TPTP Problem File: ALG400-1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : ALG400-1 : TPTP v8.2.0. Released v4.1.0.
% Domain : General Algebra
% Problem : Fundamental theorem of algebra 0677_41
% Version : Especial.
% English :
% Refs : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe
% : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% Source : [Nip10]
% Names : Fundamental_Theorem_Algebra-0677_41 [Nip10]
% Status : Unsatisfiable
% Rating : 0.30 v8.2.0, 0.24 v8.1.0, 0.16 v7.5.0, 0.32 v7.4.0, 0.24 v7.3.0, 0.33 v7.1.0, 0.25 v7.0.0, 0.33 v6.4.0, 0.27 v6.3.0, 0.18 v6.2.0, 0.40 v6.1.0, 0.43 v6.0.0, 0.40 v5.5.0, 0.60 v5.3.0, 0.61 v5.2.0, 0.62 v5.1.0, 0.59 v5.0.0, 0.50 v4.1.0
% Syntax : Number of clauses : 604 ( 115 unt; 169 nHn; 479 RR)
% Number of literals : 2209 ( 215 equ;1424 neg)
% Maximal clause size : 7 ( 3 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 42 ( 41 usr; 0 prp; 1-5 aty)
% Number of functors : 18 ( 18 usr; 6 con; 0-3 aty)
% Number of variables : 1531 ( 71 sgn)
% SPC : CNF_UNS_RFO_SEQ_NHN
% Comments :
%------------------------------------------------------------------------------
cnf(cls_divide__eq__eq__number__of1_1,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_Int_Onumber__class_Onumber__of(V_w,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_divide__eq__eq__number__of_1,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) != c_Int_Onumber__class_Onumber__of(V_w,T_a)
| c_Int_Onumber__class_Onumber__of(V_w,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_divide__eq__eq__number__of_2,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_Int_Onumber__class_Onumber__of(V_w,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_Int_Onumber__class_Onumber__of(V_w,T_a) ) ).
cnf(cls_eq__divide__eq__number__of_1,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_Int_Onumber__class_Onumber__of(V_w,T_a) != c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_Int_Onumber__class_Onumber__of(V_w,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_eq__divide__eq__number__of_2,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_Int_Onumber__class_Onumber__of(V_w,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| c_Int_Onumber__class_Onumber__of(V_w,T_a) = c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_eq__divide__eq__number__of1_2,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_Int_Onumber__class_Onumber__of(V_w,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ).
cnf(cls_le__number__of__eq__not__less_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(c_Int_Onumber__class_Onumber__of(V_v,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_Int_Onumber__class_Onumber__of(V_v,T_a),T_a) ) ).
cnf(cls_le__number__of__eq__not__less_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ class_Int_Onumber(T_a)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_Int_Onumber__class_Onumber__of(V_v,T_a),T_a)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(V_v,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ).
cnf(cls_eq__number__of_0,axiom,
( ~ class_Int_Oring__char__0(T_a)
| ~ class_Int_Onumber__ring(T_a)
| c_Int_Onumber__class_Onumber__of(V_x,T_a) != c_Int_Onumber__class_Onumber__of(V_y,T_a)
| V_x = V_y ) ).
cnf(cls_less__divide__eq__number__of_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_less__divide__eq__number__of_2,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ).
cnf(cls_divide__less__eq__number__of_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_divide__less__eq__number__of_2,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ).
cnf(cls_less__divide__eq__number__of1_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ).
cnf(cls_less__divide__eq__number__of1_2,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) ) ).
cnf(cls_divide__less__eq__number__of1_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ).
cnf(cls_divide__less__eq__number__of1_2,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a) ) ).
