%------------------------------------------------------------------------------
% File     : ALG368-1 : TPTP v8.2.0. Released v4.1.0.
% Domain   : General Algebra
% Problem  : Fundamental theorem of algebra 0348_33
% Version  : Especial.
% English  :

% Refs     : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe
%          : [BN10]  Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% Source   : [Nip10]
% Names    : Fundamental_Theorem_Algebra-0348_33 [Nip10]

% Status   : Unsatisfiable
% Rating   : 0.20 v8.2.0, 0.14 v8.1.0, 0.16 v7.5.0, 0.37 v7.4.0, 0.24 v7.3.0, 0.25 v7.1.0, 0.17 v7.0.0, 0.40 v6.3.0, 0.27 v6.2.0, 0.40 v6.1.0, 0.57 v6.0.0, 0.60 v5.5.0, 0.80 v5.3.0, 0.83 v5.2.0, 0.75 v5.1.0, 0.76 v5.0.0, 0.71 v4.1.0
% Syntax   : Number of clauses     : 1044 ( 222 unt; 128 nHn; 692 RR)
%            Number of literals    : 2728 ( 485 equ;1575 neg)
%            Maximal clause size   :    6 (   2 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of predicates  :   73 (  72 usr;   0 prp; 1-3 aty)
%            Number of functors    :   65 (  65 usr;  13 con; 0-3 aty)
%            Number of variables   : 2430 ( 131 sgn)
% SPC      : CNF_UNS_RFO_SEQ_NHN

% Comments :
%------------------------------------------------------------------------------
cnf(cls_real__add__mult__distrib_0,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_z1,V_z2,tc_RealDef_Oreal),V_w,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_z1,V_w,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_z2,V_w,tc_RealDef_Oreal),tc_RealDef_Oreal) ).

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

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

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

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

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

cnf(cls_right__inverse__eq_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a)
    | V_b = c_HOL_Ozero__class_Ozero(T_a)
    | V_a = V_b ) ).

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

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

cnf(cls_real__vector_Oscale__one_0,axiom,
    ( ~ class_RealVector_Oreal__vector(T_a)
    | c_RealVector_OscaleR__class_OscaleR(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_x,T_a) = V_x ) ).

cnf(cls_power__less__power__Suc_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ).

cnf(cls_cnj_Oadd_0,axiom,
    c_Complex_Ocnj(c_HOL_Oplus__class_Oplus(V_x,V_y,tc_Complex_Ocomplex)) = c_HOL_Oplus__class_Oplus(c_Complex_Ocnj(V_x),c_Complex_Ocnj(V_y),tc_Complex_Ocomplex) ).

cnf(cls_cos__le__one_0,axiom,
    c_lessequals(c_Transcendental_Ocos(V_x),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ).

cnf(cls_real__squared__diff__one__factored_0,axiom,
    c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(V_x,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ).

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

cnf(cls_mult__frac__frac_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Oinverse__class_Odivide(V_z,V_w,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),c_HOL_Otimes__class_Otimes(V_y,V_w,T_a),T_a) ) ).

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

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

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

cnf(cls_real__add__left__mono_0,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(V_z,V_x,tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(V_z,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal) ) ).

cnf(cls_scaleR__left__diff__distrib_0,axiom,
    ( ~ class_RealVector_Oreal__vector(T_a)
    | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ominus__class_Ominus(V_a,V_b,tc_RealDef_Oreal),V_x,T_a) = c_HOL_Ominus__class_Ominus(c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),c_RealVector_OscaleR__class_OscaleR(V_b,V_x,T_a),T_a) ) ).

cnf(cls_scaleR__left_Odiff_0,axiom,
    ( ~ class_RealVector_Oreal__vector(T_a)
    | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal),V_xa,T_a) = c_HOL_Ominus__class_Ominus(c_RealVector_OscaleR__class_OscaleR(V_x,V_xa,T_a),c_RealVector_OscaleR__class_OscaleR(V_y,V_xa,T_a),T_a) ) ).

cnf(cls_scaleR_Odiff__left_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ominus__class_Ominus(V_a,V_a_H,tc_RealDef_Oreal),V_b,T_a) = c_HOL_Ominus__class_Ominus(c_RealVector_OscaleR__class_OscaleR(V_a,V_b,T_a),c_RealVector_OscaleR__class_OscaleR(V_a_H,V_b,T_a),T_a) ) ).

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),c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ).

cnf(cls_LIMSEQ__inverse__realpow__zero__lemma_0,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(V_n,tc_nat),V_x,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_Power_Opower__class_Opower(c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),V_n,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).

cnf(cls_power__divide_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) ).

cnf(cls_divide__le__0__1__iff_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_divide__le__0__1__iff_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_norm__power__ineq_0,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra__1(T_a)
    | c_lessequals(c_RealVector_Onorm__class_Onorm(c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a),c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(V_x,T_a),V_n,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_sin__add_0,axiom,
    c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(V_x,V_y,tc_RealDef_Oreal)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(V_x),c_Transcendental_Ocos(V_y),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(V_x),c_Transcendental_Osin(V_y),tc_RealDef_Oreal),tc_RealDef_Oreal) ).

cnf(cls_real__sqrt__eq__1__iff_0,axiom,
    ( c_NthRoot_Osqrt(V_x) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
    | V_x = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ) ).

cnf(cls_zero__le__divide__1__iff_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) ) ).

cnf(cls_zero__le__divide__1__iff_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),T_a) ) ).

cnf(cls_sin__cos__squared__add3_0,axiom,
    c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(V_x),c_Transcendental_Ocos(V_x),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(V_x),c_Transcendental_Osin(V_x),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ).

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

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

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

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

cnf(cls_real__mult__1_0,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) = V_z ).

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

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

cnf(cls_power__one__over_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a),V_n,T_a) ) ).

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

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

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

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

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

cnf(cls_sin__le__one_0,axiom,
    c_lessequals(c_Transcendental_Osin(V_x),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ).

cnf(cls_abs__cos__le__one_0,axiom,
    c_lessequals(c_HOL_Oabs__class_Oabs(c_Transcendental_Ocos(V_x),tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ).

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

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

cnf(cls_power__Suc__less_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a),c_Power_Opower__class_Opower(V_a,V_n,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_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_gt__half__sum_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(T_a),c_HOL_Oone__class_Oone(T_a),T_a),T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).

cnf(cls_less__half__sum_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(T_a),c_HOL_Oone__class_Oone(T_a),T_a),T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).

cnf(cls_add__frac__num_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),V_z,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),T_a),V_y,T_a)
    | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_add__num__frac_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oplus__class_Oplus(V_z,c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),T_a),V_y,T_a)
    | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ).

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

cnf(cls_divide__1_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ).

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

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

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

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

cnf(cls_scaleR_Oprod__diff__prod_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | c_HOL_Ominus__class_Ominus(c_RealVector_OscaleR__class_OscaleR(V_x,V_y,T_a),c_RealVector_OscaleR__class_OscaleR(V_a,V_b,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_RealVector_OscaleR__class_OscaleR(c_HOL_Ominus__class_Ominus(V_x,V_a,tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(V_y,V_b,T_a),T_a),c_RealVector_OscaleR__class_OscaleR(c_HOL_Ominus__class_Ominus(V_x,V_a,tc_RealDef_Oreal),V_b,T_a),T_a),c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ominus__class_Ominus(V_y,V_b,T_a),T_a),T_a) ) ).

cnf(cls_norm__one_0,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra__1(T_a)
    | c_RealVector_Onorm__class_Onorm(c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ) ).

cnf(cls_abs__sin__le__one_0,axiom,
    c_lessequals(c_HOL_Oabs__class_Oabs(c_Transcendental_Osin(V_x),tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ).

cnf(cls_cos__zero_0,axiom,
    c_Transcendental_Ocos(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ).

cnf(cls_mult_OscaleR__left_0,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(V_r,V_a,T_a),V_b,T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ).

cnf(cls_mult__left_OscaleR_0,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(V_r,V_x,T_a),V_y,T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) ) ).

cnf(cls_mult_OscaleR__right_0,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_HOL_Otimes__class_Otimes(V_a,c_RealVector_OscaleR__class_OscaleR(V_r,V_b,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ).

cnf(cls_mult__right_OscaleR_0,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_HOL_Otimes__class_Otimes(V_xa,c_RealVector_OscaleR__class_OscaleR(V_r,V_x,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),T_a) ) ).

cnf(cls_mult__scaleR__left_0,axiom,
    ( ~ class_RealVector_Oreal__algebra(T_a)
    | c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),V_y,T_a) = c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) ) ).

cnf(cls_mult__scaleR__right_0,axiom,
    ( ~ class_RealVector_Oreal__algebra(T_a)
    | c_HOL_Otimes__class_Otimes(V_x,c_RealVector_OscaleR__class_OscaleR(V_a,V_y,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) ) ).

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

cnf(cls_norm__diff__ineq_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | c_lessequals(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(V_a,T_a),c_RealVector_Onorm__class_Onorm(V_b,T_a),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a),tc_RealDef_Oreal) ) ).

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

cnf(cls_divide_OscaleR_0,axiom,
    ( ~ class_RealVector_Oreal__normed__field(T_a)
    | c_HOL_Oinverse__class_Odivide(c_RealVector_OscaleR__class_OscaleR(V_r,V_x,T_a),V_y,T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) ) ).

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

cnf(cls_cos__one__sin__zero_0,axiom,
    ( c_Transcendental_Ocos(V_x) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
    | c_Transcendental_Osin(V_x) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).

cnf(cls_sin__diff2_0,axiom,
    c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(V_y),c_Transcendental_Osin(V_x),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(V_y),c_Transcendental_Ocos(V_x),tc_RealDef_Oreal),tc_RealDef_Oreal) ).

cnf(cls_DERIV__mult__lemma_0,axiom,
    ( ~ class_RealVector_Oreal__field(T_a)
    | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_c,V_d,T_a),T_a),V_h,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(V_b,V_d,T_a),V_h,T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(V_a,V_c,T_a),V_h,T_a),V_d,T_a),T_a) ) ).

cnf(cls_sin__zero__abs__cos__one_0,axiom,
    ( c_Transcendental_Osin(V_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_HOL_Oabs__class_Oabs(c_Transcendental_Ocos(V_x),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ) ).

