TPTP Problem File: ALG409-1.p
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- Solve Problem
%------------------------------------------------------------------------------
% File : ALG409-1 : TPTP v8.2.0. Released v4.1.0.
% Domain : General Algebra
% Problem : Fundamental theorem of algebra 0745_66
% Version : Especial.
% English :
% Refs : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe
% : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% Source : [Nip10]
% Names : Fundamental_Theorem_Algebra-0745_66 [Nip10]
% Status : Unsatisfiable
% Rating : 0.40 v8.2.0, 0.38 v8.1.0, 0.42 v7.5.0, 0.47 v7.3.0, 0.33 v7.0.0, 0.53 v6.4.0, 0.47 v6.3.0, 0.45 v6.2.0, 0.50 v6.1.0, 0.57 v6.0.0, 0.60 v5.5.0, 0.80 v5.3.0, 0.78 v5.2.0, 0.81 v5.1.0, 0.82 v5.0.0, 0.71 v4.1.0
% Syntax : Number of clauses : 893 ( 189 unt; 81 nHn; 584 RR)
% Number of literals : 2221 ( 474 equ;1264 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 9 ( 1 avg)
% Number of predicates : 72 ( 71 usr; 0 prp; 1-3 aty)
% Number of functors : 27 ( 27 usr; 9 con; 0-3 aty)
% Number of variables : 2051 ( 51 sgn)
% SPC : CNF_UNS_RFO_SEQ_NHN
% Comments :
%------------------------------------------------------------------------------
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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_power__0__Suc_0,axiom,
( ~ class_Ring__and__Field_Osemiring__0(T_a)
| ~ class_Power_Opower(T_a)
| c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Suc(V_n),T_a) = c_HOL_Ozero__class_Ozero(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_abs__le__interval__iff_1,axiom,
( c_lessequals(V_x,V_r,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_x,tc_RealDef_Oreal),V_r,tc_RealDef_Oreal) ) ).
cnf(cls_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_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_Suc__eq__plus1__left_0,axiom,
c_Suc(V_n) = c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_nat),V_n,tc_nat) ).
cnf(cls_Suc__eq__plus1_0,axiom,
c_Suc(V_n) = c_HOL_Oplus__class_Oplus(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat) ).
cnf(cls_neg__less__0__iff__less_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_neg__less__0__iff__less_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_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_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_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_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_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_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_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_abs__eq__0_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_comm__monoid__add_Omult__left__commute_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) ) ).
cnf(cls_comm__monoid__add_Omult__assoc_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ).
cnf(cls_class__semiring_Oadd__a_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),V_z,T_a) ) ).
cnf(cls_nat__add__assoc_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),V_k,tc_nat) = c_HOL_Oplus__class_Oplus(V_m,c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat),tc_nat) ).
cnf(cls_nat__add__left__commute_0,axiom,
c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(V_y,c_HOL_Oplus__class_Oplus(V_x,V_z,tc_nat),tc_nat) ).
cnf(cls_add__cancel__21_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_y,c_HOL_Oplus__class_Oplus(V_x,V_z,T_a),T_a) ) ).
cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom,
( ~ class_OrderedGroup_Oab__semigroup__add(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I25_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_d,T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I23_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_b,T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I22_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_c,c_HOL_Oplus__class_Oplus(V_a,V_d,T_a),T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I21_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ).
cnf(cls_neg__0__equal__iff__equal_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Ouminus__class_Ouminus(V_a,T_a)
| c_HOL_Ozero__class_Ozero(T_a) = V_a ) ).
cnf(cls_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_norm__triangle__ineq3_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(V_a,T_a),c_RealVector_Onorm__class_Onorm(V_b,T_a),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a),tc_RealDef_Oreal) ) ).
cnf(cls_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_power__mono_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_lessequals(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(V_a,V_b,T_a) ) ).
cnf(cls_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_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_power__le__zero__eq_3,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| V_x = c_HOL_Ozero__class_Ozero(T_a)
| c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_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_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_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_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_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_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_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_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_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_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_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__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_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_neg__equal__iff__equal_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| c_HOL_Ouminus__class_Ouminus(V_a,T_a) != c_HOL_Ouminus__class_Ouminus(V_b,T_a)
| V_a = V_b ) ).
cnf(cls_compl__eq__compl__iff_0,axiom,
( ~ class_Lattices_Oboolean__algebra(T_a)
| c_HOL_Ouminus__class_Ouminus(V_x,T_a) != c_HOL_Ouminus__class_Ouminus(V_y,T_a)
| V_x = V_y ) ).