cnf(cls_divide__eq__eq__number__of_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a) != c_Int_Onumber__class_Onumber__of(V_w,T_a)
| V_b = c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a)
| V_c = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_divide__eq__eq__number__of1_4,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_divide__eq__eq__number__of_3,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_c,T_a) = c_Int_Onumber__class_Onumber__of(V_w,T_a)
| V_c = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_eq__divide__eq__number__of1_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) = V_b
| c_Int_Onumber__class_Onumber__of(V_w,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_divide__eq__eq__number__of1_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| c_Int_Onumber__class_Onumber__of(V_w,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_eq__divide__eq__number__of_3,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_Int_Onumber__class_Onumber__of(V_w,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_c,T_a)
| V_c = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_divide__eq__eq__number__of_4,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_Int_Onumber__class_Onumber__of(V_w,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_c,T_a) = c_Int_Onumber__class_Onumber__of(V_w,T_a) ) ).
cnf(cls_eq__divide__eq__number__of_4,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_Int_Onumber__class_Onumber__of(V_w,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| c_Int_Onumber__class_Onumber__of(V_w,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_c,T_a) ) ).
cnf(cls_eq__divide__eq__number__of_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_Int_Onumber__class_Onumber__of(V_w,T_a) != c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a)
| c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a) = V_b
| V_c = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_eq__divide__eq__number__of1_3,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| c_Int_Onumber__class_Onumber__of(V_w,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_divide__eq__eq__number__of1_3,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) = V_a
| c_Int_Onumber__class_Onumber__of(V_w,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_eq__divide__eq__number__of1_4,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ).
cnf(cls_inverse__eq__divide__number__of_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oinverse__class_Oinverse(c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ).
cnf(cls_le__divide__eq__number__of_2,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ).
cnf(cls_le__divide__eq__number__of_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_le__divide__eq__number__of1_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
| ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ).
cnf(cls_le__divide__eq__number__of1_2,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) ) ).
cnf(cls_divide__le__eq__number__of1_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ).
cnf(cls_divide__le__eq__number__of1_2,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a) ) ).
cnf(cls_divide__le__eq__number__of_2,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ).
cnf(cls_divide__le__eq__number__of_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_less__divide__eq__number__of_8,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a) ) ).
cnf(cls_less__divide__eq__number__of_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_less__divide__eq__number__of_1,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ).
cnf(cls_less__divide__eq__number__of_9,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a) ) ).
cnf(cls_less__divide__eq__number__of_7,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a) ) ).
cnf(cls_less__divide__eq__number__of_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_divide__less__eq__number__of_9,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a) ) ).
cnf(cls_less__divide__eq__number__of1_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ).
cnf(cls_divide__less__eq__number__of1_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ).
cnf(cls_divide__less__eq__number__of_7,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a) ) ).
cnf(cls_divide__less__eq__number__of_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_less__divide__eq__number__of1_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ).
cnf(cls_less__divide__eq__number__of1_1,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) ) ).
cnf(cls_divide__less__eq__number__of1_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ).
cnf(cls_divide__less__eq__number__of1_1,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a) ) ).
cnf(cls_divide__less__eq__number__of_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a) ) ).
cnf(cls_divide__less__eq__number__of_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ).
cnf(cls_less__divide__eq__number__of_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a) ) ).
cnf(cls_less__divide__eq__number__of_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ).
cnf(cls_divide__less__eq__number__of_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_divide__less__eq__number__of_1,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ).
cnf(cls_less__divide__eq__number__of1_9,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a) ) ).
cnf(cls_divide__less__eq__number__of1_9,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) ) ).
cnf(cls_divide__less__eq__number__of_8,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a) ) ).
cnf(cls_less__divide__eq__number__of1_7,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a) ) ).
cnf(cls_divide__less__eq__number__of1_7,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) ) ).
cnf(cls_less__divide__eq__number__of1_8,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a) ) ).
cnf(cls_divide__less__eq__number__of1_8,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) ) ).
cnf(cls_less__divide__eq__number__of1_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a) ) ).
cnf(cls_less__divide__eq__number__of1_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) ) ).
cnf(cls_divide__less__eq__number__of1_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) ) ).
cnf(cls_divide__less__eq__number__of1_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a) ) ).
