%------------------------------------------------------------------------------
% File     : ALG434-1 : TPTP v8.2.0. Released v4.1.0.
% Domain   : General Algebra
% Problem  : Fundamental theorem of algebra 1005_24
% Version  : Especial.
% English  :

% Refs     : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe
%          : [BN10]  Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% Source   : [Nip10]
% Names    : Fundamental_Theorem_Algebra-1005_24 [Nip10]

% Status   : Unsatisfiable
% Rating   : 0.00 v7.0.0, 0.07 v6.4.0, 0.00 v6.0.0, 0.10 v5.5.0, 0.20 v5.4.0, 0.15 v5.3.0, 0.17 v5.2.0, 0.19 v5.1.0, 0.24 v5.0.0, 0.07 v4.1.0
% Syntax   : Number of clauses     :  441 (  35 unt;  28 nHn; 187 RR)
%            Number of literals    : 1034 ( 388 equ; 568 neg)
%            Maximal clause size   :    6 (   2 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of predicates  :   43 (  42 usr;   0 prp; 1-5 aty)
%            Number of functors    :   19 (  19 usr;   4 con; 0-3 aty)
%            Number of variables   : 1248 (  86 sgn)
% SPC      : CNF_UNS_RFO_SEQ_NHN

% Comments :
%------------------------------------------------------------------------------
cnf(cls_synthetic__div__unique_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
    | c_HOL_Oplus__class_Oplus(V_p,c_Polynomial_Osmult(V_c,V_q,T_a),tc_Polynomial_Opoly(T_a)) != c_Polynomial_OpCons(V_r,V_q,T_a)
    | V_r = c_Polynomial_Opoly(V_p,V_c,T_a) ) ).

cnf(cls_poly__pCons_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
    | c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) ).

cnf(cls_order__root_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_poly__0_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
    | c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_poly__smult_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
    | c_Polynomial_Opoly(c_Polynomial_Osmult(V_a,V_p,T_a),V_x,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Polynomial_Opoly(V_p,V_x,T_a),T_a) ) ).

cnf(cls_poly__mult_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
    | c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(V_p,V_x,T_a),c_Polynomial_Opoly(V_q,V_x,T_a),T_a) ) ).

cnf(cls_poly__add_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
    | c_Polynomial_Opoly(c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(V_p,V_x,T_a),c_Polynomial_Opoly(V_q,V_x,T_a),T_a) ) ).

cnf(cls_poly__minus_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(T_a)
    | c_Polynomial_Opoly(c_HOL_Ouminus__class_Ouminus(V_p,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Opoly(V_p,V_x,T_a),T_a) ) ).

cnf(cls_poly__diff_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(T_a)
    | c_Polynomial_Opoly(c_HOL_Ominus__class_Ominus(V_p,V_q,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(V_p,V_x,T_a),c_Polynomial_Opoly(V_q,V_x,T_a),T_a) ) ).

cnf(cls_diff__pCons_0,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(T_a)
    | c_HOL_Ominus__class_Ominus(c_Polynomial_OpCons(V_a,V_p,T_a),c_Polynomial_OpCons(V_b,V_q,T_a),tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ominus__class_Ominus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) ) ).

cnf(cls_minus__pCons_0,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(T_a)
    | c_HOL_Ouminus__class_Ouminus(c_Polynomial_OpCons(V_a,V_p,T_a),tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_p,tc_Polynomial_Opoly(T_a)),T_a) ) ).

cnf(cls_synthetic__div__unique__lemma_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
    | c_Polynomial_Osmult(V_c,V_p,T_a) != c_Polynomial_OpCons(V_a,V_p,T_a)
    | V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_add__pCons_0,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | c_HOL_Oplus__class_Oplus(c_Polynomial_OpCons(V_a,V_p,T_a),c_Polynomial_OpCons(V_b,V_q,T_a),tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) ) ).

cnf(cls_smult__pCons_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
    | c_Polynomial_Osmult(V_a,c_Polynomial_OpCons(V_b,V_p,T_a),T_a) = c_Polynomial_OpCons(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_Polynomial_Osmult(V_a,V_p,T_a),T_a) ) ).

cnf(cls_pCons__eq__0__iff_0,axiom,
    ( ~ class_HOL_Ozero(T_a)
    | c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_pCons__0__0_0,axiom,
    ( ~ class_HOL_Ozero(T_a)
    | c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_pCons__eq__0__iff_1,axiom,
    ( ~ class_HOL_Ozero(T_a)
    | c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_pCons__eq__iff_0,axiom,
    ( ~ class_HOL_Ozero(T_a)
    | c_Polynomial_OpCons(V_a,V_p,T_a) != c_Polynomial_OpCons(V_b,V_q,T_a)
    | V_a = V_b ) ).

cnf(cls_pCons__eq__iff_1,axiom,
    ( ~ class_HOL_Ozero(T_a)
    | c_Polynomial_OpCons(V_a,V_p,T_a) != c_Polynomial_OpCons(V_b,V_q,T_a)
    | V_p = V_q ) ).

cnf(cls_poly__eq__0__iff__dvd_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | c_Polynomial_Opoly(V_p,V_c,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(V_c,T_a),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a),V_p,tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_poly__eq__0__iff__dvd_0,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | c_Polynomial_Opoly(V_p,V_c,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(V_c,T_a),c_Polynomial_OpCons(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a),V_p,tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_dvd__iff__poly__eq__0_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | c_Polynomial_Opoly(V_p,c_HOL_Ouminus__class_Ouminus(V_c,T_a),T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(V_c,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a),V_p,tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_dvd__iff__poly__eq__0_0,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | c_Polynomial_Opoly(V_p,c_HOL_Ouminus__class_Ouminus(V_c,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_OpCons(V_c,c_Polynomial_OpCons(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a),V_p,tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_offset__poly__eq__0__lemma_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
    | c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(V_c,V_p,T_a),c_Polynomial_OpCons(V_a,V_p,T_a),tc_Polynomial_Opoly(T_a)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_no__zero__divisors_0,axiom,
    ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
    | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | V_b = c_HOL_Ozero__class_Ozero(T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_mult__eq__0__iff_0,axiom,
    ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a)
    | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | V_b = c_HOL_Ozero__class_Ozero(T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_one__neq__zero_0,axiom,
    ( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
    | c_HOL_Oone__class_Oone(T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_div__mult__self1__is__id_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),V_b,T_a) = V_a
    | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_div__mult__self2__is__id_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_b,T_a) = V_a
    | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_neg__equal__0__iff__equal_0,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | c_HOL_Ouminus__class_Ouminus(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_class__semiring_Osemiring__rules_I13_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),c_HOL_Otimes__class_Otimes(V_ly,V_ry,T_a),T_a) ) ).

