%------------------------------------------------------------------------------
% File     : ALG397-1 : TPTP v8.2.0. Released v4.1.0.
% Domain   : General Algebra
% Problem  : Fundamental theorem of algebra 0653_38
% Version  : Especial.
% English  :

% Refs     : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe
%          : [BN10]  Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% Source   : [Nip10]
% Names    : Fundamental_Theorem_Algebra-0653_38 [Nip10]

% Status   : Unsatisfiable
% Rating   : 0.05 v7.4.0, 0.06 v7.3.0, 0.00 v7.0.0, 0.07 v6.3.0, 0.00 v6.2.0, 0.10 v6.1.0, 0.00 v5.5.0, 0.05 v5.3.0, 0.06 v5.1.0, 0.12 v5.0.0, 0.14 v4.1.0
% Syntax   : Number of clauses     :  713 ( 166 unt;  67 nHn; 479 RR)
%            Number of literals    : 1719 ( 409 equ; 965 neg)
%            Maximal clause size   :    6 (   2 avg)
%            Maximal term depth    :    8 (   2 avg)
%            Number of predicates  :   65 (  64 usr;   0 prp; 1-3 aty)
%            Number of functors    :   43 (  43 usr;  10 con; 0-5 aty)
%            Number of variables   : 1554 (  95 sgn)
% SPC      : CNF_UNS_RFO_SEQ_NHN

% Comments :
%------------------------------------------------------------------------------
cnf(cls_zero__le__square_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_a),T_a) ) ).

cnf(cls_mult__nonpos__nonpos_0,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),T_a)
    | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_split__mult__pos__le_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),T_a)
    | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_split__mult__pos__le_0,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_xt1_I11_J_0,axiom,
    ( ~ class_Orderings_Oorder(T_a)
    | c_HOL_Oord__class_Oless(V_b,V_a,T_a)
    | V_a = V_b
    | ~ c_lessequals(V_b,V_a,T_a) ) ).

cnf(cls_xt1_I12_J_0,axiom,
    ( ~ class_Orderings_Oorder(T_a)
    | c_HOL_Oord__class_Oless(V_b,V_a,T_a)
    | ~ c_lessequals(V_b,V_a,T_a)
    | V_a = V_b ) ).

cnf(cls_linorder__antisym__conv2_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | V_x = V_y
    | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | ~ c_lessequals(V_x,V_y,T_a) ) ).

cnf(cls_linorder__antisym__conv1_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | V_x = V_y
    | ~ c_lessequals(V_x,V_y,T_a)
    | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).

cnf(cls_order__neq__le__trans_0,axiom,
    ( ~ class_Orderings_Oorder(T_a)
    | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ c_lessequals(V_a,V_b,T_a)
    | V_a = V_b ) ).

cnf(cls_order__le__neq__trans_0,axiom,
    ( ~ class_Orderings_Oorder(T_a)
    | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | V_a = V_b
    | ~ c_lessequals(V_a,V_b,T_a) ) ).

cnf(cls_order__le__less_0,axiom,
    ( ~ class_Orderings_Oorder(T_a)
    | V_x = V_y
    | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | ~ c_lessequals(V_x,V_y,T_a) ) ).

cnf(cls_order__less__le_2,axiom,
    ( ~ class_Orderings_Oorder(T_a)
    | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | V_x = V_y
    | ~ c_lessequals(V_x,V_y,T_a) ) ).

cnf(cls_add__is__1_1,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ).

cnf(cls_add__is__1_2,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | V_m = c_HOL_Ozero__class_Ozero(tc_nat)
    | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).

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

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

cnf(cls_zero__le__mult__iff_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_zero__le__mult__iff_5,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),T_a)
    | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_mult__nonneg__nonneg_0,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

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

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

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

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

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

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

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

cnf(cls_poly__rec__pCons_0,axiom,
    ( ~ class_HOL_Ozero(T_b)
    | hAPP(hAPP(hAPP(V_f,c_HOL_Ozero__class_Ozero(T_b)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z) != V_z
    | c_Polynomial_Opoly__rec(V_z,V_f,c_Polynomial_OpCons(V_a,V_p,T_b),T_a,T_b) = hAPP(hAPP(hAPP(V_f,V_a),V_p),c_Polynomial_Opoly__rec(V_z,V_f,V_p,T_a,T_b)) ) ).

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

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

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

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

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

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

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

cnf(cls_zero__le__mult__iff_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),T_a) ) ).

cnf(cls_zero__le__mult__iff_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),T_a) ) ).

cnf(cls_zero__le__mult__iff_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),T_a) ) ).

cnf(cls_zero__le__mult__iff_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),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_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_zero__less__power__eq_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_HOL_Ozero__class_Ozero(tc_nat)),T_a) ) ).

cnf(cls_sum__squares__gt__zero__iff_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Ozero__class_Ozero(T_a))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Ozero__class_Ozero(T_a))),T_a) ) ).

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

cnf(cls_zero__less__two_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Oone__class_Oone(T_a)),c_HOL_Oone__class_Oone(T_a)),T_a) ) ).

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

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

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

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

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

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

cnf(cls_mult__mono_0,axiom,
    ( ~ class_Ring__and__Field_Opordered__semiring(T_a)
    | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_d),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | ~ c_lessequals(V_c,V_d,T_a)
    | ~ c_lessequals(V_a,V_b,T_a) ) ).

cnf(cls_mult__mono_H_0,axiom,
    ( ~ class_Ring__and__Field_Opordered__semiring(T_a)
    | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_d),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_lessequals(V_c,V_d,T_a)
    | ~ c_lessequals(V_a,V_b,T_a) ) ).

cnf(cls_power__inject__base_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Suc(V_n)) != hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Suc(V_n))
    | V_a = V_b
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_smult__monom_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
    | c_Polynomial_Osmult(V_a,c_Polynomial_Omonom(V_b,V_n,T_a),T_a) = c_Polynomial_Omonom(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),V_n,T_a) ) ).

cnf(cls_power__Suc__less_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_mult__less__cancel__left__disj_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b),T_a) ) ).

cnf(cls_mult__less__cancel__left__disj_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_HOL_Oord__class_Oless(V_b,V_a,T_a)
    | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b),T_a) ) ).

cnf(cls_mult__less__cancel__right__disj_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c),T_a) ) ).

cnf(cls_mult__less__cancel__right__disj_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_HOL_Oord__class_Oless(V_b,V_a,T_a)
    | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c),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_offset__poly__single_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
    | c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(V_a,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),V_h,T_a) = c_Polynomial_OpCons(V_a,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) ) ).

cnf(cls_add__monom_0,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),c_Polynomial_Omonom(V_a,V_n,T_a)),c_Polynomial_Omonom(V_b,V_n,T_a)) = c_Polynomial_Omonom(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_n,T_a) ) ).

cnf(cls_mult__left__le__one__le_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_y),V_x),V_x,T_a)
    | ~ c_lessequals(V_y,c_HOL_Oone__class_Oone(T_a),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ).

cnf(cls_mult__right__le__one__le_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_y),V_x,T_a)
    | ~ c_lessequals(V_y,c_HOL_Oone__class_Oone(T_a),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ).

cnf(cls_nat__add__right__cancel_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_k) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k)
    | V_m = V_n ) ).

cnf(cls_nat__add__left__cancel_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n)
    | V_m = V_n ) ).

cnf(cls_natgb_Oadd__cancel_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_y) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_z)
    | V_y = V_z ) ).

cnf(cls_not__square__less__zero_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_mult__le__0__iff_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_mult__le__0__iff_5,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_split__mult__neg__le_0,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
    | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_split__mult__neg__le_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
    | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_mult__nonneg__nonpos_0,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
    | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_mult__nonpos__nonneg_0,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
    | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_mult__nonneg__nonpos2_0,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
    | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_add__nonneg__pos_0,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_add__pos__nonneg_0,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_add__Suc__shift_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(V_m)),V_n) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_Suc(V_n)) ).

cnf(cls_of__nat__Suc_0,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(T_a)
    | c_Nat_Osemiring__1__class_Oof__nat(c_Suc(V_m),T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Oone__class_Oone(T_a)),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a)) ) ).

cnf(cls_one__is__add_3,axiom,
    ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)
    | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).

cnf(cls_one__is__add_0,axiom,
    ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)
    | V_m = c_HOL_Ozero__class_Ozero(tc_nat)
    | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ).

cnf(cls_coeff__add_0,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | hAPP(c_Polynomial_Ocoeff(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),V_p),V_q),T_a),V_n) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(c_Polynomial_Ocoeff(V_p,T_a),V_n)),hAPP(c_Polynomial_Ocoeff(V_q,T_a),V_n)) ) ).