cnf(cls_le__divide__eq__number__of1_9,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
| ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a) ) ).
cnf(cls_divide__le__eq__number__of1_9,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a)
| ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) ) ).
cnf(cls_le__divide__eq__number__of_9,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a) ) ).
cnf(cls_divide__le__eq__number__of_9,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a)
| ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_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_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_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_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_mult__neg__pos_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_mult__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__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__less__cancel__left__disj_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ).
cnf(cls_mult__less__cancel__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_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__left__disj_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ).
cnf(cls_mult__less__cancel__left__disj_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ).
cnf(cls_mult__less__cancel__right__disj_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ).
cnf(cls_mult__less__cancel__right__disj_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ).
cnf(cls_divide__left__mono_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_c,V_a,T_a),c_HOL_Oinverse__class_Odivide(V_c,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(V_b,V_a,T_a) ) ).
cnf(cls_divide__left__mono__neg_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_c,V_a,T_a),c_HOL_Oinverse__class_Odivide(V_c,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_a,V_b,T_a) ) ).
cnf(cls_divide__le__eq_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ).
cnf(cls_divide__le__eq_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ).
cnf(cls_le__divide__eq_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ).
cnf(cls_le__divide__eq_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ).
cnf(cls_mult__imp__div__pos__le_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),V_z,T_a)
| ~ c_lessequals(V_x,c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ).
cnf(cls_mult__imp__le__div__pos_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_lessequals(V_z,c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),V_x,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ).
cnf(cls_divide__le__eq_8,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
| ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ).
cnf(cls_le__divide__eq_8,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ).
cnf(cls_divide__le__eq_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_divide__le__eq_7,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ).
cnf(cls_le__divide__eq_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_le__divide__eq_7,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ).
cnf(cls_divide__le__eq_1,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ).
cnf(cls_divide__le__eq_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_le__divide__eq_1,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ).
cnf(cls_le__divide__eq_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_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_div__smult__left_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Divides_Odiv__class_Odiv(c_Polynomial_Osmult(V_a,V_x,T_a),V_y,tc_Polynomial_Opoly(T_a)) = c_Polynomial_Osmult(V_a,c_Divides_Odiv__class_Odiv(V_x,V_y,tc_Polynomial_Opoly(T_a)),T_a) ) ).
cnf(cls_pdivmod__rel__smult__left_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Polynomial_Opdivmod__rel(c_Polynomial_Osmult(V_a,V_x,T_a),V_y,c_Polynomial_Osmult(V_a,V_q,T_a),c_Polynomial_Osmult(V_a,V_r,T_a),T_a)
| ~ c_Polynomial_Opdivmod__rel(V_x,V_y,V_q,V_r,T_a) ) ).
cnf(cls_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_mult__frac__num_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),V_z,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),V_y,T_a) ) ).
cnf(cls_mult__frac__frac_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Oinverse__class_Odivide(V_z,V_w,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),c_HOL_Otimes__class_Otimes(V_y,V_w,T_a),T_a) ) ).
cnf(cls_div__by__1_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Odiv(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ).
cnf(cls_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__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_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_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_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__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_divide__le__eq_9,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
| ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ).
cnf(cls_le__divide__eq_9,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ).
cnf(cls_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_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_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__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__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__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__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_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_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_order__less__le_2,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| V_x = V_y
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_order__le__less_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| V_x = V_y
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_order__le__neq__trans_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| V_a = V_b
| ~ c_lessequals(V_a,V_b,T_a) ) ).
cnf(cls_order__neq__le__trans_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| V_a = V_b ) ).
cnf(cls_linorder__antisym__conv1_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| V_x = V_y
| ~ c_lessequals(V_x,V_y,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_divide__le__eq__number__of1_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a) ) ).
cnf(cls_divide__le__eq__number__of1_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) ) ).
cnf(cls_le__divide__eq__number__of1_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) ) ).
cnf(cls_le__divide__eq__number__of1_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a) ) ).