cnf(cls_class__semiring_Osemiring__rules_I14_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a),T_a) ) ).

cnf(cls_class__semiring_Osemiring__rules_I15_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_ry,T_a),T_a) ) ).

cnf(cls_neg__equal__iff__equal_0,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | c_HOL_Ouminus__class_Ouminus(V_a,T_a) != c_HOL_Ouminus__class_Ouminus(V_b,T_a)
    | V_a = V_b ) ).

cnf(cls_compl__eq__compl__iff_0,axiom,
    ( ~ class_Lattices_Oboolean__algebra(T_a)
    | c_HOL_Ouminus__class_Ouminus(V_x,T_a) != c_HOL_Ouminus__class_Ouminus(V_y,T_a)
    | V_x = V_y ) ).

cnf(cls_pdivmod__rel__unique_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | V_q1 = V_q2
    | ~ c_Polynomial_Opdivmod__rel(V_x,V_y,V_q2,V_r2,T_a)
    | ~ c_Polynomial_Opdivmod__rel(V_x,V_y,V_q1,V_r1,T_a) ) ).

cnf(cls_pdivmod__rel__unique_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | V_r1 = V_r2
    | ~ c_Polynomial_Opdivmod__rel(V_x,V_y,V_q2,V_r2,T_a)
    | ~ c_Polynomial_Opdivmod__rel(V_x,V_y,V_q1,V_r1,T_a) ) ).

cnf(cls_dvd__mult__cancel__left_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a),T_a) ) ).

cnf(cls_dvd__mult__cancel__right_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a),T_a) ) ).

cnf(cls_poly__gcd__0__0_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_abs__mult_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a) ) ).

cnf(cls_minus__mult__left_0,axiom,
    ( ~ class_Ring__and__Field_Oring(T_a)
    | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) ).

cnf(cls_minus__mult__right_0,axiom,
    ( ~ class_Ring__and__Field_Oring(T_a)
    | c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ).

cnf(cls_mult__left__idem_0,axiom,
    ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a)
    | c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_x,V_y,T_a) ) ).

cnf(cls_power__eq__0__iff_0,axiom,
    ( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
    | ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
    | ~ class_Ring__and__Field_Omult__zero(T_a)
    | ~ class_Power_Opower(T_a)
    | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_field__power__not__zero_0,axiom,
    ( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(T_a)
    | c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_div__mult__div__if__dvd_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_x,V_y,T_a),c_Divides_Odiv__class_Odiv(V_w,V_z,T_a),T_a) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_x,V_w,T_a),c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_w,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a) ) ).

cnf(cls_pdivmod__rel__by__0__iff_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | V_r = V_x
    | ~ c_Polynomial_Opdivmod__rel(V_x,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q,V_r,T_a) ) ).

cnf(cls_div__mult__mult1__if_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_mod__add__self1_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_b,V_a,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a) ) ).

cnf(cls_mod__add__self2_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a) ) ).

cnf(cls_add__minus__cancel_0,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a),T_a) = V_b ) ).

cnf(cls_poly__mod__mult__right_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Divides_Odiv__class_Omod(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_y,c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Odiv(V_x,V_y,tc_Polynomial_Opoly(T_a)),V_z,tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)),c_Divides_Odiv__class_Omod(V_x,V_y,tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_class__ringb_Oadd__scale__eq__noteq_0,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_r,V_c,T_a),T_a) != c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_r,V_d,T_a),T_a)
    | V_c = V_d
    | V_r = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_sum__squares__eq__zero__iff_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_sum__squares__eq__zero__iff_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_mult__idem_0,axiom,
    ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a)
    | c_HOL_Otimes__class_Otimes(V_x,V_x,T_a) = V_x ) ).

cnf(cls_pdivmod__rel__def_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | ~ c_Polynomial_Opdivmod__rel(V_x,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q,V_r,T_a)
    | V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_pdivmod__rel__0__iff_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_y,V_q,V_r,T_a) ) ).

cnf(cls_pdivmod__rel__0__iff_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | V_r = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_y,V_q,V_r,T_a) ) ).

cnf(cls_pdivmod__rel__by__0__iff_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | ~ c_Polynomial_Opdivmod__rel(V_x,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q,V_r,T_a) ) ).

cnf(cls_class__semiring_Opwr__mul_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_q,T_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_q,T_a),c_Power_Opower__class_Opower(V_y,V_q,T_a),T_a) ) ).

cnf(cls_power__mult__distrib_0,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__mult(T_a)
    | c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_n,T_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) ).

cnf(cls_zmod__simps_I2_J_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) ) ).

cnf(cls_zmod__simps_I1_J_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) ) ).

cnf(cls_inf__period_I4_J_0,axiom,
    ( ~ class_Ring__and__Field_Odvd(T_a)
    | ~ class_Ring__and__Field_Ocomm__ring(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_x,c_HOL_Otimes__class_Otimes(V_k,V_D,T_a),T_a),V_t,T_a),T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(V_x,V_t,T_a),T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_D,T_a) ) ).

cnf(cls_inf__period_I4_J_1,axiom,
    ( ~ class_Ring__and__Field_Odvd(T_a)
    | ~ class_Ring__and__Field_Ocomm__ring(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(V_x,V_t,T_a),T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_x,c_HOL_Otimes__class_Otimes(V_k,V_D,T_a),T_a),V_t,T_a),T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_D,T_a) ) ).

cnf(cls_mod__div__decomp_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | V_a = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a) ) ).

cnf(cls_mod__div__equality_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a) = V_a ) ).

cnf(cls_mod__div__equality2_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a) = V_a ) ).

cnf(cls_class__ring_Oneg__mul_0,axiom,
    ( ~ class_Int_Onumber__ring(T_a)
    | c_HOL_Ouminus__class_Ouminus(V_x,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a),V_x,T_a) ) ).

cnf(cls_dvd__div__neg_0,axiom,
    ( ~ class_Divides_Oring__div(T_a)
    | c_Divides_Odiv__class_Odiv(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(V_x,V_y,T_a),T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a) ) ).

cnf(cls_dvd__neg__div_0,axiom,
    ( ~ class_Divides_Oring__div(T_a)
    | c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(V_x,V_y,T_a),T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a) ) ).

cnf(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0,axiom,
    ( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ).

