%------------------------------------------------------------------------------
% File     : SWV596-1 : TPTP v8.2.0. Released v4.1.0.
% Domain   : Software Verification
% Problem  : Fast Fourier Transform 134_34
% Version  : Especial.
% English  : Formalization of a functional implementation of the FFT algorithm
%            over the complex numbers, and its inverse. Both are shown
%            equivalent to the usual definitions of these operations through
%            Vandermonde matrices. They are also shown to be inverse to each
%            other, more precisely, that composition of the inverse and the
%            transformation yield the identity up to a scalar.

% Refs     : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe
%          : [BN10]  Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% Source   : [Nip10]
% Names    : FFT-134_34 [Nip10]

% Status   : Unsatisfiable
% Rating   : 0.20 v8.2.0, 0.24 v8.1.0, 0.05 v7.5.0, 0.16 v7.4.0, 0.12 v7.3.0, 0.17 v7.1.0, 0.08 v7.0.0, 0.27 v6.3.0, 0.18 v6.2.0, 0.30 v6.1.0, 0.43 v6.0.0, 0.40 v5.5.0, 0.70 v5.3.0, 0.67 v5.2.0, 0.69 v5.1.0, 0.71 v5.0.0, 0.57 v4.1.0
% Syntax   : Number of clauses     : 1255 ( 188 unt; 151 nHn; 753 RR)
%            Number of literals    : 3465 ( 711 equ;2068 neg)
%            Maximal clause size   :    6 (   2 avg)
%            Maximal term depth    :    6 (   1 avg)
%            Number of predicates  :   81 (  80 usr;   0 prp; 1-3 aty)
%            Number of functors    :   34 (  34 usr;   5 con; 0-3 aty)
%            Number of variables   : 3353 ( 161 sgn)
% SPC      : CNF_UNS_RFO_SEQ_NHN

% Comments :
%------------------------------------------------------------------------------
cnf(cls_DERIV__inverse__lemma_0,axiom,
    ( ~ class_RealVector_Oreal__normed__field(T_a)
    | c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a),V_h,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_h,T_a),T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a),T_a)
    | V_b = c_HOL_Ozero__class_Ozero(T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_inverse__negative__imp__negative_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_inverse__divide_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_b,V_a,T_a) ) ).

cnf(cls_minus__max__eq__min_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_HOL_Ouminus__class_Ouminus(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) = c_Orderings_Oord__class_Omin(c_HOL_Ouminus__class_Ouminus(V_x,T_a),c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) ) ).

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_sup__eq__if_1,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_Lattices_Oupper__semilattice__class_Osup(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = V_a
    | c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_ge__one__powr__ge__zero_0,axiom,
    ( c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Log_Opowr(V_x,V_a),tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_a,tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).

cnf(cls_prts_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | V_a = c_HOL_Oplus__class_Oplus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a,T_a),T_a) ) ).

cnf(cls_class__ringb_Oadd__scale__eq__noteq_0,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | 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_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_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_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_inverse__unique_0,axiom,
    ( ~ class_Ring__and__Field_Odivision__ring(T_a)
    | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a)
    | c_HOL_Oinverse__class_Oinverse(V_a,T_a) = V_b ) ).

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_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_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_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_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_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_le__supE_0,axiom,
    ( ~ class_Lattices_Oupper__semilattice(T_a)
    | c_lessequals(V_a,V_x,T_a)
    | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),V_x,T_a) ) ).

cnf(cls_le__supE_1,axiom,
    ( ~ class_Lattices_Oupper__semilattice(T_a)
    | c_lessequals(V_b,V_x,T_a)
    | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),V_x,T_a) ) ).

cnf(cls_le__supI1_0,axiom,
    ( ~ class_Lattices_Oupper__semilattice(T_a)
    | c_lessequals(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),T_a)
    | ~ c_lessequals(V_x,V_a,T_a) ) ).

cnf(cls_le__supI2_0,axiom,
    ( ~ class_Lattices_Oupper__semilattice(T_a)
    | c_lessequals(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),T_a)
    | ~ c_lessequals(V_x,V_b,T_a) ) ).

cnf(cls_le__sup__iff_0,axiom,
    ( ~ class_Lattices_Oupper__semilattice(T_a)
    | c_lessequals(V_x,V_z,T_a)
    | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a) ) ).

cnf(cls_le__sup__iff_1,axiom,
    ( ~ class_Lattices_Oupper__semilattice(T_a)
    | c_lessequals(V_y,V_z,T_a)
    | ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,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_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_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_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_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_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_inverse__eq__iff__eq_0,axiom,
    ( ~ class_Ring__and__Field_Odivision__ring(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Oinverse__class_Oinverse(V_b,T_a)
    | V_a = V_b ) ).

cnf(cls_of__real__mult_0,axiom,
    ( ~ class_RealVector_Oreal__algebra__1(T_a)
    | c_RealVector_Oof__real(c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),T_a) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(V_x,T_a),c_RealVector_Oof__real(V_y,T_a),T_a) ) ).

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

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

cnf(cls_real__sqrt__eq__iff_0,axiom,
    ( c_NthRoot_Osqrt(V_x) != c_NthRoot_Osqrt(V_y)
    | V_x = V_y ) ).

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_of__real__inverse_0,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_RealVector_Oreal__div__algebra(T_a)
    | c_RealVector_Oof__real(c_HOL_Oinverse__class_Oinverse(V_x,tc_RealDef_Oreal),T_a) = c_HOL_Oinverse__class_Oinverse(c_RealVector_Oof__real(V_x,T_a),T_a) ) ).

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

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

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

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

cnf(cls_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_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__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_sup__inf__distrib2_0,axiom,
    ( ~ class_Lattices_Odistrib__lattice(T_a)
    | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),V_x,T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_y,V_x,T_a),c_Lattices_Oupper__semilattice__class_Osup(V_z,V_x,T_a),T_a) ) ).

cnf(cls_sup__inf__distrib1_0,axiom,
    ( ~ class_Lattices_Odistrib__lattice(T_a)
    | c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),c_Lattices_Oupper__semilattice__class_Osup(V_x,V_z,T_a),T_a) ) ).

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

cnf(cls_abs__le__D2_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
    | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a)
    | ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ).

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_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_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_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_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_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_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_mod__add__self2_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a) ) ).

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

cnf(cls_abs__less__iff_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).

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_inf__greatest_0,axiom,
    ( ~ class_Lattices_Olower__semilattice(T_a)
    | c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a)
    | ~ c_lessequals(V_x,V_z,T_a)
    | ~ c_lessequals(V_x,V_y,T_a) ) ).

cnf(cls_le__inf__iff_2,axiom,
    ( ~ class_Lattices_Olower__semilattice(T_a)
    | c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a)
    | ~ c_lessequals(V_x,V_z,T_a)
    | ~ c_lessequals(V_x,V_y,T_a) ) ).

cnf(cls_le__infI_0,axiom,
    ( ~ class_Lattices_Olower__semilattice(T_a)
    | c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),T_a)
    | ~ c_lessequals(V_x,V_b,T_a)
    | ~ c_lessequals(V_x,V_a,T_a) ) ).

cnf(cls_inf__le2_0,axiom,
    ( ~ class_Lattices_Olower__semilattice(T_a)
    | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_y,T_a) ) ).

cnf(cls_inf__le1_0,axiom,
    ( ~ class_Lattices_Olower__semilattice(T_a)
    | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_x,T_a) ) ).

cnf(cls_inf__sup__ord_I2_J_0,axiom,
    ( ~ class_Lattices_Olattice(T_a)
    | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_y,T_a) ) ).

cnf(cls_inf__sup__ord_I1_J_0,axiom,
    ( ~ class_Lattices_Olattice(T_a)
    | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_x,T_a) ) ).

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

cnf(cls_real__mult__is__one_0,axiom,
    ( c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
    | V_x = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | V_x = c_HOL_Oone__class_Oone(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_neg__le__0__iff__le_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

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

cnf(cls_one__less__inverse__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_x,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,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_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_le__eq__neg_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

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

cnf(cls_real__add__le__0__iff_0,axiom,
    ( c_lessequals(V_y,c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_x,V_y,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_real__add__le__0__iff_1,axiom,
    ( c_lessequals(c_HOL_Oplus__class_Oplus(V_x,V_y,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_lessequals(V_y,c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

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

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

cnf(cls_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_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_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_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_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_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__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_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_dvd__mult__cancel__right_1,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a),T_a) ) ).

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

cnf(cls_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_dvd__trans_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ).

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

cnf(cls_less__infI2_0,axiom,
    ( ~ class_Lattices_Olower__semilattice(T_a)
    | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_x,T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,V_x,T_a) ) ).

cnf(cls_less__infI1_0,axiom,
    ( ~ class_Lattices_Olower__semilattice(T_a)
    | c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_x,T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,V_x,T_a) ) ).

cnf(cls_inf__sup__absorb_0,axiom,
    ( ~ class_Lattices_Olattice(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) = V_x ) ).