cnf(cls_real__le__antisym_0,axiom,
( V_z = V_w
| ~ c_lessequals(V_w,V_z,tc_RealDef_Oreal)
| ~ c_lessequals(V_z,V_w,tc_RealDef_Oreal) ) ).
cnf(cls_order__antisym_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| V_x = V_y
| ~ c_lessequals(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_order__eq__iff_2,axiom,
( ~ class_Orderings_Oorder(T_a)
| V_x = V_y
| ~ c_lessequals(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_order__antisym__conv_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| V_x = V_y
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_x,T_a) ) ).
cnf(cls_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_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_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__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_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__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_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_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_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_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__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__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__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__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_abs__eq__mult_0,axiom,
( ~ class_Ring__and__Field_Opordered__ring__abs(T_a)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_abs__eq__mult_1,axiom,
( ~ class_Ring__and__Field_Opordered__ring__abs(T_a)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_abs__eq__mult_2,axiom,
( ~ class_Ring__and__Field_Opordered__ring__abs(T_a)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_abs__eq__mult_3,axiom,
( ~ class_Ring__and__Field_Opordered__ring__abs(T_a)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_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_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_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_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_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_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_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_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_mult__le__0__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_mult__le__0__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_mult__le__0__iff_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_mult__le__0__iff_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_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_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_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_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_cnj_Oadd_0,axiom,
c_Complex_Ocnj(c_HOL_Oplus__class_Oplus(V_x,V_y,tc_Complex_Ocomplex)) = c_HOL_Oplus__class_Oplus(c_Complex_Ocnj(V_x),c_Complex_Ocnj(V_y),tc_Complex_Ocomplex) ).
cnf(cls_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_ath_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),V_t,tc_RealDef_Oreal),tc_RealDef_Oreal),V_x,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(V_t,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(V_x,V_t,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ) ).
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_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_n__not__Suc__n_0,axiom,
V_n != c_Suc(V_n) ).
cnf(cls_Suc__n__not__n_0,axiom,
c_Suc(V_n) != V_n ).
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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_power__inject__base_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a) != c_Power_Opower__class_Opower(V_b,c_Suc(V_n),T_a)
| V_a = V_b
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_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_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_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_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_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_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__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_realpow__Suc__le__self_0,axiom,
( c_lessequals(c_Power_Opower__class_Opower(V_r,c_Suc(V_n),tc_RealDef_Oreal),V_r,tc_RealDef_Oreal)
| ~ c_lessequals(V_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),V_r,tc_RealDef_Oreal) ) ).
cnf(cls_real__sum__square__gt__zero2_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| V_y = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
cnf(cls_real__sum__square__gt__zero_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_y,V_y,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal) ) ).
cnf(cls_real__vector_Oscale__left__distrib_0,axiom,
( ~ class_RealVector_Oreal__vector(T_a)
| c_RealVector_OscaleR__class_OscaleR(c_HOL_Oplus__class_Oplus(V_a,V_b,tc_RealDef_Oreal),V_x,T_a) = c_HOL_Oplus__class_Oplus(c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),c_RealVector_OscaleR__class_OscaleR(V_b,V_x,T_a),T_a) ) ).
cnf(cls_scaleR__right_Oadd_0,axiom,
( ~ class_RealVector_Oreal__vector(T_a)
| c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),c_RealVector_OscaleR__class_OscaleR(V_a,V_y,T_a),T_a) ) ).
cnf(cls_scaleR_Oadd__right_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Oplus__class_Oplus(V_b,V_b_H,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_RealVector_OscaleR__class_OscaleR(V_a,V_b,T_a),c_RealVector_OscaleR__class_OscaleR(V_a,V_b_H,T_a),T_a) ) ).
cnf(cls_scaleR__left_Oadd_0,axiom,
( ~ class_RealVector_Oreal__vector(T_a)
| c_RealVector_OscaleR__class_OscaleR(c_HOL_Oplus__class_Oplus(V_x,V_y,tc_RealDef_Oreal),V_xa,T_a) = c_HOL_Oplus__class_Oplus(c_RealVector_OscaleR__class_OscaleR(V_x,V_xa,T_a),c_RealVector_OscaleR__class_OscaleR(V_y,V_xa,T_a),T_a) ) ).
