class_Rings_Olinordered__idom(_757203), -(class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(_757203)))], (12188 ^ _319074) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex))], (12300 ^ _319074) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (12310 ^ _319074) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (2226 ^ _319074) ^ [_392391, _392393, _392395] : [class_Orderings_Opreorder(_392391), c_Orderings_Oord__class_Oless(_392391, _392393, _392395), c_Orderings_Oord__class_Oless(_392391, _392395, _392393)], (11786 ^ _319074) ^ [_726870, _726872, _726874, _726876, _726878] : [class_Groups_Oordered__ab__group__add(_726870), c_Groups_Ominus__class_Ominus(_726870, _726872, _726874) = c_Groups_Ominus__class_Ominus(_726870, _726876, _726878), 11793 ^ _319074 : [(11800 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_726870, _726876, _726878), -(c_Orderings_Oord__class_Oless__eq(_726870, _726872, _726874))], (11794 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_726870, _726872, _726874), -(c_Orderings_Oord__class_Oless__eq(_726870, _726876, _726878))]]], (4919 ^ _319074) ^ [_486225, _486227, _486229] : [class_Rings_Olinordered__ring__strict(_486225), 4922 ^ _319074 : [(4937 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_486225, c_Groups_Ozero__class_Ozero(_486225), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_486225), _486227), _486229))), 4938 ^ _319074 : [(4945 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_486225, _486227, c_Groups_Ozero__class_Ozero(_486225)), c_Orderings_Oord__class_Oless__eq(_486225, _486229, c_Groups_Ozero__class_Ozero(_486225))], (4939 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_486225, c_Groups_Ozero__class_Ozero(_486225), _486227), c_Orderings_Oord__class_Oless__eq(_486225, c_Groups_Ozero__class_Ozero(_486225), _486229)]]], (4923 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_486225, c_Groups_Ozero__class_Ozero(_486225), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_486225), _486227), _486229)), 4928 ^ _319074 : [(4931 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_486225, c_Groups_Ozero__class_Ozero(_486225), _486229))], (4929 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_486225, c_Groups_Ozero__class_Ozero(_486225), _486227))]], 4932 ^ _319074 : [(4935 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_486225, _486229, c_Groups_Ozero__class_Ozero(_486225)))], (4933 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(_486225, _486227, c_Groups_Ozero__class_Ozero(_486225)))]]]]], (12908 ^ _319074) ^ [_764233] : [class_Groups_Ocomm__monoid__add(_764233), -(class_Groups_Omonoid__add(tc_Polynomial_Opoly(_764233)))], (8162 ^ _319074) ^ [_599106, _599108, _599110] : [class_Rings_Ocomm__semiring__1(_599106), -(c_Rings_Odvd__class_Odvd(_599106, _599108, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_599106), _599108), _599110)))], (5761 ^ _319074) ^ [_513932, _513934, _513936, _513938] : [class_Fields_Ofield__inverse__zero(_513932), -(_513934 = c_Groups_Ozero__class_Ozero(_513932)), -(c_Groups_Oplus__class_Oplus(_513932, c_Rings_Oinverse__class_Odivide(_513932, _513936, _513934), _513938) = c_Rings_Oinverse__class_Odivide(_513932, c_Groups_Oplus__class_Oplus(_513932, _513936, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_513932), _513938), _513934)), _513934))], (12878 ^ _319074) ^ [_763283] : [class_Rings_Olinordered__idom(_763283), -(class_Rings_Oordered__ring(tc_Polynomial_Opoly(_763283)))], (4583 ^ _319074) ^ [_473466, _473468, _473470, _473472] : [class_Groups_Oab__semigroup__mult(_473466), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_473466), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_473466), _473468), _473470)), _473472) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_473466), _473468), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_473466), _473470), _473472)))], (12174 ^ _319074) ^ [_742859, _742861] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _742859, _742861), c_Nat_OSuc(_742859)))], (1894 ^ _319074) ^ [_381158, _381160, _381162, _381164] : [class_Rings_Ocomm__semiring__1(_381158), -(c_Groups_Oplus__class_Oplus(_381158, c_Groups_Oplus__class_Oplus(_381158, _381160, _381162), _381164) = c_Groups_Oplus__class_Oplus(_381158, c_Groups_Oplus__class_Oplus(_381158, _381160, _381164), _381162))], (1918 ^ _319074) ^ [_382264, _382266, _382268] : [class_Rings_Ocomm__semiring__1(_382264), -(c_Groups_Oplus__class_Oplus(_382264, _382266, _382268) = c_Groups_Oplus__class_Oplus(_382264, _382268, _382266))], (10619 ^ _319074) ^ [_683537, _683539] : [-(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _683537, _683539)), 10620 ^ _319074 : [(10627 ^ _319074) ^ [] : [_683537 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _683539 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (10621 ^ _319074) ^ [] : [_683537 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _683539 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (12348 ^ _319074) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (7877 ^ _319074) ^ [_589174, _589176, _589178] : [class_Rings_Olinordered__semidom(_589174), c_Orderings_Oord__class_Oless(_589174, c_Groups_Oone__class_Oone(_589174), _589176), c_Orderings_Oord__class_Oless(_589174, c_Groups_Oone__class_Oone(_589174), _589178), -(c_Orderings_Oord__class_Oless(_589174, c_Groups_Oone__class_Oone(_589174), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_589174), _589176), _589178)))], (10037 ^ _319074) ^ [_662941, _662943] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _662941), _662943) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_662943 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_662941 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (2400 ^ _319074) ^ [_397904, _397906, _397908] : [class_Groups_Ogroup__add(_397904), 2403 ^ _319074 : [(2410 ^ _319074) ^ [] : [_397908 = c_Groups_Ouminus__class_Ouminus(_397904, _397906), -(_397906 = c_Groups_Ouminus__class_Ouminus(_397904, _397908))], (2404 ^ _319074) ^ [] : [_397906 = c_Groups_Ouminus__class_Ouminus(_397904, _397908), -(_397908 = c_Groups_Ouminus__class_Ouminus(_397904, _397906))]]], (1535 ^ _319074) ^ [_368987, _368989, _368991, _368993] : [class_Orderings_Opreorder(_368987), c_Orderings_Oord__class_Oless__eq(_368987, _368989, _368991), c_Orderings_Oord__class_Oless__eq(_368987, _368991, _368993), -(c_Orderings_Oord__class_Oless__eq(_368987, _368989, _368993))], (2636 ^ _319074) ^ [_405522, _405524, _405526] : [class_Groups_Oordered__ab__group__add(_405522), c_Orderings_Oord__class_Oless__eq(_405522, _405524, _405526), -(c_Orderings_Oord__class_Oless__eq(_405522, c_Groups_Ouminus__class_Ouminus(_405522, _405526), c_Groups_Ouminus__class_Ouminus(_405522, _405524)))], (12014 ^ _319074) ^ [_736618, _736620, _736622, _736624, _736626] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _736618, _736620), 12017 ^ _319074 : [(12024 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _736624, 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, _736620, _736618)), _736622), _736626)), -(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), _736618), _736622), _736624), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _736620), _736622), _736626)))], (12018 ^ _319074) ^ [] : [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), _736618), _736622), _736624), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _736620), _736622), _736626)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _736624, 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, _736620, _736618)), _736622), _736626)))]]], (9010 ^ _319074) ^ [_627996, _627998] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _627996, _627998), -(_627996 = _627998), 9017 ^ _319074 : [(9020 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _627998, _627996)], (9018 ^ _319074) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _627996, _627998))]]], (9342 ^ _319074) ^ [_638572] : [_638572 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), -(c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, _638572) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (928 ^ _319074) ^ [_348052, _348054, _348056, _348058, _348060, _348062] : [-(c_Polynomial_Osynthetic__div(_348062, _348058, _348054) = c_Polynomial_Osynthetic__div(_348060, _348056, _348052)), _348062 = _348060, _348058 = _348056, _348054 = _348052], (3622 ^ _319074) ^ [_437943, _437945, _437947] : [class_Groups_Oordered__comm__monoid__add(_437943), c_Orderings_Oord__class_Oless__eq(_437943, _437945, c_Groups_Ozero__class_Ozero(_437943)), c_Orderings_Oord__class_Oless(_437943, _437947, c_Groups_Ozero__class_Ozero(_437943)), -(c_Orderings_Oord__class_Oless(_437943, c_Groups_Oplus__class_Oplus(_437943, _437945, _437947), c_Groups_Ozero__class_Ozero(_437943)))], (10537 ^ _319074) ^ [_680713, _680715, _680717] : [class_Groups_Omonoid__mult(_680713), -(hAPP(hAPP(c_Power_Opower__class_Opower(_680713), _680715), c_Nat_OSuc(_680717)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_680713), hAPP(hAPP(c_Power_Opower__class_Opower(_680713), _680715), _680717)), _680715))], (2352 ^ _319074) ^ [_396374, _396376, _396378] : [class_Groups_Oordered__ab__group__add(_396374), 2355 ^ _319074 : [(2362 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_396374, c_Groups_Ouminus__class_Ouminus(_396374, _396378), _396376), -(c_Orderings_Oord__class_Oless(_396374, c_Groups_Ouminus__class_Ouminus(_396374, _396376), _396378))], (2356 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_396374, c_Groups_Ouminus__class_Ouminus(_396374, _396376), _396378), -(c_Orderings_Oord__class_Oless(_396374, c_Groups_Ouminus__class_Ouminus(_396374, _396378), _396376))]]], (220 ^ _319074) ^ [_325909, _325911] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_325909)), _325911 = _325909, class_Groups_Oordered__cancel__ab__semigroup__add(_325911)], (10808 ^ _319074) ^ [_690171] : [-(c_Nat_OSuc(_690171) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _690171))], (9380 ^ _319074) ^ [_639874, _639876, _639878, _639880] : [class_Groups_Ocomm__monoid__mult(_639874), -(hAPP(hAPP(c_Power_Opower__class_Opower(_639874), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_639874), _639876), _639878)), _639880) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_639874), hAPP(hAPP(c_Power_Opower__class_Opower(_639874), _639876), _639880)), hAPP(hAPP(c_Power_Opower__class_Opower(_639874), _639878), _639880)))], (4565 ^ _319074) ^ [_472582, _472584, _472586, _472588] : [class_Rings_Ocomm__semiring__1(_472582), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_472582), _472584), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_472582), _472586), _472588)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_472582), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_472582), _472584), _472586)), _472588))], (12614 ^ _319074) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex))], (12202 ^ _319074) ^ [_744033, _744035] : [class_Orderings_Opreorder(_744033), -(class_Orderings_Opreorder(tc_fun(_744035, _744033)))], (12582 ^ _319074) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex))], (11374 ^ _319074) ^ [_709974, _709976, _709978] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _709974), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _709976, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _709978, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oabs__class_Oabs(tc_Int_Oint, c_Groups_Ominus__class_Ominus(tc_Int_Oint, _709978, _709976)), c_Groups_Oone__class_Oone(tc_Int_Oint))), _709974))))], (12570 ^ _319074) ^ [] : [-(class_Power_Opower(tc_RealDef_Oreal))], (8268 ^ _319074) ^ [_602922, _602924, _602926] : [class_Rings_Olinordered__idom(_602922), 8271 ^ _319074 : [(8278 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(_602922, _602924, _602926), -(c_Rings_Odvd__class_Odvd(_602922, c_Groups_Oabs__class_Oabs(_602922, _602924), _602926))], (8272 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(_602922, c_Groups_Oabs__class_Oabs(_602922, _602924), _602926), -(c_Rings_Odvd__class_Odvd(_602922, _602924, _602926))]]], (12154 ^ _319074) ^ [_742079, _742081, _742083] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _742079, _742081), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _742079, _742083), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _742083, _742081), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _742083, _742079)))], (11496 ^ _319074) ^ [_714470, _714472, _714474, _714476] : [class_RealVector_Oreal__normed__algebra(_714470), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_714470), c_Groups_Ominus__class_Ominus(_714470, _714472, _714474)), _714476) = c_Groups_Ominus__class_Ominus(_714470, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_714470), _714472), _714476), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_714470), _714474), _714476)))], (12550 ^ _319074) ^ [] : [-(class_Orderings_Oorder(tc_RealDef_Oreal))], (4263 ^ _319074) ^ [_460005] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _460005))], (12354 ^ _319074) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (11386 ^ _319074) ^ [_710514, _710516, _710518] : [class_Groups_Oordered__ab__group__add(_710514), 11389 ^ _319074 : [(11396 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_710514, c_Groups_Ominus__class_Ominus(_710514, _710516, _710518), c_Groups_Ozero__class_Ozero(_710514)), -(c_Orderings_Oord__class_Oless(_710514, _710516, _710518))], (11390 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_710514, _710516, _710518), -(c_Orderings_Oord__class_Oless(_710514, c_Groups_Ominus__class_Ominus(_710514, _710516, _710518), c_Groups_Ozero__class_Ozero(_710514)))]]], (12536 ^ _319074) ^ [] : [-(class_Groups_Omonoid__mult(tc_RealDef_Oreal))], (4453 ^ _319074) ^ [_467097, _467099] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _467097, _467099) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _467099, _467097))], (8618 ^ _319074) ^ [_615515, _615517] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _615515), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _615515, _615517), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _615517, _615515)], (7733 ^ _319074) ^ [_584183] : [class_Rings_Ozero__neq__one(_584183), c_Groups_Oone__class_Oone(_584183) = c_Groups_Ozero__class_Ozero(_584183)], (7486 ^ _319074) ^ [_573497, _573499, _573501, _573503] : [class_Rings_Ocomm__semiring__0(_573497), -(c_Polynomial_Opcompose(_573497, c_Polynomial_OpCons(_573497, _573499, _573501), _573503) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(_573497), c_Polynomial_OpCons(_573497, _573499, c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_573497))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_573497)), _573503), c_Polynomial_Opcompose(_573497, _573501, _573503))))], (9062 ^ _319074) ^ [_629654, _629656, _629658] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _629654, _629656), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _629656, _629658), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _629654, _629658))], (10265 ^ _319074) ^ [_670589, _670591] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _670589, _670591), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _670589, c_Nat_OSuc(_670591)))], (11351 ^ _319074) ^ [_709102, _709104] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _709102), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _709104), 11359 ^ _319074 : [(11364 ^ _319074) ^ [_709606] : [-(_709606 = 11358 ^ [_709102, _709104]), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _709606), hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), _709606), _709102) = _709104], (11362 ^ _319074) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal), 11358 ^ [_709102, _709104]), _709102) = _709104)], (11360 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 11358 ^ [_709102, _709104]))]]], (11018 ^ _319074) ^ [_697398, _697400] : [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), _697398), _697400)), -(_697400 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _697398))], (12456 ^ _319074) ^ [] : [-(class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal))], (12266 ^ _319074) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (12302 ^ _319074) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (12836 ^ _319074) ^ [_761953] : [class_Rings_Olinordered__idom(_761953), -(class_Rings_Olinordered__ring(tc_Polynomial_Opoly(_761953)))], (12396 ^ _319074) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (7383 ^ _319074) ^ [_569807, _569809, _569811, _569813] : [class_RealVector_Oreal__normed__vector(_569807), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _569809, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_569807, _569811), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _569809), c_RealVector_Onorm__class_Onorm(_569807, _569813))), -(_569811 = c_Groups_Ozero__class_Ozero(_569807))], (10291 ^ _319074) ^ [_671454, _671456] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _671454, c_Nat_OSuc(_671456)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _671454, _671456)), -(_671454 = _671456)], (9879 ^ _319074) ^ [_657778] : [c_Groups_Oabs__class_Oabs(tc_Int_Oint, _657778) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _657778, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (1191 ^ _319074) ^ [_357851, _357853, _357855, _357857] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_357851), 1194 ^ _319074 : [(1201 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_357851, _357853, _357857), -(c_Orderings_Oord__class_Oless__eq(_357851, c_Groups_Oplus__class_Oplus(_357851, _357853, _357855), c_Groups_Oplus__class_Oplus(_357851, _357857, _357855)))], (1195 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_357851, c_Groups_Oplus__class_Oplus(_357851, _357853, _357855), c_Groups_Oplus__class_Oplus(_357851, _357857, _357855)), -(c_Orderings_Oord__class_Oless__eq(_357851, _357853, _357857))]]], (7270 ^ _319074) ^ [_565601, _565603, _565605] : [class_Rings_Ocomm__ring(_565601), -(hAPP(c_Polynomial_Opoly(_565601, c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(_565601), _565603)), _565605) = c_Groups_Ouminus__class_Ouminus(_565601, hAPP(c_Polynomial_Opoly(_565601, _565603), _565605)))], (12280 ^ _319074) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (1014 ^ _319074) ^ [_351137, _351139] : [_351139 = _351137, -(c_Power_Opower__class_Opower(_351139) = c_Power_Opower__class_Opower(_351137))], (7138 ^ _319074) ^ [_560846, _560848, _560850] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _560846, _560848), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _560850), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _560846), _560850), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _560848), _560850)))], (3692 ^ _319074) ^ [_440158, _440160, _440162] : [class_Rings_Olinordered__idom(_440158), 3695 ^ _319074 : [(3708 ^ _319074) ^ [] : [-(c_Polynomial_Opos__poly(_440158, c_Polynomial_OpCons(_440158, _440160, _440162))), 3709 ^ _319074 : [(3712 ^ _319074) ^ [] : [_440162 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_440158)), c_Orderings_Oord__class_Oless(_440158, c_Groups_Ozero__class_Ozero(_440158), _440160)], (3710 ^ _319074) ^ [] : [c_Polynomial_Opos__poly(_440158, _440162)]]], (3696 ^ _319074) ^ [] : [c_Polynomial_Opos__poly(_440158, c_Polynomial_OpCons(_440158, _440160, _440162)), -(c_Polynomial_Opos__poly(_440158, _440162)), 3703 ^ _319074 : [(3706 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_440158, c_Groups_Ozero__class_Ozero(_440158), _440160))], (3704 ^ _319074) ^ [] : [-(_440162 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_440158)))]]]]], (1681 ^ _319074) ^ [_373581, _373583, _373585] : [class_Orderings_Olinorder(_373581), -(c_Orderings_Oord__class_Oless__eq(_373581, _373583, _373585)), -(c_Orderings_Oord__class_Oless__eq(_373581, _373585, _373583))], (4329 ^ _319074) ^ [_462421, _462423, _462425] : [class_RealVector_Oreal__normed__field(_462421), -(_462423 = c_Groups_Ozero__class_Ozero(_462421)), -(c_RealVector_Onorm__class_Onorm(_462421, c_Rings_Oinverse__class_Odivide(_462421, _462425, _462423)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_462421, _462425), c_RealVector_Onorm__class_Onorm(_462421, _462423)))], (10671 ^ _319074) ^ [_685175, _685177] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _685175), _685177) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 10674 ^ _319074 : [(10677 ^ _319074) ^ [] : [-(_685177 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (10675 ^ _319074) ^ [] : [-(_685175 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (8836 ^ _319074) ^ [_622457, _622459] : [class_RealVector_Oreal__normed__vector(_622457), 8839 ^ _319074 : [(8846 ^ _319074) ^ [] : [-(_622459 = c_Groups_Ozero__class_Ozero(_622457)), -(c_RealVector_Onorm__class_Onorm(_622457, c_Groups_Osgn__class_Osgn(_622457, _622459)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (8840 ^ _319074) ^ [] : [_622459 = c_Groups_Ozero__class_Ozero(_622457), -(c_RealVector_Onorm__class_Onorm(_622457, c_Groups_Osgn__class_Osgn(_622457, _622459)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))]]], (11818 ^ _319074) ^ [_728001, _728003, _728005] : [class_Groups_Oab__group__add(_728001), -(c_Groups_Ouminus__class_Ouminus(_728001, c_Groups_Ominus__class_Ominus(_728001, _728003, _728005)) = c_Groups_Ominus__class_Ominus(_728001, _728005, _728003))], (6143 ^ _319074) ^ [_526850, _526852, _526854, _526856] : [class_Rings_Olinordered__ring__strict(_526850), c_Orderings_Oord__class_Oless(_526850, c_Groups_Ozero__class_Ozero(_526850), _526852), 6150 ^ _319074 : [(6157 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_526850, _526854, _526856), -(c_Orderings_Oord__class_Oless__eq(_526850, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_526850), _526852), _526854), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_526850), _526852), _526856)))], (6151 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_526850, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_526850), _526852), _526854), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_526850), _526852), _526856)), -(c_Orderings_Oord__class_Oless__eq(_526850, _526854, _526856))]]], (12444 ^ _319074) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal))], (1802 ^ _319074) ^ [_377813] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _377813, _377813))], (12336 ^ _319074) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (1163 ^ _319074) ^ [_356766, _356768, _356770] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _356766, _356768), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _356770, _356766), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _356770, _356768)))], (2480 ^ _319074) ^ [_400356, _400358] : [class_Orderings_Opreorder(_400356), c_Orderings_Oord__class_Oless(_400356, _400358, _400358)], (140 ^ _319074) ^ [_323549, _323551] : [-(class_RealVector_Oreal__normed__algebra(_323549)), _323551 = _323549, class_RealVector_Oreal__normed__algebra(_323551)], (2620 ^ _319074) ^ [_405035, _405037] : [class_Groups_Olinordered__ab__group__add(_405035), 2623 ^ _319074 : [(2630 ^ _319074) ^ [] : [_405037 = c_Groups_Ozero__class_Ozero(_405035), -(c_Groups_Ouminus__class_Ouminus(_405035, _405037) = _405037)], (2624 ^ _319074) ^ [] : [c_Groups_Ouminus__class_Ouminus(_405035, _405037) = _405037, -(_405037 = c_Groups_Ozero__class_Ozero(_405035))]]], (8606 ^ _319074) ^ [_614967, _614969] : [class_Rings_Ocomm__semiring__1(_614967), -(hAPP(hAPP(c_Power_Opower__class_Opower(_614967), _614969), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_614967))], (12244 ^ _319074) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (3720 ^ _319074) ^ [_441007, _441009, _441011] : [class_Lattices_Oboolean__algebra(_441007), c_Orderings_Oord__class_Oless__eq(_441007, _441009, _441011), -(c_Orderings_Oord__class_Oless__eq(_441007, c_Groups_Ouminus__class_Ouminus(_441007, _441011), c_Groups_Ouminus__class_Ouminus(_441007, _441009)))], (10107 ^ _319074) ^ [_665349, _665351] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _665349, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _665351, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless(tc_Int_Oint, _665349, _665351)), -(_665349 = _665351)], (3606 ^ _319074) ^ [_437388, _437390] : [class_Groups_Oordered__ab__group__add__abs(_437388), c_Orderings_Oord__class_Oless__eq(_437388, _437390, c_Groups_Ozero__class_Ozero(_437388)), -(c_Groups_Oabs__class_Oabs(_437388, _437390) = c_Groups_Ouminus__class_Ouminus(_437388, _437390))], (7600 ^ _319074) ^ [_578325, _578327, _578329] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _578325, _578327), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _578325, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _578327, _578329)))], (8238 ^ _319074) ^ [_601915, _601917] : [class_Rings_Ocomm__semiring__1(_601915), -(c_Rings_Odvd__class_Odvd(_601915, _601917, _601917))], (3496 ^ _319074) ^ [_433513, _433515, _433517, _433519, _433521] : [class_Groups_Oordered__cancel__ab__semigroup__add(_433513), c_Orderings_Oord__class_Oless__eq(_433513, _433515, _433517), c_Orderings_Oord__class_Oless(_433513, _433519, _433521), -(c_Orderings_Oord__class_Oless(_433513, c_Groups_Oplus__class_Oplus(_433513, _433515, _433519), c_Groups_Oplus__class_Oplus(_433513, _433517, _433521)))], (6401 ^ _319074) ^ [_535757, _535759, _535761] : [class_RealVector_Oreal__normed__field(_535757), -(c_Rings_Oinverse__class_Odivide(_535757, c_Groups_Ouminus__class_Ouminus(_535757, _535759), _535761) = c_Groups_Ouminus__class_Ouminus(_535757, c_Rings_Oinverse__class_Odivide(_535757, _535759, _535761)))], (12232 ^ _319074) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (10281 ^ _319074) ^ [_671135, _671137, _671139] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _671135, _671137), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _671137, _671139), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Nat_OSuc(_671135), _671139))], (830 ^ _319074) ^ [_343940, _343942, _343944, _343946, _343948, _343950] : [-(c_Orderings_Oord__class_Oless__eq(_343948, _343944, _343940)), c_Orderings_Oord__class_Oless__eq(_343950, _343946, _343942), _343950 = _343948, _343946 = _343944, _343942 = _343940], (12458 ^ _319074) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal))], (9546 ^ _319074) ^ [_646050, _646052, _646054] : [class_Fields_Ofield__inverse__zero(_646050), -(c_Rings_Oinverse__class_Odivide(_646050, c_Groups_Oone__class_Oone(_646050), hAPP(hAPP(c_Power_Opower__class_Opower(_646050), _646052), _646054)) = hAPP(hAPP(c_Power_Opower__class_Opower(_646050), c_Rings_Oinverse__class_Odivide(_646050, c_Groups_Oone__class_Oone(_646050), _646052)), _646054))], (7522 ^ _319074) ^ [_574973, _574975, _574977, _574979] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _574973), _574975), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _574977), _574975), _574979)) = 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, _574973, _574977)), _574975), _574979))], (5751 ^ _319074) ^ [_513532, _513534, _513536, _513538] : [class_Fields_Ofield(_513532), -(_513534 = c_Groups_Ozero__class_Ozero(_513532)), -(c_Groups_Oplus__class_Oplus(_513532, _513536, c_Rings_Oinverse__class_Odivide(_513532, _513538, _513534)) = c_Rings_Oinverse__class_Odivide(_513532, c_Groups_Oplus__class_Oplus(_513532, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_513532), _513534), _513536), _513538), _513534))], (4063 ^ _319074) ^ [_453421, _453423, _453425] : [class_Rings_Odivision__ring(_453421), -(c_Groups_Ouminus__class_Ouminus(_453421, c_Rings_Oinverse__class_Odivide(_453421, _453423, _453425)) = c_Rings_Oinverse__class_Odivide(_453421, c_Groups_Ouminus__class_Ouminus(_453421, _453423), _453425))], (4577 ^ _319074) ^ [_473192, _473194, _473196] : [class_Rings_Ocomm__semiring__1(_473192), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_473192), _473194), _473196) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_473192), _473196), _473194))], (12860 ^ _319074) ^ [_762713] : [class_Rings_Ocomm__semiring__0(_762713), -(class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(_762713)))], (10255 ^ _319074) ^ [_670279, _670281] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _670279, _670281)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _670279, c_Nat_OSuc(_670281)), -(_670281 = _670279)], (3934 ^ _319074) ^ [_448462, _448464, _448466] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _448462, _448464), _448466), 3937 ^ _319074 : [(3940 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _448464, _448466))], (3938 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _448462, _448466))]]], (12132 ^ _319074) ^ [_741262, _741264] : [c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _741262, _741264) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _741264, _741262) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_741262 = _741264)], (10353 ^ _319074) ^ [_673728, _673730] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _673728, c_Nat_OSuc(_673730)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _673728, _673730)), -(_673728 = c_Nat_OSuc(_673730))], (5001 ^ _319074) ^ [_488771, _488773, _488775] : [class_Rings_Oordered__cancel__semiring(_488771), c_Orderings_Oord__class_Oless__eq(_488771, c_Groups_Ozero__class_Ozero(_488771), _488773), c_Orderings_Oord__class_Oless__eq(_488771, _488775, c_Groups_Ozero__class_Ozero(_488771)), -(c_Orderings_Oord__class_Oless__eq(_488771, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_488771), _488773), _488775), c_Groups_Ozero__class_Ozero(_488771)))], (4261 ^ _319074) ^ [_459923] : [-(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _459923) = _459923)], (1102 ^ _319074) ^ [_354336, _354338] : [_354338 = _354336, -(tc_Polynomial_Opoly(_354338) = tc_Polynomial_Opoly(_354336))], (4253 ^ _319074) ^ [_459652, _459654] : [4254 ^ _319074 : [(4257 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _459654)], (4255 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _459652)]], -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _459652, _459654)))], (730 ^ _319074) ^ [_340954, _340956] : [-(class_Groups_Ominus(_340954)), _340956 = _340954, class_Groups_Ominus(_340956)], (8594 ^ _319074) ^ [_614379, _614381, _614383, _614385] : [class_Rings_Ocomm__semiring__1(_614379), -(hAPP(c_Polynomial_Opoly(_614379, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(_614379)), _614381), _614383)), _614385) = hAPP(hAPP(c_Power_Opower__class_Opower(_614379), hAPP(c_Polynomial_Opoly(_614379, _614381), _614385)), _614383))], (10203 ^ _319074) ^ [_668574, _668576] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _668576, c_Nat_OSuc(_668574)), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _668574, _668576)], (9961 ^ _319074) ^ [_660532, _660534, _660536, _660538, _660540] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _660532, _660534), 9964 ^ _319074 : [(9971 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _660532, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _660536, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _660540), _660534)), _660538)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _660532, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _660536, _660538)))], (9965 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _660532, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _660536, _660538)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _660532, c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _660536, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _660540), _660534)), _660538)))]]], (8001 ^ _319074) ^ [_593342, _593344, _593346] : [class_Rings_Olinordered__idom(_593342), c_Orderings_Oord__class_Oless__eq(_593342, c_Groups_Ozero__class_Ozero(_593342), _593344), c_Orderings_Oord__class_Oless__eq(_593342, c_Groups_Ozero__class_Ozero(_593342), _593346), c_Orderings_Oord__class_Oless__eq(_593342, _593346, c_Groups_Oone__class_Oone(_593342)), -(c_Orderings_Oord__class_Oless__eq(_593342, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_593342), _593344), _593346), _593344))], (590 ^ _319074) ^ [_336824, _336826] : [-(class_Groups_Ogroup__add(_336824)), _336826 = _336824, class_Groups_Ogroup__add(_336826)], (1042 ^ _319074) ^ [_352150, _352152] : [_352152 = _352150, -(c_Nat_OSuc(_352152) = c_Nat_OSuc(_352150))], (3336 ^ _319074) ^ [_428377, _428379] : [class_Groups_Oab__group__add(_428377), -(c_Groups_Oplus__class_Oplus(_428377, c_Groups_Ouminus__class_Ouminus(_428377, _428379), _428379) = c_Groups_Ozero__class_Ozero(_428377))], (4541 ^ _319074) ^ [_471244, _471246, _471248, _471250, _471252] : [class_Rings_Ocomm__semiring__1(_471244), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_471244), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_471244), _471246), _471248)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_471244), _471250), _471252)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_471244), _471250), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_471244), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_471244), _471246), _471248)), _471252)))], (12658 ^ _319074) ^ [] : [-(class_Groups_Ozero(tc_Complex_Ocomplex))], (4571 ^ _319074) ^ [_472894, _472896, _472898, _472900] : [class_Rings_Ocomm__semiring__1(_472894), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_472894), _472896), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_472894), _472898), _472900)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_472894), _472898), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_472894), _472896), _472900)))], (3330 ^ _319074) ^ [_428151, _428153] : [class_Groups_Ogroup__add(_428151), -(c_Groups_Oplus__class_Oplus(_428151, c_Groups_Ouminus__class_Ouminus(_428151, _428153), _428153) = c_Groups_Ozero__class_Ozero(_428151))], (10371 ^ _319074) ^ [_674319, _674321] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _674319, _674321)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Nat_OSuc(_674321), _674319))], (4339 ^ _319074) ^ [_462769, _462771] : [class_RealVector_Oreal__normed__vector(_462769), 4342 ^ _319074 : [(4349 ^ _319074) ^ [] : [-(_462771 = c_Groups_Ozero__class_Ozero(_462769)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_462769, _462771)))], (4343 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_462769, _462771)), _462771 = c_Groups_Ozero__class_Ozero(_462769)]]], (2878 ^ _319074) ^ [_413437, _413439, _413441] : [class_Orderings_Oorder(_413437), -(_413439 = _413441), c_Orderings_Oord__class_Oless__eq(_413437, _413441, _413439), -(c_Orderings_Oord__class_Oless(_413437, _413441, _413439))], (11858 ^ _319074) ^ [_729797, _729799, _729801, _729803, _729805, _729807] : [class_Rings_Oring(_729797), 11861 ^ _319074 : [(11868 ^ _319074) ^ [] : [c_Groups_Oplus__class_Oplus(_729797, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_729797), c_Groups_Ominus__class_Ominus(_729797, _729799, _729805)), _729801), _729803) = _729807, -(c_Groups_Oplus__class_Oplus(_729797, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_729797), _729799), _729801), _729803) = c_Groups_Oplus__class_Oplus(_729797, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_729797), _729805), _729801), _729807))], (11862 ^ _319074) ^ [] : [c_Groups_Oplus__class_Oplus(_729797, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_729797), _729799), _729801), _729803) = c_Groups_Oplus__class_Oplus(_729797, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_729797), _729805), _729801), _729807), -(c_Groups_Oplus__class_Oplus(_729797, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_729797), c_Groups_Ominus__class_Ominus(_729797, _729799, _729805)), _729801), _729803) = _729807)]]], (3276 ^ _319074) ^ [_426446, _426448] : [class_Groups_Oordered__ab__group__add(_426446), 3279 ^ _319074 : [(3286 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_426446, c_Groups_Ozero__class_Ozero(_426446), _426448), -(c_Orderings_Oord__class_Oless__eq(_426446, c_Groups_Ouminus__class_Ouminus(_426446, _426448), c_Groups_Ozero__class_Ozero(_426446)))], (3280 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_426446, c_Groups_Ouminus__class_Ouminus(_426446, _426448), c_Groups_Ozero__class_Ozero(_426446)), -(c_Orderings_Oord__class_Oless__eq(_426446, c_Groups_Ozero__class_Ozero(_426446), _426448))]]], (1309 ^ _319074) ^ [_361806, _361808] : [class_Groups_Omonoid__add(_361806), -(c_Groups_Oplus__class_Oplus(_361806, c_Groups_Ozero__class_Ozero(_361806), _361808) = _361808)], (12528 ^ _319074) ^ [] : [-(class_Rings_Ozero__neq__one(tc_RealDef_Oreal))], (3674 ^ _319074) ^ [_439555, _439557, _439559, _439561] : [class_Rings_Olinordered__semidom(_439555), c_Orderings_Oord__class_Oless(_439555, c_Groups_Ozero__class_Ozero(_439555), _439557), c_Orderings_Oord__class_Oless(_439555, _439559, _439561), -(c_Orderings_Oord__class_Oless(_439555, _439559, c_Groups_Oplus__class_Oplus(_439555, _439557, _439561)))], (7613 ^ _319074) ^ [_578873, _578875] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 7611 ^ [_578873, _578875]))], (7070 ^ _319074) ^ [_558316, _558318] : [class_Rings_Ocomm__semiring__0(_558316), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(_558316)), _558318), c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_558316))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(_558316)))], (12462 ^ _319074) ^ [] : [-(class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal))], (8346 ^ _319074) ^ [_605376, _605378] : [class_Rings_Ocomm__semiring__1(_605376), c_Rings_Odvd__class_Odvd(_605376, c_Groups_Ozero__class_Ozero(_605376), _605378), -(_605378 = c_Groups_Ozero__class_Ozero(_605376))], (7040 ^ _319074) ^ [_556974, _556976, _556978] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _556974, _556976)), _556978) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _556974), _556978), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _556976), _556978)))], (7621 ^ _319074) ^ [_579216, _579218] : [class_RealVector_Oreal__normed__field(_579216), 7625 ^ _319074 : [(7628 ^ _319074) ^ [_579507] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_579216, c_Rings_Oinverse__class_Odivide(_579216, _579507, _579218)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(_579216, _579507)), 7624 ^ [_579216, _579218])))], (7626 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), 7624 ^ [_579216, _579218]))]]], (6125 ^ _319074) ^ [_526263, _526265, _526267, _526269] : [class_Fields_Olinordered__field__inverse__zero(_526263), c_Orderings_Oord__class_Oless__eq(_526263, _526265, _526267), c_Orderings_Oord__class_Oless__eq(_526263, _526269, c_Groups_Ozero__class_Ozero(_526263)), c_Orderings_Oord__class_Oless(_526263, c_Groups_Ozero__class_Ozero(_526263), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_526263), _526265), _526267)), -(c_Orderings_Oord__class_Oless__eq(_526263, c_Rings_Oinverse__class_Odivide(_526263, _526269, _526265), c_Rings_Oinverse__class_Odivide(_526263, _526269, _526267)))], (12552 ^ _319074) ^ [] : [-(class_Int_Oring__char__0(tc_RealDef_Oreal))], (10195 ^ _319074) ^ [_668263] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_668263)], (7292 ^ _319074) ^ [_566403, _566405, _566407] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _566403), 7295 ^ _319074 : [(7302 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _566405, _566407), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _566403), _566405), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _566403), _566407)))], (7296 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _566403), _566405), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _566403), _566407)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _566405, _566407))]]], (3314 ^ _319074) ^ [_427650, _427652, _427654] : [class_Groups_Ogroup__add(_427650), 3317 ^ _319074 : [(3324 ^ _319074) ^ [] : [c_Groups_Oplus__class_Oplus(_427650, _427652, _427654) = c_Groups_Ozero__class_Ozero(_427650), -(_427652 = c_Groups_Ouminus__class_Ouminus(_427650, _427654))], (3318 ^ _319074) ^ [] : [_427652 = c_Groups_Ouminus__class_Ouminus(_427650, _427654), -(c_Groups_Oplus__class_Oplus(_427650, _427652, _427654) = c_Groups_Ozero__class_Ozero(_427650))]]], (1848 ^ _319074) ^ [_379426, _379428, _379430] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_379426), 1851 ^ _319074 : [(1858 ^ _319074) ^ [] : [_379430 = c_Groups_Ozero__class_Ozero(_379426), -(_379428 = c_Groups_Oplus__class_Oplus(_379426, _379428, _379430))], (1852 ^ _319074) ^ [] : [_379428 = c_Groups_Oplus__class_Oplus(_379426, _379428, _379430), -(_379430 = c_Groups_Ozero__class_Ozero(_379426))]]], (11604 ^ _319074) ^ [_719367, _719369, _719371, _719373] : [class_Rings_Ocomm__ring(_719367), class_Rings_Odvd(_719367), c_Rings_Odvd__class_Odvd(_719367, _719369, _719371), 11615 ^ _319074 : [(11622 ^ _319074) ^ [_720008, _720010] : [c_Rings_Odvd__class_Odvd(_719367, _719369, c_Groups_Oplus__class_Oplus(_719367, c_Groups_Ominus__class_Ominus(_719367, _720010, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_719367), _720008), _719371)), _719373)), -(c_Rings_Odvd__class_Odvd(_719367, _719369, c_Groups_Oplus__class_Oplus(_719367, _720010, _719373)))], (11616 ^ _319074) ^ [_719770, _719772] : [c_Rings_Odvd__class_Odvd(_719367, _719369, c_Groups_Oplus__class_Oplus(_719367, _719772, _719373)), -(c_Rings_Odvd__class_Odvd(_719367, _719369, c_Groups_Oplus__class_Oplus(_719367, c_Groups_Ominus__class_Ominus(_719367, _719772, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_719367), _719770), _719371)), _719373)))]]], (8316 ^ _319074) ^ [_604431, _604433, _604435] : [class_Rings_Ocomm__ring__1(_604431), 8319 ^ _319074 : [(8326 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(_604431, _604433, _604435), -(c_Rings_Odvd__class_Odvd(_604431, c_Groups_Ouminus__class_Ouminus(_604431, _604433), _604435))], (8320 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(_604431, c_Groups_Ouminus__class_Ouminus(_604431, _604433), _604435), -(c_Rings_Odvd__class_Odvd(_604431, _604433, _604435))]]], (2216 ^ _319074) ^ [_392065, _392067, _392069] : [class_Orderings_Oorder(_392065), c_Orderings_Oord__class_Oless(_392065, _392067, _392069), c_Orderings_Oord__class_Oless(_392065, _392069, _392067)], (11638 ^ _319074) ^ [_720735, _720737, _720739, _720741] : [class_Fields_Ofield(_720735), -(_720737 = c_Groups_Ozero__class_Ozero(_720735)), -(c_Groups_Ominus__class_Ominus(_720735, c_Rings_Oinverse__class_Odivide(_720735, _720739, _720737), _720741) = c_Rings_Oinverse__class_Odivide(_720735, c_Groups_Ominus__class_Ominus(_720735, _720739, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_720735), _720737), _720741)), _720737))], (4595 ^ _319074) ^ [_473982, _473984] : [class_Rings_Ocomm__semiring__1(_473982), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_473982), _473984), c_Groups_Ozero__class_Ozero(_473982)) = c_Groups_Ozero__class_Ozero(_473982))], (9326 ^ _319074) ^ [_638095] : [-(_638095 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), 9329 ^ _319074 : [(9336 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _638095)), -(c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, _638095) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))], (9330 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _638095), -(c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, _638095) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))]]], (8964 ^ _319074) ^ [_626553, _626555] : [-(_626553 = _626555), c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _626553, _626555), 8971 ^ _319074 : [(8974 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _626555, _626553)], (8972 ^ _319074) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _626553, _626555))]]], (3746 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____)))], (4601 ^ _319074) ^ [_474214, _474216] : [class_Rings_Omult__zero(_474214), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_474214), c_Groups_Ozero__class_Ozero(_474214)), _474216) = c_Groups_Ozero__class_Ozero(_474214))], (7407 ^ _319074) ^ [_570619] : [-(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _570619), _570619))), -(_570619 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))], (4437 ^ _319074) ^ [_466442, _466444, _466446] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _466442, _466444) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _466442, _466446), -(_466444 = _466446)], (11218 ^ _319074) ^ [_704336, _704338, _704340, _704342, _704344, _704346] : [c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _704336), _704338), _704340) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _704342), _704344), _704346), 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), _704342), _704344), _704346), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _704340, _704336), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _704346), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _704342), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _704342, _704336), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _704344, _704338))], (7739 ^ _319074) ^ [_584394, _584396] : [class_Rings_Odivision__ring(_584394), -(c_Rings_Oinverse__class_Odivide(_584394, _584396, c_Groups_Oone__class_Oone(_584394)) = _584396)], (4191 ^ _319074) ^ [_457593] : [-(_457593 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _457593))], (4395 ^ _319074) ^ [_464642, _464644, _464646, _464648, _464650] : [class_Fields_Ofield__inverse__zero(_464642), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_464642), c_Rings_Oinverse__class_Odivide(_464642, _464644, _464646)), c_Rings_Oinverse__class_Odivide(_464642, _464648, _464650)) = c_Rings_Oinverse__class_Odivide(_464642, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_464642), _464644), _464648), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_464642), _464646), _464650)))], (10125 ^ _319074) ^ [_665940, _665942] : [c_Orderings_Oord__class_Oless(tc_Int_Oint, _665940, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _665942, c_Groups_Oone__class_Oone(tc_Int_Oint))), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _665940, _665942))], (2492 ^ _319074) ^ [_400776, _400778] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, _400778, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _400776)), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _400776, _400778), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (9300 ^ _319074) ^ [_637149, _637151, _637153] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _637149), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _637151, _637153)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _637149), _637151)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _637149), _637153)))], (12292 ^ _319074) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (7865 ^ _319074) ^ [_588749] : [class_Rings_Olinordered__semidom(_588749), c_Orderings_Oord__class_Oless(_588749, c_Groups_Oone__class_Oone(_588749), c_Groups_Ozero__class_Ozero(_588749))], (7815 ^ _319074) ^ [_587129, _587131] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _587129), _587131), 7818 ^ _319074 : [(7821 ^ _319074) ^ [] : [-(_587131 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (7819 ^ _319074) ^ [] : [-(_587129 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (4635 ^ _319074) ^ [_475386, _475388, _475390] : [class_Rings_Ono__zero__divisors(_475386), -(_475388 = c_Groups_Ozero__class_Ozero(_475386)), -(_475390 = c_Groups_Ozero__class_Ozero(_475386)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_475386), _475388), _475390) = c_Groups_Ozero__class_Ozero(_475386)], (10405 ^ _319074) ^ [_675479] : [_675479 = c_Nat_OSuc(_675479)], (5127 ^ _319074) ^ [_493011, _493013, _493015, _493017, _493019] : [class_Rings_Oordered__semiring(_493011), c_Orderings_Oord__class_Oless__eq(_493011, _493013, _493015), c_Orderings_Oord__class_Oless__eq(_493011, _493017, _493019), c_Orderings_Oord__class_Oless__eq(_493011, c_Groups_Ozero__class_Ozero(_493011), _493013), c_Orderings_Oord__class_Oless__eq(_493011, c_Groups_Ozero__class_Ozero(_493011), _493017), -(c_Orderings_Oord__class_Oless__eq(_493011, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_493011), _493013), _493017), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_493011), _493015), _493019)))], (2026 ^ _319074) ^ [_385926, _385928, _385930, _385932, _385934] : [class_Groups_Ozero(_385926), 2029 ^ _319074 : [(2038 ^ _319074) ^ [] : [-(c_Polynomial_OpCons(_385926, _385928, _385930) = c_Polynomial_OpCons(_385926, _385932, _385934)), _385928 = _385932, _385930 = _385934], (2030 ^ _319074) ^ [] : [c_Polynomial_OpCons(_385926, _385928, _385930) = c_Polynomial_OpCons(_385926, _385932, _385934), 2033 ^ _319074 : [(2036 ^ _319074) ^ [] : [-(_385930 = _385934)], (2034 ^ _319074) ^ [] : [-(_385928 = _385932)]]]]], (12308 ^ _319074) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (7775 ^ _319074) ^ [_585566, _585568] : [class_Rings_Ocomm__semiring__1(_585566), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_585566), c_Groups_Oone__class_Oone(_585566)), _585568) = _585568)], (3436 ^ _319074) ^ [_431615, _431617] : [class_Groups_Olinordered__ab__group__add(_431615), 3439 ^ _319074 : [(3446 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_431615, _431617, c_Groups_Ozero__class_Ozero(_431615)), -(c_Orderings_Oord__class_Oless(_431615, c_Groups_Oplus__class_Oplus(_431615, _431617, _431617), c_Groups_Ozero__class_Ozero(_431615)))], (3440 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_431615, c_Groups_Oplus__class_Oplus(_431615, _431617, _431617), c_Groups_Ozero__class_Ozero(_431615)), -(c_Orderings_Oord__class_Oless(_431615, _431617, c_Groups_Ozero__class_Ozero(_431615)))]]], (8628 ^ _319074) ^ [_615864, _615866, _615868] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _615864), _615866), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _615864), _615868)), -(_615864 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _615866, _615868))], (12776 ^ _319074) ^ [_760053] : [class_Groups_Ocancel__comm__monoid__add(_760053), -(class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(_760053)))], (2160 ^ _319074) ^ [_390295, _390297, _390299, _390301] : [class_Orderings_Oorder(_390295), c_Orderings_Oord__class_Oless(_390295, _390297, _390299), _390297 = _390301, -(c_Orderings_Oord__class_Oless(_390295, _390301, _390299))], (1315 ^ _319074) ^ [_362026, _362028] : [class_Groups_Oordered__ab__group__add__abs(_362026), 1318 ^ _319074 : [(1325 ^ _319074) ^ [] : [_362028 = c_Groups_Ozero__class_Ozero(_362026), -(c_Groups_Oabs__class_Oabs(_362026, _362028) = c_Groups_Ozero__class_Ozero(_362026))], (1319 ^ _319074) ^ [] : [c_Groups_Oabs__class_Oabs(_362026, _362028) = c_Groups_Ozero__class_Ozero(_362026), -(_362028 = c_Groups_Ozero__class_Ozero(_362026))]]], (10543 ^ _319074) ^ [_680994] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _680994), -(_680994 = c_Nat_OSuc(10546 ^ [_680994]))], (4559 ^ _319074) ^ [_472270, _472272, _472274, _472276] : [class_Rings_Ocomm__semiring__1(_472270), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_472270), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_472270), _472272), _472274)), _472276) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_472270), _472272), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_472270), _472274), _472276)))], (12566 ^ _319074) ^ [] : [-(class_Groups_Ominus(tc_RealDef_Oreal))], (10185 ^ _319074) ^ [_667868] : [c_Nat_OSuc(_667868) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (620 ^ _319074) ^ [_337709, _337711] : [-(class_Int_Oring__char__0(_337709)), _337711 = _337709, class_Int_Oring__char__0(_337711)], (6861 ^ _319074) ^ [_550735, _550737, _550739] : [class_Rings_Olinordered__ring__strict(_550735), 6864 ^ _319074 : [(6865 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_550735, c_Groups_Ozero__class_Ozero(_550735), c_Groups_Oplus__class_Oplus(_550735, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_550735), _550737), _550737), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_550735), _550739), _550739))), _550737 = c_Groups_Ozero__class_Ozero(_550735), _550739 = c_Groups_Ozero__class_Ozero(_550735)], (6875 ^ _319074) ^ [] : [6876 ^ _319074 : [(6879 ^ _319074) ^ [] : [-(_550739 = c_Groups_Ozero__class_Ozero(_550735))], (6877 ^ _319074) ^ [] : [-(_550737 = c_Groups_Ozero__class_Ozero(_550735))]], -(c_Orderings_Oord__class_Oless(_550735, c_Groups_Ozero__class_Ozero(_550735), c_Groups_Oplus__class_Oplus(_550735, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_550735), _550737), _550737), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_550735), _550739), _550739))))]]], (12368 ^ _319074) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (12362 ^ _319074) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (12346 ^ _319074) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (12250 ^ _319074) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (11490 ^ _319074) ^ [_714158, _714160, _714162, _714164] : [class_RealVector_Oreal__normed__algebra(_714158), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_714158), _714160), c_Groups_Ominus__class_Ominus(_714158, _714162, _714164)) = c_Groups_Ominus__class_Ominus(_714158, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_714158), _714160), _714162), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_714158), _714160), _714164)))], (12190 ^ _319074) ^ [] : [-(class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal))], (7504 ^ _319074) ^ [_574356, _574358, _574360] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _574356), _574358) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _574356), _574360), -(_574356 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_574358 = _574360)], (12242 ^ _319074) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (12234 ^ _319074) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (10938 ^ _319074) ^ [_694532, _694534, _694536] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _694532), _694534), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _694536), _694534)), -(_694534 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Rings_Odvd__class_Odvd(tc_Int_Oint, _694532, _694536))], (7218 ^ _319074) ^ [_563640, _563642] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _563640), c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _563642), -(c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _563640), _563642)))], (12938 ^ _319074) ^ [_765183] : [class_Rings_Olinordered__idom(_765183), -(class_Orderings_Oorder(tc_Polynomial_Opoly(_765183)))], (11062 ^ _319074) ^ [_698956, _698958, _698960] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, _698956, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _698958, _698960)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint, _698958, c_Groups_Oplus__class_Oplus(tc_Int_Oint, _698956, _698960)))], (3984 ^ _319074) ^ [_450272, _450274, _450276] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _450272, _450274), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _450272, _450276), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _450274, _450276)))], (10193 ^ _319074) ^ [_668184] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Nat_OSuc(_668184)], (3378 ^ _319074) ^ [_429808, _429810, _429812] : [class_Groups_Oordered__ab__group__add__abs(_429808), c_Orderings_Oord__class_Oless__eq(_429808, _429810, _429812), c_Orderings_Oord__class_Oless__eq(_429808, c_Groups_Ouminus__class_Ouminus(_429808, _429810), _429812), -(c_Orderings_Oord__class_Oless__eq(_429808, c_Groups_Oabs__class_Oabs(_429808, _429810), _429812))], (12914 ^ _319074) ^ [_764423] : [class_Rings_Ocomm__semiring__0(_764423), -(class_Rings_Osemiring__0(tc_Polynomial_Opoly(_764423)))], (9314 ^ _319074) ^ [_637715] : [c_Orderings_Oord__class_Oless(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _637715), -(c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal, _637715) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal))], (3420 ^ _319074) ^ [_431127, _431129] : [class_Groups_Olinordered__ab__group__add(_431127), 3423 ^ _319074 : [(3430 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_431127, c_Groups_Ozero__class_Ozero(_431127), _431129), -(c_Orderings_Oord__class_Oless(_431127, c_Groups_Ozero__class_Ozero(_431127), c_Groups_Oplus__class_Oplus(_431127, _431129, _431129)))], (3424 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_431127, c_Groups_Ozero__class_Ozero(_431127), c_Groups_Oplus__class_Oplus(_431127, _431129, _431129)), -(c_Orderings_Oord__class_Oless(_431127, c_Groups_Ozero__class_Ozero(_431127), _431129))]]], (9172 ^ _319074) ^ [_633034, _633036, _633038] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _633034, _633036), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _633036, _633034)), _633036 = _633038, 9183 ^ _319074 : [(9186 ^ _319074) ^ [] : [c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _633038, _633034)], (9184 ^ _319074) ^ [] : [-(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _633034, _633038))]]], (12226 ^ _319074) ^ [_744881, _744883] : [class_Groups_Ominus(_744881), -(class_Groups_Ominus(tc_fun(_744883, _744881)))], (12620 ^ _319074) ^ [] : [-(class_RealVector_Oreal__field(tc_Complex_Ocomplex))], (6249 ^ _319074) ^ [_530380, _530382, _530384, _530386, _530388] : [class_Rings_Olinordered__semiring__strict(_530380), c_Orderings_Oord__class_Oless__eq(_530380, _530382, _530384), c_Orderings_Oord__class_Oless(_530380, _530386, _530388), c_Orderings_Oord__class_Oless(_530380, c_Groups_Ozero__class_Ozero(_530380), _530382), c_Orderings_Oord__class_Oless__eq(_530380, c_Groups_Ozero__class_Ozero(_530380), _530386), -(c_Orderings_Oord__class_Oless(_530380, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_530380), _530382), _530386), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_530380), _530384), _530388)))], (4649 ^ _319074) ^ [_475835, _475837, _475839] : [class_Rings_Ono__zero__divisors(_475835), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_475835), _475837), _475839) = c_Groups_Ozero__class_Ozero(_475835), -(_475837 = c_Groups_Ozero__class_Ozero(_475835)), -(_475839 = c_Groups_Ozero__class_Ozero(_475835))], (11896 ^ _319074) ^ [_731583, _731585, _731587, _731589, _731591] : [class_Rings_Oring(_731583), -(c_Groups_Ominus__class_Ominus(_731583, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_731583), _731585), _731587), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_731583), _731589), _731591)) = c_Groups_Oplus__class_Oplus(_731583, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_731583), _731585), c_Groups_Ominus__class_Ominus(_731583, _731587, _731591)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_731583), c_Groups_Ominus__class_Ominus(_731583, _731585, _731589)), _731591)))], (1092 ^ _319074) ^ [_354005, _354007, _354009, _354011] : [-(tc_fun(_354011, _354007) = tc_fun(_354009, _354005)), _354011 = _354009, _354007 = _354005], (1549 ^ _319074) ^ [_369421, _369423, _369425] : [class_Orderings_Oorder(_369421), c_Orderings_Oord__class_Oless__eq(_369421, _369423, _369425), c_Orderings_Oord__class_Oless__eq(_369421, _369425, _369423), -(_369423 = _369425)], (2838 ^ _319074) ^ [_412198, _412200, _412202] : [class_Orderings_Olinorder(_412198), c_Orderings_Oord__class_Oless__eq(_412198, _412200, _412202), 2845 ^ _319074 : [(2852 ^ _319074) ^ [] : [_412200 = _412202, c_Orderings_Oord__class_Oless(_412198, _412200, _412202)], (2846 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_412198, _412200, _412202)), -(_412200 = _412202)]]], (848 ^ _319074) ^ [_345005, _345007, _345009, _345011] : [-(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_345011, _345007) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(_345009, _345005)), _345011 = _345009, _345007 = _345005], (6723 ^ _319074) ^ [_546229, _546231, _546233] : [-(c_RealVector_Onorm__class_Onorm(_546229, c_Rings_Oinverse__class_Odivide(_546229, _546231, _546233)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_546229, _546231), c_RealVector_Onorm__class_Onorm(_546229, _546233))), class_Fields_Ofield__inverse__zero(_546229), class_RealVector_Oreal__normed__field(_546229)], (10149 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (12318 ^ _319074) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (4355 ^ _319074) ^ [_463247, _463249] : [class_RealVector_Oreal__normed__vector(_463247), 4358 ^ _319074 : [(4365 ^ _319074) ^ [] : [_463249 = c_Groups_Ozero__class_Ozero(_463247), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_463247, _463249), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)))], (4359 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_RealVector_Onorm__class_Onorm(_463247, _463249), c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), -(_463249 = c_Groups_Ozero__class_Ozero(_463247))]]], (3586 ^ _319074) ^ [_436700, _436702] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _436700), _436702), 3589 ^ _319074 : [(3592 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _436700, _436702))], (3590 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _436702), _436700))]]], (4413 ^ _319074) ^ [_465440, _465442] : [class_Lattices_Oab__semigroup__idem__mult(_465440), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_465440), _465442), _465442) = _465442)], (12358 ^ _319074) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (3752 ^ _319074) ^ [_442030, _442032] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _442030, _442032), _442032)], (12272 ^ _319074) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (11200 ^ _319074) ^ [_703699, _703701, _703703, _703705, _703707] : [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), _703699), _703701), _703703), c_Groups_Oplus__class_Oplus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _703699), _703705), _703707)), c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _703707, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Orderings_Oord__class_Oless(tc_Int_Oint, _703699, _703707), c_Orderings_Oord__class_Oless(tc_Int_Oint, _703699, _703703), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _703705, _703701))], (500 ^ _319074) ^ [_334169, _334171] : [-(class_Rings_Ocomm__semiring(_334169)), _334171 = _334169, class_Rings_Ocomm__semiring(_334171)], (4203 ^ _319074) ^ [_458020, _458022] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _458020, _458022), _458022 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (8600 ^ _319074) ^ [_614687, _614689, _614691, _614693] : [class_Rings_Ocomm__semiring__1(_614687), -(hAPP(hAPP(c_Power_Opower__class_Opower(_614687), hAPP(hAPP(c_Power_Opower__class_Opower(_614687), _614689), _614691)), _614693) = hAPP(hAPP(c_Power_Opower__class_Opower(_614687), _614689), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _614691), _614693)))], (5581 ^ _319074) ^ [_507783, _507785, _507787] : [class_Rings_Olinordered__semiring__strict(_507783), c_Orderings_Oord__class_Oless(_507783, c_Groups_Ozero__class_Ozero(_507783), _507785), c_Orderings_Oord__class_Oless(_507783, _507787, c_Groups_Ozero__class_Ozero(_507783)), -(c_Orderings_Oord__class_Oless(_507783, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_507783), _507787), _507785), c_Groups_Ozero__class_Ozero(_507783)))], (9610 ^ _319074) ^ [_648493, _648495, _648497] : [class_Rings_Olinordered__semidom(_648493), c_Orderings_Oord__class_Oless(_648493, c_Groups_Oone__class_Oone(_648493), _648495), -(c_Orderings_Oord__class_Oless(_648493, c_Groups_Oone__class_Oone(_648493), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_648493), _648495), hAPP(hAPP(c_Power_Opower__class_Opower(_648493), _648495), _648497))))], (12890 ^ _319074) ^ [_763663] : [class_Rings_Olinordered__idom(_763663), -(class_Orderings_Olinorder(tc_Polynomial_Opoly(_763663)))], (5263 ^ _319074) ^ [_497355, _497357, _497359, _497361] : [class_Fields_Olinordered__field__inverse__zero(_497355), 5266 ^ _319074 : [(5267 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_497355, c_Rings_Oinverse__class_Odivide(_497355, _497357, _497359), _497361), 5270 ^ _319074 : [(5277 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_497355, c_Groups_Ozero__class_Ozero(_497355), _497359)), 5280 ^ _319074 : [(5287 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_497355, _497359, c_Groups_Ozero__class_Ozero(_497355))), -(c_Orderings_Oord__class_Oless(_497355, c_Groups_Ozero__class_Ozero(_497355), _497361))], (5281 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_497355, _497359, c_Groups_Ozero__class_Ozero(_497355)), -(c_Orderings_Oord__class_Oless(_497355, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_497355), _497361), _497359), _497357))]]], (5271 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_497355, c_Groups_Ozero__class_Ozero(_497355), _497359), -(c_Orderings_Oord__class_Oless(_497355, _497357, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_497355), _497361), _497359)))]]], (5293 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_497355, c_Rings_Oinverse__class_Odivide(_497355, _497357, _497359), _497361)), 5296 ^ _319074 : [(5299 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_497355, _497357, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_497355), _497361), _497359))], (5297 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_497355, c_Groups_Ozero__class_Ozero(_497355), _497359))]], 5300 ^ _319074 : [(5303 ^ _319074) ^ [] : [5304 ^ _319074 : [(5307 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_497355, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_497355), _497361), _497359), _497357)], (5305 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(_497355, _497359, c_Groups_Ozero__class_Ozero(_497355)))]], 5308 ^ _319074 : [(5311 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_497355, c_Groups_Ozero__class_Ozero(_497355), _497361)], (5309 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_497355, _497359, c_Groups_Ozero__class_Ozero(_497355))]]], (5301 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_497355, c_Groups_Ozero__class_Ozero(_497355), _497359)]]]]], (7318 ^ _319074) ^ [_567257, _567259, _567261] : [7319 ^ _319074 : [(7322 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _567257, _567261)], (7320 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _567259))]], -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _567257), _567259), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _567261), _567259)))], (11319 ^ _319074) ^ [_707884, _707886] : [-(hBOOL(hAPP(_707884, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_707884, _707886)), 11327 ^ _319074 : [(11330 ^ _319074) ^ [_708320] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _708320, 11326 ^ [_707884, _707886]), hBOOL(hAPP(_707884, _708320))], (11336 ^ _319074) ^ [] : [-(hBOOL(hAPP(_707884, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, 11326 ^ [_707884, _707886], c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (11328 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, 11326 ^ [_707884, _707886], _707886))]]], (12998 ^ _319074) ^ [_767083] : [class_Groups_Ozero(_767083), -(class_Groups_Ozero(tc_Polynomial_Opoly(_767083)))], (10784 ^ _319074) ^ [_689137, _689139, _689141] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _689139, _689141), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_689137)), _689139), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Nat_OSuc(_689137)), _689141)))], (12884 ^ _319074) ^ [_763473] : [class_Rings_Olinordered__idom(_763473), -(class_Orderings_Opreorder(tc_Polynomial_Opoly(_763473)))], (12236 ^ _319074) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (6609 ^ _319074) ^ [_542507, _542509, _542511] : [class_Fields_Olinordered__field(_542507), c_Orderings_Oord__class_Oless(_542507, c_Groups_Ozero__class_Ozero(_542507), _542509), c_Orderings_Oord__class_Oless(_542507, _542511, c_Groups_Ozero__class_Ozero(_542507)), -(c_Orderings_Oord__class_Oless(_542507, c_Rings_Oinverse__class_Odivide(_542507, _542509, _542511), c_Groups_Ozero__class_Ozero(_542507)))], (9997 ^ _319074) ^ [_661726, _661728] : [c_Rings_Odvd__class_Odvd(tc_Int_Oint, _661726, _661728), c_Orderings_Oord__class_Oless(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _661728), -(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint, _661726, _661728))], (3902 ^ _319074) ^ [_447331, _447333] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _447331, _447333), _447333 = _447331], (11028 ^ _319074) ^ [_697666, _697668] : [11029 ^ _319074 : [(11032 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _697666)], (11030 ^ _319074) ^ [] : [_697668 = 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), _697666), _697668)))], (1281 ^ _319074) ^ [_360884, _360886] : [class_Groups_Omonoid__add(_360884), -(c_Groups_Oplus__class_Oplus(_360884, _360886, c_Groups_Ozero__class_Ozero(_360884)) = _360886)], (12650 ^ _319074) ^ [] : [-(class_Rings_Oring__1(tc_Complex_Ocomplex))], (7787 ^ _319074) ^ [_586022, _586024] : [class_Groups_Omonoid__mult(_586022), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_586022), _586024), c_Groups_Oone__class_Oone(_586022)) = _586024)], (11508 ^ _319074) ^ [_715065, _715067, _715069] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _715065), c_Groups_Ominus__class_Ominus(tc_Int_Oint, _715067, _715069)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _715065), _715067), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _715065), _715069)))], (1870 ^ _319074) ^ [_380138, _380140] : [class_Rings_Ocomm__semiring__1(_380138), -(c_Groups_Oplus__class_Oplus(_380138, c_Groups_Ozero__class_Ozero(_380138), _380140) = _380140)], (2060 ^ _319074) ^ [_387172, _387174] : [class_Groups_Olinordered__ab__group__add(_387172), 2063 ^ _319074 : [(2070 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_387172, c_Groups_Ozero__class_Ozero(_387172), _387174), -(c_Orderings_Oord__class_Oless(_387172, c_Groups_Ouminus__class_Ouminus(_387172, _387174), _387174))], (2064 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_387172, c_Groups_Ouminus__class_Ouminus(_387172, _387174), _387174), -(c_Orderings_Oord__class_Oless(_387172, c_Groups_Ozero__class_Ozero(_387172), _387174))]]], (2782 ^ _319074) ^ [_410503, _410505, _410507, _410509] : [class_Orderings_Opreorder(_410503), c_Orderings_Oord__class_Oless(_410503, _410505, _410507), c_Orderings_Oord__class_Oless__eq(_410503, _410507, _410509), -(c_Orderings_Oord__class_Oless(_410503, _410505, _410509))], (7156 ^ _319074) ^ [_561503, _561505, _561507] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _561503), _561505), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _561507), _561505))), c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _561505), c_Orderings_Oord__class_Oless(tc_Nat_Onat, _561503, _561507)], (9386 ^ _319074) ^ [_640174, _640176] : [class_Groups_Omonoid__mult(_640174), -(hAPP(hAPP(c_Power_Opower__class_Opower(_640174), c_Groups_Oone__class_Oone(_640174)), _640176) = c_Groups_Oone__class_Oone(_640174))], (1804 ^ _319074) ^ [_377921, _377923] : [class_Groups_Oordered__ab__group__add__abs(_377921), -(c_Groups_Oabs__class_Oabs(_377921, c_Groups_Oabs__class_Oabs(_377921, _377923)) = c_Groups_Oabs__class_Oabs(_377921, _377923))], (610 ^ _319074) ^ [_337414, _337416] : [-(class_Orderings_Oorder(_337414)), _337416 = _337414, class_Orderings_Oorder(_337416)], (12196 ^ _319074) ^ [_743821, _743823] : [class_Lattices_Oboolean__algebra(_743821), -(class_Lattices_Oboolean__algebra(tc_fun(_743823, _743821)))], (4731 ^ _319074) ^ [_479270, _479272, _479274, _479276] : [class_Rings_Ocomm__semiring(_479270), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_479270), c_Groups_Oplus__class_Oplus(_479270, _479272, _479274)), _479276) = c_Groups_Oplus__class_Oplus(_479270, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_479270), _479272), _479276), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_479270), _479274), _479276)))], (2706 ^ _319074) ^ [_407895, _407897, _407899] : [class_Groups_Ogroup__add(_407895), -(c_Groups_Ouminus__class_Ouminus(_407895, c_Groups_Oplus__class_Oplus(_407895, _407897, _407899)) = c_Groups_Oplus__class_Oplus(_407895, c_Groups_Ouminus__class_Ouminus(_407895, _407899), c_Groups_Ouminus__class_Ouminus(_407895, _407897)))], (2588 ^ _319074) ^ [_404083, _404085] : [class_Groups_Olinordered__ab__group__add(_404083), 2591 ^ _319074 : [(2598 ^ _319074) ^ [] : [_404085 = c_Groups_Ozero__class_Ozero(_404083), -(_404085 = c_Groups_Ouminus__class_Ouminus(_404083, _404085))], (2592 ^ _319074) ^ [] : [_404085 = c_Groups_Ouminus__class_Ouminus(_404083, _404085), -(_404085 = c_Groups_Ozero__class_Ozero(_404083))]]], (12630 ^ _319074) ^ [] : [-(class_Groups_Omonoid__mult(tc_Complex_Ocomplex))], (6383 ^ _319074) ^ [_534975, _534977] : [class_RealVector_Oreal__normed__field(_534975), -(c_Rings_Oinverse__class_Odivide(_534975, c_Groups_Ozero__class_Ozero(_534975), _534977) = c_Groups_Ozero__class_Ozero(_534975))], (12572 ^ _319074) ^ [] : [-(class_Groups_Ozero(tc_RealDef_Oreal))], (3580 ^ _319074) ^ [_436441, _436443] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal, _436441), _436443), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, _436441, _436443)))], (11118 ^ _319074) ^ [_700967] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _700967, c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_700967 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_700967 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (2012 ^ _319074) ^ [_385458, _385460, _385462] : [class_Groups_Oordered__comm__monoid__add(_385458), c_Orderings_Oord__class_Oless(_385458, _385460, c_Groups_Ozero__class_Ozero(_385458)), c_Orderings_Oord__class_Oless__eq(_385458, _385462, c_Groups_Ozero__class_Ozero(_385458)), -(c_Orderings_Oord__class_Oless(_385458, c_Groups_Oplus__class_Oplus(_385458, _385460, _385462), c_Groups_Ozero__class_Ozero(_385458)))], (11274 ^ _319074) ^ [] : [-(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)))], (10455 ^ _319074) ^ [_677229] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _677229) = _677229)], (12340 ^ _319074) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (12288 ^ _319074) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (1149 ^ _319074) ^ [] : [v_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))], (1379 ^ _319074) ^ [_364081, _364083, _364085] : [class_Groups_Oordered__comm__monoid__add(_364081), c_Orderings_Oord__class_Oless__eq(_364081, c_Groups_Ozero__class_Ozero(_364081), _364083), c_Orderings_Oord__class_Oless__eq(_364081, c_Groups_Ozero__class_Ozero(_364081), _364085), 1390 ^ _319074 : [(1399 ^ _319074) ^ [] : [-(c_Groups_Oplus__class_Oplus(_364081, _364083, _364085) = c_Groups_Ozero__class_Ozero(_364081)), _364083 = c_Groups_Ozero__class_Ozero(_364081), _364085 = c_Groups_Ozero__class_Ozero(_364081)], (1391 ^ _319074) ^ [] : [c_Groups_Oplus__class_Oplus(_364081, _364083, _364085) = c_Groups_Ozero__class_Ozero(_364081), 1394 ^ _319074 : [(1397 ^ _319074) ^ [] : [-(_364085 = c_Groups_Ozero__class_Ozero(_364081))], (1395 ^ _319074) ^ [] : [-(_364083 = c_Groups_Ozero__class_Ozero(_364081))]]]]], (12030 ^ _319074) ^ [_737278, _737280, _737282, _737284, _737286] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _737278, _737280), -(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), _737278), _737282), _737284), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _737280), _737282), _737286)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat, _737284, 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, _737280, _737278)), _737282), _737286)))], (3846 ^ _319074) ^ [_445418, _445420, _445422, _445424] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _445418, _445420), c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _445422, _445420) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _445418, _445424), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _445422, _445424))], (4691 ^ _319074) ^ [_477448, _477450, _477452, _477454] : [class_Rings_Ocomm__semiring__1(_477448), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_477448), c_Groups_Oplus__class_Oplus(_477448, _477450, _477452)), _477454) = c_Groups_Oplus__class_Oplus(_477448, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_477448), _477450), _477454), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_477448), _477452), _477454)))], (10531 ^ _319074) ^ [_680433, _680435, _680437] : [class_Power_Opower(_680433), -(hAPP(hAPP(c_Power_Opower__class_Opower(_680433), _680435), c_Nat_OSuc(_680437)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_680433), _680435), hAPP(hAPP(c_Power_Opower__class_Opower(_680433), _680435), _680437)))], (3754 ^ _319074) ^ [_442173, _442175] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _442173, _442175), 3757 ^ _319074 : [(3760 ^ _319074) ^ [] : [_442173 = _442175], (3758 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _442173, _442175))]]], (1924 ^ _319074) ^ [] : [c_Polynomial_OpCons(tc_Complex_Ocomplex, v_c____, v_cs____) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))], (7246 ^ _319074) ^ [_564608, _564610] : [-(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _564608), _564608), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal), _564610), _564610)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)), _564608 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal), _564610 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)], (9104 ^ _319074) ^ [_630981, _630983] : [_630981 = _630983, c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _630981, _630983), -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat, _630983, _630981))], (3748 ^ _319074) ^ [] : [-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v_da____), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_aa____)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_c____)), c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, v_z____)))], (11574 ^ _319074) ^ [_718121, _718123, _718125] : [class_Groups_Oordered__ab__group__add__abs(_718121), -(c_Orderings_Oord__class_Oless__eq(_718121, c_Groups_Oabs__class_Oabs(_718121, c_Groups_Ominus__class_Ominus(_718121, _718123, _718125)), c_Groups_Oplus__class_Oplus(_718121, c_Groups_Oabs__class_Oabs(_718121, _718123), c_Groups_Oabs__class_Oabs(_718121, _718125))))], (11762 ^ _319074) ^ [_725828, _725830, _725832] : [class_Groups_Oab__group__add(_725828), -(c_Groups_Ominus__class_Ominus(_725828, _725830, _725832) = c_Groups_Oplus__class_Oplus(_725828, _725830, c_Groups_Ouminus__class_Ouminus(_725828, _725832)))], (7372 ^ _319074) ^ [_569275, _569277] : [-(v_cs____ = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex))), 7376 ^ _319074 : [(7377 ^ _319074) ^ [_569504] : [c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, 7375 ^ [_569275, _569277], c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, _569504)), -(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, _569275, c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex, c_Polynomial_OpCons(tc_Complex_Ocomplex, _569277, v_cs____)), _569504))))]]], (6637 ^ _319074) ^ [_543387, _543389, _543391] : [class_Fields_Olinordered__field(_543387), c_Orderings_Oord__class_Oless(_543387, _543389, c_Groups_Ozero__class_Ozero(_543387)), c_Orderings_Oord__class_Oless(_543387, _543391, c_Groups_Ozero__class_Ozero(_543387)), -(c_Orderings_Oord__class_Oless(_543387, c_Groups_Ozero__class_Ozero(_543387), c_Rings_Oinverse__class_Odivide(_543387, _543389, _543391)))], (2892 ^ _319074) ^ [_413858, _413860, _413862] : [class_Orderings_Oorder(_413858), -(_413860 = _413862), c_Orderings_Oord__class_Oless__eq(_413858, _413860, _413862), -(c_Orderings_Oord__class_Oless(_413858, _413860, _413862))], (10433 ^ _319074) ^ [_676483] : [-(c_Groups_Oplus__class_Oplus(tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint, _676483), _676483) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (5999 ^ _319074) ^ [_522072, _522074, _522076, _522078] : [class_Fields_Olinordered__field(_522072), c_Orderings_Oord__class_Oless(_522072, c_Groups_Ozero__class_Ozero(_522072), _522074), 6006 ^ _319074 : [(6013 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_522072, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_522072), _522076), _522074), _522078), -(c_Orderings_Oord__class_Oless__eq(_522072, _522076, c_Rings_Oinverse__class_Odivide(_522072, _522078, _522074)))], (6007 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(_522072, _522076, c_Rings_Oinverse__class_Odivide(_522072, _522078, _522074)), -(c_Orderings_Oord__class_Oless__eq(_522072, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_522072), _522076), _522074), _522078))]]], (8065 ^ _319074) ^ [_595408, _595410] : [-(c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex, c_Complex_Orcis(_595408, _595410)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, _595408))], (10403 ^ _319074) ^ [_675400] : [c_Nat_OSuc(_675400) = _675400], (11998 ^ _319074) ^ [_735964, _735966, _735968, _735970, _735972] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _735964, _735966), 12001 ^ _319074 : [(12008 ^ _319074) ^ [] : [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, _735966, _735964)), _735968), _735970) = _735972, -(c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _735966), _735968), _735970) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _735964), _735968), _735972))], (12002 ^ _319074) ^ [] : [c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _735966), _735968), _735970) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _735964), _735968), _735972), -(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, _735966, _735964)), _735968), _735970) = _735972)]]], (8736 ^ _319074) ^ [_619423, _619425] : [class_Rings_Olinordered__idom(_619423), 8739 ^ _319074 : [(8746 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(_619423, c_Groups_Ozero__class_Ozero(_619423), _619425), -(c_Groups_Osgn__class_Osgn(_619423, _619425) = c_Groups_Oone__class_Oone(_619423))], (8740 ^ _319074) ^ [] : [c_Groups_Osgn__class_Osgn(_619423, _619425) = c_Groups_Oone__class_Oone(_619423), -(c_Orderings_Oord__class_Oless(_619423, c_Groups_Ozero__class_Ozero(_619423), _619425))]]], (2712 ^ _319074) ^ [_408157, _408159, _408161] : [class_Groups_Oab__group__add(_408157), -(c_Groups_Ouminus__class_Ouminus(_408157, c_Groups_Oplus__class_Oplus(_408157, _408159, _408161)) = c_Groups_Oplus__class_Oplus(_408157, c_Groups_Ouminus__class_Ouminus(_408157, _408159), c_Groups_Ouminus__class_Ouminus(_408157, _408161)))], (7973 ^ _319074) ^ [_592467, _592469] : [class_Rings_Odivision__ring__inverse__zero(_592467), 7976 ^ _319074 : [(7983 ^ _319074) ^ [] : [-(_592469 = c_Groups_Ozero__class_Ozero(_592467)), -(c_Rings_Oinverse__class_Odivide(_592467, _592469, _592469) = c_Groups_Oone__class_Oone(_592467))], (7977 ^ _319074) ^ [] : [_592469 = c_Groups_Ozero__class_Ozero(_592467), -(c_Rings_Oinverse__class_Odivide(_592467, _592469, _592469) = c_Groups_Ozero__class_Ozero(_592467))]]], (7853 ^ _319074) ^ [_588352] : [class_Rings_Olinordered__semidom(_588352), c_Orderings_Oord__class_Oless__eq(_588352, c_Groups_Oone__class_Oone(_588352), c_Groups_Ozero__class_Ozero(_588352))], (4233 ^ _319074) ^ [_458989] : [_458989 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _458989, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (12332 ^ _319074) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (10197 ^ _319074) ^ [_668401, _668403] : [-(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _668401, _668403)), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _668403, c_Nat_OSuc(_668401)))], (12356 ^ _319074) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (9290 ^ _319074) ^ [_636714, _636716] : [9291 ^ _319074 : [(9294 ^ _319074) ^ [] : [_636716 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (9292 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _636714)]], -(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), _636714), _636716)))], (3808 ^ _319074) ^ [_443995, _443997, _443999] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, _443995, _443997), -(c_Orderings_Oord__class_Oless(tc_Nat_Onat, _443995, c_Groups_Oplus__class_Oplus(tc_Nat_Onat, _443997, _443999)))], (8548 ^ _319074) ^ [_612530, _612532] : [class_RealVector_Oreal__normed__vector(_612530), 8551 ^ _319074 : [(8558 ^ _319074) ^ [] : [_612532 = c_Groups_Ozero__class_Ozero(_612530), -(c_Groups_Osgn__class_Osgn(_612530, _612532) = c_Groups_Ozero__class_Ozero(_612530))], (8552 ^ _319074) ^ [] : [c_Groups_Osgn__class_Osgn(_612530, _612532) = c_Groups_Ozero__class_Ozero(_612530), -(_612532 = c_Groups_Ozero__class_Ozero(_612530))]]], (12450 ^ _319074) ^ [] : [-(class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal))], (7438 ^ _319074) ^ [_571887, _571889, _571891] : [c_Orderings_Oord__class_Oless(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _571887), 7441 ^ _319074 : [(7448 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _571889, _571891), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _571887), _571889), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _571887), _571891)))], (7442 ^ _319074) ^ [] : [c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _571887), _571889), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _571887), _571891)), -(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat, _571889, _571891))]]], (6107 ^ _319074) ^ [_525676, _525678, _525680, _525682] : [class_Fields_Olinordered__field(_525676), c_Orderings_Oord__class_Oless__eq(_525676, _525678, _525680), c_Orderings_Oord__class_Oless__eq(_525676, c_Groups_Ozero__class_Ozero(_525676), _525682), c_Orderings_Oord__class_Oless(_525676, c_Groups_Ozero__class_Ozero(_525676), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_525676), _525680), _525678)), -(c_Orderings_Oord__class_Oless__eq(_525676, c_Rings_Oinverse__class_Odivide(_525676, _525682, _525680), c_Rings_Oinverse__class_Odivide(_525676, _525682, _525678)))], (12510 ^ _319074) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal))], (12428 ^ _319074) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (12468 ^ _319074) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal))]], input).
% 61.55/59.43  ncf('1',plain,[c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_da____, v_mazh)],start(13044 ^ 0)).
% 61.55/59.43  ncf('1.1',plain,[-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_da____, v_mazh)), 3396 : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v_da____), v_mazh), 3396 : class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)],extension(3392 ^ 1,bind([[_430240, _430242, _430244], [tc_RealDef_Oreal, v_da____, v_mazh]]))).
% 61.55/59.43  ncf('1.1.1',plain,[-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v_da____), v_mazh)), class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v_da____), v_ma), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v_mazh, v_ma))],extension(1820 ^ 4,bind([[_378540, _378542, _378544, _378546], [tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v_da____), v_ma, v_mazh]]))).
% 61.55/59.43  ncf('1.1.1.1',plain,[-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal))],extension(12442 ^ 5)).
% 61.55/59.43  ncf('1.1.1.2',plain,[-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v_da____), v_ma), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v_mazh, v_ma))), class_Orderings_Oorder(tc_RealDef_Oreal), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_mzh, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v_mazh, v_ma)), c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v_da____), v_ma), v_mzh)],extension(1507 ^ 5,bind([[_368121, _368123, _368125, _368127], [tc_RealDef_Oreal, v_mzh, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v_mazh, v_ma), c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v_da____), v_ma)]]))).
% 61.55/59.43  ncf('1.1.1.2.1',plain,[-(class_Orderings_Oorder(tc_RealDef_Oreal))],extension(12550 ^ 6)).
% 61.55/59.43  ncf('1.1.1.2.2',plain,[-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, v_mzh, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, v_mazh, v_ma)))],extension(13040 ^ 6)).
% 61.55/59.43  ncf('1.1.1.2.3',plain,[-(c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal, c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal, c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal, v_da____), v_ma), v_mzh))],extension(13042 ^ 6)).
% 61.55/59.43  ncf('1.1.2',plain,[-(class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal))],extension(12460 ^ 2)).
% 61.55/59.43  %-----------------------------------------------------
% 61.55/59.43  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------