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_min__max_Osup__idem_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_Orderings_Oord__class_Omax(V_x,V_x,T_a) = V_x ) ).

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

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

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

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

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

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

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

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

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

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

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

cnf(cls_cos__monotone__minus__pi__0_H_0,axiom,
    ( c_lessequals(c_Transcendental_Ocos(V_y),c_Transcendental_Ocos(V_x),tc_RealDef_Oreal)
    | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_lessequals(V_y,V_x,tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal),V_y,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_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_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_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_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__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_min__max_Oinf__idem_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_Orderings_Oord__class_Omin(V_x,V_x,T_a) = V_x ) ).

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_distrib__sup__le_0,axiom,
    ( ~ class_Lattices_Olattice(T_a)
    | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),c_Lattices_Oupper__semilattice__class_Osup(V_x,V_z,T_a),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_zero__le__iff__zero__nprt_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_zero__le__iff__zero__nprt_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_inverse__less__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_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a)
    | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_abs__lattice_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a)
    | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ).

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_inf__period_I4_J_0,axiom,
    ( ~ class_Ring__and__Field_Odvd(T_a)
    | ~ class_Ring__and__Field_Ocomm__ring(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_x,c_HOL_Otimes__class_Otimes(V_k,V_D,T_a),T_a),V_t,T_a),T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(V_x,V_t,T_a),T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_D,T_a) ) ).

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

cnf(cls_min__max_Osup__inf__distrib1_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),c_Orderings_Oord__class_Omax(V_x,V_z,T_a),T_a) ) ).

cnf(cls_min__max_Osup__inf__distrib2_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(V_y,V_z,T_a),V_x,T_a) = c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(V_y,V_x,T_a),c_Orderings_Oord__class_Omax(V_z,V_x,T_a),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_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_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_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__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_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_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_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_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_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_inverse__minus__eq_0,axiom,
    ( ~ class_Ring__and__Field_Odivision__ring(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) ).

cnf(cls_split__mult__pos__le_0,axiom,
    ( ~ class_Ring__and__Field_Opordered__ring(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),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_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_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_real__0__less__add__iff_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal),V_y,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_real__0__less__add__iff_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) ) ).

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

cnf(cls_of__real__def_0,axiom,
    ( ~ class_RealVector_Oreal__algebra__1(T_a)
    | c_RealVector_Oof__real(V_r,T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,c_HOL_Oone__class_Oone(T_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_class__semiring_Osemiring__rules_I8_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ).

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

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

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

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

cnf(cls_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_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_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_tan__minus_0,axiom,
    c_Transcendental_Otan(c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Otan(V_x),tc_RealDef_Oreal) ).

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_less__supI1_0,axiom,
    ( ~ class_Lattices_Oupper__semilattice(T_a)
    | c_HOL_Oord__class_Oless(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_a,T_a) ) ).

cnf(cls_less__supI2_0,axiom,
    ( ~ class_Lattices_Oupper__semilattice(T_a)
    | c_HOL_Oord__class_Oless(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_b,T_a) ) ).

cnf(cls_minus__divide__right_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ).

cnf(cls_minus__divide__left_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) ).

cnf(cls_one__le__inverse__iff_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a)
    | ~ c_lessequals(V_x,c_HOL_Oone__class_Oone(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,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_min__max_Osup__left__idem_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) = c_Orderings_Oord__class_Omax(V_x,V_y,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_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_nonzero__inverse__eq__divide_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

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

cnf(cls_real__eq__refl_0,axiom,
    c_HOL_Oeq__class_Oeq(V_x,V_x,tc_RealDef_Oreal) ).

cnf(cls_eq__class_Oeq__refl_0,axiom,
    ( ~ class_HOL_Oeq(T_a)
    | c_HOL_Oeq__class_Oeq(V_x,V_x,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_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_mult_Ominus__left_0,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ).

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

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

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

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

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

cnf(cls_real__mult__inverse__left_0,axiom,
    ( c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_x,tc_RealDef_Oreal),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_field__inverse_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_left__inverse_0,axiom,
    ( ~ class_Ring__and__Field_Odivision__ring(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a) = c_HOL_Oone__class_Oone(T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_right__inverse_0,axiom,
    ( ~ class_Ring__and__Field_Odivision__ring(T_a)
    | c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oone__class_Oone(T_a)
    | V_a = c_HOL_Ozero__class_Ozero(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_max__add__distrib__left_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
    | c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) = c_Orderings_Oord__class_Omax(c_HOL_Oplus__class_Oplus(V_x,V_z,T_a),c_HOL_Oplus__class_Oplus(V_y,V_z,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_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_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_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_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_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_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_of__real__minus_0,axiom,
    ( ~ class_RealVector_Oreal__algebra__1(T_a)
    | c_RealVector_Oof__real(c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal),T_a) = c_HOL_Ouminus__class_Ouminus(c_RealVector_Oof__real(V_x,T_a),T_a) ) ).

cnf(cls_of__real_Ominus_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | ~ class_RealVector_Oreal__algebra__1(T_a)
    | c_RealVector_Oof__real(c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal),T_a) = c_HOL_Ouminus__class_Ouminus(c_RealVector_Oof__real(V_x,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__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_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__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_pprt__neg_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_x,T_a),T_a) ) ).

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

cnf(cls_NthRoot_Oroot__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_min__max_Osup__inf__absorb_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a) = V_x ) ).

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_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_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_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_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_sup__0__imp__0_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_Lattices_Oupper__semilattice__class_Osup(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_sum__squares__le__zero__iff_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
    | c_lessequals(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_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_neg__less__iff__less_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).

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

cnf(cls_nonzero__inverse__scaleR__distrib_0,axiom,
    ( ~ class_RealVector_Oreal__div__algebra(T_a)
    | c_HOL_Oinverse__class_Oinverse(c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Oinverse__class_Oinverse(V_a,tc_RealDef_Oreal),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a)
    | V_x = c_HOL_Ozero__class_Ozero(T_a)
    | V_a = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).

cnf(cls_inverse__scaleR__distrib_0,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_RealVector_Oreal__div__algebra(T_a)
    | c_HOL_Oinverse__class_Oinverse(c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(c_HOL_Oinverse__class_Oinverse(V_a,tc_RealDef_Oreal),c_HOL_Oinverse__class_Oinverse(V_x,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_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_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_inf__left__commute_0,axiom,
    ( ~ class_Lattices_Olower__semilattice(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,T_a),T_a) ) ).

cnf(cls_inf__assoc_0,axiom,
    ( ~ class_Lattices_Olower__semilattice(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ).

cnf(cls_inf__sup__aci_I3_J_0,axiom,
    ( ~ class_Lattices_Olattice(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,T_a),T_a) ) ).

cnf(cls_inf__sup__aci_I2_J_0,axiom,
    ( ~ class_Lattices_Olattice(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ).

cnf(cls_abs__less__iff_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__idom(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,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_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_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_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_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_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_powr__minus_0,axiom,
    c_Log_Opowr(V_x,c_HOL_Ouminus__class_Ouminus(V_a,tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Oinverse(c_Log_Opowr(V_x,V_a),tc_RealDef_Oreal) ).

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_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_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_powr__mono2_0,axiom,
    ( c_lessequals(c_Log_Opowr(V_x,V_a),c_Log_Opowr(V_y,V_a),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_x,tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_a,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_abs__of__neg_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
    | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_abs__if_0,axiom,
    ( ~ class_Ring__and__Field_Oabs__if(T_a)
    | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_abs__if__lattice_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a)
    | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

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

cnf(cls_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__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__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__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__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_real__add__minus__iff_0,axiom,
    ( c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ouminus__class_Ouminus(V_a,tc_RealDef_Oreal),tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | V_x = V_a ) ).

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_inverse__le__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_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a)
    | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(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_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_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_arctan__monotone_H_0,axiom,
    ( c_lessequals(c_Transcendental_Oarctan(V_x),c_Transcendental_Oarctan(V_y),tc_RealDef_Oreal)
    | ~ c_lessequals(V_x,V_y,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_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_minus__min__eq__max_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_HOL_Ouminus__class_Ouminus(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a) = c_Orderings_Oord__class_Omax(c_HOL_Ouminus__class_Ouminus(V_x,T_a),c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) ) ).