cnf(cls_scaleR_Oadd__left_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_RealVector_OscaleR__class_OscaleR(c_HOL_Oplus__class_Oplus(V_a,V_a_H,tc_RealDef_Oreal),V_b,T_a) = c_HOL_Oplus__class_Oplus(c_RealVector_OscaleR__class_OscaleR(V_a,V_b,T_a),c_RealVector_OscaleR__class_OscaleR(V_a_H,V_b,T_a),T_a) ) ).
cnf(cls_complex__mod__triangle__ineq2_0,axiom,
c_lessequals(c_HOL_Ominus__class_Ominus(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(V_b,V_a,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(V_b,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_a,tc_Complex_Ocomplex),tc_RealDef_Oreal) ).
cnf(cls_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_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_mult__smult__right_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_HOL_Otimes__class_Otimes(V_p,c_Polynomial_Osmult(V_a,V_q,T_a),tc_Polynomial_Opoly(T_a)) = c_Polynomial_Osmult(V_a,c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) ) ).
cnf(cls_mult__smult__left_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(V_a,V_p,T_a),V_q,tc_Polynomial_Opoly(T_a)) = c_Polynomial_Osmult(V_a,c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) ) ).
cnf(cls_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_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_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_m_I1_J_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal) ).
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_cnj_Ominus_0,axiom,
c_Complex_Ocnj(c_HOL_Ouminus__class_Ouminus(V_x,tc_Complex_Ocomplex)) = c_HOL_Ouminus__class_Ouminus(c_Complex_Ocnj(V_x),tc_Complex_Ocomplex) ).
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_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_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_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_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__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_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_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_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_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_add__strict__right__mono_0,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_add__less__cancel__right_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_add__less__cancel__right_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ).
cnf(cls_add__strict__left__mono_0,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_add__less__cancel__left_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_add__less__cancel__left_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a) ) ).
cnf(cls_order__less__imp__le_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| c_lessequals(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_order__le__less_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_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_less__le__not__le_2,axiom,
( ~ class_Orderings_Opreorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| c_lessequals(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_abs__less__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ).
cnf(cls_xt1_I11_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| V_a = V_b
| ~ c_lessequals(V_b,V_a,T_a) ) ).
cnf(cls_xt1_I12_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| V_a = V_b ) ).
cnf(cls_linorder__antisym__conv2_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| V_x = V_y
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_linorder__antisym__conv1_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| V_x = V_y
| ~ c_lessequals(V_x,V_y,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_order__neq__le__trans_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| V_a = V_b ) ).
cnf(cls_order__le__neq__trans_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| V_a = V_b
| ~ c_lessequals(V_a,V_b,T_a) ) ).
cnf(cls_order__le__less_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| V_x = V_y
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_order__less__le_2,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| V_x = V_y
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_less__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_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_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_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_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_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_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_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_smult__monom_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_Polynomial_Osmult(V_a,c_Polynomial_Omonom(V_b,V_n,T_a),T_a) = c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_n,T_a) ) ).
cnf(cls_smult__1__left_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Polynomial_Osmult(c_HOL_Oone__class_Oone(T_a),V_p,T_a) = V_p ) ).
cnf(cls_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_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_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_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_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_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_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_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_nat__add__right__cancel_0,axiom,
( c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat) != c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat)
| V_m = V_n ) ).
cnf(cls_nat__add__left__cancel_0,axiom,
( c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat)
| V_m = V_n ) ).
cnf(cls_natgb_Oadd__cancel_0,axiom,
( c_HOL_Oplus__class_Oplus(V_x,V_y,tc_nat) != c_HOL_Oplus__class_Oplus(V_x,V_z,tc_nat)
| V_y = V_z ) ).
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_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_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_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_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_mult__monom_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_HOL_Otimes__class_Otimes(c_Polynomial_Omonom(V_a,V_m,T_a),c_Polynomial_Omonom(V_b,V_n,T_a),tc_Polynomial_Opoly(T_a)) = c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),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_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_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_add__Suc__shift_0,axiom,
c_HOL_Oplus__class_Oplus(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_m,c_Suc(V_n),tc_nat) ).