cnf(cls_class__semiring_Osemiring__rules_I16_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) ).

cnf(cls_class__semiring_Osemiring__rules_I17_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,V_rx,T_a),T_a) ) ).

cnf(cls_class__semiring_Osemiring__rules_I18_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ry,T_a) ) ).

cnf(cls_class__semiring_Osemiring__rules_I19_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a) ) ).

cnf(cls_class__semiring_Omul__a_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_z,T_a) ) ).

cnf(cls_class__semiring_Osemiring__rules_I8_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ).

cnf(cls_mult__right_Oadd_0,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),c_HOL_Otimes__class_Otimes(V_xa,V_y,T_a),T_a) ) ).

cnf(cls_mult_Oadd__right_0,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oplus__class_Oplus(V_b,V_b_H,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a,V_b_H,T_a),T_a) ) ).

cnf(cls_mult__left_Oadd_0,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),V_ya,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_ya,T_a),c_HOL_Otimes__class_Otimes(V_y,V_ya,T_a),T_a) ) ).

cnf(cls_mult_Oadd__left_0,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_a_H,T_a),V_b,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a_H,V_b,T_a),T_a) ) ).

cnf(cls_mult__poly__add__left_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),V_r,tc_Polynomial_Opoly(T_a)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_p,V_r,tc_Polynomial_Opoly(T_a)),c_HOL_Otimes__class_Otimes(V_q,V_r,tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_class__semiring_Omul__d_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a) ) ).

cnf(cls_comm__semiring__class_Odistrib_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ).

cnf(cls_abs__minus__commute_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
    | c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),T_a) ) ).

cnf(cls_poly__gcd__zero__iff_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Polynomial_Opoly__gcd(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | V_x = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_poly__gcd__zero__iff_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Polynomial_Opoly__gcd(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | V_y = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_neg__equal__zero_0,axiom,
    ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a)
    | c_HOL_Ouminus__class_Ouminus(V_a,T_a) != V_a
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_div__add__self1_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_b,V_a,T_a),V_b,T_a) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),c_HOL_Oone__class_Oone(T_a),T_a)
    | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_div__add__self2_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),c_HOL_Oone__class_Oone(T_a),T_a)
    | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_abs__one_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) ).

cnf(cls_class__semiring_Osemiring__rules_I1_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),c_HOL_Otimes__class_Otimes(V_b,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_m,T_a) ) ).

cnf(cls_mult_Ominus__left_0,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ).

cnf(cls_mult__left_Ominus_0,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) ) ).

cnf(cls_mult_Ominus__right_0,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ).

cnf(cls_mult__right_Ominus_0,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),T_a) ) ).

cnf(cls_square__eq__iff_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_b,V_b,T_a) ) ).

cnf(cls_minus__mult__minus_0,axiom,
    ( ~ class_Ring__and__Field_Oring(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) ) ).

cnf(cls_div__mult__mult1_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) = c_Divides_Odiv__class_Odiv(V_a,V_b,T_a)
    | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_div__mult__mult2_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) = c_Divides_Odiv__class_Odiv(V_a,V_b,T_a)
    | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_mod__minus__eq_0,axiom,
    ( ~ class_Divides_Oring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a),V_b,T_a) ) ).

cnf(cls_group__add__class_Odiff__0_0,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a) ) ).

cnf(cls_diff__poly__code_I1_J_0,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(T_a)
    | c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q,tc_Polynomial_Opoly(T_a)) = c_HOL_Ouminus__class_Ouminus(V_q,tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_mult__pCons__left_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
    | c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(V_a,V_p,T_a),V_q,tc_Polynomial_Opoly(T_a)) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(V_a,V_q,T_a),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a),tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_mult__pCons__right_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
    | c_HOL_Otimes__class_Otimes(V_p,c_Polynomial_OpCons(V_a,V_q,T_a),tc_Polynomial_Opoly(T_a)) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(V_a,V_p,T_a),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a),tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_no__zero__divirors__neq0_0,axiom,
    ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
    | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a)
    | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_div__by__0_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Odiv(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_div__0_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_double__eq__0__iff_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_HOL_Oplus__class_Oplus(V_a,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_diff__poly__code_I2_J_0,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(T_a)
    | c_HOL_Ominus__class_Ominus(V_p,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) = V_p ) ).

cnf(cls_eq__iff__diff__eq__0_0,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(T_a)
    | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_right__minus__eq_1,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_diff__0__right_0,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | c_HOL_Ominus__class_Ominus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ).

cnf(cls_diff__self_0,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | c_HOL_Ominus__class_Ominus(V_a,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_class__ringb_Osubr0__iff_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_square__eq__iff_0,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) != c_HOL_Otimes__class_Otimes(V_b,V_b,T_a)
    | V_a = c_HOL_Ouminus__class_Ouminus(V_b,T_a)
    | V_a = V_b ) ).

cnf(cls_class__ringb_Oadd__r0__iff_0,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_dvd__power_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a),T_a) ) ).

cnf(cls_pdivmod__rel__def_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | V_x = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_q,V_y,tc_Polynomial_Opoly(T_a)),V_r,tc_Polynomial_Opoly(T_a))
    | ~ c_Polynomial_Opdivmod__rel(V_x,V_y,V_q,V_r,T_a) ) ).

cnf(cls_smult__add__left_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
    | c_Polynomial_Osmult(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_p,T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(V_a,V_p,T_a),c_Polynomial_Osmult(V_b,V_p,T_a),tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_eq__add__iff2_1,axiom,
    ( ~ class_Ring__and__Field_Oring(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a) ) ).

cnf(cls_div__add_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),V_z,T_a) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(V_x,V_z,T_a),c_Divides_Odiv__class_Odiv(V_y,V_z,T_a),T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_y,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_x,T_a) ) ).

cnf(cls_zmod__simps_I4_J_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) ) ).

cnf(cls_mult__1__right_0,axiom,
    ( ~ class_OrderedGroup_Omonoid__mult(T_a)
    | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ).

cnf(cls_mult__1__left_0,axiom,
    ( ~ class_OrderedGroup_Omonoid__mult(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ).

cnf(cls_mult__1_0,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__mult(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ).

cnf(cls_class__semiring_Omul__1_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_x,T_a) = V_x ) ).

cnf(cls_class__semiring_Osemiring__rules_I12_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ).

cnf(cls_class__semiring_Osemiring__rules_I11_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ).