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

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

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

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

cnf(cls_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_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_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_powr__powr__swap_0,axiom,
    c_Log_Opowr(c_Log_Opowr(V_x,V_a),V_b) = c_Log_Opowr(c_Log_Opowr(V_x,V_b),V_a) ).

cnf(cls_add__eq__inf__sup_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_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_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_scaleR__minus__right_0,axiom,
    ( ~ class_RealVector_Oreal__vector(T_a)
    | c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),T_a) ) ).

cnf(cls_scaleR_Ominus__right_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(V_a,V_b,T_a),T_a) ) ).

cnf(cls_scaleR__minus__left_0,axiom,
    ( ~ class_RealVector_Oreal__vector(T_a)
    | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ouminus__class_Ouminus(V_a,tc_RealDef_Oreal),V_x,T_a) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),T_a) ) ).

cnf(cls_scaleR__left_Ominus_0,axiom,
    ( ~ class_RealVector_Oreal__vector(T_a)
    | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal),V_xa,T_a) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(V_x,V_xa,T_a),T_a) ) ).

cnf(cls_scaleR_Ominus__left_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | c_RealVector_OscaleR__class_OscaleR(c_HOL_Ouminus__class_Ouminus(V_a,tc_RealDef_Oreal),V_b,T_a) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(V_a,V_b,T_a),T_a) ) ).

cnf(cls_min__max_Oinf__sup__distrib2_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(V_y,V_z,T_a),V_x,T_a) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(V_y,V_x,T_a),c_Orderings_Oord__class_Omin(V_z,V_x,T_a),T_a) ) ).

cnf(cls_min__max_Oinf__sup__distrib1_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_Orderings_Oord__class_Omin(V_x,c_Orderings_Oord__class_Omax(V_y,V_z,T_a),T_a) = c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),c_Orderings_Oord__class_Omin(V_x,V_z,T_a),T_a) ) ).

cnf(cls_abs__minus__le__zero_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
    | c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(V_a,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_of__real__eq__iff_0,axiom,
    ( ~ class_RealVector_Oreal__algebra__1(T_a)
    | c_RealVector_Oof__real(V_x,T_a) != c_RealVector_Oof__real(V_y,T_a)
    | V_x = V_y ) ).

cnf(cls_min__max_Ole__sup__iff_2,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a)
    | ~ c_lessequals(V_y,V_z,T_a)
    | ~ c_lessequals(V_x,V_z,T_a) ) ).

cnf(cls_min__max_Osup__least_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(c_Orderings_Oord__class_Omax(V_y,V_z,T_a),V_x,T_a)
    | ~ c_lessequals(V_z,V_x,T_a)
    | ~ c_lessequals(V_y,V_x,T_a) ) ).

cnf(cls_min__max_Ole__supI_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(c_Orderings_Oord__class_Omax(V_a,V_b,T_a),V_x,T_a)
    | ~ c_lessequals(V_b,V_x,T_a)
    | ~ c_lessequals(V_a,V_x,T_a) ) ).

cnf(cls_le__maxI1_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(V_x,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) ) ).

cnf(cls_le__maxI2_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(V_y,c_Orderings_Oord__class_Omax(V_x,V_y,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_neg__le__iff__le_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_lessequals(V_a,V_b,T_a)
    | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ).

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

cnf(cls_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_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_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__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_inverse__eq__divide_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ).

cnf(cls_class__fieldgb_Oinverse__divide_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | c_HOL_Oinverse__class_Oinverse(V_x,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_x,T_a) ) ).

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

cnf(cls_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_compl__sup_0,axiom,
    ( ~ class_Lattices_Oboolean__algebra(T_a)
    | c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(V_x,T_a),c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) ) ).

cnf(cls_neg__sup__eq__inf_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),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_zero__le__pprt_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a,T_a),T_a) ) ).

cnf(cls_min__max_Odistrib__inf__le_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),c_Orderings_Oord__class_Omin(V_x,V_z,T_a),T_a),c_Orderings_Oord__class_Omin(V_x,c_Orderings_Oord__class_Omax(V_y,V_z,T_a),T_a),T_a) ) ).

cnf(cls_of__real__1_0,axiom,
    ( ~ class_RealVector_Oreal__algebra__1(T_a)
    | c_RealVector_Oof__real(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),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_one__less__inverse__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_x,c_HOL_Oone__class_Oone(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) ) ).

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

cnf(cls_inverse__add_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a)
    | V_b = c_HOL_Ozero__class_Ozero(T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_division__ring__inverse__add_0,axiom,
    ( ~ class_Ring__and__Field_Odivision__ring(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a)
    | V_b = c_HOL_Ozero__class_Ozero(T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_min__max_Osup__commute_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_Orderings_Oord__class_Omax(V_x,V_y,T_a) = c_Orderings_Oord__class_Omax(V_y,V_x,T_a) ) ).

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_cos__arctan__not__zero_0,axiom,
    c_Transcendental_Ocos(c_Transcendental_Oarctan(V_x)) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ).

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_real__sum__squares__cancel__a_0,axiom,
    ( c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_y,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).

cnf(cls_real__sum__squares__cancel__a_1,axiom,
    ( c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal) != c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_y,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | V_y = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).

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_Deriv_Oinverse__diff__inverse_0,axiom,
    ( ~ class_Ring__and__Field_Odivision__ring(T_a)
    | c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a),T_a)
    | V_b = c_HOL_Ozero__class_Ozero(T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_real__diff__def_0,axiom,
    c_HOL_Ominus__class_Ominus(V_r,V_s,tc_RealDef_Oreal) = c_HOL_Oplus__class_Oplus(V_r,c_HOL_Ouminus__class_Ouminus(V_s,tc_RealDef_Oreal),tc_RealDef_Oreal) ).

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

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

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

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

cnf(cls_nonzero__minus__divide__divide_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a)
    | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ).

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

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

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

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

cnf(cls_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_le__infE_0,axiom,
    ( ~ class_Lattices_Olower__semilattice(T_a)
    | c_lessequals(V_x,V_a,T_a)
    | ~ c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),T_a) ) ).

cnf(cls_le__infE_1,axiom,
    ( ~ class_Lattices_Olower__semilattice(T_a)
    | c_lessequals(V_x,V_b,T_a)
    | ~ c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),T_a) ) ).

cnf(cls_le__infI1_0,axiom,
    ( ~ class_Lattices_Olower__semilattice(T_a)
    | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_x,T_a)
    | ~ c_lessequals(V_a,V_x,T_a) ) ).

cnf(cls_le__infI2_0,axiom,
    ( ~ class_Lattices_Olower__semilattice(T_a)
    | c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_x,T_a)
    | ~ c_lessequals(V_b,V_x,T_a) ) ).

cnf(cls_le__inf__iff_0,axiom,
    ( ~ class_Lattices_Olower__semilattice(T_a)
    | c_lessequals(V_x,V_y,T_a)
    | ~ c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ).

cnf(cls_le__inf__iff_1,axiom,
    ( ~ class_Lattices_Olower__semilattice(T_a)
    | c_lessequals(V_x,V_z,T_a)
    | ~ c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,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_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_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_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_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_powr__mono_0,axiom,
    ( c_lessequals(c_Log_Opowr(V_x,V_a),c_Log_Opowr(V_x,V_b),tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal)
    | ~ c_lessequals(V_a,V_b,tc_RealDef_Oreal) ) ).

cnf(cls_min__add__distrib__left_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
    | c_HOL_Oplus__class_Oplus(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) = c_Orderings_Oord__class_Omin(c_HOL_Oplus__class_Oplus(V_x,V_z,T_a),c_HOL_Oplus__class_Oplus(V_y,V_z,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_abs__leI_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
    | c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a)
    | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a)
    | ~ c_lessequals(V_a,V_b,T_a) ) ).

cnf(cls_abs__le__iff_2,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
    | c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a)
    | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a)
    | ~ c_lessequals(V_a,V_b,T_a) ) ).

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

cnf(cls_real__less__sum__gt__zero_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(V_S,c_HOL_Ouminus__class_Ouminus(V_W,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(V_W,V_S,tc_RealDef_Oreal) ) ).

cnf(cls_real__sum__gt__zero__less_0,axiom,
    ( c_HOL_Oord__class_Oless(V_W,V_S,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(V_S,c_HOL_Ouminus__class_Ouminus(V_W,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

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_powr__gt__zero_0,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Log_Opowr(V_x,V_a),tc_RealDef_Oreal) ).

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_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_inverse__mult__distrib_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ).

cnf(cls_nonzero__inverse__mult__distrib_0,axiom,
    ( ~ class_Ring__and__Field_Odivision__ring(T_a)
    | c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a)
    | V_b = c_HOL_Ozero__class_Ozero(T_a)
    | V_a = c_HOL_Ozero__class_Ozero(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_cos__monotone__minus__pi__0_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Transcendental_Ocos(V_y),c_Transcendental_Ocos(V_x),tc_RealDef_Oreal)
    | ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(V_y,V_x,tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(c_Transcendental_Opi,tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) ) ).

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_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_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_dvd__imp__mod__0_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(V_b,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ).