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_of__nat__1_0,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(T_a)
    | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),T_a) = c_HOL_Oone__class_Oone(T_a) ) ).

cnf(cls_one__is__add_5,axiom,
    c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) ).

cnf(cls_offset__poly__eq__0__iff_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
    | c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,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_neg__0__le__iff__le_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ).

cnf(cls_neg__0__le__iff__le_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
    | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

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

cnf(cls_coeff__monom_0,axiom,
    ( ~ class_HOL_Ozero(T_a)
    | hAPP(c_Polynomial_Ocoeff(c_Polynomial_Omonom(V_a,V_x,T_a),T_a),V_x) = V_a ) ).

cnf(cls_power__Suc__less__one_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Suc(V_n)),c_HOL_Oone__class_Oone(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_comm__monoid__add_Opower__add_0,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),T_a),V_a),V_n)) ) ).

cnf(cls_add__mono_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a)
    | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d),T_a)
    | ~ c_lessequals(V_c,V_d,T_a)
    | ~ c_lessequals(V_a,V_b,T_a) ) ).

cnf(cls_leading__coeff__0__iff_1,axiom,
    ( ~ class_HOL_Ozero(T_a)
    | hAPP(c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a)) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_power__0__left_0,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0(T_a)
    | ~ class_Power_Opower(T_a)
    | hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(T_a) ) ).

cnf(cls_add__strict__increasing_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
    | ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | c_HOL_Oord__class_Oless(V_b,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a)
    | ~ c_lessequals(V_b,V_c,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_zero__le__power__iff_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_zero__le__power_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_le__minus__self__iff_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ).

cnf(cls_le__minus__self__iff_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
    | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_minus__le__self__iff_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) ) ).

cnf(cls_minus__le__self__iff_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_less__eq__neg__nonpos_0,axiom,
    ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a)
    | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ).

cnf(cls_less__eq__neg__nonpos_1,axiom,
    ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a)
    | c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
    | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_neg__less__eq__nonneg_0,axiom,
    ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) ) ).

cnf(cls_neg__less__eq__nonneg_1,axiom,
    ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a)
    | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_degree__pCons__0_0,axiom,
    ( ~ class_HOL_Ozero(T_a)
    | c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a) = c_HOL_Ozero__class_Ozero(tc_nat) ) ).

cnf(cls_one__le__power_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_lessequals(c_HOL_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),T_a)
    | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ).

cnf(cls_coeff__pCons__Suc_0,axiom,
    ( ~ class_HOL_Ozero(T_a)
    | hAPP(c_Polynomial_Ocoeff(c_Polynomial_OpCons(V_a,V_p,T_a),T_a),c_Suc(V_n)) = hAPP(c_Polynomial_Ocoeff(V_p,T_a),V_n) ) ).

cnf(cls_add__Suc_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(V_m)),V_n) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)) ).

cnf(cls_add__Suc__right_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_Suc(V_n)) = c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)) ).

cnf(cls_norm__minus__cancel_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_RealVector_Onorm__class_Onorm(V_x,T_a) ) ).

cnf(cls_nat__add__commute_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m) ).

cnf(cls_foldl__assoc_0,axiom,
    ( ~ class_OrderedGroup_Osemigroup__add(T_a)
    | c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y),V_zs,T_a,T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),V_y,V_zs,T_a,T_a)) ) ).

cnf(cls_power_Opower_Opower__Suc_0,axiom,
    hAPP(hAPP(c_Power_Opower_Opower(V_one,V_times,T_a),V_a),c_Suc(V_n)) = hAPP(hAPP(V_times,V_a),hAPP(hAPP(c_Power_Opower_Opower(V_one,V_times,T_a),V_a),V_n)) ).

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

cnf(cls_degree__smult__eq_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | c_Polynomial_Odegree(c_Polynomial_Osmult(V_a,V_p,T_a),T_a) = c_Polynomial_Odegree(V_p,T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_of__nat__add_0,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(T_a)
    | c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a)),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)) ) ).

cnf(cls_coeff__inject_0,axiom,
    ( ~ class_HOL_Ozero(T_a)
    | c_Polynomial_Ocoeff(V_x,T_a) != c_Polynomial_Ocoeff(V_y,T_a)
    | V_x = V_y ) ).

cnf(cls_monom__0_0,axiom,
    ( ~ class_HOL_Ozero(T_a)
    | c_Polynomial_Omonom(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_Polynomial_OpCons(V_a,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) ) ).

cnf(cls_mult__strict__mono_H_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_d),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).

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

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(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),c_Polynomial_Osmult(V_a,V_p,T_a),T_a) ) ).

cnf(cls_Suc__n__not__n_0,axiom,
    c_Suc(V_n) != V_n ).

cnf(cls_n__not__Suc__n_0,axiom,
    V_n != c_Suc(V_n) ).

cnf(cls_mult__right__mono__neg_0,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(T_a)
    | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c),T_a)
    | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(V_b,V_a,T_a) ) ).

cnf(cls_mult__left__mono__neg_0,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(T_a)
    | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b),T_a)
    | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(V_b,V_a,T_a) ) ).

cnf(cls_mult__right__mono_0,axiom,
    ( ~ class_Ring__and__Field_Omult__mono(T_a)
    | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_lessequals(V_a,V_b,T_a) ) ).

cnf(cls_mult__left__mono_0,axiom,
    ( ~ class_Ring__and__Field_Omult__mono(T_a)
    | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_lessequals(V_a,V_b,T_a) ) ).

cnf(cls_mult__mono1_0,axiom,
    ( ~ class_Ring__and__Field_Omult__mono1(T_a)
    | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_lessequals(V_a,V_b,T_a) ) ).

cnf(cls_power__less__power__Suc_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,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_add__minus__cancel_0,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a)),V_b)) = V_b ) ).

cnf(cls_mult__pos__neg2_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_mult__pos__neg_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_mult__neg__pos_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_mult__le__0__iff_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_mult__le__0__iff_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_mult__le__0__iff_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_mult__le__0__iff_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_psize__def_1,axiom,
    ( ~ class_HOL_Ozero(T_a)
    | c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(V_p,T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a))
    | V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_class__semiring_Opwr__0_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(T_a) ) ).

cnf(cls_power__0_0,axiom,
    ( ~ class_Power_Opower(T_a)
    | hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oone__class_Oone(T_a) ) ).

cnf(cls_neg__le__0__iff__le_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_neg__le__0__iff__le_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

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

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

cnf(cls_less__add__one_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_HOL_Oord__class_Oless(V_a,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Oone__class_Oone(T_a)),T_a) ) ).

cnf(cls_le__eq__neg_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a)
    | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_le__eq__neg_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ).