cnf(cls_divide__le__eq__number__of_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_divide__le__eq__number__of_1,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ).
cnf(cls_le__divide__eq__number__of_8,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a) ) ).
cnf(cls_le__divide__eq__number__of_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a) ) ).
cnf(cls_le__divide__eq__number__of_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ).
cnf(cls_le__divide__eq__number__of_7,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a) ) ).
cnf(cls_le__divide__eq__number__of_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_divide__le__eq__number__of1_7,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) ) ).
cnf(cls_le__divide__eq__number__of1_7,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
| ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a) ) ).
cnf(cls_divide__le__eq__number__of_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a) ) ).
cnf(cls_divide__le__eq__number__of_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ).
cnf(cls_divide__le__eq__number__of1_8,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a)
| ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) ) ).
cnf(cls_le__divide__eq__number__of1_8,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a) ) ).
cnf(cls_divide__le__eq__number__of_8,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a)
| ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a) ) ).
cnf(cls_divide__le__eq__number__of1_1,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a) ) ).
cnf(cls_divide__le__eq__number__of1_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ).
cnf(cls_le__divide__eq__number__of1_1,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a) ) ).
cnf(cls_le__divide__eq__number__of1_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ).
cnf(cls_le__divide__eq__number__of_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_le__divide__eq__number__of_1,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ).
cnf(cls_divide__le__eq__number__of1_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ).
cnf(cls_le__divide__eq__number__of1_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
| ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a) ) ).
cnf(cls_divide__le__eq__number__of_7,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),T_a) ) ).
cnf(cls_divide__le__eq__number__of_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| ~ class_Int_Onumber(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),V_c,T_a),V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_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_not__one__le__zero_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| ~ c_lessequals(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_zero__le__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_div__self_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Odiv(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_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_divide__eq__eq_4,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a),V_c,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_frac__eq__eq_1,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_HOL_Otimes__class_Otimes(V_x,V_z,T_a) != c_HOL_Otimes__class_Otimes(V_w,V_y,T_a)
| V_z = c_HOL_Ozero__class_Ozero(T_a)
| V_y = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a) ) ).
cnf(cls_frac__eq__eq_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) != c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a)
| V_z = c_HOL_Ozero__class_Ozero(T_a)
| V_y = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Otimes__class_Otimes(V_x,V_z,T_a) = c_HOL_Otimes__class_Otimes(V_w,V_y,T_a) ) ).
cnf(cls_zero__le__divide__iff_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_zero__le__divide__iff_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_eq__divide__eq_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b
| V_c = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_divide__eq__eq_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a)
| V_c = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_eq__divide__eq_4,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a),V_c,T_a) ) ).
cnf(cls_divide__le__0__iff_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_divide__le__0__iff_2,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_divide__le__0__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_divide__le__0__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_divide__right__mono__neg_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),T_a)
| ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_a,V_b,T_a) ) ).
cnf(cls_divide__right__mono_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a) ) ).
cnf(cls_eq__divide__imp_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| V_c = c_HOL_Ozero__class_Ozero(T_a)
| V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) ).
cnf(cls_divide__eq__imp_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| V_c = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) = V_a ) ).
cnf(cls_eq__divide__eq_3,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a)
| V_c = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_divide__eq__eq_3,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) = V_a
| V_c = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_divide__le__0__iff_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_divide__le__0__iff_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_zero__le__divide__iff_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ).
cnf(cls_zero__le__divide__iff_2,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ).
cnf(cls_zero__le__divide__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ).
cnf(cls_zero__le__divide__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ).
cnf(cls_mult__divide__mult__cancel__right_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a)
| V_c = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_mult__divide__mult__cancel__left_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a)
| V_c = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_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_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_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_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_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_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_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_class__fieldgb_Odivide__inverse_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Int_Onumber__ring(T_a)
| c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,T_a),T_a) ) ).
cnf(cls_divide__inverse_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a) ) ).