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_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_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_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_norm__scaleR_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_RealVector_Onorm__class_Onorm(c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x,T_a),tc_RealDef_Oreal) ) ).
cnf(cls_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_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_power__Suc__less__one_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a),c_HOL_Oone__class_Oone(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_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_zero__le__power__abs_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(V_a,T_a),V_n,T_a),T_a) ) ).
cnf(cls_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_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_rabs__ratiotest__lemma_0,axiom,
( V_x = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_x,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(V_c,c_HOL_Oabs__class_Oabs(V_y,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).
cnf(cls_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_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_abs__add__one__gt__zero_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_HOL_Oabs__class_Oabs(V_x,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ).
cnf(cls_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_zero__le__power__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_zero__le__power_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_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_one__le__power_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_lessequals(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
| ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ).
cnf(cls_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_add__Suc_0,axiom,
c_HOL_Oplus__class_Oplus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)) ).
cnf(cls_add__Suc__right_0,axiom,
c_HOL_Oplus__class_Oplus(V_m,c_Suc(V_n),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)) ).
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_complex__cnj__cnj_0,axiom,
c_Complex_Ocnj(c_Complex_Ocnj(V_z)) = V_z ).
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_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_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_nat__add__commute_0,axiom,
c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat) ).
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_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_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_less__add__iff2_0,axiom,
( ~ class_Ring__and__Field_Opordered__ring(T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a) ) ).
cnf(cls_less__add__iff1_1,axiom,
( ~ class_Ring__and__Field_Opordered__ring(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a) ) ).
cnf(cls_less__add__iff1_0,axiom,
( ~ class_Ring__and__Field_Opordered__ring(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a) ) ).
cnf(cls_sum__squares__gt__zero__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),T_a),T_a) ) ).
cnf(cls_mult__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_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_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__strict__mono_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_mult__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_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_inv0_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ).
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_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_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_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_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_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_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__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_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__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__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_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_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_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_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_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__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__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_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_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_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_mult_Oadd__left_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_a_H,T_a),V_b,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a_H,V_b,T_a),T_a) ) ).
cnf(cls_mult__left_Oadd_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),V_ya,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_ya,T_a),c_HOL_Otimes__class_Otimes(V_y,V_ya,T_a),T_a) ) ).
cnf(cls_mult_Oadd__right_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oplus__class_Oplus(V_b,V_b_H,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a,V_b_H,T_a),T_a) ) ).
cnf(cls_mult__right_Oadd_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),c_HOL_Otimes__class_Otimes(V_xa,V_y,T_a),T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I8_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ).
cnf(cls_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_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_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_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__1__right_0,axiom,
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ).
cnf(cls_mult__1__left_0,axiom,
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ).
cnf(cls_mult__1_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__mult(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ).
cnf(cls_class__semiring_Omul__1_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_x,T_a) = V_x ) ).
cnf(cls_class__semiring_Osemiring__rules_I12_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ).
cnf(cls_class__semiring_Osemiring__rules_I11_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a) = V_a ) ).
cnf(cls_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_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_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_smult__smult_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_Polynomial_Osmult(V_a,c_Polynomial_Osmult(V_b,V_p,T_a),T_a) = c_Polynomial_Osmult(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_p,T_a) ) ).
cnf(cls_power__gt1_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ).
cnf(cls_power__less__imp__less__base_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) ).
cnf(cls_power__minus_0,axiom,
( ~ class_Ring__and__Field_Oring__1(T_a)
| c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_n,T_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(T_a),T_a),V_n,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) ).
cnf(cls_power__one__right_0,axiom,
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| c_Power_Opower__class_Opower(V_a,c_HOL_Oone__class_Oone(tc_nat),T_a) = V_a ) ).
cnf(cls_class__semiring_Osemiring__rules_I33_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Power_Opower__class_Opower(V_x,c_HOL_Oone__class_Oone(tc_nat),T_a) = V_x ) ).
cnf(cls_power__one_0,axiom,
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a) = c_HOL_Oone__class_Oone(T_a) ) ).
cnf(cls_power__inverse_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_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a) ) ).
cnf(cls_field__power__not__zero_0,axiom,
( ~ class_Ring__and__Field_Oring__1__no__zero__divisors(T_a)
| c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_power__eq__0__iff_0,axiom,
( ~ class_Ring__and__Field_Ozero__neq__one(T_a)
| ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| ~ class_Ring__and__Field_Omult__zero(T_a)
| ~ class_Power_Opower(T_a)
| c_Power_Opower__class_Opower(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_power__abs_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(V_a,T_a),V_n,T_a) ) ).
cnf(cls_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_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_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_poly__replicate__append_0,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(T_a)
| c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(c_Polynomial_Omonom(c_HOL_Oone__class_Oone(T_a),V_n,T_a),V_p,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_Polynomial_Opoly(V_p,V_x,T_a),T_a) ) ).