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

cnf(cls_complex__cnj__cnj_0,axiom,
    c_Complex_Ocnj(c_Complex_Ocnj(V_z)) = V_z ).

cnf(cls_real__sqrt__power_0,axiom,
    c_NthRoot_Osqrt(c_Power_Opower__class_Opower(V_x,V_k,tc_RealDef_Oreal)) = c_Power_Opower__class_Opower(c_NthRoot_Osqrt(V_x),V_k,tc_RealDef_Oreal) ).

cnf(cls_scaleR_OscaleR__right_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | c_RealVector_OscaleR__class_OscaleR(V_a,c_RealVector_OscaleR__class_OscaleR(V_r,V_b,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,c_RealVector_OscaleR__class_OscaleR(V_a,V_b,T_a),T_a) ) ).

cnf(cls_scaleR__left__commute_0,axiom,
    ( ~ class_RealVector_Oreal__vector(T_a)
    | c_RealVector_OscaleR__class_OscaleR(V_a,c_RealVector_OscaleR__class_OscaleR(V_b,V_x,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_b,c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),T_a) ) ).

cnf(cls_scaleR__right_OscaleR_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | c_RealVector_OscaleR__class_OscaleR(V_ra,c_RealVector_OscaleR__class_OscaleR(V_r,V_x,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,c_RealVector_OscaleR__class_OscaleR(V_ra,V_x,T_a),T_a) ) ).

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

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

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

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

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

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

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

cnf(cls_add__frac__eq_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),c_HOL_Otimes__class_Otimes(V_w,V_y,T_a),T_a),c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a)
    | V_z = c_HOL_Ozero__class_Ozero(T_a)
    | V_y = 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)
    | c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),V_m,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oone__class_Oone(T_a),T_a),V_m,T_a) ) ).

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

cnf(cls_abs__add__one__not__less__self_0,axiom,
    ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(V_x,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ).

cnf(cls_norm__triangle__ineq_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),T_a),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(V_x,T_a),c_RealVector_Onorm__class_Onorm(V_y,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_tan__periodic__pi_0,axiom,
    c_Transcendental_Otan(c_HOL_Oplus__class_Oplus(V_x,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_Transcendental_Otan(V_x) ).

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

cnf(cls_complex__cnj__cancel__iff_0,axiom,
    ( c_Complex_Ocnj(V_x) != c_Complex_Ocnj(V_y)
    | V_x = V_y ) ).

cnf(cls_real__sqrt__one_0,axiom,
    c_NthRoot_Osqrt(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ).

cnf(cls_nonzero__power__divide_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a) = c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a)
    | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ).

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

cnf(cls_cos__diff2_0,axiom,
    c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(V_y),c_Transcendental_Ocos(V_x),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(V_y),c_Transcendental_Osin(V_x),tc_RealDef_Oreal),tc_RealDef_Oreal) ).

cnf(cls_cos__diff_0,axiom,
    c_Transcendental_Ocos(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(V_x),c_Transcendental_Ocos(V_y),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(V_x),c_Transcendental_Osin(V_y),tc_RealDef_Oreal),tc_RealDef_Oreal) ).

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

cnf(cls_norm__power_0,axiom,
    ( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
    | c_RealVector_Onorm__class_Onorm(c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(V_x,T_a),V_n,tc_RealDef_Oreal) ) ).

cnf(cls_complex__mod__triangle__sub_0,axiom,
    c_lessequals(c_RealVector_Onorm__class_Onorm(V_w,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(V_w,V_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ).

cnf(cls_sin__diff_0,axiom,
    c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(V_x),c_Transcendental_Ocos(V_y),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(V_x),c_Transcendental_Osin(V_y),tc_RealDef_Oreal),tc_RealDef_Oreal) ).

cnf(cls_norm__diff__triangle__ineq_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a),T_a),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_a,V_c,T_a),T_a),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_b,V_d,T_a),T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_abs__add__one__gt__zero_0,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(V_x,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ).

cnf(cls_tan__periodic__nat_0,axiom,
    c_Transcendental_Otan(c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(V_n,tc_nat),c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal)) = c_Transcendental_Otan(V_x) ).

cnf(cls_ln__add__one__self__le__self_0,axiom,
    ( c_lessequals(c_Transcendental_Oln(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)),V_x,tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).

cnf(cls_exp__ge__add__one__self__aux_0,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal),c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).

cnf(cls_divide__less__0__iff_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(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),V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_divide__less__0__iff_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(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_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_divide__less__0__iff_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oord__class_Oless(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_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_divide__less__0__iff_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_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(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_add__neg__neg_0,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_b,T_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(V_a,c_HOL_Ozero__class_Ozero(T_a),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(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_even__less__0__iff_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_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(c_HOL_Oplus__class_Oplus(V_a,V_a,T_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(c_HOL_Oplus__class_Oplus(V_a,V_a,T_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(c_HOL_Oplus__class_Oplus(V_a,V_a,T_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_pos__add__strict_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),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_zero__less__divide__iff_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(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),V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ).

cnf(cls_zero__less__divide__iff_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(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)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ).

cnf(cls_zero__less__divide__iff_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(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),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ).

cnf(cls_zero__less__divide__iff_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(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_b,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),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),c_HOL_Oplus__class_Oplus(V_a,V_a,T_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),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_divide__less__eq_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(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,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(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ).

cnf(cls_divide__less__eq_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,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,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) ) ).

cnf(cls_less__divide__eq_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),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(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ).

cnf(cls_less__divide__eq_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),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) ) ).

cnf(cls_divide__neg__neg_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_divide__pos__pos_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ).

cnf(cls_zero__less__divide__iff_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,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(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_zero__less__divide__iff_5,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,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_divide__strict__right__mono_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,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(V_a,V_b,T_a) ) ).

cnf(cls_divide__strict__right__mono__neg_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),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_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),c_Power_Opower__class_Opower(V_a,V_n,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_Omult__assoc_0,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ).

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

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

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

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

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

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

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

cnf(cls_cos__add_0,axiom,
    c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(V_x,V_y,tc_RealDef_Oreal)) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Transcendental_Ocos(V_x),c_Transcendental_Ocos(V_y),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Transcendental_Osin(V_x),c_Transcendental_Osin(V_y),tc_RealDef_Oreal),tc_RealDef_Oreal) ).

cnf(cls_right__inverse__eq_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | V_x = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oinverse__class_Odivide(V_x,V_x,T_a) = c_HOL_Oone__class_Oone(T_a) ) ).

cnf(cls_divide__self_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_divide__self__if_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_real__vector_Oscale__scale_0,axiom,
    ( ~ class_RealVector_Oreal__vector(T_a)
    | c_RealVector_OscaleR__class_OscaleR(V_a,c_RealVector_OscaleR__class_OscaleR(V_b,V_x,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Otimes__class_Otimes(V_a,V_b,tc_RealDef_Oreal),V_x,T_a) ) ).

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

cnf(cls_sgn__one_0,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra__1(T_a)
    | c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) ).

cnf(cls_pos__poly__pCons_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_Polynomial_Opos__poly(c_Polynomial_OpCons(V_a,V_p,T_a),T_a)
    | ~ c_Polynomial_Opos__poly(V_p,T_a) ) ).

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

cnf(cls_abs__divide_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a) ) ).

cnf(cls_real__vector_Oscale__left__distrib_0,axiom,
    ( ~ class_RealVector_Oreal__vector(T_a)
    | c_RealVector_OscaleR__class_OscaleR(c_HOL_Oplus__class_Oplus(V_a,V_b,tc_RealDef_Oreal),V_x,T_a) = c_HOL_Oplus__class_Oplus(c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),c_RealVector_OscaleR__class_OscaleR(V_b,V_x,T_a),T_a) ) ).

cnf(cls_scaleR__right_Oadd_0,axiom,
    ( ~ class_RealVector_Oreal__vector(T_a)
    | c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),c_RealVector_OscaleR__class_OscaleR(V_a,V_y,T_a),T_a) ) ).

cnf(cls_scaleR_Oadd__right_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Oplus__class_Oplus(V_b,V_b_H,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_RealVector_OscaleR__class_OscaleR(V_a,V_b,T_a),c_RealVector_OscaleR__class_OscaleR(V_a,V_b_H,T_a),T_a) ) ).

cnf(cls_scaleR__left_Oadd_0,axiom,
    ( ~ class_RealVector_Oreal__vector(T_a)
    | c_RealVector_OscaleR__class_OscaleR(c_HOL_Oplus__class_Oplus(V_x,V_y,tc_RealDef_Oreal),V_xa,T_a) = c_HOL_Oplus__class_Oplus(c_RealVector_OscaleR__class_OscaleR(V_x,V_xa,T_a),c_RealVector_OscaleR__class_OscaleR(V_y,V_xa,T_a),T_a) ) ).

cnf(cls_scaleR_Oadd__left_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | c_RealVector_OscaleR__class_OscaleR(c_HOL_Oplus__class_Oplus(V_a,V_a_H,tc_RealDef_Oreal),V_b,T_a) = c_HOL_Oplus__class_Oplus(c_RealVector_OscaleR__class_OscaleR(V_a,V_b,T_a),c_RealVector_OscaleR__class_OscaleR(V_a_H,V_b,T_a),T_a) ) ).

cnf(cls_complex__mod__triangle__ineq2_0,axiom,
    c_lessequals(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(V_b,V_a,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(V_b,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_a,tc_Complex_Ocomplex),tc_RealDef_Oreal) ).

cnf(cls_mult__frac__num_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),V_z,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),V_y,T_a) ) ).

cnf(cls_real__mult__is__one_1,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ).

cnf(cls_add__divide__distrib_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ).

cnf(cls_divide_Oadd_0,axiom,
    ( ~ class_RealVector_Oreal__normed__field(T_a)
    | c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),V_ya,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_x,V_ya,T_a),c_HOL_Oinverse__class_Odivide(V_y,V_ya,T_a),T_a) ) ).

cnf(cls_eq__divide__eq_2,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_scaleR__cancel__right_0,axiom,
    ( ~ class_RealVector_Oreal__vector(T_a)
    | c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a) != c_RealVector_OscaleR__class_OscaleR(V_b,V_x,T_a)
    | V_x = c_HOL_Ozero__class_Ozero(T_a)
    | V_a = V_b ) ).

cnf(cls_scaleR__cancel__right_1,axiom,
    ( ~ class_RealVector_Oreal__vector(T_a)
    | c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

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

cnf(cls_divide__self__if_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

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

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

cnf(cls_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_double__eq__0__iff_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_HOL_Oplus__class_Oplus(V_a,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

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

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

cnf(cls_scaleR_Ozero__right_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_scaleR__eq__0__iff_2,axiom,
    ( ~ class_RealVector_Oreal__vector(T_a)
    | c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_divide__zero__left_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_divide__eq__eq_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_divide__zero_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_divide_Ozero_0,axiom,
    ( ~ class_RealVector_Oreal__normed__field(T_a)
    | c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

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

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

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

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

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

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

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

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

cnf(cls_zero__less__divide__1__iff_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) ) ).

cnf(cls_zero__less__divide__1__iff_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(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),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),T_a) ) ).

cnf(cls_divide__less__0__1__iff_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_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) ) ).

cnf(cls_divide__less__0__1__iff_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(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_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

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),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(T_a),c_HOL_Oone__class_Oone(T_a),T_a),T_a) ) ).