cnf(cls_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_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_complex__divide__def_0,axiom,
c_HOL_Oinverse__class_Odivide(V_x,V_y,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ).
cnf(cls_divide__strict__left__mono__neg_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_c,V_a,T_a),c_HOL_Oinverse__class_Odivide(V_c,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_divide__strict__left__mono_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_c,V_a,T_a),c_HOL_Oinverse__class_Odivide(V_c,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ).
cnf(cls_frac__le_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_x,V_z,T_a),c_HOL_Oinverse__class_Odivide(V_y,V_w,T_a),T_a)
| ~ c_lessequals(V_w,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_w,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ).
cnf(cls_less__divide__eq_7,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ).
cnf(cls_less__divide__eq_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_less__divide__eq_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_less__divide__eq_1,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ).
cnf(cls_divide__less__eq_7,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ).
cnf(cls_divide__less__eq_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_divide__less__eq_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_divide__less__eq_1,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ).
cnf(cls_divide__nonpos__neg_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_divide__nonneg__pos_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ).
cnf(cls_less__divide__eq_9,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ).
cnf(cls_less__divide__eq_8,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ).
cnf(cls_divide__less__eq_9,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ).
cnf(cls_divide__less__eq_8,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ).
cnf(cls_frac__less_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_x,V_z,T_a),c_HOL_Oinverse__class_Odivide(V_y,V_w,T_a),T_a)
| ~ c_lessequals(V_w,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_w,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ).
cnf(cls_divide__nonpos__pos_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
| ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_divide__nonneg__neg_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ).
cnf(cls_mult__imp__less__div__pos_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_HOL_Oord__class_Oless(V_z,c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),V_x,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ).
cnf(cls_mult__imp__div__pos__less_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ).
cnf(cls_less__divide__eq_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ).
cnf(cls_less__divide__eq_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ).
cnf(cls_divide__less__eq_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ).
cnf(cls_divide__less__eq_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ).
cnf(cls_frac__less2_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_x,V_z,T_a),c_HOL_Oinverse__class_Odivide(V_y,V_w,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_w,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_w,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ).
cnf(cls_le__divide__eq_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_le__divide__eq_2,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ).
cnf(cls_divide__le__eq_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_divide__le__eq_2,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ).
cnf(cls_divide__le__0__1__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_divide__le__0__1__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_zero__le__divide__1__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) ) ).
cnf(cls_zero__le__divide__1__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),T_a) ) ).
cnf(cls_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_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_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_lessequals(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(V_a,V_b,T_a) ) ).
cnf(cls_inverse__le__imp__le_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_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_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_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_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_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_linorder__antisym__conv2_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| V_x = V_y
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_xt1_I12_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| V_a = V_b ) ).
cnf(cls_xt1_I11_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| V_a = V_b
| ~ c_lessequals(V_b,V_a,T_a) ) ).
cnf(cls_mult__less__cancel__left__disj_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ).
cnf(cls_mult__less__cancel__right__disj_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_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_order__le__less_1,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_order__less__imp__le_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| c_lessequals(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_order__le__less__trans_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_order__less__le__trans_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_xt1_I8_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a)
| ~ c_lessequals(V_y,V_x,T_a) ) ).
cnf(cls_xt1_I7_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a)
| ~ c_lessequals(V_z,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
cnf(cls_mult__le__cancel__left__neg_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_lessequals(V_b,V_a,T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_mult__le__cancel__left__neg_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_mult__le__cancel__left__pos_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_mult__le__cancel__left__pos_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_mult__left__le__imp__le_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
| c_lessequals(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ).
cnf(cls_mult__right__le__imp__le_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
| c_lessequals(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ).
cnf(cls_mult__strict__mono_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_mult__left__less__imp__less_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring(T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ).
cnf(cls_mult__right__less__imp__less_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring(T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ).
cnf(cls_mult__less__imp__less__left_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ).
cnf(cls_mult__less__imp__less__right_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ).
cnf(cls_mult__strict__mono_H_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_mult__le__less__imp__less_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a)
| ~ c_lessequals(V_a,V_b,T_a) ) ).