cnf(cls_zero__less__norm__iff_1,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(V_x,T_a),tc_RealDef_Oreal)
| V_x = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_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_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__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_abs__norm__cancel_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_HOL_Oabs__class_Oabs(c_RealVector_Onorm__class_Onorm(V_a,T_a),tc_RealDef_Oreal) = c_RealVector_Onorm__class_Onorm(V_a,T_a) ) ).
cnf(cls_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_complex__mod__cnj_0,axiom,
c_RealVector_Onorm__class_Onorm(c_Complex_Ocnj(V_z),tc_Complex_Ocomplex) = c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex) ).
cnf(cls_complex__cnj__mult_0,axiom,
c_Complex_Ocnj(c_HOL_Otimes__class_Otimes(V_x,V_y,tc_Complex_Ocomplex)) = c_HOL_Otimes__class_Otimes(c_Complex_Ocnj(V_x),c_Complex_Ocnj(V_y),tc_Complex_Ocomplex) ).
cnf(cls_complex__cnj__complex__of__real_0,axiom,
c_Complex_Ocnj(c_RealVector_Oof__real(V_x,tc_Complex_Ocomplex)) = c_RealVector_Oof__real(V_x,tc_Complex_Ocomplex) ).
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_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_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_real__mult__left__cancel_0,axiom,
( c_HOL_Otimes__class_Otimes(V_c,V_a,tc_RealDef_Oreal) != c_HOL_Otimes__class_Otimes(V_c,V_b,tc_RealDef_Oreal)
| V_c = c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_a = V_b ) ).
cnf(cls_real__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_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_nat_Oinject_0,axiom,
( c_Suc(V_nat) != c_Suc(V_nat_H)
| V_nat = V_nat_H ) ).
cnf(cls_Suc__inject_0,axiom,
( c_Suc(V_x) != c_Suc(V_y)
| V_x = V_y ) ).
cnf(cls_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_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_nonzero__power__inverse_0,axiom,
( ~ class_Ring__and__Field_Odivision__ring(T_a)
| c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a)
| V_a = c_HOL_Ozero__class_Ozero(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_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_abs__power__minus_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_n,T_a),T_a) = c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) ).
cnf(cls_complex__cnj__one_0,axiom,
c_Complex_Ocnj(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ).
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_abs__add__one__not__less__self_0,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(V_x,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),V_x,tc_RealDef_Oreal) ).
cnf(cls_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_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_real__le__eq__diff_1,axiom,
( c_lessequals(V_x,V_y,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).
cnf(cls_real__le__eq__diff_0,axiom,
( c_lessequals(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_RealDef_Oreal),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(V_x,V_y,tc_RealDef_Oreal) ) ).
cnf(cls_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_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_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_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_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_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_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_neg__0__equal__iff__equal_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_power__le__imp__le__base_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_lessequals(c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a),c_Power_Opower__class_Opower(V_b,c_Suc(V_n),T_a),T_a) ) ).
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_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_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_complex__cnj__cancel__iff_0,axiom,
( c_Complex_Ocnj(V_x) != c_Complex_Ocnj(V_y)
| V_x = V_y ) ).
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_minus__zero_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_neg__equal__zero_1,axiom,
( ~ class_OrderedGroup_Oordered__ab__group__add(T_a)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_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_real__abs__def_1,axiom,
( c_HOL_Oabs__class_Oabs(V_r,tc_RealDef_Oreal) = V_r
| c_HOL_Oord__class_Oless(V_r,c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).
cnf(cls_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_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_abs__add__abs_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a) ) ).
cnf(cls_abs__eq__0_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_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_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_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_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_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_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_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_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_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__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_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_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_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_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_complex__mod__triangle__sub_0,axiom,
c_lessequals(c_RealVector_Onorm__class_Onorm(V_w,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(V_w,V_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ).
cnf(cls_realpow__increasing_0,axiom,
( c_lessequals(V_x,V_y,tc_RealDef_Oreal)
| ~ c_lessequals(c_Power_Opower__class_Opower(V_x,c_Suc(V_n),tc_RealDef_Oreal),c_Power_Opower__class_Opower(V_y,c_Suc(V_n),tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ 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),V_x,tc_RealDef_Oreal) ) ).