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

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

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(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,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(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).

cnf(cls_scaleR__right_Odiff_0,axiom,
    ( ~ class_RealVector_Oreal__vector(T_a)
    | c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ominus__class_Ominus(V_x,V_y,T_a),T_a) = c_HOL_Ominus__class_Ominus(c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),c_RealVector_OscaleR__class_OscaleR(V_a,V_y,T_a),T_a) ) ).

cnf(cls_scaleR_Odiff__right_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ominus__class_Ominus(V_b,V_b_H,T_a),T_a) = c_HOL_Ominus__class_Ominus(c_RealVector_OscaleR__class_OscaleR(V_a,V_b,T_a),c_RealVector_OscaleR__class_OscaleR(V_a,V_b_H,T_a),T_a) ) ).

cnf(cls_diff__divide__distrib_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ).

cnf(cls_divide_Odiff_0,axiom,
    ( ~ class_RealVector_Oreal__normed__field(T_a)
    | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(V_x,V_y,T_a),V_ya,T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(V_x,V_ya,T_a),c_HOL_Oinverse__class_Odivide(V_y,V_ya,T_a),T_a) ) ).

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

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

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

cnf(cls_scaleR__cancel__left_0,axiom,
    ( ~ class_RealVector_Oreal__vector(T_a)
    | c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a) != c_RealVector_OscaleR__class_OscaleR(V_a,V_y,T_a)
    | V_a = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | V_x = V_y ) ).

cnf(cls_scaleR__cancel__left_1,axiom,
    ( ~ class_RealVector_Oreal__vector(T_a)
    | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,T_a) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,T_a) ) ).

cnf(cls_tan__zero_0,axiom,
    c_Transcendental_Otan(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ).

cnf(cls_real__zero__not__eq__one_0,axiom,
    c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ).

cnf(cls_sin__zero_0,axiom,
    c_Transcendental_Osin(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ).

cnf(cls_norm__add__less_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),T_a),c_HOL_Oplus__class_Oplus(V_r,V_s,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(V_y,T_a),V_s,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(V_x,T_a),V_r,tc_RealDef_Oreal) ) ).

cnf(cls_not__pos__poly__0_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | ~ c_Polynomial_Opos__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) ) ).

cnf(cls_complex__mod__cnj_0,axiom,
    c_RealVector_Onorm__class_Onorm(c_Complex_Ocnj(V_z),tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex) ).

cnf(cls_cnj_Odiff_0,axiom,
    c_Complex_Ocnj(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_Complex_Ocomplex)) = c_HOL_Ominus__class_Ominus(c_Complex_Ocnj(V_x),c_Complex_Ocnj(V_y),tc_Complex_Ocomplex) ).

cnf(cls_frac__le_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_x,V_z,T_a),c_HOL_Oinverse__class_Odivide(V_y,V_w,T_a),T_a)
    | ~ c_lessequals(V_w,V_z,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_w,T_a)
    | ~ c_lessequals(V_x,V_y,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,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,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),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_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),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),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__nonneg__pos_0,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),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_divide__nonpos__neg_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_divide__nonneg__pos_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(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_frac__less_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_x,V_z,T_a),c_HOL_Oinverse__class_Odivide(V_y,V_w,T_a),T_a)
    | ~ c_lessequals(V_w,V_z,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_w,T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ).

cnf(cls_divide__nonpos__pos_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
    | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_divide__nonneg__neg_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ).

cnf(cls_add__nonpos__neg_0,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_b,T_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_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(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),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_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(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) ).

cnf(cls_frac__less2_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_x,V_z,T_a),c_HOL_Oinverse__class_Odivide(V_y,V_w,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_w,V_z,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_w,T_a)
    | ~ c_lessequals(V_x,V_y,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),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,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),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_le__divide__eq_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),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) ) ).

cnf(cls_le__divide__eq_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),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_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ).

cnf(cls_divide__le__eq_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,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) ) ).

cnf(cls_divide__le__eq_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,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_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ).

cnf(cls_divide__strict__left__mono__neg_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_c,V_a,T_a),c_HOL_Oinverse__class_Odivide(V_c,V_b,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),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) ) ).

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_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),c_HOL_Oplus__class_Oplus(V_a,V_b,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(c_HOL_Ozero__class_Ozero(T_a),V_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_divide__neg__pos_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_divide__pos__neg_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ).

cnf(cls_divide__less__0__iff_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_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_divide__less__0__iff_5,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),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_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(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_power__mono_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semidom(T_a)
    | c_lessequals(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),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_zero__le__divide__iff_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(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),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ).

cnf(cls_zero__le__divide__iff_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(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),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ).

cnf(cls_zero__le__divide__iff_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(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),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ).

cnf(cls_zero__le__divide__iff_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(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),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),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)
    | c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_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,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),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,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),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_divide__le__0__iff_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_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_divide__le__0__iff_5,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_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(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_add__nonneg__eq__0__iff_0,axiom,
    ( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
    | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != 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)
    | c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != 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_divide__right__mono_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),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_divide__right__mono__neg_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),T_a)
    | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(V_a,V_b,T_a) ) ).

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

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),c_HOL_Oplus__class_Oplus(V_a,V_a,T_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),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a)
    | ~ c_lessequals(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),c_Power_Opower__class_Opower(V_a,V_n,T_a),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),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_divide__le__0__iff_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(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_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_divide__le__0__iff_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(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(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_divide__le__0__iff_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(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(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_divide__le__0__iff_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(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(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),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_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_zero__le__divide__iff_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,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),V_a,T_a) ) ).

cnf(cls_zero__le__divide__iff_5,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,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_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(c_HOL_Oplus__class_Oplus(V_a,V_a,T_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(c_HOL_Oplus__class_Oplus(V_a,V_a,T_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(c_HOL_Oplus__class_Oplus(V_a,V_b,T_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(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_mult__divide__mult__cancel__left_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a)
    | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_mult__divide__mult__cancel__right_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a)
    | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_divide__eq__eq_3,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) = V_a
    | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_eq__divide__eq_3,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a)
    | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_divide__eq__imp_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | V_c = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) = V_a ) ).

cnf(cls_eq__divide__imp_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | V_c = c_HOL_Ozero__class_Ozero(T_a)
    | V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) ).

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

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

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

cnf(cls_eq__divide__eq_4,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a),V_c,T_a) ) ).

cnf(cls_divide__eq__eq_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a)
    | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_eq__divide__eq_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b
    | V_c = c_HOL_Ozero__class_Ozero(T_a) ) ).

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

cnf(cls_frac__eq__eq_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) != c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a)
    | V_z = c_HOL_Ozero__class_Ozero(T_a)
    | V_y = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Otimes__class_Otimes(V_x,V_z,T_a) = c_HOL_Otimes__class_Otimes(V_w,V_y,T_a) ) ).

cnf(cls_frac__eq__eq_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_HOL_Otimes__class_Otimes(V_x,V_z,T_a) != c_HOL_Otimes__class_Otimes(V_w,V_y,T_a)
    | V_z = c_HOL_Ozero__class_Ozero(T_a)
    | V_y = c_HOL_Ozero__class_Ozero(T_a)
    | c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a) ) ).

cnf(cls_divide__eq__eq_4,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a),V_c,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

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

cnf(cls_add__less__le__mono_0,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a)
    | ~ c_lessequals(V_c,V_d,T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).

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),c_HOL_Otimes__class_Otimes(V_m,V_n,T_a),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_scaleR__eq__0__iff_1,axiom,
    ( ~ class_RealVector_Oreal__vector(T_a)
    | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_scaleR_Ozero__left_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_scaleR__eq__0__iff_0,axiom,
    ( ~ class_RealVector_Oreal__vector(T_a)
    | c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | V_x = c_HOL_Ozero__class_Ozero(T_a)
    | V_a = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).

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

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

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

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

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

cnf(cls_nonzero__abs__divide_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a)
    | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_abs__triangle__ineq_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
    | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a) ) ).

cnf(cls_estimate__by__abs_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a)
    | c_lessequals(V_a,c_HOL_Oplus__class_Oplus(V_c,c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) ) ).

cnf(cls_mult_Ononneg__bounded_0,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1(V_vskULp,T_a),tc_RealDef_Oreal) ) ).

cnf(cls_mult__right_Ononneg__bounded_0,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__right__Xnonneg__bounded__1__1(V_x,T_a),tc_RealDef_Oreal) ) ).

cnf(cls_mult__left_Ononneg__bounded_0,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__left__Xnonneg__bounded__1__1(V_y,T_a),tc_RealDef_Oreal) ) ).

cnf(cls_real__le__eq__diff_1,axiom,
    ( c_lessequals(V_x,V_y,tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_real__le__eq__diff_0,axiom,
    ( c_lessequals(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal) ) ).

cnf(cls_real__sum__squares__cancel_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).

cnf(cls_real__sum__squares__cancel2_0,axiom,
    ( c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | V_y = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).

cnf(cls_real__two__squares__add__zero__iff_2,axiom,
    c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ).

cnf(cls_sin__pi_0,axiom,
    c_Transcendental_Osin(c_Transcendental_Opi) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ).

cnf(cls_tan__pi_0,axiom,
    c_Transcendental_Otan(c_Transcendental_Opi) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ).

cnf(cls_exp__zero_0,axiom,
    ( ~ class_SEQ_Obanach(T_a)
    | ~ class_RealVector_Oreal__normed__field(T_a)
    | c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) ).

cnf(cls_real__sqrt__le__1__iff_1,axiom,
    ( c_lessequals(c_NthRoot_Osqrt(V_x),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_lessequals(V_x,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_real__sqrt__le__1__iff_0,axiom,
    ( c_lessequals(V_x,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_lessequals(c_NthRoot_Osqrt(V_x),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_real__sqrt__ge__1__iff_1,axiom,
    ( c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) ) ).

cnf(cls_real__sqrt__ge__1__iff_0,axiom,
    ( c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) ) ).

cnf(cls_real__sqrt__ge__one_0,axiom,
    ( c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x),tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).