cnf(cls_pdivmod__rel_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Polynomial_Opdivmod__rel(V_x,V_y,c_Divides_Odiv__class_Odiv(V_x,V_y,tc_Polynomial_Opoly(T_a)),c_Divides_Odiv__class_Omod(V_x,V_y,tc_Polynomial_Opoly(T_a)),T_a) ) ).

cnf(cls_mod__0_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_class__ringb_Oadd__mul__solve_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) ) ).

cnf(cls_class__ringb_Onoteq__reduce_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_c,T_a),c_HOL_Otimes__class_Otimes(V_x,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_d,T_a),c_HOL_Otimes__class_Otimes(V_x,V_c,T_a),T_a) ) ).

cnf(cls_poly__gcd__left__commute_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Polynomial_Opoly__gcd(V_x,c_Polynomial_Opoly__gcd(V_y,V_z,T_a),T_a) = c_Polynomial_Opoly__gcd(V_y,c_Polynomial_Opoly__gcd(V_x,V_z,T_a),T_a) ) ).

cnf(cls_poly__gcd__assoc_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Polynomial_Opoly__gcd(c_Polynomial_Opoly__gcd(V_x,V_y,T_a),V_z,T_a) = c_Polynomial_Opoly__gcd(V_x,c_Polynomial_Opoly__gcd(V_y,V_z,T_a),T_a) ) ).

cnf(cls_diff__add__cancel_0,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_b,T_a) = V_a ) ).

cnf(cls_poly__gcd__minus__right_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Polynomial_Opoly__gcd(V_x,c_HOL_Ouminus__class_Ouminus(V_y,tc_Polynomial_Opoly(T_a)),T_a) = c_Polynomial_Opoly__gcd(V_x,V_y,T_a) ) ).

cnf(cls_poly__gcd__minus__left_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Polynomial_Opoly__gcd(c_HOL_Ouminus__class_Ouminus(V_x,tc_Polynomial_Opoly(T_a)),V_y,T_a) = c_Polynomial_Opoly__gcd(V_x,V_y,T_a) ) ).

cnf(cls_class__semiring_Omul__c_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_HOL_Otimes__class_Otimes(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_y,V_x,T_a) ) ).

cnf(cls_double__eq__0__iff_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_class__semiring_Osemiring__rules_I7_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ).

cnf(cls_mod__add__eq_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ).

cnf(cls_abs__eq__0_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
    | c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_comm__monoid__add_Omult__left__commute_0,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) ) ).

cnf(cls_comm__monoid__add_Omult__assoc_0,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ).

cnf(cls_class__semiring_Oadd__a_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),V_z,T_a) ) ).

cnf(cls_add__cancel__21_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(T_a)
    | c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_y,c_HOL_Oplus__class_Oplus(V_x,V_z,T_a),T_a) ) ).

cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom,
    ( ~ class_OrderedGroup_Oab__semigroup__add(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ).

cnf(cls_class__semiring_Osemiring__rules_I25_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_d,T_a) ) ).

cnf(cls_class__semiring_Osemiring__rules_I23_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_b,T_a) ) ).

cnf(cls_class__semiring_Osemiring__rules_I22_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_c,c_HOL_Oplus__class_Oplus(V_a,V_d,T_a),T_a) ) ).

cnf(cls_class__semiring_Osemiring__rules_I21_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ).

cnf(cls_neg__0__equal__iff__equal_0,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Ouminus__class_Ouminus(V_a,T_a)
    | c_HOL_Ozero__class_Ozero(T_a) = V_a ) ).

cnf(cls_poly__div__minus__right_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Divides_Odiv__class_Odiv(V_x,c_HOL_Ouminus__class_Ouminus(V_y,tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(V_x,V_y,tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_poly__div__minus__left_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(V_x,tc_Polynomial_Opoly(T_a)),V_y,tc_Polynomial_Opoly(T_a)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(V_x,V_y,tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_mod__add__right__eq_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ).

cnf(cls_mod__add__left__eq_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) ) ).

cnf(cls_eq__eqI_0,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(T_a)
    | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
    | V_x_H = V_y_H ) ).

cnf(cls_eq__eqI_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(T_a)
    | c_HOL_Ominus__class_Ominus(V_xa,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x,V_x,T_a)
    | V_xa = V_y ) ).

cnf(cls_mod__poly__eq_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Divides_Odiv__class_Omod(V_x,V_y,tc_Polynomial_Opoly(T_a)) = V_r
    | ~ c_Polynomial_Opdivmod__rel(V_x,V_y,V_q,V_r,T_a) ) ).

cnf(cls_mult_Oprod__diff__prod_0,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_x,V_a,T_a),c_HOL_Ominus__class_Ominus(V_y,V_b,T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_x,V_a,T_a),V_b,T_a),T_a),c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ominus__class_Ominus(V_y,V_b,T_a),T_a),T_a) ) ).

cnf(cls_combine__common__factor_0,axiom,
    ( ~ class_Ring__and__Field_Osemiring(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) ) ).

cnf(cls_eq__neg__iff__add__eq__0_0,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_ab__left__minus_0,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_right__minus_0,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_left__minus_0,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_eq__iff__diff__eq__0_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(T_a)
    | c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | V_a = V_b ) ).

cnf(cls_right__minus__eq_0,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | V_a = V_b ) ).

cnf(cls_class__ringb_Osubr0__iff_0,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | V_x = V_y ) ).

cnf(cls_mult__right_Odiff_0,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Ominus__class_Ominus(V_x,V_y,T_a),T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),c_HOL_Otimes__class_Otimes(V_xa,V_y,T_a),T_a) ) ).

cnf(cls_mult_Odiff__right_0,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ominus__class_Ominus(V_b,V_b_H,T_a),T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a,V_b_H,T_a),T_a) ) ).

cnf(cls_mult_Odiff__left_0,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_a_H,T_a),V_b,T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a_H,V_b,T_a),T_a) ) ).

cnf(cls_mult__left_Odiff_0,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_x,V_y,T_a),V_ya,T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_x,V_ya,T_a),c_HOL_Otimes__class_Otimes(V_y,V_ya,T_a),T_a) ) ).

cnf(cls_Deriv_Oadd__diff__add_0,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(T_a)
    | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ominus__class_Ominus(V_c,V_d,T_a),T_a) ) ).

cnf(cls_dvd__div__mult_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),V_c,T_a) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),V_a,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ).

cnf(cls_power__abs_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(V_a,T_a),V_n,T_a) ) ).

cnf(cls_mod__mult__right__eq_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ).

cnf(cls_mod__mult__left__eq_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) ) ).