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

cnf(cls_nonzero__norm__inverse_0,axiom,
    ( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
    | c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oinverse__class_Oinverse(c_RealVector_Onorm__class_Onorm(V_a,T_a),tc_RealDef_Oreal)
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_distrib__inf__le_0,axiom,
    ( ~ class_Lattices_Olattice(T_a)
    | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,T_a),T_a),c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a),T_a) ) ).

cnf(cls_inf__sup__ord_I3_J_0,axiom,
    ( ~ class_Lattices_Olattice(T_a)
    | c_lessequals(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) ) ).

cnf(cls_inf__sup__ord_I4_J_0,axiom,
    ( ~ class_Lattices_Olattice(T_a)
    | c_lessequals(V_y,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) ) ).

cnf(cls_le__supI_0,axiom,
    ( ~ class_Lattices_Oupper__semilattice(T_a)
    | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),V_x,T_a)
    | ~ c_lessequals(V_b,V_x,T_a)
    | ~ c_lessequals(V_a,V_x,T_a) ) ).

cnf(cls_sup__ge1_0,axiom,
    ( ~ class_Lattices_Oupper__semilattice(T_a)
    | c_lessequals(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) ) ).

cnf(cls_sup__ge2_0,axiom,
    ( ~ class_Lattices_Oupper__semilattice(T_a)
    | c_lessequals(V_y,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) ) ).

cnf(cls_sup__least_0,axiom,
    ( ~ class_Lattices_Oupper__semilattice(T_a)
    | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),V_x,T_a)
    | ~ c_lessequals(V_z,V_x,T_a)
    | ~ c_lessequals(V_y,V_x,T_a) ) ).

cnf(cls_le__sup__iff_2,axiom,
    ( ~ class_Lattices_Oupper__semilattice(T_a)
    | c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a)
    | ~ c_lessequals(V_y,V_z,T_a)
    | ~ c_lessequals(V_x,V_z,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_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_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_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_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_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_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_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__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_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_min__max_Oinf__assoc_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) = c_Orderings_Oord__class_Omin(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),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_min__max_Oinf__greatest_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a)
    | ~ c_lessequals(V_x,V_z,T_a)
    | ~ c_lessequals(V_x,V_y,T_a) ) ).

cnf(cls_min__max_Ole__inf__iff_2,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a)
    | ~ c_lessequals(V_x,V_z,T_a)
    | ~ c_lessequals(V_x,V_y,T_a) ) ).

cnf(cls_min__max_Ole__infI_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_a,V_b,T_a),T_a)
    | ~ c_lessequals(V_x,V_b,T_a)
    | ~ c_lessequals(V_x,V_a,T_a) ) ).

cnf(cls_min__max_Oinf__le2_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_y,T_a) ) ).

cnf(cls_min__max_Oinf__le1_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_x,T_a) ) ).

cnf(cls_max__less__iff__conj_2,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a)
    | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_z,T_a) ) ).

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_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_cos__periodic__pi_0,axiom,
    c_Transcendental_Ocos(c_HOL_Oplus__class_Oplus(V_x,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Ocos(V_x),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_dvd__triv__right_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a) ) ).

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

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

cnf(cls_abs__prts_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a)
    | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ominus__class_Ominus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a,T_a),T_a) ) ).

cnf(cls_arctan_2,axiom,
    c_Transcendental_Otan(c_Transcendental_Oarctan(V_y)) = V_y ).

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_nonzero__minus__divide__right_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a)
    | V_b = c_HOL_Ozero__class_Ozero(T_a) ) ).

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

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

cnf(cls_min__less__iff__conj_2,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a)
    | ~ c_HOL_Oord__class_Oless(V_z,V_x,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_arctan__minus_0,axiom,
    c_Transcendental_Oarctan(c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Oarctan(V_x),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_min__max_Oinf__left__idem_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_Orderings_Oord__class_Omin(V_x,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a) = c_Orderings_Oord__class_Omin(V_x,V_y,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_norm__inverse_0,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | ~ class_RealVector_Oreal__normed__div__algebra(T_a)
    | c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oinverse__class_Oinverse(c_RealVector_Onorm__class_Onorm(V_a,T_a),tc_RealDef_Oreal) ) ).

cnf(cls_inverse__inverse__eq_0,axiom,
    ( ~ class_Ring__and__Field_Odivision__ring(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = V_a ) ).

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_inf__sup__distrib2_0,axiom,
    ( ~ class_Lattices_Odistrib__lattice(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),V_x,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_y,V_x,T_a),c_Lattices_Olower__semilattice__class_Oinf(V_z,V_x,T_a),T_a) ) ).

cnf(cls_inf__sup__distrib1_0,axiom,
    ( ~ class_Lattices_Odistrib__lattice(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,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_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_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_Osemiring__rules_I7_J_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ).

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

cnf(cls_add__sup__distrib__right_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add__join(T_a)
    | c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),V_c,T_a) = c_Lattices_Oupper__semilattice__class_Osup(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__sup__distrib__left_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add__join(T_a)
    | c_HOL_Oplus__class_Oplus(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_b,V_c,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) ) ).

cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I4_J_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_HOL_Oplus__class_Oplus(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_b,V_c,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) ) ).

cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I3_J_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),V_c,T_a) = c_Lattices_Oupper__semilattice__class_Osup(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_sup__idem_0,axiom,
    ( ~ class_Lattices_Oupper__semilattice(T_a)
    | c_Lattices_Oupper__semilattice__class_Osup(V_x,V_x,T_a) = V_x ) ).

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_comm__monoid__add_Omult__left__commute_0,axiom,
    ( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
    | c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) ) ).

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

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

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

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

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

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

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

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

cnf(cls_scaleR__conv__of__real_0,axiom,
    ( ~ class_RealVector_Oreal__algebra__1(T_a)
    | c_RealVector_OscaleR__class_OscaleR(V_r,V_x,T_a) = c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(V_r,T_a),V_x,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_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_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_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_mod__add__right__eq_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ).

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

cnf(cls_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_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_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_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_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_min__max_Oinf__sup__absorb_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_Orderings_Oord__class_Omin(V_x,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) = V_x ) ).

cnf(cls_inverse__le__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_Oone__class_Oone(T_a),V_x,T_a)
    | c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) ) ).

cnf(cls_diff__eq_0,axiom,
    ( ~ class_Lattices_Oboolean__algebra(T_a)
    | c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_HOL_Ouminus__class_Ouminus(V_y,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__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__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__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__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__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_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_sup__left__commute_0,axiom,
    ( ~ class_Lattices_Oupper__semilattice(T_a)
    | c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_z,T_a),T_a) ) ).

cnf(cls_sup__assoc_0,axiom,
    ( ~ class_Lattices_Oupper__semilattice(T_a)
    | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) ) ).

cnf(cls_inf__sup__aci_I7_J_0,axiom,
    ( ~ class_Lattices_Olattice(T_a)
    | c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_z,T_a),T_a) ) ).

cnf(cls_inf__sup__aci_I6_J_0,axiom,
    ( ~ class_Lattices_Olattice(T_a)
    | c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) ) ).

cnf(cls_minus__divide__divide_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_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) ) ).

cnf(cls_divide_Ominus_0,axiom,
    ( ~ class_RealVector_Oreal__normed__field(T_a)
    | c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) ) ).

cnf(cls_min__max_Oinf__left__commute_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_Orderings_Oord__class_Omin(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a) = c_Orderings_Oord__class_Omin(V_y,c_Orderings_Oord__class_Omin(V_x,V_z,T_a),T_a) ) ).

cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_c,T_a) = c_Lattices_Olower__semilattice__class_Oinf(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_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_HOL_Oplus__class_Oplus(V_a,c_Lattices_Olower__semilattice__class_Oinf(V_b,V_c,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) ) ).

cnf(cls_add__inf__distrib__left_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add__meet(T_a)
    | c_HOL_Oplus__class_Oplus(V_a,c_Lattices_Olower__semilattice__class_Oinf(V_b,V_c,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) ) ).

cnf(cls_add__inf__distrib__right_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add__meet(T_a)
    | c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_c,T_a) = c_Lattices_Olower__semilattice__class_Oinf(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_neg__0__le__iff__le_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ).

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

cnf(cls_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_min__max_Ole__iff__inf_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_Orderings_Oord__class_Omin(V_x,V_y,T_a) = V_x
    | ~ c_lessequals(V_x,V_y,T_a) ) ).

cnf(cls_min__max_Ole__iff__inf_1,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_Orderings_Oord__class_Omin(V_x,V_y,T_a) != V_x
    | c_lessequals(V_x,V_y,T_a) ) ).

cnf(cls_min__max_Oinf__absorb2_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_Orderings_Oord__class_Omin(V_x,V_y,T_a) = V_y
    | ~ c_lessequals(V_y,V_x,T_a) ) ).

cnf(cls_nonzero__abs__inverse_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(V_a,T_a),T_a)
    | V_a = c_HOL_Ozero__class_Ozero(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_inverse__positive__imp__positive_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),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_mult__le__prts_0,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(T_a)
    | c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a2,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_b2,T_a),T_a),c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a1,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_b2,T_a),T_a),T_a),c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a2,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_b1,T_a),T_a),T_a),c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a1,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_b1,T_a),T_a),T_a),T_a)
    | ~ c_lessequals(V_b,V_b2,T_a)
    | ~ c_lessequals(V_b1,V_b,T_a)
    | ~ c_lessequals(V_a,V_a2,T_a)
    | ~ c_lessequals(V_a1,V_a,T_a) ) ).

cnf(cls_min__max_Ole__iff__sup_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_Orderings_Oord__class_Omax(V_x,V_y,T_a) = V_y
    | ~ c_lessequals(V_x,V_y,T_a) ) ).