cnf(cls_real__sqrt__gt__1__iff_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) ) ).

cnf(cls_real__sqrt__gt__1__iff_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) ) ).

cnf(cls_real__sqrt__lt__1__iff_1,axiom,
    ( c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(V_x),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_real__sqrt__lt__1__iff_0,axiom,
    ( c_HOL_Oord__class_Oless(V_x,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(V_x),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_exp__add_0,axiom,
    ( ~ class_SEQ_Obanach(T_a)
    | ~ class_RealVector_Oreal__normed__field(T_a)
    | c_Transcendental_Oexp(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(V_x,T_a),c_Transcendental_Oexp(V_y,T_a),T_a) ) ).

cnf(cls_mult__exp__exp_0,axiom,
    ( ~ class_SEQ_Obanach(T_a)
    | ~ class_RealVector_Oreal__normed__field(T_a)
    | c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(V_x,T_a),c_Transcendental_Oexp(V_y,T_a),T_a) = c_Transcendental_Oexp(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),T_a) ) ).

cnf(cls_exp__diff_0,axiom,
    ( ~ class_SEQ_Obanach(T_a)
    | ~ class_RealVector_Oreal__normed__field(T_a)
    | c_Transcendental_Oexp(c_HOL_Ominus__class_Ominus(V_x,V_y,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Oexp(V_x,T_a),c_Transcendental_Oexp(V_y,T_a),T_a) ) ).

cnf(cls_pos__poly__pCons_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
    | c_Polynomial_Opos__poly(V_p,T_a)
    | ~ c_Polynomial_Opos__poly(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) ) ).

cnf(cls_ln__one_0,axiom,
    c_Transcendental_Oln(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ).

cnf(cls_exp__eq__one__iff_0,axiom,
    ( c_Transcendental_Oexp(V_x,tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
    | V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).

cnf(cls_exp__eq__one__iff_1,axiom,
    c_Transcendental_Oexp(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ).

cnf(cls_dist__triangle_0,axiom,
    ( ~ class_RealVector_Ometric__space(T_a)
    | c_lessequals(c_RealVector_Odist__class_Odist(V_x,V_z,T_a),c_HOL_Oplus__class_Oplus(c_RealVector_Odist__class_Odist(V_x,V_y,T_a),c_RealVector_Odist__class_Odist(V_y,V_z,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_dist__triangle2_0,axiom,
    ( ~ class_RealVector_Ometric__space(T_a)
    | c_lessequals(c_RealVector_Odist__class_Odist(V_x,V_y,T_a),c_HOL_Oplus__class_Oplus(c_RealVector_Odist__class_Odist(V_x,V_z,T_a),c_RealVector_Odist__class_Odist(V_y,V_z,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_dist__triangle3_0,axiom,
    ( ~ class_RealVector_Ometric__space(T_a)
    | c_lessequals(c_RealVector_Odist__class_Odist(V_x,V_y,T_a),c_HOL_Oplus__class_Oplus(c_RealVector_Odist__class_Odist(V_a,V_x,T_a),c_RealVector_Odist__class_Odist(V_a,V_y,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_lemma__interval__lt_2,axiom,
    ( c_HOL_Oord__class_Oless(V_y,V_b,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Deriv_Osko__Deriv__Xlemma__interval__lt__1__1(V_a,V_b,V_x),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(V_x,V_b,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(V_a,V_x,tc_RealDef_Oreal) ) ).

cnf(cls_lemma__interval__lt_1,axiom,
    ( c_HOL_Oord__class_Oless(V_a,V_y,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Deriv_Osko__Deriv__Xlemma__interval__lt__1__1(V_a,V_b,V_x),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(V_x,V_b,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(V_a,V_x,tc_RealDef_Oreal) ) ).

cnf(cls_divide__strict__left__mono_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_c,V_a,T_a),c_HOL_Oinverse__class_Odivide(V_c,V_b,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,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(V_b,V_a,T_a) ) ).

cnf(cls_less__divide__eq_7,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),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_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ).

cnf(cls_less__divide__eq_5,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).

cnf(cls_less__divide__eq_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),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,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).

cnf(cls_less__divide__eq_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),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(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ).

cnf(cls_divide__less__eq_7,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,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,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ).

cnf(cls_divide__less__eq_5,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,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_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).

cnf(cls_divide__less__eq_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,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_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).

cnf(cls_divide__less__eq_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),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(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ).

cnf(cls_less__divide__eq_9,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ).

cnf(cls_less__divide__eq_8,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),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,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ).

cnf(cls_divide__less__eq_9,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,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_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ).

cnf(cls_divide__less__eq_8,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,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_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),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),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),T_a),T_a) ) ).

cnf(cls_mult__imp__less__div__pos_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | c_HOL_Oord__class_Oless(V_z,c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),V_x,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ).

cnf(cls_mult__imp__div__pos__less_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),V_z,T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ).

cnf(cls_less__divide__eq_6,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,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(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ).

cnf(cls_less__divide__eq_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),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,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ).

cnf(cls_divide__less__eq_6,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),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(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ).

cnf(cls_divide__less__eq_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,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(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_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(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

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),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),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),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),T_a)
    | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_mult__right__le__one__le_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_lessequals(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),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__left__le__one__le_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_lessequals(c_HOL_Otimes__class_Otimes(V_y,V_x,T_a),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_sum__squares__le__zero__iff_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),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),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),T_a) ) ).

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(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),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(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_le__divide__eq_9,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ).

cnf(cls_divide__le__eq_9,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
    | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ).

cnf(cls_diff__frac__eq_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),c_HOL_Otimes__class_Otimes(V_w,V_y,T_a),T_a),c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a)
    | V_z = c_HOL_Ozero__class_Ozero(T_a)
    | V_y = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_less__add__iff2_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a) ) ).

cnf(cls_less__add__iff2_0,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(T_a)
    | c_HOL_Oord__class_Oless(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a) ) ).

cnf(cls_less__add__iff1_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a) ) ).

cnf(cls_less__add__iff1_0,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a) ) ).

cnf(cls_le__add__iff2_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(T_a)
    | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)
    | ~ c_lessequals(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a) ) ).

cnf(cls_le__add__iff2_0,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(T_a)
    | c_lessequals(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a) ) ).

cnf(cls_le__add__iff1_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(T_a)
    | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a) ) ).

cnf(cls_le__add__iff1_0,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(T_a)
    | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a) ) ).

cnf(cls_abs__div__pos_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(V_x,T_a),V_y,T_a) = c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ).

cnf(cls_zero__le__power__abs_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(V_a,T_a),V_n,T_a),T_a) ) ).

cnf(cls_sgn__1__pos_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_HOL_Osgn__class_Osgn(V_a,T_a) != c_HOL_Oone__class_Oone(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_sgn__pos_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_HOL_Osgn__class_Osgn(V_a,T_a) = c_HOL_Oone__class_Oone(T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_sgn__if_1,axiom,
    ( ~ class_Ring__and__Field_Osgn__if(T_a)
    | c_HOL_Osgn__class_Osgn(V_x,T_a) = c_HOL_Oone__class_Oone(T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)
    | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_abs__diff__less__iff_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_HOL_Oord__class_Oless(V_x,c_HOL_Oplus__class_Oplus(V_a,V_r,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_x,V_a,T_a),T_a),V_r,T_a) ) ).

cnf(cls_abs__diff__less__iff_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_x,V_a,T_a),T_a),V_r,T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Oplus__class_Oplus(V_a,V_r,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_r,T_a),V_x,T_a) ) ).

cnf(cls_abs__triangle__ineq4_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
    | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a) ) ).

cnf(cls_abs__diff__triangle__ineq_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
    | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a),T_a),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_a,V_c,T_a),T_a),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_b,V_d,T_a),T_a),T_a),T_a) ) ).

cnf(cls_pos__poly__pCons_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | c_Polynomial_Opos__poly(V_p,T_a)
    | ~ c_Polynomial_Opos__poly(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) ) ).

cnf(cls_real__mult__self__sum__ge__zero_0,axiom,
    c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ).

cnf(cls_real__sum__square__gt__zero2_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
    | V_y = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).

cnf(cls_real__sum__square__gt__zero_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
    | V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).

cnf(cls_norm__triangle__ineq2_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | c_lessequals(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(V_a,T_a),c_RealVector_Onorm__class_Onorm(V_b,T_a),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a),tc_RealDef_Oreal) ) ).

cnf(cls_norm__triangle__ineq4_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(V_a,T_a),c_RealVector_Onorm__class_Onorm(V_b,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_norm__sgn_1,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | c_RealVector_Onorm__class_Onorm(c_HOL_Osgn__class_Osgn(V_x,T_a),T_a) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
    | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_cos__monotone__0__pi_H_0,axiom,
    ( c_lessequals(c_Transcendental_Ocos(V_x),c_Transcendental_Ocos(V_y),tc_RealDef_Oreal)
    | ~ c_lessequals(V_x,c_Transcendental_Opi,tc_RealDef_Oreal)
    | ~ c_lessequals(V_y,V_x,tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) ) ).

cnf(cls_sin__ge__zero_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Osin(V_x),tc_RealDef_Oreal)
    | ~ c_lessequals(V_x,c_Transcendental_Opi,tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).

cnf(cls_sin__gt__zero__pi_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Osin(V_x),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(V_x,c_Transcendental_Opi,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).

cnf(cls_le__real__sqrt__sumsq_0,axiom,
    c_lessequals(V_x,c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal) ).

cnf(cls_ln__ge__zero_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x),tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).

cnf(cls_exp__le__one__iff_1,axiom,
    ( c_lessequals(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_exp__le__one__iff_0,axiom,
    ( c_lessequals(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_lessequals(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_one__le__exp__iff_1,axiom,
    ( c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).

cnf(cls_one__le__exp__iff_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_ln__eq__zero__iff_1,axiom,
    ( ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | c_Transcendental_Oln(c_HOL_Oone__class_Oone(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).

cnf(cls_ln__eq__zero__iff_0,axiom,
    ( c_Transcendental_Oln(V_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
    | V_x = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ) ).

cnf(cls_ln__less__zero__iff_0,axiom,
    ( c_HOL_Oord__class_Oless(V_x,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_Transcendental_Oln(V_x),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).

cnf(cls_ln__less__zero_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Transcendental_Oln(V_x),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).

cnf(cls_ln__gt__zero_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).

cnf(cls_ln__gt__zero__imp__gt__one_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x),tc_RealDef_Oreal) ) ).

cnf(cls_ln__gt__zero__iff_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).

cnf(cls_ln__gt__zero__iff_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).

cnf(cls_exp__less__one__iff_1,axiom,
    ( c_HOL_Oord__class_Oless(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_exp__less__one__iff_0,axiom,
    ( c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_one__less__exp__iff_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_exp__gt__one_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).

cnf(cls_norm__scaleR_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | c_RealVector_Onorm__class_Onorm(c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x,T_a),tc_RealDef_Oreal) ) ).