cnf(cls_pdivmod__rel__mult_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Polynomial_Opdivmod__rel(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,tc_Polynomial_Opoly(T_a)),V_q_H,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_y,V_r_H,tc_Polynomial_Opoly(T_a)),V_r,tc_Polynomial_Opoly(T_a)),T_a)
    | ~ c_Polynomial_Opdivmod__rel(V_q,V_z,V_q_H,V_r_H,T_a)
    | ~ c_Polynomial_Opdivmod__rel(V_x,V_y,V_q,V_r,T_a) ) ).

cnf(cls_add__cancel__end_0,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(T_a)
    | c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) != V_y
    | V_x = c_HOL_Ouminus__class_Ouminus(V_z,T_a) ) ).

cnf(cls_dvd__mult__div__cancel_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),T_a) = V_b
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ).

cnf(cls_dvd__div__mult__self_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),V_a,T_a) = V_b
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ).

cnf(cls_diff__minus__eq__add_0,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | c_HOL_Ominus__class_Ominus(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) ) ).

cnf(cls_mod__mult__self2_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a) ) ).

cnf(cls_mod__mult__self1_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a) ) ).

cnf(cls_dvd__mult__cancel__right_0,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
    | V_c = c_HOL_Ozero__class_Ozero(T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ).

cnf(cls_dvd__mult__cancel__left_0,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
    | V_c = c_HOL_Ozero__class_Ozero(T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ).

cnf(cls_add__poly__code_I1_J_0,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q,tc_Polynomial_Opoly(T_a)) = V_q ) ).

cnf(cls_add__poly__code_I2_J_0,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | c_HOL_Oplus__class_Oplus(V_p,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) = V_p ) ).

cnf(cls_monoid__add__class_Oadd__0__right_0,axiom,
    ( ~ class_OrderedGroup_Omonoid__add(T_a)
    | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ).

cnf(cls_add__0__left_0,axiom,
    ( ~ class_OrderedGroup_Omonoid__add(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a ) ).

cnf(cls_comm__monoid__add_Omult__1__right_0,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ).

cnf(cls_class__ringb_Oadd__r0__iff_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | V_x = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_class__semiring_Oadd__0_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = V_x ) ).

cnf(cls_comm__monoid__add_Omult__1_0,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a ) ).

cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ).

cnf(cls_class__semiring_Osemiring__rules_I5_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a ) ).

cnf(cls_add__diff__cancel_0,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = V_a ) ).

cnf(cls_minus__equation__iff_1,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = V_b ) ).

cnf(cls_equation__minus__iff_1,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | V_a = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ).

cnf(cls_equation__minus__iff_0,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | V_b = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ).

cnf(cls_double__compl_0,axiom,
    ( ~ class_Lattices_Oboolean__algebra(T_a)
    | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = V_x ) ).

cnf(cls_minus__minus_0,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = V_a ) ).

cnf(cls_div__by__1_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Odiv(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ).

cnf(cls_minus__diff__eq_0,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(T_a)
    | c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_HOL_Ominus__class_Ominus(V_b,V_a,T_a) ) ).

cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a) ) ).

cnf(cls_diff__def_0,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(T_a)
    | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) ) ).

cnf(cls_class__ring_Osub__add_0,axiom,
    ( ~ class_Int_Onumber__ring(T_a)
    | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) ) ).

cnf(cls_diff__minus_0,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ).

cnf(cls_ab__diff__minus_0,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(T_a)
    | c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ).

cnf(cls_mod__diff__eq_0,axiom,
    ( ~ class_Divides_Oring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ).

cnf(cls_abs__minus__cancel_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
    | c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Oabs__class_Oabs(V_a,T_a) ) ).

cnf(cls_class__ringb_Oadd__cancel_0,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Oplus__class_Oplus(V_x,V_z,T_a)
    | V_y = V_z ) ).

cnf(cls_add__imp__eq_0,axiom,
    ( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(T_a)
    | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)
    | V_b = V_c ) ).

cnf(cls_add__left__cancel_0,axiom,
    ( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a)
    | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)
    | V_b = V_c ) ).

cnf(cls_add__right__cancel_0,axiom,
    ( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a)
    | c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) != c_HOL_Oplus__class_Oplus(V_c,V_a,T_a)
    | V_b = V_c ) ).

cnf(cls_pdivmod__rel__0_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_y,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) ) ).

cnf(cls_dvd__imp__mod__0_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(V_b,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ).

cnf(cls_dvd__eq__mod__eq__0_1,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(V_b,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ).

cnf(cls_zero__neq__one_0,axiom,
    ( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
    | c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Oone__class_Oone(T_a) ) ).

cnf(cls_power__one_0,axiom,
    ( ~ class_OrderedGroup_Omonoid__mult(T_a)
    | c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a) = c_HOL_Oone__class_Oone(T_a) ) ).

cnf(cls_mod__diff__left__eq_0,axiom,
    ( ~ class_Divides_Oring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) ) ).

cnf(cls_mod__diff__right__eq_0,axiom,
    ( ~ class_Divides_Oring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ).

cnf(cls_smult__eq__0__iff_0,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | c_Polynomial_Osmult(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_add__cancel__21_0,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(T_a)
    | c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) != c_HOL_Oplus__class_Oplus(V_y,V_u,T_a)
    | c_HOL_Oplus__class_Oplus(V_x,V_z,T_a) = V_u ) ).

cnf(cls_mod__smult__right_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Divides_Odiv__class_Omod(V_x,c_Polynomial_Osmult(V_a,V_y,T_a),tc_Polynomial_Opoly(T_a)) = c_Divides_Odiv__class_Omod(V_x,V_y,tc_Polynomial_Opoly(T_a))
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_pdivmod__rel__def_6,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_y,tc_Polynomial_Opoly(T_a)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)),V_y,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) ) ).

cnf(cls_pdivmod__rel__def_5,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)),V_r,tc_Polynomial_Opoly(T_a)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_r,T_a) ) ).

cnf(cls_mod__mod__trivial_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a) ) ).

cnf(cls_div__self_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Odiv(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_smult__minus__left_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(T_a)
    | c_Polynomial_Osmult(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_p,T_a) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(V_a,V_p,T_a),tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_eq__add__iff1_1,axiom,
    ( ~ class_Ring__and__Field_Oring(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),T_a) ) ).

cnf(cls_abs__idempotent_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
    | c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) = c_HOL_Oabs__class_Oabs(V_a,T_a) ) ).

cnf(cls_eq__add__iff1_0,axiom,
    ( ~ class_Ring__and__Field_Oring(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) = V_d ) ).