cnf(cls_min__max_Ole__iff__sup_1,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_Orderings_Oord__class_Omax(V_x,V_y,T_a) != V_y
    | c_lessequals(V_x,V_y,T_a) ) ).

cnf(cls_min__max_Osup__absorb1_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_Orderings_Oord__class_Omax(V_x,V_y,T_a) = V_x
    | ~ c_lessequals(V_y,V_x,T_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_nprt__neg_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_x,T_a),T_a) ) ).

cnf(cls_le__zero__iff__pprt__id_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a,T_a) = V_a
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_le__zero__iff__pprt__id_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a,T_a) != V_a
    | c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_inverse__less__imp__less_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(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_a,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ).

cnf(cls_less__imp__inverse__less_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,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(V_a,V_b,T_a) ) ).

cnf(cls_inverse__less__imp__less__neg_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | c_HOL_Oord__class_Oless(V_b,V_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_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ).

cnf(cls_less__imp__inverse__less__neg_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,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,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_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_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_powr__less__cancel__iff_1,axiom,
    ( c_HOL_Oord__class_Oless(c_Log_Opowr(V_x,V_a),c_Log_Opowr(V_x,V_b),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(V_a,V_b,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).

cnf(cls_powr__less__cancel__iff_0,axiom,
    ( c_HOL_Oord__class_Oless(V_a,V_b,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_Log_Opowr(V_x,V_a),c_Log_Opowr(V_x,V_b),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).

cnf(cls_powr__less__cancel_0,axiom,
    ( c_HOL_Oord__class_Oless(V_a,V_b,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_Log_Opowr(V_x,V_a),c_Log_Opowr(V_x,V_b),tc_RealDef_Oreal) ) ).

cnf(cls_powr__less__mono_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Log_Opowr(V_x,V_a),c_Log_Opowr(V_x,V_b),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(V_a,V_b,tc_RealDef_Oreal) ) ).

cnf(cls_inverse__nonnegative__iff__nonnegative_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_a,T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) ).

cnf(cls_inverse__nonnegative__iff__nonnegative_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_Oinverse(V_a,T_a),T_a)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_sup__eq__if_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_Lattices_Oupper__semilattice__class_Osup(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_inf__0__imp__0_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_powr__le__cancel__iff_1,axiom,
    ( c_lessequals(c_Log_Opowr(V_x,V_a),c_Log_Opowr(V_x,V_b),tc_RealDef_Oreal)
    | ~ c_lessequals(V_a,V_b,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).

cnf(cls_powr__le__cancel__iff_0,axiom,
    ( c_lessequals(V_a,V_b,tc_RealDef_Oreal)
    | ~ c_lessequals(c_Log_Opowr(V_x,V_a),c_Log_Opowr(V_x,V_b),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).

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_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_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_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_mod__mod__trivial_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a) ) ).

cnf(cls_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_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_powr__mult_0,axiom,
    ( c_Log_Opowr(c_HOL_Otimes__class_Otimes(V_x,V_y,tc_RealDef_Oreal),V_a) = c_HOL_Otimes__class_Otimes(c_Log_Opowr(V_x,V_a),c_Log_Opowr(V_y,V_a),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_powr__one__gt__zero__iff_1,axiom,
    ( c_Log_Opowr(V_x,c_HOL_Oone__class_Oone(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_powr__one__gt__zero__iff_0,axiom,
    ( c_Log_Opowr(V_x,c_HOL_Oone__class_Oone(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_arctan__monotone_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Transcendental_Oarctan(V_x),c_Transcendental_Oarctan(V_y),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_RealDef_Oreal) ) ).

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

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

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

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

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

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

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

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

cnf(cls_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_dvd__mult__cancel__left_2,axiom,
    ( ~ class_Ring__and__Field_Oidom(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ).

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

cnf(cls_real__add__less__0__iff_0,axiom,
    ( c_HOL_Oord__class_Oless(V_y,c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_x,V_y,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_real__add__less__0__iff_1,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_x,V_y,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ouminus__class_Ouminus(V_x,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_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_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_norm__minus__cancel_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | c_RealVector_Onorm__class_Onorm(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_RealVector_Onorm__class_Onorm(V_x,T_a) ) ).

cnf(cls_real__sqrt__minus_0,axiom,
    c_NthRoot_Osqrt(c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_NthRoot_Osqrt(V_x),tc_RealDef_Oreal) ).

cnf(cls_le__zero__iff__zero__pprt_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
    | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_le__zero__iff__zero__pprt_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

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_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_mult__ge__prts_0,axiom,
    ( ~ class_Ring__and__Field_Olordered__ring(T_a)
    | c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a1,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_b2,T_a),T_a),c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a2,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_b2,T_a),T_a),T_a),c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a1,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_b1,T_a),T_a),T_a),c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a2,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_b1,T_a),T_a),T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
    | ~ c_lessequals(V_b,V_b2,T_a)
    | ~ c_lessequals(V_b1,V_b,T_a)
    | ~ c_lessequals(V_a,V_a2,T_a)
    | ~ c_lessequals(V_a1,V_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_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_inverse__le__imp__le_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | c_lessequals(V_b,V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ).

cnf(cls_le__imp__inverse__le_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
    | ~ c_lessequals(V_a,V_b,T_a) ) ).

cnf(cls_inverse__le__imp__le__neg_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | c_lessequals(V_b,V_a,T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ).

cnf(cls_le__imp__inverse__le__neg_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_lessequals(V_a,V_b,T_a) ) ).

cnf(cls_real__mult__inverse__cancel_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_x,tc_RealDef_Oreal),V_y,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_x1,tc_RealDef_Oreal),V_u,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_x1,V_y,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_u,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x1,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).

cnf(cls_real__mult__inverse__cancel2_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_y,c_HOL_Oinverse__class_Oinverse(V_x,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_u,c_HOL_Oinverse__class_Oinverse(V_x1,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_x1,V_y,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_u,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x1,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).

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

cnf(cls_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_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_inf__absorb2_0,axiom,
    ( ~ class_Lattices_Olower__semilattice(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y
    | ~ c_lessequals(V_y,V_x,T_a) ) ).

cnf(cls_le__iff__inf_1,axiom,
    ( ~ class_Lattices_Olower__semilattice(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) != V_x
    | c_lessequals(V_x,V_y,T_a) ) ).

cnf(cls_le__iff__inf_0,axiom,
    ( ~ class_Lattices_Olower__semilattice(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_x
    | ~ c_lessequals(V_x,V_y,T_a) ) ).

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__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_one__le__inverse__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_x,T_a)
    | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) ) ).

cnf(cls_max__less__iff__conj_1,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_HOL_Oord__class_Oless(V_y,V_z,T_a)
    | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) ) ).

cnf(cls_max__less__iff__conj_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_HOL_Oord__class_Oless(V_x,V_z,T_a)
    | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) ) ).

cnf(cls_less__max__iff__disj_2,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a) ) ).

cnf(cls_less__max__iff__disj_1,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_z,V_x,T_a) ) ).

cnf(cls_min__max_Oless__supI2_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_HOL_Oord__class_Oless(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_b,T_a) ) ).

cnf(cls_min__max_Oless__supI1_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_HOL_Oord__class_Oless(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_a,T_a) ) ).

cnf(cls_inf__commute_0,axiom,
    ( ~ class_Lattices_Olower__semilattice(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,V_x,T_a) ) ).

cnf(cls_inf__sup__aci_I1_J_0,axiom,
    ( ~ class_Lattices_Olattice(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,V_x,T_a) ) ).

cnf(cls_min__max_Oinf__commute_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_Orderings_Oord__class_Omin(V_x,V_y,T_a) = c_Orderings_Oord__class_Omin(V_y,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_eq__neg__iff__add__eq__0_0,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

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

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

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

cnf(cls_real__add__eq__0__iff_1,axiom,
    c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(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_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_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_min__less__iff__disj_2,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a)
    | ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a) ) ).

cnf(cls_min__less__iff__disj_1,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,V_z,T_a) ) ).

cnf(cls_min__less__iff__conj_1,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_HOL_Oord__class_Oless(V_z,V_y,T_a)
    | ~ c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a) ) ).

cnf(cls_min__less__iff__conj_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_HOL_Oord__class_Oless(V_z,V_x,T_a)
    | ~ c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omin(V_x,V_y,T_a),T_a) ) ).

cnf(cls_min__max_Oless__infI2_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_a,V_b,T_a),V_x,T_a)
    | ~ c_HOL_Oord__class_Oless(V_b,V_x,T_a) ) ).

cnf(cls_min__max_Oless__infI1_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_a,V_b,T_a),V_x,T_a)
    | ~ c_HOL_Oord__class_Oless(V_a,V_x,T_a) ) ).