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

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

cnf(cls_add__le__cancel__right_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
    | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a)
    | ~ c_lessequals(V_a,V_b,T_a) ) ).

cnf(cls_add__le__cancel__right_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
    | c_lessequals(V_a,V_b,T_a)
    | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a) ) ).

cnf(cls_add__le__cancel__left_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
    | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a)
    | ~ c_lessequals(V_a,V_b,T_a) ) ).

cnf(cls_add__le__cancel__left_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
    | c_lessequals(V_a,V_b,T_a)
    | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a) ) ).

cnf(cls_add__right__mono_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a)
    | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a)
    | ~ c_lessequals(V_a,V_b,T_a) ) ).

cnf(cls_add__left__mono_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a)
    | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a)
    | ~ c_lessequals(V_a,V_b,T_a) ) ).

cnf(cls_leading__coeff__0__iff_0,axiom,
    ( ~ class_HOL_Ozero(T_a)
    | hAPP(c_Polynomial_Ocoeff(V_p,T_a),c_Polynomial_Odegree(V_p,T_a)) != c_HOL_Ozero__class_Ozero(T_a)
    | V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_linorder__neqE__ordered__idom_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_HOL_Oord__class_Oless(V_y,V_x,T_a)
    | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | V_x = V_y ) ).

cnf(cls_not__less__iff__gr__or__eq_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | V_x = V_y
    | c_HOL_Oord__class_Oless(V_y,V_x,T_a)
    | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).

cnf(cls_linorder__antisym__conv3_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | V_x = V_y
    | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).

cnf(cls_linorder__less__linear_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_HOL_Oord__class_Oless(V_y,V_x,T_a)
    | V_x = V_y
    | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).

cnf(cls_order__antisym__conv_0,axiom,
    ( ~ class_Orderings_Oorder(T_a)
    | V_x = V_y
    | ~ c_lessequals(V_x,V_y,T_a)
    | ~ c_lessequals(V_y,V_x,T_a) ) ).

cnf(cls_order__eq__iff_2,axiom,
    ( ~ class_Orderings_Oorder(T_a)
    | V_x = V_y
    | ~ c_lessequals(V_y,V_x,T_a)
    | ~ c_lessequals(V_x,V_y,T_a) ) ).

cnf(cls_linorder__neqE_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_HOL_Oord__class_Oless(V_y,V_x,T_a)
    | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | V_x = V_y ) ).

cnf(cls_order__antisym_0,axiom,
    ( ~ class_Orderings_Oorder(T_a)
    | V_x = V_y
    | ~ c_lessequals(V_y,V_x,T_a)
    | ~ c_lessequals(V_x,V_y,T_a) ) ).

cnf(cls_real__le__antisym_0,axiom,
    ( V_z = V_w
    | ~ c_lessequals(V_w,V_z,tc_RealDef_Oreal)
    | ~ c_lessequals(V_z,V_w,tc_RealDef_Oreal) ) ).

cnf(cls_power__gt1__lemma_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ).

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_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_class__semiring_Osemiring__rules_I15_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_ry)) ) ).

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

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

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_sum__squares__le__zero__iff_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Ozero__class_Ozero(T_a))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Ozero__class_Ozero(T_a))),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_add__nonpos__neg_0,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_add__neg__nonpos_0,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_neg__less__iff__less_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).

cnf(cls_neg__less__iff__less_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ).

cnf(cls_not__sum__squares__lt__zero_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_y),V_y)),c_HOL_Ozero__class_Ozero(T_a),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_degree__smult__eq_0,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | c_Polynomial_Odegree(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(T_a),V_p,T_a),T_a) = c_HOL_Ozero__class_Ozero(tc_nat) ) ).

cnf(cls_power__less__imp__less__base_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n),T_a) ) ).

cnf(cls_zero__less__mult__pos2_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_a),T_a) ) ).

cnf(cls_zero__less__mult__pos_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),T_a) ) ).

cnf(cls_mult__pos__pos_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_mult__neg__neg_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_mult__eq__0__iff_0,axiom,
    ( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a)
    | hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b) != 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_no__zero__divisors_0,axiom,
    ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
    | hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b) != 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_no__zero__divirors__neq0_0,axiom,
    ( ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
    | hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b) != 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_offset__poly__eq__0__lemma_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),c_Polynomial_Osmult(V_c,V_p,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_add__is__0_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != c_HOL_Ozero__class_Ozero(tc_nat)
    | V_m = c_HOL_Ozero__class_Ozero(tc_nat) ) ).

cnf(cls_add__is__0_1,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != c_HOL_Ozero__class_Ozero(tc_nat)
    | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).

cnf(cls_class__semiring_Omul__pwr_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_p),V_q)) ) ).

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

cnf(cls_mult__less__imp__less__right_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
    | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c),T_a) ) ).

cnf(cls_mult__less__imp__less__left_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
    | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b),T_a) ) ).

cnf(cls_mult__right__less__imp__less_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring(T_a)
    | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c),T_a) ) ).

cnf(cls_mult__left__less__imp__less_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring(T_a)
    | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b),T_a) ) ).

cnf(cls_natgb_Oadd__r0__iff_0,axiom,
    ( V_x != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_a)
    | V_a = c_HOL_Ozero__class_Ozero(tc_nat) ) ).

cnf(cls_add__eq__self__zero_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != V_m
    | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).

cnf(cls_of__nat__eq__iff_0,axiom,
    ( ~ class_Nat_Osemiring__char__0(T_a)
    | c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a) != c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)
    | V_m = V_n ) ).

cnf(cls_power__power__power_0,axiom,
    ( ~ class_Power_Opower(T_a)
    | c_Power_Opower__class_Opower(T_a) = c_Power_Opower_Opower(c_HOL_Oone__class_Oone(T_a),c_HOL_Otimes__class_Otimes(T_a),T_a) ) ).

cnf(cls_sum__squares__ge__zero_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_y),V_y)),T_a) ) ).

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

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

cnf(cls_nat_Osimps_I2_J_0,axiom,
    c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H) ).

cnf(cls_Zero__neq__Suc_0,axiom,
    c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m) ).

cnf(cls_neg__le__iff__le_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_lessequals(V_a,V_b,T_a)
    | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ).

cnf(cls_le__imp__neg__le_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
    | ~ c_lessequals(V_a,V_b,T_a) ) ).

cnf(cls_power__0__Suc_0,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0(T_a)
    | ~ class_Power_Opower(T_a)
    | hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_Suc(V_n)) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_mult__strict__mono_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_d),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).

cnf(cls_comm__monoid__add_Opower__one__right_0,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),T_a),V_a),c_HOL_Oone__class_Oone(tc_nat)) = V_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_power__commutes_0,axiom,
    ( ~ class_OrderedGroup_Omonoid__mult(T_a)
    | hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ).

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

cnf(cls_nat_Oinject_0,axiom,
    ( c_Suc(V_nat) != c_Suc(V_nat_H)
    | V_nat = V_nat_H ) ).

cnf(cls_Suc__inject_0,axiom,
    ( c_Suc(V_x) != c_Suc(V_y)
    | V_x = V_y ) ).