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

cnf(cls_exp__real__of__nat__mult_0,axiom,
    c_Transcendental_Oexp(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(V_n,tc_nat),V_x,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Power_Opower__class_Opower(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),V_n,tc_RealDef_Oreal) ).

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

cnf(cls_le__divide__eq_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).

cnf(cls_le__divide__eq_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),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_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ).

cnf(cls_divide__le__eq_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).

cnf(cls_divide__le__eq_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),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(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ).

cnf(cls_le__divide__eq_7,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ).

cnf(cls_le__divide__eq_5,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).

cnf(cls_divide__le__eq_7,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ).

cnf(cls_divide__le__eq_5,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).

cnf(cls_le__divide__eq_8,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ).

cnf(cls_divide__le__eq_8,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
    | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ).

cnf(cls_mult__imp__le__div__pos_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | c_lessequals(V_z,c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),V_x,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ).

cnf(cls_mult__imp__div__pos__le_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),V_z,T_a)
    | ~ c_lessequals(V_x,c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ).

cnf(cls_le__divide__eq_6,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ).

cnf(cls_le__divide__eq_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ).

cnf(cls_divide__le__eq_6,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ).

cnf(cls_divide__le__eq_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ).

cnf(cls_divide__left__mono__neg_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_c,V_a,T_a),c_HOL_Oinverse__class_Odivide(V_c,V_b,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
    | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(V_a,V_b,T_a) ) ).

cnf(cls_divide__left__mono_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | c_lessequals(c_HOL_Oinverse__class_Odivide(V_c,V_a,T_a),c_HOL_Oinverse__class_Odivide(V_c,V_b,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
    | ~ c_lessequals(V_b,V_a,T_a) ) ).

cnf(cls_lemma__tan__total_2,axiom,
    ( c_HOL_Oord__class_Oless(V_y,c_Transcendental_Otan(c_Transcendental_Osko__Transcendental__Xlemma__tan__total__1__1(V_y)),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) ) ).

cnf(cls_mult__right_Ononneg__bounded_1,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(V_x,V_K,T_a),T_a),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_K,T_a),c_RealVector_Osko__RealVector__Xmult__right__Xnonneg__bounded__1__1(V_x,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_mult_Ononneg__bounded_1,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_a,T_a),c_RealVector_Onorm__class_Onorm(V_b,T_a),tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1(V_vskULp,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_mult__right_Obounded_0,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(V_x,V_K,T_a),T_a),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_K,T_a),c_RealVector_Osko__RealVector__Xmult__right__Xbounded__1__1(V_x,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_mult__left_Ononneg__bounded_1,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(V_K,V_y,T_a),T_a),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_K,T_a),c_RealVector_Osko__RealVector__Xmult__left__Xnonneg__bounded__1__1(V_y,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_mult__left_Obounded_0,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(V_K,V_y,T_a),T_a),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_K,T_a),c_RealVector_Osko__RealVector__Xmult__left__Xbounded__1__1(V_y,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_mult_Obounded_0,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_a,T_a),c_RealVector_Onorm__class_Onorm(V_b,T_a),tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__Xbounded__1__1(V_vskULj,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_pos__poly__pCons_3,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_Polynomial_Opos__poly(c_Polynomial_OpCons(V_a,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_reals__Archimedean6_1,axiom,
    ( c_HOL_Oord__class_Oless(V_r,c_RealDef_Oreal(c_RComplete_Osko__RComplete__Xreals__Archimedean6__1__1(V_r),tc_nat),tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_r,tc_RealDef_Oreal) ) ).

cnf(cls_cos__monotone__0__pi_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Transcendental_Ocos(V_x),c_Transcendental_Ocos(V_y),tc_RealDef_Oreal)
    | ~ c_lessequals(V_x,c_Transcendental_Opi,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(V_y,V_x,tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) ) ).

cnf(cls_reals__Archimedean3_0,axiom,
    ( c_HOL_Oord__class_Oless(V_y,c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(c_RComplete_Osko__RComplete__Xreals__Archimedean3__1__1(V_x,V_y),tc_nat),V_x,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).

cnf(cls_real__sqrt__mult__self__sum__ge__zero_0,axiom,
    c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)),tc_RealDef_Oreal) ).

cnf(cls_sin__npi_0,axiom,
    c_Transcendental_Osin(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(V_n,tc_nat),c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ).

cnf(cls_tan__npi_0,axiom,
    c_Transcendental_Otan(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(V_n,tc_nat),c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ).

cnf(cls_sin__npi2_0,axiom,
    c_Transcendental_Osin(c_HOL_Otimes__class_Otimes(c_Transcendental_Opi,c_RealDef_Oreal(V_n,tc_nat),tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ).

cnf(cls_norm__triangle__ineq3_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(V_a,T_a),c_RealVector_Onorm__class_Onorm(V_b,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a),tc_RealDef_Oreal) ) ).

cnf(cls_ln__ge__zero__iff_0,axiom,
    ( c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).

cnf(cls_ln__ge__zero__iff_1,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x),tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).

cnf(cls_ln__ge__zero__imp__ge__one_0,axiom,
    ( c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oln(V_x),tc_RealDef_Oreal) ) ).

cnf(cls_ln__mult_0,axiom,
    ( c_Transcendental_Oln(c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal)) = c_HOL_Oplus__class_Oplus(c_Transcendental_Oln(V_x),c_Transcendental_Oln(V_y),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).

cnf(cls_lemma__interval_2,axiom,
    ( c_lessequals(V_y,V_b,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Deriv_Osko__Deriv__Xlemma__interval__1__1(V_a,V_b,V_x),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(V_x,V_b,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(V_a,V_x,tc_RealDef_Oreal) ) ).

cnf(cls_lemma__interval_1,axiom,
    ( c_lessequals(V_a,V_y,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal),c_Deriv_Osko__Deriv__Xlemma__interval__1__1(V_a,V_b,V_x),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(V_x,V_b,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(V_a,V_x,tc_RealDef_Oreal) ) ).

cnf(cls_reals__Archimedean4_0,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(c_Transcendental_Osko__Transcendental__Xreals__Archimedean4__1__1(V_x,V_y),tc_nat),V_y,tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) ) ).

cnf(cls_divide_Opos__bounded_1,axiom,
    ( ~ class_RealVector_Oreal__normed__field(T_a)
    | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(V_K,V_y,T_a),T_a),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_K,T_a),c_RealVector_Osko__RealVector__Xdivide__Xpos__bounded__1__1(V_y,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_scaleR__right_Opos__bounded_1,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | c_lessequals(c_RealVector_Onorm__class_Onorm(c_RealVector_OscaleR__class_OscaleR(V_r,V_K,T_a),T_a),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_K,T_a),c_RealVector_Osko__RealVector__XscaleR__right__Xpos__bounded__1__1(V_vskULt,V_r,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_ln__realpow_0,axiom,
    ( c_Transcendental_Oln(c_Power_Opower__class_Opower(V_x,V_n,tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(c_RealDef_Oreal(V_n,tc_nat),c_Transcendental_Oln(V_x),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).

cnf(cls_cnj_Opos__bounded_1,axiom,
    c_lessequals(c_RealVector_Onorm__class_Onorm(c_Complex_Ocnj(V_K),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_K,tc_Complex_Ocomplex),c_Complex_Osko__Complex__Xcnj__Xpos__bounded__1__1,tc_RealDef_Oreal),tc_RealDef_Oreal) ).

cnf(cls_dist__complex__def__raw_0,axiom,
    c_RealVector_Odist__class_Odist(v_x,v_y,tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_x,v_y,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ).

cnf(cls_q_I2_J_0,axiom,
    c_Polynomial_Opoly(v_q____,V_x,tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_p,c_HOL_Oplus__class_Oplus(v_z,V_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ).

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_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_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_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(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_mult__le__cancel__left__neg_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
    | ~ c_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__pos_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_lessequals(V_a,V_b,T_a)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).

cnf(cls_mult__le__cancel__left__pos_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
    | ~ c_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__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(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ).

cnf(cls_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(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ).

cnf(cls_mult__strict__mono_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)
    | ~ c_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_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(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ).

cnf(cls_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(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ).

cnf(cls_mult__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(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ).

cnf(cls_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(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ).

cnf(cls_mult__strict__mono_H_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)
    | ~ c_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__le__less__imp__less_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)
    | ~ c_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(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)
    | ~ c_HOL_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_exp__not__eq__zero_0,axiom,
    ( ~ class_SEQ_Obanach(T_a)
    | ~ class_RealVector_Oreal__normed__field(T_a)
    | c_Transcendental_Oexp(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_sgn__zero__iff_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | c_HOL_Osgn__class_Osgn(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_sgn__0__0_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_HOL_Osgn__class_Osgn(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

cnf(cls_sgn__zero_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_sgn0_0,axiom,
    ( ~ class_Ring__and__Field_Osgn__if(T_a)
    | c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_sgn__0__0_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

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

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

cnf(cls_dist__le__zero__iff_0,axiom,
    ( ~ class_RealVector_Ometric__space(T_a)
    | V_x = V_y
    | ~ c_lessequals(c_RealVector_Odist__class_Odist(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

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

cnf(cls_real__sqrt__le__0__iff_1,axiom,
    ( c_lessequals(c_NthRoot_Osqrt(V_x),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_real__sqrt__le__0__iff_0,axiom,
    ( c_lessequals(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_lessequals(c_NthRoot_Osqrt(V_x),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_real__sqrt__mult_0,axiom,
    c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) ).

cnf(cls_real__of__nat__ge__zero_0,axiom,
    c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(V_n,tc_nat),tc_RealDef_Oreal) ).

cnf(cls_not__exp__le__zero_0,axiom,
    ~ c_lessequals(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ).

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

cnf(cls_mult__left_Opos__bounded_1,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(V_K,V_y,T_a),T_a),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_K,T_a),c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1(V_y,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

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

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

cnf(cls_real__mult__commute_0,axiom,
    c_HOL_Otimes__class_Otimes(V_z,V_w,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(V_w,V_z,tc_RealDef_Oreal) ).