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_inverse__nonpositive__iff__nonpositive_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_Oinverse(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_inverse__nonpositive__iff__nonpositive_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_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

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__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_inverse__eq__1__iff_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oinverse__class_Oinverse(V_x,T_a) != c_HOL_Oone__class_Oone(T_a)
    | V_x = c_HOL_Oone__class_Oone(T_a) ) ).

cnf(cls_inverse__less__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_Oone__class_Oone(T_a),V_x,T_a)
    | c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a) ) ).

cnf(cls_powr__less__mono2_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Log_Opowr(V_x,V_a),c_Log_Opowr(V_y,V_a),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_x,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_a,tc_RealDef_Oreal) ) ).

cnf(cls_powr__less__mono2__neg_0,axiom,
    ( c_HOL_Oord__class_Oless(c_Log_Opowr(V_y,V_a),c_Log_Opowr(V_x,V_a),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_x,tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

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_abs__inverse_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_Oinverse(V_a,T_a),T_a) = c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(V_a,T_a),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_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_positive__imp__inverse__positive_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_Oinverse(V_a,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_inverse__positive__iff__positive_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_Oinverse(V_a,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).

cnf(cls_inverse__positive__iff__positive_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_a,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) ) ).

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

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

cnf(cls_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_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_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_inf__eq__neg__sup_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a),T_a) ) ).

cnf(cls_sup__commute_0,axiom,
    ( ~ class_Lattices_Oupper__semilattice(T_a)
    | c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,V_x,T_a) ) ).

cnf(cls_inf__sup__aci_I5_J_0,axiom,
    ( ~ class_Lattices_Olattice(T_a)
    | c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,V_x,T_a) ) ).

cnf(cls_neg__inf__eq__sup_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ).

cnf(cls_compl__inf_0,axiom,
    ( ~ class_Lattices_Oboolean__algebra(T_a)
    | c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(V_x,T_a),c_HOL_Ouminus__class_Ouminus(V_y,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_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_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_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_real__minus__mult__self__le_0,axiom,
    c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_u,V_u,tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),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_add__cancel__end_0,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(T_a)
    | c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) != V_y
    | V_x = c_HOL_Ouminus__class_Ouminus(V_z,T_a) ) ).

cnf(cls_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_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_sup__left__idem_0,axiom,
    ( ~ class_Lattices_Oupper__semilattice(T_a)
    | c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) ) ).

cnf(cls_inf__sup__aci_I8_J_0,axiom,
    ( ~ class_Lattices_Olattice(T_a)
    | c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) ) ).

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_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_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_abs__of__nonpos_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
    | c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a)
    | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_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_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_min__max_Osup__left__commute_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omax(V_y,V_z,T_a),T_a) = c_Orderings_Oord__class_Omax(V_y,c_Orderings_Oord__class_Omax(V_x,V_z,T_a),T_a) ) ).

cnf(cls_min__max_Osup__assoc_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_Orderings_Oord__class_Omax(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) = c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omax(V_y,V_z,T_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_nprt__le__zero_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_lessequals(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

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

cnf(cls_le__max__iff__disj_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(V_z,V_y,T_a)
    | c_lessequals(V_z,V_x,T_a)
    | ~ c_lessequals(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) ) ).

cnf(cls_powr__zero__eq__one_0,axiom,
    c_Log_Opowr(V_x,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_HOL_Oone__class_Oone(tc_RealDef_Oreal) ).

cnf(cls_min__max_Ole__infE_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(V_x,V_a,T_a)
    | ~ c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_a,V_b,T_a),T_a) ) ).

cnf(cls_min__max_Ole__infE_1,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(V_x,V_b,T_a)
    | ~ c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_a,V_b,T_a),T_a) ) ).

cnf(cls_min__max_Ole__infI1_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(c_Orderings_Oord__class_Omin(V_a,V_b,T_a),V_x,T_a)
    | ~ c_lessequals(V_a,V_x,T_a) ) ).

cnf(cls_min__max_Ole__infI2_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(c_Orderings_Oord__class_Omin(V_a,V_b,T_a),V_x,T_a)
    | ~ c_lessequals(V_b,V_x,T_a) ) ).

cnf(cls_min__le__iff__disj_1,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a)
    | ~ c_lessequals(V_x,V_z,T_a) ) ).

cnf(cls_min__le__iff__disj_2,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a)
    | ~ c_lessequals(V_y,V_z,T_a) ) ).

cnf(cls_min__max_Ole__inf__iff_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(V_x,V_y,T_a)
    | ~ c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a) ) ).

cnf(cls_min__max_Ole__inf__iff_1,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(V_x,V_z,T_a)
    | ~ c_lessequals(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),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_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_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_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_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_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_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_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_inverse__le__1__iff_2,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_lessequals(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a)
    | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),V_x,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_abs__ge__minus__self_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
    | c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ) ).

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_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_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__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__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_min__le__iff__disj_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(V_y,V_z,T_a)
    | c_lessequals(V_x,V_z,T_a)
    | ~ c_lessequals(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,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_mod__add__cong_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a)
    | c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a_H,V_b_H,T_a),V_c,T_a) ) ).

cnf(cls_min__max_Ole__supE_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(V_a,V_x,T_a)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(V_a,V_b,T_a),V_x,T_a) ) ).

cnf(cls_min__max_Ole__supE_1,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(V_b,V_x,T_a)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(V_a,V_b,T_a),V_x,T_a) ) ).

cnf(cls_min__max_Ole__supI1_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a)
    | ~ c_lessequals(V_x,V_a,T_a) ) ).

cnf(cls_min__max_Ole__supI2_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(V_x,c_Orderings_Oord__class_Omax(V_a,V_b,T_a),T_a)
    | ~ c_lessequals(V_x,V_b,T_a) ) ).

cnf(cls_le__max__iff__disj_1,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a)
    | ~ c_lessequals(V_z,V_x,T_a) ) ).

cnf(cls_le__max__iff__disj_2,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a)
    | ~ c_lessequals(V_z,V_y,T_a) ) ).

cnf(cls_min__max_Ole__sup__iff_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(V_x,V_z,T_a)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) ) ).

cnf(cls_min__max_Ole__sup__iff_1,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(V_y,V_z,T_a)
    | ~ c_lessequals(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) ) ).

cnf(cls_less__max__iff__disj_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_HOL_Oord__class_Oless(V_z,V_y,T_a)
    | c_HOL_Oord__class_Oless(V_z,V_x,T_a)
    | ~ c_HOL_Oord__class_Oless(V_z,c_Orderings_Oord__class_Omax(V_x,V_y,T_a),T_a) ) ).

cnf(cls_real__add__eq__0__iff_0,axiom,
    ( c_HOL_Oplus__class_Oplus(V_x,V_y,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | V_y = c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal) ) ).

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

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

cnf(cls_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_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_min__less__iff__disj_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_HOL_Oord__class_Oless(V_y,V_z,T_a)
    | c_HOL_Oord__class_Oless(V_x,V_z,T_a)
    | ~ c_HOL_Oord__class_Oless(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) ) ).

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

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

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

cnf(cls_nonzero__inverse__minus__eq_0,axiom,
    ( ~ class_Ring__and__Field_Odivision__ring(T_a)
    | c_HOL_Oinverse__class_Oinverse(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_powr__add_0,axiom,
    c_Log_Opowr(V_x,c_HOL_Oplus__class_Oplus(V_a,V_b,tc_RealDef_Oreal)) = c_HOL_Otimes__class_Otimes(c_Log_Opowr(V_x,V_a),c_Log_Opowr(V_x,V_b),tc_RealDef_Oreal) ).

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

cnf(cls_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_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_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_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_powr__powr_0,axiom,
    c_Log_Opowr(c_Log_Opowr(V_x,V_a),V_b) = c_Log_Opowr(V_x,c_HOL_Otimes__class_Otimes(V_a,V_b,tc_RealDef_Oreal)) ).

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_Bseq__inverse__lemma_0,axiom,
    ( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
    | c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a),c_HOL_Oinverse__class_Oinverse(V_r,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_r,tc_RealDef_Oreal)
    | ~ c_lessequals(V_r,c_RealVector_Onorm__class_Onorm(V_x,T_a),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_mod__by__1_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_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_one__le__inverse__iff_1,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_lessequals(V_x,c_HOL_Oone__class_Oone(T_a),T_a)
    | ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a) ) ).

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

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

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

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

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

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

cnf(cls_real__less__def_1,axiom,
    ~ c_HOL_Oord__class_Oless(V_x,V_x,tc_RealDef_Oreal) ).

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

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

cnf(cls_sup__inf__absorb_0,axiom,
    ( ~ class_Lattices_Olattice(T_a)
    | c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a) = V_x ) ).

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_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_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_inverse__negative__iff__negative_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_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_inverse__negative__iff__negative_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_Oinverse(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_negative__imp__inverse__negative_0,axiom,
    ( ~ class_Ring__and__Field_Oordered__field(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Oinverse(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_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_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_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_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_le__iff__sup_0,axiom,
    ( ~ class_Lattices_Oupper__semilattice(T_a)
    | c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = V_y
    | ~ c_lessequals(V_x,V_y,T_a) ) ).

cnf(cls_le__iff__sup_1,axiom,
    ( ~ class_Lattices_Oupper__semilattice(T_a)
    | c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) != V_y
    | c_lessequals(V_x,V_y,T_a) ) ).

cnf(cls_sup__absorb1_0,axiom,
    ( ~ class_Lattices_Oupper__semilattice(T_a)
    | c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = V_x
    | ~ c_lessequals(V_y,V_x,T_a) ) ).