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_monom__eq__iff_0,axiom,
( ~ class_HOL_Ozero(T_a)
| c_Polynomial_Omonom(V_a,V_n,T_a) != c_Polynomial_Omonom(V_b,V_n,T_a)
| V_a = V_b ) ).
cnf(cls_minus__add_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| c_HOL_Ouminus__class_Ouminus(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_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_complex__cnj__power_0,axiom,
c_Complex_Ocnj(c_Power_Opower__class_Opower(V_x,V_n,tc_Complex_Ocomplex)) = c_Power_Opower__class_Opower(c_Complex_Ocnj(V_x),V_n,tc_Complex_Ocomplex) ).
cnf(cls_th30_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ).
cnf(cls_t_I3_J_0,axiom,
c_HOL_Oord__class_Oless(v_t____,c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ).
cnf(cls_power__Suc__less_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_th11_0,axiom,
c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Oplus__class_Oplus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_a____,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_s____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_RealDef_Oreal),c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_s____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),tc_RealDef_Oreal) ).
cnf(cls_wm1_0,axiom,
c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_w____,v_k____,tc_Complex_Ocomplex),v_a____,tc_Complex_Ocomplex) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ).
cnf(cls_mult__less__cancel__right__disj_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ).
cnf(cls_mult__less__cancel__right__disj_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ).
cnf(cls_mult__less__cancel__left__disj_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ).
cnf(cls_mult__less__cancel__left__disj_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ).
cnf(cls_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__less__cancel__right__disj_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ).
cnf(cls_mult__less__cancel__left__disj_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ).
cnf(cls_mult__pos__neg2_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_mult__pos__neg_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_mult__neg__pos_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_zero__less__mult__pos2_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a) ) ).
cnf(cls_zero__less__mult__pos_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ).
cnf(cls_mult__pos__pos_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_mult__neg__neg_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_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_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_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_power__inject__exp_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_Power_Opower__class_Opower(V_a,V_m,T_a) != c_Power_Opower__class_Opower(V_a,V_n,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a)
| V_m = V_n ) ).
cnf(cls_zero__less__power_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_power__less__zero__eq_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I28_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_q,T_a),V_x,T_a) = c_Power_Opower__class_Opower(V_x,c_Suc(V_q),T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I27_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,V_q,T_a),T_a) = c_Power_Opower__class_Opower(V_x,c_Suc(V_q),T_a) ) ).
cnf(cls_class__semiring_Omul__pwr_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_p,T_a),c_Power_Opower__class_Opower(V_x,V_q,T_a),T_a) = c_Power_Opower__class_Opower(V_x,c_HOL_Oplus__class_Oplus(V_p,V_q,tc_nat),T_a) ) ).
cnf(cls_class__semiring_Opwr__Suc_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Power_Opower__class_Opower(V_x,c_Suc(V_n),T_a) = c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a) ) ).
cnf(cls_power__Suc2_0,axiom,
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_a,V_n,T_a),V_a,T_a) ) ).
cnf(cls_power__Suc_0,axiom,
( ~ class_Power_Opower(T_a)
| c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I35_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Power_Opower__class_Opower(V_x,c_Suc(V_q),T_a) = c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,V_q,T_a),T_a) ) ).
cnf(cls_power__add_0,axiom,
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| c_Power_Opower__class_Opower(V_a,c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),T_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,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_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_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_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_poly__mult_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(V_p,V_x,T_a),c_Polynomial_Opoly(V_q,V_x,T_a),T_a) ) ).
cnf(cls_poly__smult_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_Polynomial_Opoly(c_Polynomial_Osmult(V_a,V_p,T_a),V_x,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Polynomial_Opoly(V_p,V_x,T_a),T_a) ) ).
cnf(cls_poly__power_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Polynomial_Opoly(c_Power_Opower__class_Opower(V_p,V_n,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_Power_Opower__class_Opower(c_Polynomial_Opoly(V_p,V_x,T_a),V_n,T_a) ) ).
cnf(cls_norm__of__real_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra__1(T_a)
| c_RealVector_Onorm__class_Onorm(c_RealVector_Oof__real(V_r,T_a),T_a) = c_HOL_Oabs__class_Oabs(V_r,tc_RealDef_Oreal) ) ).
cnf(cls_t_I2_J_0,axiom,
c_HOL_Oord__class_Oless(v_t____,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ).
cnf(cls_t_I1_J_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),v_t____,tc_RealDef_Oreal) ).
cnf(cls_m_I2_J_0,axiom,
( c_lessequals(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_s____,V_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_m____,tc_RealDef_Oreal)
| ~ c_lessequals(c_RealVector_Onorm__class_Onorm(V_z,tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal) ) ).
cnf(cls_power__less__power__Suc_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ).
cnf(cls_power__gt1__lemma_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ).