cnf(cls_eq__add__iff2_0,axiom,
    ( ~ class_Ring__and__Field_Oring(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a)
    | V_c = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a) ) ).

cnf(cls_div__mod__equality_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) ) ).

cnf(cls_div__mod__equality2_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) ) ).

cnf(cls_pdivmod__rel__by__0_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Polynomial_Opdivmod__rel(V_x,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x,T_a) ) ).

cnf(cls_mod__by__0_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ).

cnf(cls_mod__self_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(V_a,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) ).

cnf(cls_class__semiring_Oadd__c_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) = c_HOL_Oplus__class_Oplus(V_y,V_x,T_a) ) ).

cnf(cls_comm__monoid__add_Omult__commute_0,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) ).

cnf(cls_power__minus_0,axiom,
    ( ~ class_Ring__and__Field_Oring__1(T_a)
    | c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_n,T_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a),V_n,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) ).

cnf(cls_mod__div__trivial_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_mod__minus__cong_0,axiom,
    ( ~ class_Divides_Oring__div(T_a)
    | c_Divides_Odiv__class_Omod(V_a,V_b,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_b,T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(V_a_H,T_a),V_b,T_a) ) ).

cnf(cls_mod__mult__eq_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ).

cnf(cls_power__commutes_0,axiom,
    ( ~ class_OrderedGroup_Omonoid__mult(T_a)
    | c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_a,V_n,T_a),V_a,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) ).

cnf(cls_div__mult__self1_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a),V_b,T_a) = c_HOL_Oplus__class_Oplus(V_c,c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),T_a)
    | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_div__mult__self2_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a),V_b,T_a) = c_HOL_Oplus__class_Oplus(V_c,c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),T_a)
    | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_class__semiring_Osemiring__rules_I4_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_HOL_Oplus__class_Oplus(V_m,V_m,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(T_a),c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) ).

cnf(cls_div__poly__eq_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Divides_Odiv__class_Odiv(V_x,V_y,tc_Polynomial_Opoly(T_a)) = V_q
    | ~ c_Polynomial_Opdivmod__rel(V_x,V_y,V_q,V_r,T_a) ) ).

cnf(cls_mod__add__cong_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a)
    | c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a_H,V_b_H,T_a),V_c,T_a) ) ).

cnf(cls_smult__diff__left_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(T_a)
    | c_Polynomial_Osmult(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_p,T_a) = c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(V_a,V_p,T_a),c_Polynomial_Osmult(V_b,V_p,T_a),tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_minus__unique_0,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Ouminus__class_Ouminus(V_a,T_a) = V_b ) ).

cnf(cls_eq__neg__iff__add__eq__0_1,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | V_a = c_HOL_Ouminus__class_Ouminus(V_b,T_a) ) ).

cnf(cls_div__power_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(V_x,V_y,T_a),V_n,T_a) = c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_Power_Opower__class_Opower(V_y,V_n,T_a),T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a) ) ).

cnf(cls_class__ringb_Onoteq__reduce_0,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_d,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
    | V_c = V_d
    | V_a = V_b ) ).

cnf(cls_class__ringb_Oadd__mul__solve_0,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_w,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_w,V_z,T_a),c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a)
    | V_y = V_z
    | V_w = V_x ) ).

cnf(cls_abs__mult__self_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) ) ).

cnf(cls_mod__mult__cong_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a)
    | c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a_H,V_b_H,T_a),V_c,T_a) ) ).

cnf(cls_class__semiring_Osemiring__rules_I9_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_class__semiring_Osemiring__rules_I10_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_mult__left_Ozero_0,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_mult_Ozero__left_0,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_mult_Ozero__right_0,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_mult__right_Ozero_0,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_HOL_Otimes__class_Otimes(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_mult__poly__0__left_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q,tc_Polynomial_Opoly(T_a)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_mult__poly__0__right_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
    | c_HOL_Otimes__class_Otimes(V_p,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_class__semiring_Omul__0_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_mult__zero__left_0,axiom,
    ( ~ class_Ring__and__Field_Omult__zero(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_mult__zero__right_0,axiom,
    ( ~ class_Ring__and__Field_Omult__zero(T_a)
    | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_mult__eq__0__iff_1,axiom,
    ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_mult__eq__0__iff_2,axiom,
    ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a)
    | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_abs__power__minus_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_n,T_a),T_a) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) ).

cnf(cls_class__semiring_Osemiring__rules_I2_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),V_m,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) ).

cnf(cls_class__semiring_Osemiring__rules_I3_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) ).

cnf(cls_mod__by__1_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_mod__diff__cong_0,axiom,
    ( ~ class_Divides_Oring__div(T_a)
    | c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a)
    | c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a_H,V_b_H,T_a),V_c,T_a) ) ).

cnf(cls_add__cancel__end_1,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_z,T_a),c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = V_y ) ).

cnf(cls_minus__add__cancel_0,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a) = V_b ) ).

cnf(cls_poly__mod__minus__right_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Divides_Odiv__class_Omod(V_x,c_HOL_Ouminus__class_Ouminus(V_y,tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) = c_Divides_Odiv__class_Omod(V_x,V_y,tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_neg__0__equal__iff__equal_1,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_poly__gcd__commute_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Polynomial_Opoly__gcd(V_x,V_y,T_a) = c_Polynomial_Opoly__gcd(V_y,V_x,T_a) ) ).

cnf(cls_minus__mult__commute_0,axiom,
    ( ~ class_Ring__and__Field_Oring(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ).

cnf(cls_minus__zero_0,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_neg__equal__zero_1,axiom,
    ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a)
    | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_minus__poly__code_I1_J_0,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(T_a)
    | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_poly__gcd__code_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Polynomial_Opoly__gcd(V_x,V_y,T_a) = c_Polynomial_Opoly__gcd(V_y,c_Divides_Odiv__class_Omod(V_x,V_y,tc_Polynomial_Opoly(T_a)),T_a)
    | V_y = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_smult__eq__0__iff_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(T_a),V_p,T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_smult__0__left_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
    | c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(T_a),V_p,T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_Lim_Ominus__diff__minus_0,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(T_a)
    | c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) ) ).

cnf(cls_poly__div__mult__right_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Divides_Odiv__class_Odiv(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(V_x,V_y,tc_Polynomial_Opoly(T_a)),V_z,tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_abs__add__abs_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
    | c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a) ) ).