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

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

cnf(cls_real__inverse__gt__one_0,axiom,
    ( c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oinverse__class_Oinverse(V_x,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_inverse__eq__1__iff_1,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) ).

cnf(cls_one__less__inverse__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(c_HOL_Oone__class_Oone(T_a),c_HOL_Oinverse__class_Oinverse(V_x,T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Oone__class_Oone(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ).

cnf(cls_inverse__1_0,axiom,
    ( ~ class_Ring__and__Field_Odivision__ring(T_a)
    | c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(T_a),T_a) = c_HOL_Oone__class_Oone(T_a) ) ).

cnf(cls_of__real__add_0,axiom,
    ( ~ class_RealVector_Oreal__algebra__1(T_a)
    | c_RealVector_Oof__real(c_HOL_Oplus__class_Oplus(V_x,V_y,tc_RealDef_Oreal),T_a) = c_HOL_Oplus__class_Oplus(c_RealVector_Oof__real(V_x,T_a),c_RealVector_Oof__real(V_y,T_a),T_a) ) ).

cnf(cls_of__real_Oadd_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | ~ class_RealVector_Oreal__algebra__1(T_a)
    | c_RealVector_Oof__real(c_HOL_Oplus__class_Oplus(V_x,V_y,tc_RealDef_Oreal),T_a) = c_HOL_Oplus__class_Oplus(c_RealVector_Oof__real(V_x,T_a),c_RealVector_Oof__real(V_y,T_a),T_a) ) ).

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

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

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

cnf(cls_real__0__le__add__iff_0,axiom,
    ( c_lessequals(c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal),V_y,tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).

cnf(cls_real__0__le__add__iff_1,axiom,
    ( c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(V_x,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal)
    | ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal),V_y,tc_RealDef_Oreal) ) ).

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

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

cnf(cls_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_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_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_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_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_id__apply_0,axiom,
    c_Fun_Oid(V_x,T_a) = V_x ).

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_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_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_minus__equation__iff_1,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = V_b ) ).

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

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

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

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

cnf(cls_add__less__le__mono_0,axiom,
    ( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
    | c_HOL_Oord__class_Oless(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_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_minus__less__iff_1,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a) ) ).

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

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

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

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

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

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

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

cnf(cls_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_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_neg__equal__zero_1,axiom,
    ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a)
    | c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

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

cnf(cls_inverse__zero__imp__zero_0,axiom,
    ( ~ class_Ring__and__Field_Odivision__ring(T_a)
    | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_inverse__nonzero__iff__nonzero_0,axiom,
    ( ~ class_Ring__and__Field_Odivision__ring(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

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

cnf(cls_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_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__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__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_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__right_Ozero_0,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_HOL_Otimes__class_Otimes(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_mult_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_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__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_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_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_dvd__0__right_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

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

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

cnf(cls_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_nonzero__inverse__inverse__eq_0,axiom,
    ( ~ class_Ring__and__Field_Odivision__ring(T_a)
    | c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a) = V_a
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

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

cnf(cls_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_neg__equal__zero_0,axiom,
    ( ~ class_OrderedGroup_Oordered__ab__group__add(T_a)
    | c_HOL_Ouminus__class_Ouminus(V_a,T_a) != V_a
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_inverse__zero_0,axiom,
    ( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_inverse__nonzero__iff__nonzero_1,axiom,
    ( ~ class_Ring__and__Field_Odivision__ring(T_a)
    | ~ class_Ring__and__Field_Odivision__by__zero(T_a)
    | c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_nonzero__inverse__eq__imp__eq_0,axiom,
    ( ~ class_Ring__and__Field_Odivision__ring(T_a)
    | c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Oinverse__class_Oinverse(V_b,T_a)
    | V_a = V_b
    | V_b = c_HOL_Ozero__class_Ozero(T_a)
    | V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_nprt__0_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

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

cnf(cls_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_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_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_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_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_pprt__0_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

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

cnf(cls_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_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_neg__0__equal__iff__equal_0,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Ouminus__class_Ouminus(V_a,T_a)
    | c_HOL_Ozero__class_Ozero(T_a) = V_a ) ).

cnf(cls_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__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_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_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_division__ring__inverse__diff_0,axiom,
    ( ~ class_Ring__and__Field_Odivision__ring(T_a)
    | c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a)
    | V_b = c_HOL_Ozero__class_Ozero(T_a)
    | V_a = c_HOL_Ozero__class_Ozero(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_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_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_nonzero__of__real__inverse_0,axiom,
    ( ~ class_RealVector_Oreal__div__algebra(T_a)
    | c_RealVector_Oof__real(c_HOL_Oinverse__class_Oinverse(V_x,tc_RealDef_Oreal),T_a) = c_HOL_Oinverse__class_Oinverse(c_RealVector_Oof__real(V_x,T_a),T_a)
    | V_x = c_HOL_Ozero__class_Ozero(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_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_cos__minus_0,axiom,
    c_Transcendental_Ocos(c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal)) = c_Transcendental_Ocos(V_x) ).

cnf(cls_eq__equals_0,axiom,
    ( ~ class_HOL_Oeq(T_a)
    | V_x = V_y
    | ~ c_HOL_Oeq__class_Oeq(V_x,V_y,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__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__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_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_powr__ge__pzero_0,axiom,
    c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Log_Opowr(V_x,V_y),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_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_minus__mult__commute_0,axiom,
    ( ~ class_Ring__and__Field_Oring(T_a)
    | c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ).

cnf(cls_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_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_divide__inverse_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ).

cnf(cls_class__fieldgb_Odivide__inverse_0,axiom,
    ( ~ class_Ring__and__Field_Ofield(T_a)
    | ~ class_Int_Onumber__ring(T_a)
    | c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,T_a),T_a) ) ).

cnf(cls_inf__sup__aci_I4_J_0,axiom,
    ( ~ class_Lattices_Olattice(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) ) ).

cnf(cls_inf__left__idem_0,axiom,
    ( ~ class_Lattices_Olower__semilattice(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) ) ).

cnf(cls_zero__le__iff__nprt__id_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a,T_a) = V_a
    | ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

cnf(cls_zero__le__iff__nprt__id_1,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a,T_a) != V_a
    | c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).

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

cnf(cls_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_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_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_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__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_mult__dvd__mono_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_c,V_d,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ).

cnf(cls_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_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_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_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_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_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_inf__idem_0,axiom,
    ( ~ class_Lattices_Olower__semilattice(T_a)
    | c_Lattices_Olower__semilattice__class_Oinf(V_x,V_x,T_a) = V_x ) ).

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_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_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__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__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__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__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__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_order__eq__refl_0,axiom,
    ( ~ class_Orderings_Opreorder(T_a)
    | c_lessequals(V_x,V_x,T_a) ) ).

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

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

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

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

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

cnf(cls_le__add__right__mono_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_lessequals(V_a,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_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_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_xt1_I8_J_0,axiom,
    ( ~ class_Orderings_Oorder(T_a)
    | c_HOL_Oord__class_Oless(V_z,V_x,T_a)
    | ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a)
    | ~ c_lessequals(V_y,V_x,T_a) ) ).

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

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

cnf(cls_inverse__less__1__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(c_HOL_Oinverse__class_Oinverse(V_x,T_a),c_HOL_Oone__class_Oone(T_a),T_a)
    | ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_x,T_a) ) ).

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

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

cnf(cls_powr__one__eq__one_0,axiom,
    c_Log_Opowr(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_a) = c_HOL_Oone__class_Oone(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_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_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_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_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__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__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_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_real__mult__is__one_2,axiom,
    c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Oone__class_Oone(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_min__max_Odistrib__sup__le_0,axiom,
    ( ~ class_Orderings_Olinorder(T_a)
    | c_lessequals(c_Orderings_Oord__class_Omax(V_x,c_Orderings_Oord__class_Omin(V_y,V_z,T_a),T_a),c_Orderings_Oord__class_Omin(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),c_Orderings_Oord__class_Omax(V_x,V_z,T_a),T_a),T_a) ) ).

cnf(cls_sup__eq__neg__inf_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
    | c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a),T_a) ) ).

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

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

cnf(cls_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_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_mod__mult__mult1_0,axiom,
    ( ~ class_Divides_Osemiring__div(T_a)
    | c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_c,c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a) ) ).

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

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

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

cnf(cls_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_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_real__sqrt__inverse_0,axiom,
    c_NthRoot_Osqrt(c_HOL_Oinverse__class_Oinverse(V_x,tc_RealDef_Oreal)) = c_HOL_Oinverse__class_Oinverse(c_NthRoot_Osqrt(V_x),tc_RealDef_Oreal) ).