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

cnf(cls_One__nat__def_0,axiom,
    c_HOL_Oone__class_Oone(tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ).

cnf(cls_class__semiring_Osemiring__rules_I33_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_HOL_Oone__class_Oone(tc_nat)) = V_x ) ).

cnf(cls_power__one__right_0,axiom,
    ( ~ class_OrderedGroup_Omonoid__mult(T_a)
    | hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_HOL_Oone__class_Oone(tc_nat)) = V_a ) ).

cnf(cls_one__is__add_2,axiom,
    ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)
    | V_m = c_HOL_Ozero__class_Ozero(tc_nat)
    | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).

cnf(cls_one__is__add_1,axiom,
    ( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)
    | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ).

cnf(cls_zero__less__power_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_poly__monom_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | hAPP(c_Polynomial_Opoly(c_Polynomial_Omonom(V_a,V_n,T_a),T_a),V_x) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ) ).

cnf(cls_not__one__less__zero_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

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

cnf(cls_degree__monom__eq_0,axiom,
    ( ~ class_HOL_Ozero(T_a)
    | c_Polynomial_Odegree(c_Polynomial_Omonom(V_a,V_n,T_a),T_a) = V_n
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_zero__le__one_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a) ) ).

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

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

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

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

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

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

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

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

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

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

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

cnf(cls_one__is__add_4,axiom,
    c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) ).

cnf(cls_linorder__neq__iff_1,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).

cnf(cls_order__less__le_1,axiom,
    ( ~ class_Orderings_Oorder(T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).

cnf(cls_order__less__irrefl_0,axiom,
    ( ~ class_Orderings_Opreorder(T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).

cnf(cls_less__le__not__le_2,axiom,
    ( ~ class_Orderings_Opreorder(T_a)
    | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | c_lessequals(V_y,V_x,T_a)
    | ~ c_lessequals(V_x,V_y,T_a) ) ).

cnf(cls_not__one__le__zero_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_add__strict__mono_0,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d),T_a)
    | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).

cnf(cls_order__le__less_1,axiom,
    ( ~ class_Orderings_Oorder(T_a)
    | c_lessequals(V_x,V_y,T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).

cnf(cls_order__less__imp__le_0,axiom,
    ( ~ class_Orderings_Opreorder(T_a)
    | c_lessequals(V_x,V_y,T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).

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

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

cnf(cls_Suc__neq__Zero_0,axiom,
    c_Suc(V_m) != c_HOL_Ozero__class_Ozero(tc_nat) ).

cnf(cls_nat_Osimps_I3_J_0,axiom,
    c_Suc(V_nat_H) != c_HOL_Ozero__class_Ozero(tc_nat) ).

cnf(cls_power__gt1_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Suc(V_n)),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ).

cnf(cls_coeff__pCons__0_0,axiom,
    ( ~ class_HOL_Ozero(T_a)
    | hAPP(c_Polynomial_Ocoeff(c_Polynomial_OpCons(V_a,V_p,T_a),T_a),c_HOL_Ozero__class_Ozero(tc_nat)) = V_a ) ).

cnf(cls_power__le__zero__eq_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_zero__less__one_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),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_power__le__imp__le__base_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_lessequals(V_a,V_b,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Suc(V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),c_Suc(V_n)),T_a) ) ).

cnf(cls_mult__le__less__imp__less_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_d),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a)
    | ~ c_lessequals(V_a,V_b,T_a) ) ).

cnf(cls_mult__less__le__imp__less_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_d),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_lessequals(V_c,V_d,T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).

cnf(cls_power__inject__exp_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m) != hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a)
    | V_m = V_n ) ).

cnf(cls_class__semiring_Osemiring__rules_I27_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Suc(V_q)) ) ).

cnf(cls_class__semiring_Osemiring__rules_I28_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Suc(V_q)) ) ).

cnf(cls_minus__mult__commute_0,axiom,
    ( ~ class_Ring__and__Field_Oring(T_a)
    | hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a)),V_b) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),c_HOL_Ouminus__class_Ouminus(V_b,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_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_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_power_Opower_Opower__0_0,axiom,
    hAPP(hAPP(c_Power_Opower_Opower(V_one,V_times,T_a),V_a),c_HOL_Ozero__class_Ozero(tc_nat)) = V_one ).

cnf(cls_add__less__cancel__left_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
    | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a) ) ).

cnf(cls_add__less__cancel__left_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).

cnf(cls_add__strict__left__mono_0,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).

cnf(cls_add__less__cancel__right_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
    | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a) ) ).

cnf(cls_add__less__cancel__right_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).

cnf(cls_add__strict__right__mono_0,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).

cnf(cls_order__eq__refl_0,axiom,
    ( ~ class_Orderings_Opreorder(T_a)
    | c_lessequals(V_x,V_x,T_a) ) ).

cnf(cls_order__eq__iff_0,axiom,
    ( ~ class_Orderings_Oorder(T_a)
    | c_lessequals(V_x,V_x,T_a) ) ).

cnf(cls_real__le__trans_0,axiom,
    ( c_lessequals(V_i,V_k,tc_RealDef_Oreal)
    | ~ c_lessequals(V_j,V_k,tc_RealDef_Oreal)
    | ~ c_lessequals(V_i,V_j,tc_RealDef_Oreal) ) ).

cnf(cls_real__le__refl_0,axiom,
    c_lessequals(V_w,V_w,tc_RealDef_Oreal) ).

cnf(cls_order__le__less__trans_0,axiom,
    ( ~ class_Orderings_Opreorder(T_a)
    | c_HOL_Oord__class_Oless(V_x,V_z,T_a)
    | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
    | ~ c_lessequals(V_x,V_y,T_a) ) ).

cnf(cls_order__less__le__trans_0,axiom,
    ( ~ class_Orderings_Opreorder(T_a)
    | c_HOL_Oord__class_Oless(V_x,V_z,T_a)
    | ~ c_lessequals(V_y,V_z,T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).

cnf(cls_le__add__right__mono_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_lessequals(V_a,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d),T_a)
    | ~ c_lessequals(V_c,V_d,T_a)
    | ~ c_lessequals(V_a,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a) ) ).

cnf(cls_order__trans_0,axiom,
    ( ~ class_Orderings_Opreorder(T_a)
    | c_lessequals(V_x,V_z,T_a)
    | ~ c_lessequals(V_y,V_z,T_a)
    | ~ c_lessequals(V_x,V_y,T_a) ) ).

cnf(cls_xt1_I8_J_0,axiom,
    ( ~ class_Orderings_Oorder(T_a)
    | c_HOL_Oord__class_Oless(V_z,V_x,T_a)
    | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a)
    | ~ c_lessequals(V_y,V_x,T_a) ) ).

cnf(cls_xt1_I7_J_0,axiom,
    ( ~ class_Orderings_Oorder(T_a)
    | c_HOL_Oord__class_Oless(V_z,V_x,T_a)
    | ~ c_lessequals(V_z,V_y,T_a)
    | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).

cnf(cls_xt1_I6_J_0,axiom,
    ( ~ class_Orderings_Oorder(T_a)
    | c_lessequals(V_z,V_x,T_a)
    | ~ c_lessequals(V_z,V_y,T_a)
    | ~ c_lessequals(V_y,V_x,T_a) ) ).

cnf(cls_add__is__1_5,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ).

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

cnf(cls_poly__rec_Osimps_0,axiom,
    ( ~ class_HOL_Ozero(T_b)
    | c_Polynomial_Opoly__rec(V_z,V_f,c_Polynomial_OpCons(V_a,V_p,T_b),T_a,T_b) = hAPP(hAPP(hAPP(V_f,V_a),V_p),c_HOL_OIf(c_fequal(V_p,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)),tc_Polynomial_Opoly(T_b)),V_z,c_Polynomial_Opoly__rec(V_z,V_f,V_p,T_a,T_b),T_a)) ) ).

cnf(cls_mult__less__cancel__left__disj_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_HOL_Oord__class_Oless(V_b,V_a,T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b),T_a) ) ).

cnf(cls_mult__less__cancel__left__disj_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b),T_a) ) ).

cnf(cls_mult__less__cancel__right__disj_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_HOL_Oord__class_Oless(V_b,V_a,T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c),T_a) ) ).

cnf(cls_mult__less__cancel__right__disj_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c),T_a) ) ).

cnf(cls_monom__Suc_0,axiom,
    ( ~ class_HOL_Ozero(T_a)
    | c_Polynomial_Omonom(V_a,c_Suc(V_n),T_a) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_Polynomial_Omonom(V_a,V_n,T_a),T_a) ) ).

cnf(cls_neg__0__less__iff__less_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ).

cnf(cls_neg__0__less__iff__less_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_less__minus__self__iff_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ).

cnf(cls_less__minus__self__iff_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_monom__eq__iff_0,axiom,
    ( ~ class_HOL_Ozero(T_a)
    | c_Polynomial_Omonom(V_a,V_n,T_a) != c_Polynomial_Omonom(V_b,V_n,T_a)
    | V_a = V_b ) ).