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

cnf(cls_abs__mult__less_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),c_HOL_Otimes__class_Otimes(V_c,V_d,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_b,T_a),V_d,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_c,T_a) ) ).

cnf(cls_exp__ge__zero_0,axiom,
    c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),tc_RealDef_Oreal) ).

cnf(cls_abs__triangle__ineq3_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
    | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a),T_a) ) ).

cnf(cls_abs__le__interval__iff_1,axiom,
    ( c_lessequals(V_x,V_r,tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_x,tc_RealDef_Oreal),V_r,tc_RealDef_Oreal) ) ).

cnf(cls_abs__le__D1_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
    | c_lessequals(V_a,V_b,T_a)
    | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ).

cnf(cls_abs__le__mult_0,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(T_a)
    | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a) ) ).

cnf(cls_norm__mult__ineq_0,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_x,T_a),c_RealVector_Onorm__class_Onorm(V_y,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_mult__sgn__abs_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(V_x,T_a),c_HOL_Oabs__class_Oabs(V_x,T_a),T_a) = V_x ) ).

cnf(cls_real__of__nat__inject_0,axiom,
    ( c_RealDef_Oreal(V_n,tc_nat) != c_RealDef_Oreal(V_m,tc_nat)
    | V_n = V_m ) ).

cnf(cls_dist__le__zero__iff_1,axiom,
    ( ~ class_RealVector_Ometric__space(T_a)
    | c_lessequals(c_RealVector_Odist__class_Odist(V_x,V_x,T_a),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

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

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

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

cnf(cls_abs__le__zero__iff_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a)
    | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_exp__le__cancel__iff_0,axiom,
    ( c_lessequals(V_x,V_y,tc_RealDef_Oreal)
    | ~ c_lessequals(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),c_Transcendental_Oexp(V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_exp__le__cancel__iff_1,axiom,
    ( c_lessequals(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),c_Transcendental_Oexp(V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal) ) ).

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_abs__less__iff_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_HOL_Oord__class_Oless(V_a,V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,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(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ).

cnf(cls_mult__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(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ).

cnf(cls_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_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_abs__minus__commute_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
    | c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),T_a) ) ).

cnf(cls_le__eqI_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
    | c_lessequals(V_y_H,V_x_H,T_a)
    | ~ c_lessequals(V_y,V_x,T_a) ) ).

cnf(cls_le__eqI_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
    | c_lessequals(V_y,V_x,T_a)
    | ~ c_lessequals(V_y_H,V_x_H,T_a) ) ).

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

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

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

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

cnf(cls_real__mult__right__cancel_0,axiom,
    ( c_HOL_Otimes__class_Otimes(V_a,V_c,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(V_b,V_c,tc_RealDef_Oreal)
    | V_c = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | V_a = V_b ) ).

cnf(cls_real__mult__left__cancel_0,axiom,
    ( c_HOL_Otimes__class_Otimes(V_c,V_a,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(V_c,V_b,tc_RealDef_Oreal)
    | V_c = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | V_a = V_b ) ).

cnf(cls_real__sqrt__eq__0__iff_0,axiom,
    ( c_NthRoot_Osqrt(V_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).

cnf(cls_pi__neq__zero_0,axiom,
    c_Transcendental_Opi != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ).

cnf(cls_real__sqrt__zero_0,axiom,
    c_NthRoot_Osqrt(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ).

cnf(cls_real__root__zero_0,axiom,
    c_NthRoot_Oroot(V_n,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ).

cnf(cls_dist__self_0,axiom,
    ( ~ class_RealVector_Ometric__space(T_a)
    | c_RealVector_Odist__class_Odist(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).

cnf(cls_dist__eq__0__iff_0,axiom,
    ( ~ class_RealVector_Ometric__space(T_a)
    | c_RealVector_Odist__class_Odist(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | V_x = V_y ) ).

cnf(cls_ln__le__cancel__iff_1,axiom,
    ( c_lessequals(c_Transcendental_Oln(V_x),c_Transcendental_Oln(V_y),tc_RealDef_Oreal)
    | ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).

cnf(cls_ln__le__cancel__iff_0,axiom,
    ( c_lessequals(V_x,V_y,tc_RealDef_Oreal)
    | ~ c_lessequals(c_Transcendental_Oln(V_x),c_Transcendental_Oln(V_y),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).

cnf(cls_real__less__all__preal_0,axiom,
    ( c_HOL_Oord__class_Oless(V_y,c_RealDef_Oreal__of__preal(V_x),tc_RealDef_Oreal)
    | ~ c_lessequals(V_y,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_exp__ln_0,axiom,
    ( c_Transcendental_Oexp(c_Transcendental_Oln(V_x),tc_RealDef_Oreal) = V_x
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).

cnf(cls_exp__ln__iff_0,axiom,
    ( c_Transcendental_Oexp(c_Transcendental_Oln(V_x),tc_RealDef_Oreal) != V_x
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).

cnf(cls_real__mult__le__cancel__iff2_1,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(V_z,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_z,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) ) ).

cnf(cls_real__mult__le__cancel__iff2_0,axiom,
    ( c_lessequals(V_x,V_y,tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_z,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_z,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) ) ).

cnf(cls_real__mult__le__cancel__iff1_1,axiom,
    ( c_lessequals(c_HOL_Otimes__class_Otimes(V_x,V_z,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_z,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) ) ).

cnf(cls_real__mult__le__cancel__iff1_0,axiom,
    ( c_lessequals(V_x,V_y,tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_x,V_z,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_z,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) ) ).

cnf(cls_real__less__def_0,axiom,
    ( c_lessequals(V_x,V_y,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) ) ).

cnf(cls_exp__less__cancel_0,axiom,
    ( c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),c_Transcendental_Oexp(V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_exp__less__mono_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),c_Transcendental_Oexp(V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) ) ).

cnf(cls_real__less__def_2,axiom,
    ( c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal)
    | V_x = V_y
    | ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal) ) ).

cnf(cls_real__sqrt__less__iff_0,axiom,
    ( c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) ) ).

cnf(cls_real__sqrt__less__iff_1,axiom,
    ( c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) ) ).

cnf(cls_norm__mult__less_0,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a),c_HOL_Otimes__class_Otimes(V_r,V_s,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(V_y,T_a),V_s,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(V_x,T_a),V_r,tc_RealDef_Oreal) ) ).

cnf(cls_abs__norm__cancel_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(V_a,T_a),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(V_a,T_a) ) ).

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

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

cnf(cls_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_diff__poly__code_I2_J_0,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(T_a)
    | c_HOL_Ominus__class_Ominus(V_p,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) = V_p ) ).

cnf(cls_poly__bound__exists_1,axiom,
    ( c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(V_p,V_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(V_p,V_r),tc_RealDef_Oreal)
    | ~ c_lessequals(c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex),V_r,tc_RealDef_Oreal) ) ).

cnf(cls_norm__ratiotest__lemma_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | V_x = c_HOL_Ozero__class_Ozero(T_a)
    | ~ c_lessequals(c_RealVector_Onorm__class_Onorm(V_x,T_a),c_HOL_Otimes__class_Otimes(V_c,c_RealVector_Onorm__class_Onorm(V_y,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

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(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ).

cnf(cls_mult__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(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ).

cnf(cls_mult__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(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ).

cnf(cls_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(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ).

cnf(cls_zero__less__abs__iff_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(T_a),T_a),T_a) ) ).

cnf(cls_abs__if_1,axiom,
    ( ~ class_Ring__and__Field_Oabs__if(T_a)
    | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_abs__if__lattice_1,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a)
    | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_abs__not__less__zero_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_zero__less__abs__iff_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

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

cnf(cls_Rational_Oordered__idom__class_Osgn__less_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(V_a,T_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_Rational_Oordered__idom__class_Osgn__less_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(c_HOL_Osgn__class_Osgn(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),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(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ).

cnf(cls_mult__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(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ).

cnf(cls_mult__pos__neg2_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_b,V_a,T_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(c_HOL_Otimes__class_Otimes(V_a,V_b,T_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__neg__pos_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),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_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),c_HOL_Otimes__class_Otimes(V_b,V_a,T_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),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),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),c_HOL_Otimes__class_Otimes(V_a,V_b,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(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),c_HOL_Otimes__class_Otimes(V_a,V_b,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_Rational_Oordered__idom__class_Osgn__greater_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Osgn__class_Osgn(V_a,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_Rational_Oordered__idom__class_Osgn__greater_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(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),c_HOL_Osgn__class_Osgn(V_a,T_a),T_a) ) ).

cnf(cls_abs__of__pos_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
    | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,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(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
    | ~ c_HOL_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(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
    | ~ c_HOL_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(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
    | ~ c_HOL_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(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
    | ~ c_HOL_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(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
    | ~ c_HOL_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(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
    | ~ c_HOL_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(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
    | ~ c_HOL_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(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
    | ~ c_HOL_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(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
    | ~ c_HOL_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(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
    | ~ c_HOL_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(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
    | ~ c_HOL_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(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
    | ~ c_HOL_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(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_le__iff__diff__le__0_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_lessequals(V_a,V_b,T_a)
    | ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_le__iff__diff__le__0_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_lessequals(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(V_a,V_b,T_a) ) ).

cnf(cls_abs__diff__less__iff_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_r,T_a),V_x,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_x,V_a,T_a),T_a),V_r,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_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_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_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_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_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_coeff__diff_0,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(T_a)
    | c_Polynomial_Ocoeff(c_HOL_Ominus__class_Ominus(V_p,V_q,tc_Polynomial_Opoly(T_a)),V_n,T_a) = c_HOL_Ominus__class_Ominus(c_Polynomial_Ocoeff(V_p,V_n,T_a),c_Polynomial_Ocoeff(V_q,V_n,T_a),T_a) ) ).

cnf(cls_abs__of__nonneg_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
    | c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

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

cnf(cls_abs__eq__mult_0,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a)
    | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a)
    | ~ 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_abs__eq__mult_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a)
    | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a)
    | ~ 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_abs__eq__mult_2,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a)
    | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a)
    | ~ 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_abs__eq__mult_3,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring__abs(T_a)
    | c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a)
    | ~ 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__left__idem_0,axiom,
    ( ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a)
    | c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_x,V_y,T_a) ) ).

cnf(cls_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(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),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(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),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(c_HOL_Otimes__class_Otimes(V_a,V_b,T_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(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_real__sqrt__ge__0__iff_1,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) ) ).

cnf(cls_real__sqrt__ge__0__iff_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) ) ).

cnf(cls_real__sqrt__ge__zero_0,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x),tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).