cnf(cls_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_poly__monom_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Polynomial_Opoly(c_Polynomial_Omonom(V_a,V_n,T_a),V_x,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a) ) ).
cnf(cls_norm__power__ineq_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra__1(T_a)
| c_lessequals(c_RealVector_Onorm__class_Onorm(c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a),c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(V_x,T_a),V_n,tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).
cnf(cls_tw_0,axiom,
c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),tc_RealDef_Oreal) ).
cnf(cls_xt1_I9_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ).
cnf(cls_not__less__iff__gr__or__eq_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
cnf(cls_order__less__asym_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_order__less__asym_H_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_complex__of__real__power_0,axiom,
c_Power_Opower__class_Opower(c_RealVector_Oof__real(V_x,tc_Complex_Ocomplex),V_n,tc_Complex_Ocomplex) = c_RealVector_Oof__real(c_Power_Opower__class_Opower(V_x,V_n,tc_RealDef_Oreal),tc_Complex_Ocomplex) ).
cnf(cls_norm__power_0,axiom,
( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
| c_RealVector_Onorm__class_Onorm(c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a) = c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(V_x,T_a),V_n,tc_RealDef_Oreal) ) ).
cnf(cls_order__less__irrefl_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).
cnf(cls_real__less__def_1,axiom,
~ c_HOL_Oord__class_Oless(V_x,V_x,tc_RealDef_Oreal) ).
cnf(cls_order__less__le_1,axiom,
( ~ class_Orderings_Oorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).
cnf(cls_linorder__neq__iff_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).
cnf(cls_power__commutes_0,axiom,
( ~ class_OrderedGroup_Omonoid__mult(T_a)
| c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_a,V_n,T_a),V_a,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a) ) ).
cnf(cls_mult__less__cancel__right__disj_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ).
cnf(cls_mult__less__cancel__left__disj_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ).
cnf(cls_of__real__power_0,axiom,
( ~ class_RealVector_Oreal__algebra__1(T_a)
| c_RealVector_Oof__real(c_Power_Opower__class_Opower(V_x,V_n,tc_RealDef_Oreal),T_a) = c_Power_Opower__class_Opower(c_RealVector_Oof__real(V_x,T_a),V_n,T_a) ) ).
cnf(cls_class__semiring_Omul__a_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_z,T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I19_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a) ) ).
cnf(cls_class__semiring_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_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_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_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_power__mult__distrib_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__mult(T_a)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_n,T_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a) ) ).
cnf(cls_class__semiring_Opwr__mul_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_q,T_a) = c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_q,T_a),c_Power_Opower__class_Opower(V_y,V_q,T_a),T_a) ) ).
cnf(cls_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__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_linorder__neqE__ordered__idom_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| V_x = V_y ) ).
cnf(cls_not__less__iff__gr__or__eq_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| V_x = V_y
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_linorder__antisym__conv3_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| V_x = V_y
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
cnf(cls_linorder__less__linear_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| V_x = V_y
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_linorder__neqE_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| V_x = V_y ) ).
cnf(cls_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_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_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_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_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_CHAINED_0,axiom,
c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_s____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ).
cnf(cls_CHAINED_0_01,axiom,
c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_t____,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_RealVector_Onorm__class_Onorm(v_w____,tc_Complex_Ocomplex),c_HOL_Oplus__class_Oplus(v_k____,c_HOL_Oone__class_Oone(tc_nat),tc_nat),tc_RealDef_Oreal),v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal) ).
cnf(cls_conjecture_0,negated_conjecture,
~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),v_k____,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Polynomial_Opoly(v_s____,c_HOL_Otimes__class_Otimes(c_RealVector_Oof__real(v_t____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v_t____,v_k____,tc_RealDef_Oreal),tc_RealDef_Oreal) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__comm__monoid__add,axiom,
( class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring,axiom,
( class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__ring(T_1) ) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__comm__monoid__add,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring,axiom,
class_Ring__and__Field_Ocomm__ring(tc_RealDef_Oreal) ).
cnf(clsarity_nat__OrderedGroup_Ocancel__comm__monoid__add,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Oordered__semiring__strict,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Ocancel__semigroup__add,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Opordered__semiring,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Oordered__semiring,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Ono__zero__divisors,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__0,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Oab__semigroup__mult,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__mult,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Oab__semigroup__add,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Ozero__neq__one,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Osemiring__0,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Omult__mono1,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Omult__zero,axiom,
class_Ring__and__Field_Omult__zero(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Omult__mono,axiom,
class_Ring__and__Field_Omult__mono(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Omonoid__mult,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Osemiring,axiom,
class_Ring__and__Field_Osemiring(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Omonoid__add,axiom,
class_OrderedGroup_Omonoid__add(tc_nat) ).