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

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

cnf(cls_order__less__asym_H_0,axiom,
    ( ~ class_Orderings_Opreorder(T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).

cnf(cls_order__less__asym_0,axiom,
    ( ~ class_Orderings_Opreorder(T_a)
    | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).

cnf(cls_linorder__linear_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(V_y,V_x,T_a)
    | c_lessequals(V_x,V_y,T_a) ) ).

cnf(cls_real__le__linear_0,axiom,
    ( c_lessequals(V_w,V_z,tc_RealDef_Oreal)
    | c_lessequals(V_z,V_w,tc_RealDef_Oreal) ) ).

cnf(cls_not__less__iff__gr__or__eq_1,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).

cnf(cls_xt1_I9_J_0,axiom,
    ( ~ class_Orderings_Oorder(T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ).

cnf(cls_degree__pCons__eq_0,axiom,
    ( ~ class_HOL_Ozero(T_a)
    | c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a))
    | V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_degree__offset__poly_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
    | c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),T_a) = c_Polynomial_Odegree(V_p,T_a) ) ).

cnf(cls_offset__poly__0_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
    | c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_h,T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).

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

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

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

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

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

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

cnf(cls_add__is__1_4,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ).

cnf(cls_Suc__eq__plus1__left_0,axiom,
    c_Suc(V_n) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),V_n) ).

cnf(cls_Suc__eq__plus1_0,axiom,
    c_Suc(V_n) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),c_HOL_Oone__class_Oone(tc_nat)) ).

cnf(cls_neg__less__0__iff__less_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_neg__less__0__iff__less_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

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

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

cnf(cls_offset__poly__pCons_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
    | c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(V_a,V_p,T_a),V_h,T_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a)),c_Polynomial_Osmult(V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),T_a)),c_Polynomial_OpCons(V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),T_a)) ) ).

cnf(cls_class__semiring_Opwr__Suc_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Suc(V_n)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ) ).

cnf(cls_power__Suc2_0,axiom,
    ( ~ class_OrderedGroup_Omonoid__mult(T_a)
    | hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Suc(V_n)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) ) ).

cnf(cls_power__Suc_0,axiom,
    ( ~ class_Power_Opower(T_a)
    | hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Suc(V_n)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ).

cnf(cls_class__semiring_Osemiring__rules_I35_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Suc(V_q)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) ) ).

cnf(cls_comm__monoid__add_Opower__Suc_0,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),T_a),V_a),c_Suc(V_n)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),T_a),V_a),V_n)) ) ).

cnf(cls_comm__monoid__add_Opower__Suc2_0,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),T_a),V_a),c_Suc(V_n)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),T_a),V_a),V_n)),V_a) ) ).

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

cnf(cls_add__is__0_2,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(tc_nat) ).

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

cnf(cls_zero__less__power__eq_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | V_n = c_HOL_Ozero__class_Ozero(tc_nat)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_n),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_xt1_I10_J_0,axiom,
    ( ~ class_Orderings_Oorder(T_a)
    | c_HOL_Oord__class_Oless(V_z,V_x,T_a)
    | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a)
    | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).

cnf(cls_order__less__trans_0,axiom,
    ( ~ class_Orderings_Opreorder(T_a)
    | c_HOL_Oord__class_Oless(V_x,V_z,T_a)
    | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).

cnf(cls_coeff__smult_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
    | hAPP(c_Polynomial_Ocoeff(c_Polynomial_Osmult(V_a,V_p,T_a),T_a),V_n) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),hAPP(c_Polynomial_Ocoeff(V_p,T_a),V_n)) ) ).

cnf(cls_coeff__monom_1,axiom,
    ( ~ class_HOL_Ozero(T_a)
    | hAPP(c_Polynomial_Ocoeff(c_Polynomial_Omonom(V_a,V_m,T_a),T_a),V_n) = c_HOL_Ozero__class_Ozero(T_a)
    | V_m = V_n ) ).

cnf(cls_nat__add__assoc_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)),V_k) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k)) ).

cnf(cls_nat__add__left__commute_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z)) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_z)) ).

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_power__add_0,axiom,
    ( ~ class_OrderedGroup_Omonoid__mult(T_a)
    | hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)) = hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ).

cnf(cls_less__le__not__le_1,axiom,
    ( ~ class_Orderings_Opreorder(T_a)
    | ~ c_lessequals(V_y,V_x,T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).

cnf(cls_not__leE_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | c_lessequals(V_y,V_x,T_a) ) ).

cnf(cls_linorder__antisym__conv2_1,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | ~ c_lessequals(V_x,V_x,T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).

cnf(cls_linorder__antisym__conv1_1,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_HOL_Oord__class_Oless(V_x,V_x,T_a)
    | c_lessequals(V_x,V_x,T_a) ) ).

cnf(cls_linorder__not__less_1,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | ~ c_lessequals(V_y,V_x,T_a) ) ).

cnf(cls_linorder__not__less_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(V_y,V_x,T_a)
    | c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).

cnf(cls_linorder__not__le_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_HOL_Oord__class_Oless(V_y,V_x,T_a)
    | c_lessequals(V_x,V_y,T_a) ) ).

cnf(cls_linorder__not__le_1,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | ~ c_lessequals(V_x,V_y,T_a)
    | ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).

cnf(cls_add__strict__increasing2_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
    | ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | c_HOL_Oord__class_Oless(V_b,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_power__mono_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_lessequals(V_a,V_b,T_a) ) ).

cnf(cls_power__less__zero__eq_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_power__le__zero__eq_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | V_x = c_HOL_Ozero__class_Ozero(T_a)
    | c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_mult__right__le__imp__le_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
    | c_lessequals(V_a,V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c),T_a) ) ).

cnf(cls_mult__left__le__imp__le_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
    | c_lessequals(V_a,V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b),T_a) ) ).

cnf(cls_mult__le__cancel__left__pos_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b),T_a)
    | ~ c_lessequals(V_a,V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).

cnf(cls_mult__le__cancel__left__pos_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_lessequals(V_a,V_b,T_a)
    | ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).

cnf(cls_mult__le__cancel__left__neg_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b),T_a)
    | ~ c_lessequals(V_b,V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_mult__le__cancel__left__neg_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_lessequals(V_b,V_a,T_a)
    | ~ c_lessequals(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b),T_a)
    | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

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

cnf(cls_sum__squares__le__zero__iff_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | V_y = c_HOL_Ozero__class_Ozero(T_a)
    | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_y),V_y)),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_sum__squares__le__zero__iff_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | V_x = c_HOL_Ozero__class_Ozero(T_a)
    | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_y),V_y)),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_add__is__1_0,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | V_m = c_HOL_Ozero__class_Ozero(tc_nat)
    | V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ).

cnf(cls_add__is__1_3,axiom,
    ( hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
    | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).

cnf(cls_sum__squares__gt__zero__iff_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_y),V_y)),T_a)
    | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_sum__squares__gt__zero__iff_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_y),V_y)),T_a)
    | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ).