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_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_real__sqrt__eq__iff_0,axiom,
    ( c_NthRoot_Osqrt(V_x) != c_NthRoot_Osqrt(V_y)
    | V_x = V_y ) ).

cnf(cls_exp__inj__iff_0,axiom,
    ( c_Transcendental_Oexp(V_x,tc_RealDef_Oreal) != c_Transcendental_Oexp(V_y,tc_RealDef_Oreal)
    | V_x = V_y ) ).

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

cnf(cls_mult__right__mono_0,axiom,
    ( ~ class_Ring__and__Field_Omult__mono(T_a)
    | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
    | ~ c_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__neg_0,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(T_a)
    | c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
    | ~ c_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__neg_0,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(T_a)
    | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
    | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(V_b,V_a,T_a) ) ).

cnf(cls_zero__le__dist_0,axiom,
    ( ~ class_RealVector_Ometric__space(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(V_x,V_y,T_a),tc_RealDef_Oreal) ) ).

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

cnf(cls_abs__real__of__nat__cancel_0,axiom,
    c_HOL_Oabs__class_Oabs(c_RealDef_Oreal(V_x,tc_nat),tc_RealDef_Oreal) = c_RealDef_Oreal(V_x,tc_nat) ).

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

cnf(cls_split__mult__pos__le_0,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,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),V_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),c_HOL_Otimes__class_Otimes(V_a,V_b,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_mult__nonpos__nonpos_0,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,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_zero__le__square_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_a,T_a),T_a) ) ).

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),c_HOL_Otimes__class_Otimes(V_a,V_b,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),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),c_HOL_Otimes__class_Otimes(V_a,V_b,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_mult__nonneg__nonneg_0,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,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),V_a,T_a) ) ).

cnf(cls_abs__triangle__ineq2_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
    | c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a),T_a) ) ).

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

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

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

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

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

cnf(cls_real__mult__assoc_0,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_z1,V_z2,tc_RealDef_Oreal),V_z3,tc_RealDef_Oreal) = c_HOL_Otimes__class_Otimes(V_z1,c_HOL_Otimes__class_Otimes(V_z2,V_z3,tc_RealDef_Oreal),tc_RealDef_Oreal) ).

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

cnf(cls_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),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),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),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),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),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),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),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ).

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

cnf(cls_mult__mono_0,axiom,
    ( ~ class_Ring__and__Field_Opordered__semiring(T_a)
    | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)
    | ~ c_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(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)
    | ~ c_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_diff__pCons_0,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(T_a)
    | c_HOL_Ominus__class_Ominus(c_Polynomial_OpCons(V_a,V_p,T_a),c_Polynomial_OpCons(V_b,V_q,T_a),tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ominus__class_Ominus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) ) ).

cnf(cls_sgn__sgn_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(V_a,T_a),T_a) = c_HOL_Osgn__class_Osgn(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(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_n,T_a) ) ).

cnf(cls_abs__sgn_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_HOL_Oabs__class_Oabs(V_k,T_a) = c_HOL_Otimes__class_Otimes(V_k,c_HOL_Osgn__class_Osgn(V_k,T_a),T_a) ) ).

cnf(cls_mult_Opos__bounded_1,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_a,T_a),c_RealVector_Onorm__class_Onorm(V_b,T_a),tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1(V_vskULn,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_mult__right_Opos__bounded_1,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(V_x,V_K,T_a),T_a),c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_K,T_a),c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1(V_x,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_mult__le__0__iff_4,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_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_mult__le__0__iff_5,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_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(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(c_HOL_Otimes__class_Otimes(V_a,V_b,T_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_split__mult__neg__le_1,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
    | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_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(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(c_HOL_Otimes__class_Otimes(V_a,V_b,T_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_mult__nonpos__nonneg_0,axiom,
    ( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
    | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_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(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(c_HOL_Otimes__class_Otimes(V_b,V_a,T_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_abs__le__zero__iff_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
    | c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_ln__unique_0,axiom,
    c_Transcendental_Oln(c_Transcendental_Oexp(V_y,tc_RealDef_Oreal)) = V_y ).

cnf(cls_exp__ln__eq_0,axiom,
    c_Transcendental_Oln(c_Transcendental_Oexp(V_u,tc_RealDef_Oreal)) = V_u ).

cnf(cls_ln__exp_0,axiom,
    c_Transcendental_Oln(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal)) = V_x ).

cnf(cls_dist__commute_0,axiom,
    ( ~ class_RealVector_Ometric__space(T_a)
    | c_RealVector_Odist__class_Odist(V_x,V_y,T_a) = c_RealVector_Odist__class_Odist(V_y,V_x,T_a) ) ).

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

cnf(cls_real__sqrt__eq__zero__cancel_0,axiom,
    ( c_NthRoot_Osqrt(V_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
    | V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).

cnf(cls_real__sqrt__le__iff_1,axiom,
    ( c_lessequals(c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal)
    | ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal) ) ).

cnf(cls_real__sqrt__le__iff_0,axiom,
    ( c_lessequals(V_x,V_y,tc_RealDef_Oreal)
    | ~ c_lessequals(c_NthRoot_Osqrt(V_x),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) ) ).

cnf(cls_rabs__ratiotest__lemma_0,axiom,
    ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_c,c_HOL_Oabs__class_Oabs(V_y,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

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

cnf(cls_norm__mult_0,axiom,
    ( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
    | c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(V_x,T_a),c_RealVector_Onorm__class_Onorm(V_y,T_a),tc_RealDef_Oreal) ) ).

cnf(cls_abs__ge__self_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
    | c_lessequals(V_a,c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ) ).

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

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

cnf(cls_abs__exp__cancel_0,axiom,
    c_HOL_Oabs__class_Oabs(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_Transcendental_Oexp(V_x,tc_RealDef_Oreal) ).

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

cnf(cls_abs__mult__pos_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_y,T_a),V_x,T_a) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_y,V_x,T_a),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ).

cnf(cls_real__sqrt__abs2_0,axiom,
    c_NthRoot_Osqrt(c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal)) = c_HOL_Oabs__class_Oabs(V_x,tc_RealDef_Oreal) ).

cnf(cls_diff__monom_0,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(T_a)
    | c_HOL_Ominus__class_Ominus(c_Polynomial_Omonom(V_a,V_n,T_a),c_Polynomial_Omonom(V_b,V_n,T_a),tc_Polynomial_Opoly(T_a)) = c_Polynomial_Omonom(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_n,T_a) ) ).

cnf(cls_pi__ge__zero_0,axiom,
    c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal) ).

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__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_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_sgn__mult_0,axiom,
    ( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
    | c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(V_x,T_a),c_HOL_Osgn__class_Osgn(V_y,T_a),T_a) ) ).

cnf(cls_sgn__times_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(V_a,T_a),c_HOL_Osgn__class_Osgn(V_b,T_a),T_a) ) ).

cnf(cls_abs__ge__zero_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,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_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_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_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_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_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_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_coeff__0_0,axiom,
    ( ~ class_HOL_Ozero(T_a)
    | c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_real__less__all__real2_0,axiom,
    ( c_HOL_Oord__class_Oless(V_y,c_RealDef_Oreal__of__preal(V_x),tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) ) ).

cnf(cls_pi__gt__zero_0,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal) ).

cnf(cls_not__real__square__gt__zero_0,axiom,
    ( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_real__abs__def_1,axiom,
    ( c_HOL_Oabs__class_Oabs(V_r,tc_RealDef_Oreal) = V_r
    | c_HOL_Oord__class_Oless(V_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_mult__right_Opos__bounded_0,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1(V_x,T_a),tc_RealDef_Oreal) ) ).

cnf(cls_Re_Opos__bounded_0,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_Osko__Complex__XRe__Xpos__bounded__1__1,tc_RealDef_Oreal) ).

cnf(cls_mult__left_Opos__bounded_0,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1(V_y,T_a),tc_RealDef_Oreal) ) ).

cnf(cls_not__real__square__gt__zero_1,axiom,
    ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ).

cnf(cls_divide_Opos__bounded_0,axiom,
    ( ~ class_RealVector_Oreal__normed__field(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xdivide__Xpos__bounded__1__1(V_y,T_a),tc_RealDef_Oreal) ) ).

cnf(cls_real__of__preal__zero__less_0,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal__of__preal(V_m),tc_RealDef_Oreal) ).

cnf(cls_real__gt__zero__preal__Ex_1,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal__of__preal(V_xa),tc_RealDef_Oreal) ).

cnf(cls_scaleR__right_Opos__bounded_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__XscaleR__right__Xpos__bounded__1__1(V_vskULt,V_r,T_a),tc_RealDef_Oreal) ) ).

cnf(cls_lemma__tan__total_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Osko__Transcendental__Xlemma__tan__total__1__1(V_y),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) ) ).

cnf(cls_real__lbound__gt__zero_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Osko__RealDef__Xreal__lbound__gt__zero__1__1(V_d1,V_d2),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d2,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d1,tc_RealDef_Oreal) ) ).

cnf(cls_realpow__pos__nth2_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osko__NthRoot__Xrealpow__pos__nth2__1__1(V_a,V_n),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_a,tc_RealDef_Oreal) ) ).

cnf(cls_lemma__interval_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Deriv_Osko__Deriv__Xlemma__interval__1__1(V_a,V_b,V_x),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(V_x,V_b,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(V_a,V_x,tc_RealDef_Oreal) ) ).

cnf(cls_real__sqrt__gt__zero_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_x),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).

cnf(cls_real__sqrt__gt__0__iff_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal) ) ).

cnf(cls_real__sqrt__gt__0__iff_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_y),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) ) ).

cnf(cls_ln__less__cancel__iff_1,axiom,
    ( c_HOL_Oord__class_Oless(c_Transcendental_Oln(V_x),c_Transcendental_Oln(V_y),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).

cnf(cls_ln__less__cancel__iff_0,axiom,
    ( c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_Transcendental_Oln(V_x),c_Transcendental_Oln(V_y),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).

cnf(cls_poly__bound__exists_0,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1(V_p,V_r),tc_RealDef_Oreal) ).

cnf(cls_ln__inj__iff_0,axiom,
    ( c_Transcendental_Oln(V_x) != c_Transcendental_Oln(V_y)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
    | V_x = V_y ) ).

cnf(cls_ln__less__self_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Transcendental_Oln(V_x),V_x,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).

cnf(cls_root__def_2,axiom,
    ( c_NthRoot_Oroot(V_n,V_x) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).

cnf(cls_scaleR_Opos__bounded_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__XscaleR__Xpos__bounded__1__1(V_vskULo,T_a),tc_RealDef_Oreal) ) ).