cnf(clsarity_nat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_nat) ).
cnf(clsarity_nat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_nat) ).
cnf(clsarity_nat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_nat) ).
cnf(clsarity_nat__Power_Opower,axiom,
class_Power_Opower(tc_nat) ).
cnf(clsarity_nat__HOL_Ozero,axiom,
class_HOL_Ozero(tc_nat) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oring__1__no__zero__divisors,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs,axiom,
class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_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__Ring__and__Field_Ocomm__semiring__0,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring,axiom,
class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field,axiom,
class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring,axiom,
class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_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__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__Ring__and__Field_Osemiring__0,axiom,
class_Ring__and__Field_Osemiring__0(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1,axiom,
class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__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__OrderedGroup_Omonoid__mult,axiom,
class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Osemiring,axiom,
class_Ring__and__Field_Osemiring(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__RealVector_Oreal__algebra,axiom,
class_RealVector_Oreal__algebra(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__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_Oring__1,axiom,
class_Ring__and__Field_Oring__1(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__Ring__and__Field_Ofield,axiom,
class_Ring__and__Field_Ofield(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oring,axiom,
class_Ring__and__Field_Oring(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oidom,axiom,
class_Ring__and__Field_Oidom(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Power_Opower,axiom,
class_Power_Opower(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__HOL_Ozero,axiom,
class_HOL_Ozero(tc_RealDef_Oreal) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__div__algebra,axiom,
class_RealVector_Oreal__div__algebra(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0,axiom,
class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1,axiom,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero,axiom,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__algebra,axiom,
class_RealVector_Oreal__algebra(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__RealVector_Oreal__vector,axiom,
class_RealVector_Oreal__vector(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1,axiom,
class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ofield,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oring,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Power_Opower,axiom,
class_Power_Opower(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__HOL_Ozero,axiom,
class_HOL_Ozero(tc_Complex_Ocomplex) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__comm__semiring__strict,axiom,
( class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__cancel__semiring,axiom,
( class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1__no__zero__divisors,axiom,
( class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oidom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring__strict,axiom,
( class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add__abs,axiom,
( class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__comm__monoid__add,axiom,
( class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors,axiom,
( class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oidom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict,axiom,
( class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add,axiom,
( class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add,axiom,
( class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__semiring,axiom,
( class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring__abs,axiom,
( class_Ring__and__Field_Opordered__ring__abs(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring,axiom,
( class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors,axiom,
( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oidom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semidom,axiom,
( class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1,axiom,
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0,axiom,
( class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult,axiom,
( class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult,axiom,
( class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add,axiom,
( class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(T_1))
| ~ class_OrderedGroup_Ocomm__monoid__add(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring,axiom,
( class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring,axiom,
( class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__add,axiom,
( class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1))
| ~ class_OrderedGroup_Ocomm__monoid__add(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one,axiom,
( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom,axiom,
( class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1,axiom,
( class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__ring__1(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring__0,axiom,
( class_Ring__and__Field_Osemiring__0(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono1,axiom,
( class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add,axiom,
( class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(T_1))
| ~ class_OrderedGroup_Oab__group__add(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero,axiom,
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono,axiom,
( class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult,axiom,
( class_OrderedGroup_Omonoid__mult(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring,axiom,
( class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add,axiom,
( class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(T_1))
| ~ class_OrderedGroup_Ocomm__monoid__add(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add,axiom,
( class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(T_1))
| ~ class_OrderedGroup_Oab__group__add(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1,axiom,
( class_Ring__and__Field_Oring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__ring__1(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oabs__if,axiom,
( class_Ring__and__Field_Oabs__if(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oring,axiom,
( class_Ring__and__Field_Oring(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__ring(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oidom,axiom,
( class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oidom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Orderings_Opreorder,axiom,
( class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Orderings_Olinorder,axiom,
( class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Orderings_Oorder,axiom,
( class_Orderings_Oorder(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Int_Onumber__ring,axiom,
( class_Int_Onumber__ring(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__ring__1(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Power_Opower,axiom,
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__HOL_Ozero,axiom,
( class_HOL_Ozero(tc_Polynomial_Opoly(T_1))
| ~ class_HOL_Ozero(T_1) ) ).
%------------------------------------------------------------------------------