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

cnf(cls_of__nat__less__0__iff_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | ~ c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

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

cnf(cls_mult__strict__left__mono__comm_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T_a)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).

cnf(cls_mult__less__cancel__right__disj_5,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c),T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_mult__less__cancel__right__disj_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).

cnf(cls_mult__strict__right__mono_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).

cnf(cls_mult__strict__right__mono__neg_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_b),V_c),T_a)
    | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ).

cnf(cls_mult__less__cancel__left__disj_5,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b),T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_mult__less__cancel__left__disj_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).

cnf(cls_mult__strict__left__mono_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).

cnf(cls_mult__strict__left__mono__neg_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b),T_a)
    | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ).

cnf(cls_mult__less__cancel__left__pos_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).

cnf(cls_mult__less__cancel__left__pos_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).

cnf(cls_mult__less__cancel__left__neg_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b),T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_mult__less__cancel__left__neg_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_HOL_Oord__class_Oless(V_b,V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_c),V_b),T_a)
    | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

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(hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_a),V_b),V_p,T_a) ) ).

cnf(cls_zero__le__imp__of__nat_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),T_a) ) ).

cnf(cls_of__nat__0__le__iff_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a) ) ).

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

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

cnf(cls_natgb_Oadd__r0__iff_1,axiom,
    V_x = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),c_HOL_Ozero__class_Ozero(tc_nat)) ).

cnf(cls_Nat_Oadd__0__right_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_HOL_Ozero__class_Ozero(tc_nat)) = V_m ).

cnf(cls_plus__nat_Oadd__0_0,axiom,
    hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n) = V_n ).

cnf(cls_less__1__mult_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_m),V_n),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_n,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_m,T_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_add__less__le__mono_0,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d),T_a)
    | ~ c_lessequals(V_c,V_d,T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).

cnf(cls_add__le__less__mono_0,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d),T_a)
    | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a)
    | ~ c_lessequals(V_a,V_b,T_a) ) ).

cnf(cls_minus__less__iff_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a) ) ).

cnf(cls_minus__less__iff_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) ).

cnf(cls_less__minus__iff_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ).

cnf(cls_less__minus__iff_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_HOL_Oord__class_Oless(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ).

cnf(cls_minus__le__iff_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a)
    | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a) ) ).

cnf(cls_minus__le__iff_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a)
    | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) ).

cnf(cls_le__minus__iff_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a)
    | ~ c_lessequals(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ).

cnf(cls_le__minus__iff_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_lessequals(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
    | ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ).

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

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

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

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

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

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

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

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

cnf(cls_pc0_0,axiom,
    hAPP(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),v_c____) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ).

cnf(cls_poly__offset_0,axiom,
    c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1(V_a,V_p),tc_Complex_Ocomplex) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(V_p,tc_Complex_Ocomplex) ).

cnf(cls_poly__decompose__lemma_0,axiom,
    ( ~ class_Ring__and__Field_Oidom(t_a)
    | v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__lemma__2(V_p) != c_HOL_Ozero__class_Ozero(t_a)
    | hAPP(c_Polynomial_Opoly(V_p,t_a),V_z) = c_HOL_Ozero__class_Ozero(t_a)
    | V_z = c_HOL_Ozero__class_Ozero(t_a) ) ).

cnf(cls_degree__0_0,axiom,
    ( ~ class_HOL_Ozero(T_a)
    | c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_nat) ) ).

cnf(cls_coeff__0_0,axiom,
    ( ~ class_HOL_Ozero(T_a)
    | hAPP(c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),V_n) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_add__neg__neg_0,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

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

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

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

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

cnf(cls_power__eq__0__iff_1,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)
    | hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Ozero__class_Ozero(T_a) ) ).

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

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

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

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

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

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

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

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

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

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

cnf(cls_add__nonneg__eq__0__iff_2,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Ozero__class_Ozero(T_a)) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_pcompose__0_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
    | c_Polynomial_Opcompose(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q,T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_monom__eq__0_0,axiom,
    ( ~ class_HOL_Ozero(T_a)
    | c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_poly__offset__poly_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
    | hAPP(c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),T_a),V_x) = hAPP(c_Polynomial_Opoly(V_p,T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_h),V_x)) ) ).

cnf(cls_add__increasing_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
    | ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | c_lessequals(V_b,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a)
    | ~ c_lessequals(V_b,V_c,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_add__increasing2_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
    | ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | c_lessequals(V_b,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a)
    | ~ c_lessequals(V_b,V_a,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).

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

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

cnf(cls_add__nonneg__eq__0__iff_0,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)
    | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_add__nonneg__eq__0__iff_1,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y) != c_HOL_Ozero__class_Ozero(T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)
    | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_even__less__0__iff_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_even__less__0__iff_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_double__add__less__zero__iff__single__less__zero_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_double__add__less__zero__iff__single__less__zero_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_c_0,axiom,
    c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),v_c____),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(hAPP(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),V_w),tc_Complex_Ocomplex),tc_RealDef_Oreal) ).

cnf(cls_poly__rec__0_0,axiom,
    ( ~ class_HOL_Ozero(T_b)
    | hAPP(hAPP(hAPP(V_f,c_HOL_Ozero__class_Ozero(T_b)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z) != V_z
    | c_Polynomial_Opoly__rec(V_z,V_f,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)),T_a,T_b) = V_z ) ).

cnf(cls_order__root_2,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | hAPP(c_Polynomial_Opoly(V_p,T_a),V_a) = c_HOL_Ozero__class_Ozero(T_a)
    | c_Polynomial_Oorder(V_a,V_p,T_a) = c_HOL_Ozero__class_Ozero(tc_nat) ) ).

cnf(cls_power__eq__0__iff_2,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)
    | hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_n) = c_HOL_Ozero__class_Ozero(T_a)
    | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).

cnf(cls_power__0__left_1,axiom,
    ( ~ class_Ring__and__Field_Osemiring__0(T_a)
    | ~ class_Power_Opower(T_a)
    | hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_n) = c_HOL_Ozero__class_Ozero(T_a)
    | V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).

cnf(cls_comm__monoid__add_Opower__commutes_0,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),T_a),V_a),V_n)),V_a) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),T_a),V_a),V_n)) ) ).

cnf(cls_pos__add__strict_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_HOL_Oord__class_Oless(V_b,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,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)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_r),V_c)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_r),V_d))
    | 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)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_y),V_y)) != 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)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_x),V_x)),hAPP(hAPP(c_HOL_Otimes__class_Otimes(T_a),V_y),V_y)) != c_HOL_Ozero__class_Ozero(T_a)
    | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_monom__eq__0__iff_0,axiom,
    ( ~ class_HOL_Ozero(T_a)
    | c_Polynomial_Omonom(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_zero__less__double__add__iff__zero__less__single__add_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),T_a) ) ).

cnf(cls_zero__less__double__add__iff__zero__less__single__add_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

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

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

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

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

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

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

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

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_of__nat__0_0,axiom,
    ( ~ class_Ring__and__Field_Osemiring__1(T_a)
    | c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_HOL_Ozero__class_Ozero(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)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z)) != hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_u)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z) = V_u ) ).

cnf(cls_n_0,axiom,
    v_n____ = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_pa____,tc_Complex_Ocomplex) ).

cnf(cls_psize__def_0,axiom,
    ( ~ class_HOL_Ozero(T_a)
    | c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_nat) ) ).

cnf(cls_add__nonneg__nonneg_0,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_comm__monoid__add_Opower__mult__distrib_0,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),T_a),V_b),V_n)) ) ).

cnf(cls_zero__le__double__add__iff__zero__le__single__add_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),T_a) ) ).

cnf(cls_zero__le__double__add__iff__zero__le__single__add_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

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

cnf(cls_psize__eq__0__iff_0,axiom,
    ( ~ class_HOL_Ozero(T_a)
    | c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_nat)
    | V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).