cnf(cls_lemma__interval__lt_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Deriv_Osko__Deriv__Xlemma__interval__lt__1__1(V_a,V_b,V_x),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(V_x,V_b,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(V_a,V_x,tc_RealDef_Oreal) ) ).

cnf(cls_zero__less__dist__iff_1,axiom,
    ( ~ class_RealVector_Ometric__space(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(V_x,V_y,T_a),tc_RealDef_Oreal)
    | V_x = V_y ) ).

cnf(cls_of__real_Opos__bounded_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | ~ class_RealVector_Oreal__algebra__1(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xof__real__Xpos__bounded__1__1(V_vskULr,T_a),tc_RealDef_Oreal) ) ).

cnf(cls_dist__not__less__zero_0,axiom,
    ( ~ class_RealVector_Ometric__space(T_a)
    | ~ c_HOL_Oord__class_Oless(c_RealVector_Odist__class_Odist(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_Im_Opos__bounded_0,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_Osko__Complex__XIm__Xpos__bounded__1__1,tc_RealDef_Oreal) ).

cnf(cls_real__sqrt__not__eq__zero_0,axiom,
    ( c_NthRoot_Osqrt(V_x) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).

cnf(cls_not__exp__less__zero_0,axiom,
    ~ c_HOL_Oord__class_Oless(c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ).

cnf(cls_real__mult__order_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_y,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).

cnf(cls_real__lbound__gt__zero_2,axiom,
    ( c_HOL_Oord__class_Oless(c_RealDef_Osko__RealDef__Xreal__lbound__gt__zero__1__1(V_d1,V_d2),V_d2,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d2,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d1,tc_RealDef_Oreal) ) ).

cnf(cls_real__lbound__gt__zero_1,axiom,
    ( c_HOL_Oord__class_Oless(c_RealDef_Osko__RealDef__Xreal__lbound__gt__zero__1__1(V_d1,V_d2),V_d1,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d2,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_d1,tc_RealDef_Oreal) ) ).

cnf(cls_zero__less__dist__iff_0,axiom,
    ( ~ class_RealVector_Ometric__space(T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Odist__class_Odist(V_x,V_x,T_a),tc_RealDef_Oreal) ) ).

cnf(cls_not__real__of__nat__less__zero_0,axiom,
    ~ c_HOL_Oord__class_Oless(c_RealDef_Oreal(V_n,tc_nat),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ).

cnf(cls_real__sqrt__lt__0__iff_0,axiom,
    ( c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(V_x),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_real__sqrt__lt__0__iff_1,axiom,
    ( c_HOL_Oord__class_Oless(c_NthRoot_Osqrt(V_x),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_pi__not__less__zero_0,axiom,
    ~ c_HOL_Oord__class_Oless(c_Transcendental_Opi,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ).

cnf(cls_cnj_Opos__bounded_0,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Complex_Osko__Complex__Xcnj__Xpos__bounded__1__1,tc_RealDef_Oreal) ).

cnf(cls_mult_Opos__bounded_0,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1(V_vskULn,T_a),tc_RealDef_Oreal) ) ).

cnf(cls_real__mult__less__mono2_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_z,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_z,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) ) ).

cnf(cls_real__mult__less__iff1_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_x,V_z,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_z,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) ) ).

cnf(cls_real__mult__less__iff1_0,axiom,
    ( c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_x,V_z,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_z,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) ) ).

cnf(cls_exp__gt__zero_0,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Oexp(V_x,tc_RealDef_Oreal),tc_RealDef_Oreal) ).

cnf(cls_scaleR__left_Opos__bounded_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Osko__RealVector__XscaleR__left__Xpos__bounded__1__1(V_x,T_a),tc_RealDef_Oreal) ) ).

cnf(cls_dist__norm_0,axiom,
    ( ~ class_RealVector_Odist__norm(T_a)
    | c_RealVector_Odist__class_Odist(V_x,V_y,T_a) = c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_x,V_y,T_a),T_a) ) ).

cnf(cls_norm__ge__zero_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x,T_a),tc_RealDef_Oreal) ) ).

cnf(cls_th_0,axiom,
    c_Polynomial_Opoly(v_q____,c_HOL_Ominus__class_Ominus(V_w,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_Polynomial_Opoly(v_p,V_w,tc_Complex_Ocomplex) ).

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

cnf(cls_dist__complex__def_0,axiom,
    c_RealVector_Odist__class_Odist(V_x,V_y,tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ).

cnf(cls_norm__sgn_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | c_RealVector_Onorm__class_Onorm(c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(T_a),T_a),T_a) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).

cnf(cls_norm__le__zero__iff_1,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_norm__le__zero__iff_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | V_x = c_HOL_Ozero__class_Ozero(T_a)
    | ~ c_lessequals(c_RealVector_Onorm__class_Onorm(V_x,T_a),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

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_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_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_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_less__iff__diff__less__0_1,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_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_less__iff__diff__less__0_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,V_b,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_real__less__def_1,axiom,
    ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_RealDef_Oreal) ).

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_linorder__neq__iff_1,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).

cnf(cls_norm__zero_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).

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

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

cnf(cls_ep_0,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_e,tc_RealDef_Oreal) ).

cnf(cls_less__eqI_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
    | c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).

cnf(cls_less__eqI_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
    | c_HOL_Oord__class_Oless(V_x,V_y,T_a)
    | ~ c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a) ) ).

cnf(cls_zero__less__norm__iff_1,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x,T_a),tc_RealDef_Oreal)
    | V_x = c_HOL_Ozero__class_Ozero(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_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_zero__less__norm__iff_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ozero__class_Ozero(T_a),T_a),tc_RealDef_Oreal) ) ).

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

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

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

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

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

cnf(cls_norm__eq__zero_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | c_RealVector_Onorm__class_Onorm(V_x,T_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | V_x = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_norm__not__less__zero_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(V_x,T_a),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

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_eq__eqI_0,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(T_a)
    | c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
    | V_x_H = V_y_H ) ).

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

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

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

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

cnf(cls_norm__minus__commute_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),T_a) ) ).

cnf(cls_CHAINED_0,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_e,tc_RealDef_Oreal) ).

cnf(cls_conjecture_0,negated_conjecture,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(hAPP(v_x,V_xa),v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa,tc_RealDef_Oreal) ) ).

cnf(cls_conjecture_1,negated_conjecture,
    ( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(hAPP(v_x,V_xa),v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),V_xa,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa,tc_RealDef_Oreal) ) ).

cnf(cls_conjecture_2,negated_conjecture,
    ( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ominus__class_Ominus(hAPP(v_x,V_xa),v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(tc_Complex_Ocomplex)),c_HOL_Ominus__class_Ominus(v_z,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_e,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa,tc_RealDef_Oreal) ) ).

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_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_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_nat__OrderedGroup_Ocancel__comm__monoid__add,axiom,
    class_OrderedGroup_Ocancel__comm__monoid__add(tc_nat) ).

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__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__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__ab__group__add__abs,axiom,
    class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs,axiom,
    class_OrderedGroup_Olordered__ab__group__add__abs(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__RealVector_Oreal__normed__div__algebra,axiom,
    class_RealVector_Oreal__normed__div__algebra(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_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_Opordered__ring__abs,axiom,
    class_Ring__and__Field_Opordered__ring__abs(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1,axiom,
    class_RealVector_Oreal__normed__algebra__1(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_Odivision__by__zero,axiom,
    class_Ring__and__Field_Odivision__by__zero(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_Oordered__field,axiom,
    class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring,axiom,
    class_Ring__and__Field_Olordered__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__RealVector_Oreal__normed__field,axiom,
    class_RealVector_Oreal__normed__field(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__Ring__and__Field_Omult__mono1,axiom,
    class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__RealVector_Oreal__algebra__1,axiom,
    class_RealVector_Oreal__algebra__1(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__Ring__and__Field_Ocomm__ring,axiom,
    class_Ring__and__Field_Ocomm__ring(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__RealVector_Oreal__algebra,axiom,
    class_RealVector_Oreal__algebra(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__RealVector_Ometric__space,axiom,
    class_RealVector_Ometric__space(tc_RealDef_Oreal) ).

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

cnf(clsarity_RealDef__Oreal__RealVector_Oreal__vector,axiom,
    class_RealVector_Oreal__vector(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_Osgn__if,axiom,
    class_Ring__and__Field_Osgn__if(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if,axiom,
    class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__RealVector_Oreal__field,axiom,
    class_RealVector_Oreal__field(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ofield,axiom,
    class_Ring__and__Field_Ofield(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__RealVector_Odist__norm,axiom,
    class_RealVector_Odist__norm(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__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_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__SEQ_Obanach,axiom,
    class_SEQ_Obanach(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__RealVector_Oreal__normed__div__algebra,axiom,
    class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) ).

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

cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
    class_RealVector_Oreal__normed__algebra__1(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_Odivision__by__zero,axiom,
    class_Ring__and__Field_Odivision__by__zero(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__RealVector_Oreal__normed__field,axiom,
    class_RealVector_Oreal__normed__field(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__RealVector_Oreal__algebra__1,axiom,
    class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex) ).

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

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

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

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

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

cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__algebra,axiom,
    class_RealVector_Oreal__algebra(tc_Complex_Ocomplex) ).

cnf(clsarity_Complex__Ocomplex__RealVector_Ometric__space,axiom,
    class_RealVector_Ometric__space(tc_Complex_Ocomplex) ).

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

cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__vector,axiom,
    class_RealVector_Oreal__vector(tc_Complex_Ocomplex) ).

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

cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__field,axiom,
    class_RealVector_Oreal__field(tc_Complex_Ocomplex) ).

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

cnf(clsarity_Complex__Ocomplex__RealVector_Odist__norm,axiom,
    class_RealVector_Odist__norm(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__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__SEQ_Obanach,axiom,
    class_SEQ_Obanach(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__ab__group__add__abs,axiom,
    ( class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__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_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_Opordered__ring__abs,axiom,
    ( class_Ring__and__Field_Opordered__ring__abs(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__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__Ring__and__Field_Ocomm__ring,axiom,
    ( class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Ocomm__ring(T_1) ) ).

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

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

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

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

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Osgn__if,axiom,
    ( class_Ring__and__Field_Osgn__if(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).

cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oabs__if,axiom,
    ( class_Ring__and__Field_Oabs__if(tc_Polynomial_Opoly(T_1))
    | ~ class_Ring__and__Field_Oordered__idom(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__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_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) ) ).

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