cnf(cls_mult__less__le__imp__less_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(V_c,V_d,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_div__0_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_div__by__0_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Odiv(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_no__zero__divirors__neq0_0,axiom,
( ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a)
| V_b = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_no__zero__divisors_0,axiom,
( ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| V_b = c_HOL_Ozero__class_Ozero(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_mult__eq__0__iff_0,axiom,
( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a)
| c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| V_b = c_HOL_Ozero__class_Ozero(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I9_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I10_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_mult__left_Ozero_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_mult_Ozero__left_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_mult_Ozero__right_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_mult__right_Ozero_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_HOL_Otimes__class_Otimes(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_class__semiring_Omul__0_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_mult__zero__left_0,axiom,
( ~ class_Ring__and__Field_Omult__zero(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_mult__zero__right_0,axiom,
( ~ class_Ring__and__Field_Omult__zero(T_a)
| c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_mult__eq__0__iff_1,axiom,
( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_mult__eq__0__iff_2,axiom,
( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a)
| c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_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_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_div__mult__self1__is__id_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),V_b,T_a) = V_a
| V_b = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_div__mult__self2__is__id_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_b,T_a) = V_a
| V_b = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I13_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),c_HOL_Otimes__class_Otimes(V_ly,V_ry,T_a),T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I14_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a),T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I15_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_ry,T_a),T_a) ) ).
cnf(cls_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_pdivmod__rel__unique_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| V_q1 = V_q2
| ~ c_Polynomial_Opdivmod__rel(V_x,V_y,V_q2,V_r2,T_a)
| ~ c_Polynomial_Opdivmod__rel(V_x,V_y,V_q1,V_r1,T_a) ) ).
cnf(cls_pdivmod__rel__unique_1,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| V_r1 = V_r2
| ~ c_Polynomial_Opdivmod__rel(V_x,V_y,V_q2,V_r2,T_a)
| ~ c_Polynomial_Opdivmod__rel(V_x,V_y,V_q1,V_r1,T_a) ) ).
cnf(cls_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_div__mult__mult1__if_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_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_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_mult__idem_0,axiom,
( ~ class_OrderedGroup_Oab__semigroup__idem__mult(T_a)
| c_HOL_Otimes__class_Otimes(V_x,V_x,T_a) = V_x ) ).
cnf(cls_split__mult__pos__le_0,axiom,
( ~ class_Ring__and__Field_Opordered__ring(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_split__mult__pos__le_1,axiom,
( ~ class_Ring__and__Field_Opordered__ring(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_mult__nonpos__nonpos_0,axiom,
( ~ class_Ring__and__Field_Opordered__ring(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_zero__le__square_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_a,T_a),T_a) ) ).
cnf(cls_zero__le__mult__iff_4,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_zero__le__mult__iff_5,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_mult__nonneg__nonneg_0,axiom,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_ab__semigroup__mult__class_Omult__ac_I1_J_0,axiom,
( ~ class_OrderedGroup_Oab__semigroup__mult(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I16_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I17_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a) = c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,V_rx,T_a),T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I18_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ry,T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I19_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a) ) ).
cnf(cls_class__semiring_Omul__a_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_z,T_a) ) ).
cnf(cls_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_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_div__mult__mult1_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) = c_Divides_Odiv__class_Odiv(V_a,V_b,T_a)
| V_c = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_div__mult__mult2_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) = c_Divides_Odiv__class_Odiv(V_a,V_b,T_a)
| V_c = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_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_div__poly__eq_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Divides_Odiv__class_Odiv(V_x,V_y,tc_Polynomial_Opoly(T_a)) = V_q
| ~ c_Polynomial_Opdivmod__rel(V_x,V_y,V_q,V_r,T_a) ) ).
cnf(cls_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_order__trans_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_xt1_I6_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_z,V_x,T_a)
| ~ c_lessequals(V_z,V_y,T_a)
| ~ c_lessequals(V_y,V_x,T_a) ) ).