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

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

cnf(cls_comm__monoid__add_Omult__commute_0,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_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_foldl__absorb0_0,axiom,
    ( ~ class_OrderedGroup_Omonoid__add(T_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a),V_zs,T_a,T_a)) = c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),V_x,V_zs,T_a,T_a) ) ).

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

cnf(cls_calculation_0,axiom,
    ( hAPP(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),v_c____) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)
    | hAPP(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),v_sko__unknown__thm__rrS__1(v_pa____)) = c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ).

cnf(cls_psize__def__raw_0,axiom,
    ( ~ class_HOL_Ozero(t_a)
    | c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_p,t_a) = c_HOL_OIf(c_fequal(v_p,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)),tc_Polynomial_Opoly(t_a)),c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_Polynomial_Odegree(v_p,t_a)),tc_nat) ) ).

cnf(cls_comm__monoid__add_Opower__one_0,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),T_a),c_HOL_Ozero__class_Ozero(T_a)),V_n) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_comm__monoid__add_Opower__0_0,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | hAPP(hAPP(c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),T_a),V_a),c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_add__pos__pos_0,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_poly__decompose_3,axiom,
    ( ~ class_Ring__and__Field_Oidom(t_a)
    | hAPP(c_Polynomial_Opoly(V_p,t_a),V_z) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(t_a),hAPP(c_Polynomial_Opoly(V_p,t_a),c_HOL_Ozero__class_Ozero(t_a))),hAPP(hAPP(c_HOL_Otimes__class_Otimes(t_a),hAPP(hAPP(c_Power_Opower__class_Opower(t_a),V_z),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1(V_p))),hAPP(c_Polynomial_Opoly(c_Polynomial_OpCons(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__2(V_p),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__3(V_p),t_a),t_a),V_z)))
    | c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(V_p,t_a),t_a,t_a) ) ).

cnf(cls_comm__monoid__add__class_Oaxioms_0,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | c_OrderedGroup_Ocomm__monoid__add__axioms(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),T_a) ) ).

cnf(cls_poly__offset_1,axiom,
    hAPP(c_Polynomial_Opoly(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__offset__1(V_a,V_p),tc_Complex_Ocomplex),V_q) = hAPP(c_Polynomial_Opoly(V_p,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),V_a),V_q)) ).

cnf(cls_monoid__add__class_Oaxioms_0,axiom,
    ( ~ class_OrderedGroup_Omonoid__add(T_a)
    | c_OrderedGroup_Omonoid__add__axioms(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),T_a) ) ).

cnf(cls_poly__decompose_2,axiom,
    ( ~ class_Ring__and__Field_Oidom(t_a)
    | hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__3(V_p),t_a)),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1(V_p))),c_HOL_Oone__class_Oone(tc_nat)) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(V_p,t_a)
    | c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(V_p,t_a),t_a,t_a) ) ).

cnf(cls_order__root_0,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | c_Polynomial_Oorder(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_nat)
    | V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | hAPP(c_Polynomial_Opoly(V_p,T_a),V_a) != c_HOL_Ozero__class_Ozero(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_double__add__le__zero__iff__single__add__le__zero_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_double__add__le__zero__iff__single__add__le__zero_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_add__nonpos__nonpos_0,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
    | c_lessequals(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

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

cnf(cls_poly__zero_0,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | ~ class_Int_Oring__char__0(T_a)
    | c_Polynomial_Opoly(V_p,T_a) != c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a)
    | V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).

cnf(cls_poly__eq__iff_0,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | ~ class_Int_Oring__char__0(T_a)
    | c_Polynomial_Opoly(V_p,T_a) != c_Polynomial_Opoly(V_q,T_a)
    | V_p = V_q ) ).

cnf(cls_constant__def_0,axiom,
    ( hAPP(V_f,V_x) = hAPP(V_f,V_y)
    | ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(V_f,t_a,t_b) ) ).

cnf(cls_poly__decompose_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(t_a)
    | v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__1(V_p) != c_HOL_Ozero__class_Ozero(tc_nat)
    | c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(V_p,t_a),t_a,t_a) ) ).

cnf(cls_assms_0,axiom,
    ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(v_p,tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex) ).

cnf(cls_poly__pcompose_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
    | hAPP(c_Polynomial_Opoly(c_Polynomial_Opcompose(V_p,V_q,T_a),T_a),V_x) = hAPP(c_Polynomial_Opoly(V_p,T_a),hAPP(c_Polynomial_Opoly(V_q,T_a),V_x)) ) ).

cnf(cls_q_I1_J_0,axiom,
    c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_q____,tc_Complex_Ocomplex) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_pa____,tc_Complex_Ocomplex) ).

cnf(cls_q_I2_J_0,axiom,
    hAPP(c_Polynomial_Opoly(v_q____,tc_Complex_Ocomplex),V_x) = hAPP(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_Complex_Ocomplex),v_c____),V_x)) ).

cnf(cls_nc_0,axiom,
    ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(v_pa____,tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex) ).

cnf(cls_poly__decompose_0,axiom,
    ( ~ class_Ring__and__Field_Oidom(t_a)
    | v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__decompose__2(V_p) != c_HOL_Ozero__class_Ozero(t_a)
    | c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(V_p,t_a),t_a,t_a) ) ).

cnf(cls_CHAINED_0,axiom,
    ~ c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(v_q____,tc_Complex_Ocomplex),tc_Complex_Ocomplex,tc_Complex_Ocomplex) ).

cnf(cls_conjecture_0,negated_conjecture,
    c_Fundamental__Theorem__Algebra__Mirabelle_Oconstant(c_Polynomial_Opoly(v_q____,tc_Complex_Ocomplex),tc_Complex_Ocomplex,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_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__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_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add,axiom,
    class_OrderedGroup_Ocancel__comm__monoid__add(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__Ring__and__Field_Ocomm__ring,axiom,
    class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex) ).

cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__comm__monoid__add,axiom,
    class_OrderedGroup_Ocancel__comm__monoid__add(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring__1,axiom,
    class_Ring__and__Field_Ocomm__ring__1(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring,axiom,
    class_Ring__and__Field_Ocomm__ring(tc_RealDef_Oreal) ).

cnf(clsarity_nat__OrderedGroup_Ocancel__comm__monoid__add,axiom,
    class_OrderedGroup_Ocancel__comm__monoid__add(tc_nat) ).

cnf(clsarity_fun__Lattices_Oboolean__algebra,axiom,
    ( class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1))
    | ~ class_Lattices_Oboolean__algebra(T_1) ) ).

cnf(clsarity_fun__Orderings_Opreorder,axiom,
    ( class_Orderings_Opreorder(tc_fun(T_2,T_1))
    | ~ class_Orderings_Opreorder(T_1) ) ).

cnf(clsarity_fun__Orderings_Oorder,axiom,
    ( class_Orderings_Oorder(tc_fun(T_2,T_1))
    | ~ class_Orderings_Oorder(T_1) ) ).

cnf(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ).

cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ).

cnf(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ).

cnf(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ).

cnf(clsarity_nat__Ring__and__Field_Oordered__semiring__strict,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ).

cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ).

cnf(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ).

cnf(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ).

cnf(clsarity_nat__OrderedGroup_Ocancel__semigroup__add,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ).

cnf(clsarity_nat__Ring__and__Field_Opordered__semiring,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_nat) ).