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

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

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

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

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

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

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

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

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

cnf(cls_powr__not__zero_0,axiom,
    c_Log_Opowr(V_x,V_a) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ).

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_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__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_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_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_INVERSE__ZERO_0,axiom,
    c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ).

cnf(cls_arctan__zero__zero_0,axiom,
    c_Transcendental_Oarctan(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_Lim_Ominus__diff__minus_0,axiom,
    ( ~ class_OrderedGroup_Oab__group__add(T_a)
    | c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) ) ).

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

cnf(cls_min__diff__distrib__left_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omin(V_x,V_y,T_a),V_z,T_a) = c_Orderings_Oord__class_Omin(c_HOL_Ominus__class_Ominus(V_x,V_z,T_a),c_HOL_Ominus__class_Ominus(V_y,V_z,T_a),T_a) ) ).

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

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

cnf(cls_max__diff__distrib__left_0,axiom,
    ( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
    | c_HOL_Ominus__class_Ominus(c_Orderings_Oord__class_Omax(V_x,V_y,T_a),V_z,T_a) = c_Orderings_Oord__class_Omax(c_HOL_Ominus__class_Ominus(V_x,V_z,T_a),c_HOL_Ominus__class_Ominus(V_y,V_z,T_a),T_a) ) ).

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

cnf(cls_abs__minus__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_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_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_dvd__diff_0,axiom,
    ( ~ class_Ring__and__Field_Ocomm__ring__1(T_a)
    | c_Ring__and__Field_Odvd__class_Odvd(V_x,c_HOL_Ominus__class_Ominus(V_y,V_z,T_a),T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,T_a)
    | ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) ) ).

cnf(cls_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_mult__right_Odiff_0,axiom,
    ( ~ class_RealVector_Oreal__normed__algebra(T_a)
    | c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Ominus__class_Ominus(V_x,V_y,T_a),T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),c_HOL_Otimes__class_Otimes(V_xa,V_y,T_a),T_a) ) ).

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

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

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

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

cnf(cls_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_add__diff__cancel_0,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = V_a ) ).

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

cnf(cls_pprt__def__raw_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(t_a)
    | c_OrderedGroup_Olordered__ab__group__add__class_Opprt(v_x,t_a) = c_Lattices_Oupper__semilattice__class_Osup(v_x,c_HOL_Ozero__class_Ozero(t_a),t_a) ) ).

cnf(cls_nprt__def__raw_0,axiom,
    ( ~ class_OrderedGroup_Olordered__ab__group__add(t_a)
    | c_OrderedGroup_Olordered__ab__group__add__class_Onprt(v_x,t_a) = c_Lattices_Olower__semilattice__class_Oinf(v_x,c_HOL_Ozero__class_Ozero(t_a),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_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_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_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__periodic__pi2_0,axiom,
    c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(c_Transcendental_Opi,V_x,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(V_x),tc_RealDef_Oreal) ).

cnf(cls_sin__periodic__pi_0,axiom,
    c_Transcendental_Osin(c_HOL_Oplus__class_Oplus(V_x,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(V_x),tc_RealDef_Oreal) ).

cnf(cls_calculation_I2_J_0,axiom,
    ( c_Transcendental_Ocos(v_x) != c_HOL_Oone__class_Oone(tc_RealDef_Oreal)
    | v_x != c_Transcendental_Opi ) ).

cnf(cls_eq__diff__eq_H_0,axiom,
    V_y = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_y,V_z,tc_RealDef_Oreal),V_z,tc_RealDef_Oreal) ).

cnf(cls_eq__diff__eq_H_1,axiom,
    V_x = c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_x,V_z,tc_RealDef_Oreal),V_z,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_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_sin__minus_0,axiom,
    c_Transcendental_Osin(c_HOL_Ouminus__class_Ouminus(V_x,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(V_x),tc_RealDef_Oreal) ).

cnf(cls_id__def_0,axiom,
    c_Fun_Oid(v_x,t_a) = v_x ).

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_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_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_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_of__real__eq__0__iff_0,axiom,
    ( ~ class_RealVector_Oreal__algebra__1(T_a)
    | c_RealVector_Oof__real(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a)
    | V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).

cnf(cls_of__real__0_0,axiom,
    ( ~ class_RealVector_Oreal__algebra__1(T_a)
    | c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).

cnf(cls_of__real_Ozero_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | ~ class_RealVector_Oreal__algebra__1(T_a)
    | c_RealVector_Oof__real(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),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_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_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_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_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_group__add__class_Odiff__0_0,axiom,
    ( ~ class_OrderedGroup_Ogroup__add(T_a)
    | c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a) ) ).

cnf(cls_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_pi__ge__zero_0,axiom,
    c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi,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_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_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__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_eq__real__def_0,axiom,
    ( c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | ~ c_HOL_Oeq__class_Oeq(V_x,V_y,tc_RealDef_Oreal) ) ).

cnf(cls_eq__real__def_1,axiom,
    ( c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal) != c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
    | c_HOL_Oeq__class_Oeq(V_x,V_y,tc_RealDef_Oreal) ) ).

cnf(cls_of__real_Odiff_0,axiom,
    ( ~ class_RealVector_Oreal__normed__vector(T_a)
    | ~ class_RealVector_Oreal__algebra__1(T_a)
    | c_RealVector_Oof__real(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal),T_a) = c_HOL_Ominus__class_Ominus(c_RealVector_Oof__real(V_x,T_a),c_RealVector_Oof__real(V_y,T_a),T_a) ) ).

cnf(cls_of__real__diff_0,axiom,
    ( ~ class_RealVector_Oreal__algebra__1(T_a)
    | c_RealVector_Oof__real(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal),T_a) = c_HOL_Ominus__class_Ominus(c_RealVector_Oof__real(V_x,T_a),c_RealVector_Oof__real(V_y,T_a),T_a) ) ).

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_0_0,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_x,tc_RealDef_Oreal) ).

cnf(cls_pi1_0,axiom,
    c_HOL_Oord__class_Oless(c_Transcendental_Opi,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_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__periodic__pi__diff_0,axiom,
    c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(V_x,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ouminus__class_Ouminus(c_Transcendental_Osin(V_x),tc_RealDef_Oreal) ).

cnf(cls_calculation_I1_J_0,axiom,
    ( c_Transcendental_Osin(v_x) != c_HOL_Ozero__class_Ozero(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_pi__neq__zero_0,axiom,
    c_Transcendental_Opi != c_HOL_Ozero__class_Ozero(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_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_sin__pi_0,axiom,
    c_Transcendental_Osin(c_Transcendental_Opi) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ).

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_CHAINED_0,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal),c_Transcendental_Opi,tc_RealDef_Oreal) ).

cnf(cls_CHAINED_0_01,axiom,
    c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal),tc_RealDef_Oreal) ).

cnf(cls_conjecture_0,negated_conjecture,
    c_Transcendental_Osin(c_HOL_Ominus__class_Ominus(v_x,c_Transcendental_Opi,tc_RealDef_Oreal)) = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ).

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__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__Lattices_Oupper__semilattice,axiom,
    class_Lattices_Oupper__semilattice(tc_nat) ).

cnf(clsarity_nat__Lattices_Olower__semilattice,axiom,
    class_Lattices_Olower__semilattice(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__Lattices_Odistrib__lattice,axiom,
    class_Lattices_Odistrib__lattice(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__Divides_Osemiring__div,axiom,
    class_Divides_Osemiring__div(tc_nat) ).

cnf(clsarity_nat__Ring__and__Field_Odvd,axiom,
    class_Ring__and__Field_Odvd(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__Lattices_Olattice,axiom,
    class_Lattices_Olattice(tc_nat) ).

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

cnf(clsarity_nat__HOL_Oeq,axiom,
    class_HOL_Oeq(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__OrderedGroup_Olordered__ab__group__add__meet,axiom,
    class_OrderedGroup_Olordered__ab__group__add__meet(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__join,axiom,
    class_OrderedGroup_Olordered__ab__group__add__join(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_Oordered__ab__group__add,axiom,
    class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal) ).

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

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

cnf(clsarity_RealDef__Oreal__Ring__and__Field_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__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_Odivision__ring,axiom,
    class_Ring__and__Field_Odivision__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__RealVector_Oreal__div__algebra,axiom,
    class_RealVector_Oreal__div__algebra(tc_RealDef_Oreal) ).

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

cnf(clsarity_RealDef__Oreal__Lattices_Oupper__semilattice,axiom,
    class_Lattices_Oupper__semilattice(tc_RealDef_Oreal) ).

cnf(clsarity_RealDef__Oreal__Lattices_Olower__semilattice,axiom,
    class_Lattices_Olower__semilattice(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__Lattices_Odistrib__lattice,axiom,
    class_Lattices_Odistrib__lattice(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_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__Ring__and__Field_Odvd,axiom,
    class_Ring__and__Field_Odvd(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__Lattices_Olattice,axiom,
    class_Lattices_Olattice(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__HOL_Oeq,axiom,
    class_HOL_Oeq(tc_RealDef_Oreal) ).

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