cnf(cls_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_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_div__smult__right_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Divides_Odiv__class_Odiv(V_x,c_Polynomial_Osmult(V_a,V_y,T_a),tc_Polynomial_Opoly(T_a)) = c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_Divides_Odiv__class_Odiv(V_x,V_y,tc_Polynomial_Opoly(T_a)),T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_pdivmod__rel__smult__right_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Polynomial_Opdivmod__rel(V_x,c_Polynomial_Osmult(V_a,V_y,T_a),c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_q,T_a),V_r,T_a)
| ~ c_Polynomial_Opdivmod__rel(V_x,V_y,V_q,V_r,T_a)
| V_a = c_HOL_Ozero__class_Ozero(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_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_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_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_lgqr_0,axiom,
c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(v_q____,tc_Complex_Ocomplex) = c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ).
cnf(cls_qr_0,axiom,
c_Polynomial_Opoly(v_q____,V_z,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),V_z,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ).
cnf(cls_r01_0,axiom,
c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex) ).
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_eq__divide__eq_2,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_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_divide__less__0__iff_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_divide__less__0__iff_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_divide__pos__neg_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ).
cnf(cls_divide__neg__pos_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_zero__less__divide__1__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) ) ).
cnf(cls_zero__less__divide__1__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),T_a) ) ).
cnf(cls_inverse__zero__imp__zero_0,axiom,
( ~ class_Ring__and__Field_Odivision__ring(T_a)
| c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_inverse__nonzero__iff__nonzero_0,axiom,
( ~ class_Ring__and__Field_Odivision__ring(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_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_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_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__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_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_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_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_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_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_divide__less__0__1__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_divide__less__0__1__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_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_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_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_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_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_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_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_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_divide__self__if_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_divide__1_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Oone__class_Oone(T_a),T_a) = V_a ) ).
cnf(cls_divide__strict__right__mono__neg_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ).
cnf(cls_divide__strict__right__mono_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_a00_0,axiom,
c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ).
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_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_zero__less__divide__iff_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_zero__less__divide__iff_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_divide__pos__pos_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ).
cnf(cls_divide__neg__neg_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_less__divide__eq_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_less__divide__eq_2,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ).
cnf(cls_divide__less__eq_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_divide__less__eq_2,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ).
cnf(cls_nonzero__inverse__eq__divide_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_right__inverse__eq_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) != c_HOL_Oone__class_Oone(T_a)
| V_b = c_HOL_Ozero__class_Ozero(T_a)
| V_a = V_b ) ).
cnf(cls_inverse__zero_0,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_inverse__nonzero__iff__nonzero_1,axiom,
( ~ class_Ring__and__Field_Odivision__ring(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_nonzero__inverse__eq__imp__eq_0,axiom,
( ~ class_Ring__and__Field_Odivision__ring(T_a)
| c_HOL_Oinverse__class_Oinverse(V_a,T_a) != c_HOL_Oinverse__class_Oinverse(V_b,T_a)
| V_a = V_b
| V_b = c_HOL_Ozero__class_Ozero(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_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_zero__less__divide__iff_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ).
cnf(cls_zero__less__divide__iff_2,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ).
cnf(cls_zero__less__divide__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ).
cnf(cls_zero__less__divide__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ).
cnf(cls_inverse__divide_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_b,V_a,T_a) ) ).
cnf(cls_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_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_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_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_inverse__eq__divide_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_HOL_Oinverse__class_Oinverse(V_a,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a) ) ).
cnf(cls_class__fieldgb_Oinverse__divide_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Int_Onumber__ring(T_a)
| c_HOL_Oinverse__class_Oinverse(V_x,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_x,T_a) ) ).
cnf(cls_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_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_right__inverse__eq_1,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| V_x = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Oinverse__class_Odivide(V_x,V_x,T_a) = c_HOL_Oone__class_Oone(T_a) ) ).