cnf(clsarity_nat__Ring__and__Field_Oordered__semiring,axiom,
    class_Ring__and__Field_Oordered__semiring(tc_nat) ).

cnf(clsarity_nat__Ring__and__Field_Ono__zero__divisors,axiom,
    class_Ring__and__Field_Ono__zero__divisors(tc_nat) ).

cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_nat) ).

cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ).

cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__0,axiom,
    class_Ring__and__Field_Ocomm__semiring__0(tc_nat) ).

cnf(clsarity_nat__OrderedGroup_Oab__semigroup__mult,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_nat) ).

cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__mult,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ).

cnf(clsarity_nat__OrderedGroup_Oab__semigroup__add,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_nat) ).

cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_nat) ).

cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_nat) ).

cnf(clsarity_nat__Ring__and__Field_Ozero__neq__one,axiom,
    class_Ring__and__Field_Ozero__neq__one(tc_nat) ).

cnf(clsarity_nat__OrderedGroup_Osemigroup__add,axiom,
    class_OrderedGroup_Osemigroup__add(tc_nat) ).

cnf(clsarity_nat__Ring__and__Field_Osemiring__1,axiom,
    class_Ring__and__Field_Osemiring__1(tc_nat) ).

cnf(clsarity_nat__Ring__and__Field_Osemiring__0,axiom,
    class_Ring__and__Field_Osemiring__0(tc_nat) ).

cnf(clsarity_nat__Ring__and__Field_Omult__mono1,axiom,
    class_Ring__and__Field_Omult__mono1(tc_nat) ).

cnf(clsarity_nat__Ring__and__Field_Omult__zero,axiom,
    class_Ring__and__Field_Omult__zero(tc_nat) ).

cnf(clsarity_nat__Ring__and__Field_Omult__mono,axiom,
    class_Ring__and__Field_Omult__mono(tc_nat) ).

cnf(clsarity_nat__OrderedGroup_Omonoid__mult,axiom,
    class_OrderedGroup_Omonoid__mult(tc_nat) ).

cnf(clsarity_nat__Ring__and__Field_Osemiring,axiom,
    class_Ring__and__Field_Osemiring(tc_nat) ).

cnf(clsarity_nat__OrderedGroup_Omonoid__add,axiom,
    class_OrderedGroup_Omonoid__add(tc_nat) ).

cnf(clsarity_nat__Nat_Osemiring__char__0,axiom,
    class_Nat_Osemiring__char__0(tc_nat) ).

cnf(clsarity_nat__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_nat) ).

cnf(clsarity_nat__Orderings_Olinorder,axiom,
    class_Orderings_Olinorder(tc_nat) ).

cnf(clsarity_nat__Orderings_Oorder,axiom,
    class_Orderings_Oorder(tc_nat) ).

cnf(clsarity_nat__Power_Opower,axiom,
    class_Power_Opower(tc_nat) ).

cnf(clsarity_nat__HOL_Ozero,axiom,
    class_HOL_Ozero(tc_nat) ).

cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oring__1__no__zero__divisors,axiom,
    class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict,axiom,
    class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors,axiom,
    class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict,axiom,
    class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add,axiom,
    class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add,axiom,
    class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add,axiom,
    class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add,axiom,
    class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring,axiom,
    class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring,axiom,
    class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors,axiom,
    class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom,axiom,
    class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1,axiom,
    class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__0,axiom,
    class_Ring__and__Field_Ocomm__semiring__0(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom,
    class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult,axiom,
    class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
    class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult,axiom,
    class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add,axiom,
    class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring,axiom,
    class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring,axiom,
    class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add,axiom,
    class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one,axiom,
    class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom,axiom,
    class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__OrderedGroup_Osemigroup__add,axiom,
    class_OrderedGroup_Osemigroup__add(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__1,axiom,
    class_Ring__and__Field_Osemiring__1(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Osemiring__0,axiom,
    class_Ring__and__Field_Osemiring__0(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1,axiom,
    class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add,axiom,
    class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero,axiom,
    class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono,axiom,
    class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult,axiom,
    class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Osemiring,axiom,
    class_Ring__and__Field_Osemiring(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add,axiom,
    class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add,axiom,
    class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oring__1,axiom,
    class_Ring__and__Field_Oring__1(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oring,axiom,
    class_Ring__and__Field_Oring(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oidom,axiom,
    class_Ring__and__Field_Oidom(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__Nat_Osemiring__char__0,axiom,
    class_Nat_Osemiring__char__0(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__Orderings_Opreorder,axiom,
    class_Orderings_Opreorder(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__Orderings_Olinorder,axiom,
    class_Orderings_Olinorder(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__Orderings_Oorder,axiom,
    class_Orderings_Oorder(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__Int_Oring__char__0,axiom,
    class_Int_Oring__char__0(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__Int_Onumber__ring,axiom,
    class_Int_Onumber__ring(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__Power_Opower,axiom,
    class_Power_Opower(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__HOL_Ozero,axiom,
    class_HOL_Ozero(tc_RealDef_Oreal) ).

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__RealVector_Oreal__normed__vector,axiom,
    class_RealVector_Oreal__normed__vector(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__OrderedGroup_Osemigroup__add,axiom,
    class_OrderedGroup_Osemigroup__add(tc_Complex_Ocomplex) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1,axiom,
    class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex) ).

cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0,axiom,
    class_Ring__and__Field_Osemiring__0(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__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_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__Nat_Osemiring__char__0,axiom,
    class_Nat_Osemiring__char__0(tc_Complex_Ocomplex) ).

cnf(clsarity_Complex__Ocomplex__Int_Oring__char__0,axiom,
    class_Int_Oring__char__0(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__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
    ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__comm__semiring__strict,axiom,
    ( class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__cancel__semiring,axiom,
    ( class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).

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__Ring__and__Field_Oordered__semiring__strict,axiom,
    ( class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add,axiom,
    ( class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__comm__monoid__add,axiom,
    ( class_OrderedGroup_Opordered__comm__monoid__add(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_Opordered__ab__group__add,axiom,
    ( class_OrderedGroup_Opordered__ab__group__add(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_Opordered__semiring,axiom,
    ( class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring,axiom,
    ( class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Oordered__idom(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_Oordered__semidom,axiom,
    ( class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Oordered__idom(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_Opordered__ring,axiom,
    ( class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Oordered__idom(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__OrderedGroup_Osemigroup__add,axiom,
    ( class_OrderedGroup_Osemigroup__add(tc_Polynomial_Opoly(T_1))
    | ~ class_OrderedGroup_Ocomm__monoid__add(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring__1,axiom,
    ( class_Ring__and__Field_Osemiring__1(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring__0,axiom,
    ( class_Ring__and__Field_Osemiring__0(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono1,axiom,
    ( class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Oordered__idom(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_Omult__mono,axiom,
    ( class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Oordered__idom(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__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__Nat_Osemiring__char__0,axiom,
    ( class_Nat_Osemiring__char__0(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__Orderings_Opreorder,axiom,
    ( class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__Orderings_Olinorder,axiom,
    ( class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__Orderings_Oorder,axiom,
    ( class_Orderings_Oorder(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__Int_Oring__char__0,axiom,
    ( class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Oordered__idom(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) ) ).

cnf(cls_ATP__Linkup_Oequal__imp__fequal_0,axiom,
    hBOOL(c_fequal(V_x,V_x,T_a)) ).

cnf(cls_ATP__Linkup_Ofequal__imp__equal_0,axiom,
    ( V_X = V_Y
    | ~ hBOOL(c_fequal(V_X,V_Y,T_a)) ) ).

%------------------------------------------------------------------------------