cnf(cls_abs__eq__0_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
    | c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_mod__mult__self1__is__0_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_mod__mult__self2__is__0_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_semiring__div__class_Omod__div__equality_H_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a),T_a) = V_a ) ).

cnf(cls_sum__squares__eq__zero__iff_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_pdivmod__rel__def_3,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | V_y = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_q,V_y,tc_Polynomial_Opoly(T_a)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)),V_y,V_q,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) ) ).

cnf(cls_poly__mod__minus__left_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(V_x,tc_Polynomial_Opoly(T_a)),V_y,tc_Polynomial_Opoly(T_a)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(V_x,V_y,tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_mod__mult__mult1_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_c,c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a) ) ).

cnf(cls_mod__mult__mult2_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_c,T_a) ) ).

cnf(cls_minus__add_0,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ).

cnf(cls_minus__add__distrib_0,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(T_a)
    | c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ).

cnf(cls_dvd__if__abs__eq_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_HOL_Oabs__class_Oabs(V_l,T_a) != c_HOL_Oabs__class_Oabs(V_k,T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_l,V_k,T_a) ) ).

cnf(cls_mult__dvd__mono_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_c,V_d,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ).

cnf(cls_smult__0__right_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
    | c_Polynomial_Osmult(V_a,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_smult__eq__0__iff_2,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | c_Polynomial_Osmult(V_a,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_mod__mod__cancel_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(V_a,V_c,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_c,V_b,T_a) ) ).

cnf(cls_poly__gcd__greatest_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Polynomial_Opoly__gcd(V_x,V_y,T_a),tc_Polynomial_Opoly(T_a))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_y,tc_Polynomial_Opoly(T_a))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_x,tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_dvd__poly__gcd__iff_2,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Polynomial_Opoly__gcd(V_x,V_y,T_a),tc_Polynomial_Opoly(T_a))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_y,tc_Polynomial_Opoly(T_a))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_x,tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_poly__gcd__dvd1_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(V_x,V_y,T_a),V_x,tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_poly__gcd__dvd2_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(V_x,V_y,T_a),V_y,tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_smult__dvd__iff_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(T_a),V_p,T_a),V_q,tc_Polynomial_Opoly(T_a))
    | V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_dvd__abs__iff_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_m,c_HOL_Oabs__class_Oabs(V_k,T_a),T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a) ) ).

cnf(cls_dvd__abs__iff_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,c_HOL_Oabs__class_Oabs(V_k,T_a),T_a) ) ).

cnf(cls_abs__dvd__iff_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(V_m,T_a),V_k,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a) ) ).

cnf(cls_abs__dvd__iff_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(V_m,T_a),V_k,T_a) ) ).

cnf(cls_dvd__0__right_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_smult__diff__right_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(T_a)
    | c_Polynomial_Osmult(V_a,c_HOL_Ominus__class_Ominus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(V_a,V_p,T_a),c_Polynomial_Osmult(V_a,V_q,T_a),tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_dvd__poly__gcd__iff_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_k,V_y,tc_Polynomial_Opoly(T_a))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Polynomial_Opoly__gcd(V_x,V_y,T_a),tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_dvd__poly__gcd__iff_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_k,V_x,tc_Polynomial_Opoly(T_a))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Polynomial_Opoly__gcd(V_x,V_y,T_a),tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_dvd__mult__cancel__right_2,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ).

cnf(cls_dvd__mult__cancel__left_2,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ).

cnf(cls_smult__minus__right_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring(T_a)
    | c_Polynomial_Osmult(V_a,c_HOL_Ouminus__class_Ouminus(V_p,tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(V_a,V_p,T_a),tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_dvd__0__left_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_minus__dvd__iff_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) ) ).

cnf(cls_minus__dvd__iff_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) ) ).

cnf(cls_dvd__minus__iff_1,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) ) ).

cnf(cls_dvd__minus__iff_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) ) ).

cnf(cls_div__dvd__div_1,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),c_Divides_Odiv__class_Odiv(V_c,V_a,T_a),T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ).

cnf(cls_div__dvd__div_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),c_Divides_Odiv__class_Odiv(V_c,V_a,T_a),T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ).

cnf(cls_dvd__add_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ).

cnf(cls_smult__1__left_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_Polynomial_Osmult(c_HOL_Oone__class_Oone(T_a),V_p,T_a) = V_p ) ).

cnf(cls_mod__smult__left_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Divides_Odiv__class_Omod(c_Polynomial_Osmult(V_a,V_x,T_a),V_y,tc_Polynomial_Opoly(T_a)) = c_Polynomial_Osmult(V_a,c_Divides_Odiv__class_Omod(V_x,V_y,tc_Polynomial_Opoly(T_a)),T_a) ) ).

cnf(cls_dvd__smult__cancel_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
    | V_a = c_HOL_Ozero__class_Ozero(T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,c_Polynomial_Osmult(V_a,V_q,T_a),tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_smult__dvd_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(V_a,V_p,T_a),V_q,tc_Polynomial_Opoly(T_a))
    | V_a = c_HOL_Ozero__class_Ozero(T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_dvd__smult__iff_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,c_Polynomial_Osmult(V_a,V_q,T_a),tc_Polynomial_Opoly(T_a))
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_dvd__smult__iff_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_p,c_Polynomial_Osmult(V_a,V_q,T_a),tc_Polynomial_Opoly(T_a))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_smult__dvd__iff_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
    | V_a = c_HOL_Ozero__class_Ozero(T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(V_a,V_p,T_a),V_q,tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_smult__dvd__iff_2,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(V_a,V_p,T_a),V_q,tc_Polynomial_Opoly(T_a))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_smult__dvd__iff_4,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(V_a,V_p,T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_dvd__mult__right_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) ) ).

cnf(cls_dvd__mult__left_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) ) ).

cnf(cls_dvd__mult2_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ).

cnf(cls_dvd__mult_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) ) ).

cnf(cls_one__dvd_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ).

cnf(cls_dvd__trans_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ).

cnf(cls_dvd__refl_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_a,T_a) ) ).

cnf(cls_smult__dvd__iff_3,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(T_a),V_p,T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_pdivmod__rel__smult__left_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Polynomial_Opdivmod__rel(c_Polynomial_Osmult(V_a,V_x,T_a),V_y,c_Polynomial_Osmult(V_a,V_q,T_a),c_Polynomial_Osmult(V_a,V_r,T_a),T_a)
    | ~ c_Polynomial_Opdivmod__rel(V_x,V_y,V_q,V_r,T_a) ) ).

cnf(cls_dvd__diff_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_x,c_HOL_Ominus__class_Ominus(V_y,V_z,T_a),T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) ) ).

cnf(cls_smult__add__right_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
    | c_Polynomial_Osmult(V_a,c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(V_a,V_p,T_a),c_Polynomial_Osmult(V_a,V_q,T_a),tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_dvd__mod__imp__dvd_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a) ) ).

cnf(cls_dvd__mod__iff_1,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a) ) ).

cnf(cls_dvd__mod__iff_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a) ) ).

cnf(cls_dvd__mod_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a) ) ).

cnf(cls_div__smult__left_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Divides_Odiv__class_Odiv(c_Polynomial_Osmult(V_a,V_x,T_a),V_y,tc_Polynomial_Opoly(T_a)) = c_Polynomial_Osmult(V_a,c_Divides_Odiv__class_Odiv(V_x,V_y,tc_Polynomial_Opoly(T_a)),T_a) ) ).

cnf(cls_dvd__triv__right_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a) ) ).

cnf(cls_dvd__triv__left_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ).

cnf(cls_dvdI_0,axiom,
    ( ~ class_Ring__and__Field_Odvd(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_b,c_HOL_Otimes__class_Otimes(V_b,V_k,T_a),T_a) ) ).

cnf(cls_smult__dvd__cancel_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(V_a,V_p,T_a),V_q,tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_dvd__smult_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_p,c_Polynomial_Osmult(V_a,V_q,T_a),tc_Polynomial_Opoly(T_a))
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_dvd__power__same_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_Power_Opower__class_Opower(V_y,V_n,T_a),T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) ) ).

cnf(cls_mult__smult__right_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
    | c_HOL_Otimes__class_Otimes(V_p,c_Polynomial_Osmult(V_a,V_q,T_a),tc_Polynomial_Opoly(T_a)) = c_Polynomial_Osmult(V_a,c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) ) ).

cnf(cls_mult__smult__left_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
    | c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(V_a,V_p,T_a),V_q,tc_Polynomial_Opoly(T_a)) = c_Polynomial_Osmult(V_a,c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) ) ).

cnf(cls_pq_0,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ).

cnf(cls_smult__smult_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
    | c_Polynomial_Osmult(V_a,c_Polynomial_Osmult(V_b,V_p,T_a),T_a) = c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_p,T_a) ) ).

cnf(cls_CHAINED_0,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(v_q,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ).

cnf(cls_CHAINED_0_01,axiom,
    c_Ring__and__Field_Odvd__class_Odvd(v_p,v_q,tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ).

cnf(cls_conjecture_0,negated_conjecture,
    ~ c_Ring__and__Field_Odvd__class_Odvd(v_p,c_Polynomial_Osmult(v_a,v_q,tc_Complex_Ocomplex),tc_Polynomial_Opoly(tc_Complex_Ocomplex)) ).

cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__comm__monoid__add,axiom,
    ( class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1))
    | ~ class_OrderedGroup_Ocancel__comm__monoid__add(T_1) ) ).

cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add,axiom,
    class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors,axiom,
    class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors,axiom,
    class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) ).

cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ).

cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors,axiom,
    class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0,axiom,
    class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) ).

cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
    class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ).

cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) ).

cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) ).

cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) ).

cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one,axiom,
    class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1,axiom,
    class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex) ).

cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add,axiom,
    class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero,axiom,
    class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring,axiom,
    class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex) ).

cnf(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult,axiom,
    class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring,axiom,
    class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) ).

cnf(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add,axiom,
    class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) ).

cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add,axiom,
    class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1,axiom,
    class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield,axiom,
    class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring,axiom,
    class_Ring__and__Field_Oring(tc_Complex_Ocomplex) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom,axiom,
    class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Odvd,axiom,
    class_Ring__and__Field_Odvd(tc_Complex_Ocomplex) ).

cnf(clsarity_Complex__Ocomplex__Int_Onumber__ring,axiom,
    class_Int_Onumber__ring(tc_Complex_Ocomplex) ).

cnf(clsarity_Complex__Ocomplex__Power_Opower,axiom,
    class_Power_Opower(tc_Complex_Ocomplex) ).

cnf(clsarity_Complex__Ocomplex__HOL_Ozero,axiom,
    class_HOL_Ozero(tc_Complex_Ocomplex) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1__no__zero__divisors,axiom,
    ( class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Oidom(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add__abs,axiom,
    ( class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors,axiom,
    ( class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Oidom(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
    ( class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1))
    | ~ class_OrderedGroup_Ocancel__comm__monoid__add(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict,axiom,
    ( class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add,axiom,
    ( class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add,axiom,
    ( class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1))
    | ~ class_OrderedGroup_Ocancel__comm__monoid__add(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors,axiom,
    ( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Oidom(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0,axiom,
    ( class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult,axiom,
    ( class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult,axiom,
    ( class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add,axiom,
    ( class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(T_1))
    | ~ class_OrderedGroup_Ocomm__monoid__add(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring,axiom,
    ( class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__add,axiom,
    ( class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1))
    | ~ class_OrderedGroup_Ocomm__monoid__add(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one,axiom,
    ( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom,axiom,
    ( class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1,axiom,
    ( class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Ocomm__ring__1(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add,axiom,
    ( class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(T_1))
    | ~ class_OrderedGroup_Oab__group__add(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero,axiom,
    ( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring,axiom,
    ( class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Ocomm__ring(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult,axiom,
    ( class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring,axiom,
    ( class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add,axiom,
    ( class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(T_1))
    | ~ class_OrderedGroup_Ocomm__monoid__add(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add,axiom,
    ( class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(T_1))
    | ~ class_OrderedGroup_Oab__group__add(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1,axiom,
    ( class_Ring__and__Field_Oring__1(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Ocomm__ring__1(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__Divides_Osemiring__div,axiom,
    ( class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Ofield(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oring,axiom,
    ( class_Ring__and__Field_Oring(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Ocomm__ring(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oidom,axiom,
    ( class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Oidom(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Odvd,axiom,
    ( class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__Divides_Oring__div,axiom,
    ( class_Divides_Oring__div(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Ofield(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__Int_Onumber__ring,axiom,
    ( class_Int_Onumber__ring(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Ocomm__ring__1(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__Power_Opower,axiom,
    ( class_Power_Opower(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__HOL_Ozero,axiom,
    ( class_HOL_Ozero(tc_Polynomial_Opoly(T_1))
    | ~ class_HOL_Ozero(T_1) ) ).

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