cnf(cls_divide__self_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_divide__self__if_1,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a) = c_HOL_Oone__class_Oone(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_divide__zero__left_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_divide__eq__eq_1,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_divide__zero_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_divide_Ozero_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_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_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_divide__less__0__iff_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_divide__less__0__iff_2,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_divide__less__0__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_divide__less__0__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_CHAINED_0,axiom,
c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex) != c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex) ).
cnf(cls_CHAINED_0_01,axiom,
c_Polynomial_Opoly(v_q____,v_w____,tc_Complex_Ocomplex) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ).
cnf(cls_conjecture_0,negated_conjecture,
( ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_Polynomial_Opoly(v_q____,v_w____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).
cnf(cls_conjecture_1,negated_conjecture,
( c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(c_Polynomial_Osmult(c_HOL_Oinverse__class_Oinverse(c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_q____,tc_Complex_Ocomplex),v_w____,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Oinverse__class_Odivide(c_Polynomial_Opoly(v_q____,v_w____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_q____,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oidom,axiom,
( class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oidom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1,axiom,
( class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__ring__1(T_1) ) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Oidom,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oidom,axiom,
class_Ring__and__Field_Oidom(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_Int__Oint__Ring__and__Field_Oidom,axiom,
class_Ring__and__Field_Oidom(tc_Int_Oint) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Ocomm__ring__1,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Int_Oint) ).
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__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__Ring__and__Field_Ozero__neq__one,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Omult__mono1,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Omult__zero,axiom,
class_Ring__and__Field_Omult__zero(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Omult__mono,axiom,
class_Ring__and__Field_Omult__mono(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Omonoid__mult,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat) ).
cnf(clsarity_nat__Divides_Osemiring__div,axiom,
class_Divides_Osemiring__div(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__Int_Onumber,axiom,
class_Int_Onumber(tc_nat) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__comm__semiring__strict,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Int_Oint) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_Int_Oint) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Oring__no__zero__divisors,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Int_Oint) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__ring__strict,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Opordered__semiring,axiom,
class_Ring__and__Field_Opordered__semiring(tc_Int_Oint) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__semiring,axiom,
class_Ring__and__Field_Oordered__semiring(tc_Int_Oint) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__semidom,axiom,
class_Ring__and__Field_Oordered__semidom(tc_Int_Oint) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__0,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Int_Oint) ).
cnf(clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint) ).
cnf(clsarity_Int__Oint__OrderedGroup_Ocomm__monoid__mult,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Opordered__ring,axiom,
class_Ring__and__Field_Opordered__ring(tc_Int_Oint) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Ozero__neq__one,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Int_Oint) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Oordered__idom,axiom,
class_Ring__and__Field_Oordered__idom(tc_Int_Oint) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Omult__mono1,axiom,
class_Ring__and__Field_Omult__mono1(tc_Int_Oint) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Omult__zero,axiom,
class_Ring__and__Field_Omult__zero(tc_Int_Oint) ).
cnf(clsarity_Int__Oint__Ring__and__Field_Omult__mono,axiom,
class_Ring__and__Field_Omult__mono(tc_Int_Oint) ).
cnf(clsarity_Int__Oint__OrderedGroup_Omonoid__mult,axiom,
class_OrderedGroup_Omonoid__mult(tc_Int_Oint) ).
cnf(clsarity_Int__Oint__Divides_Osemiring__div,axiom,
class_Divides_Osemiring__div(tc_Int_Oint) ).
cnf(clsarity_Int__Oint__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Int_Oint) ).
cnf(clsarity_Int__Oint__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Int_Oint) ).
cnf(clsarity_Int__Oint__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_Int_Oint) ).
cnf(clsarity_Int__Oint__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_Int_Oint) ).
cnf(clsarity_Int__Oint__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_Int_Oint) ).
cnf(clsarity_Int__Oint__Int_Onumber,axiom,
class_Int_Onumber(tc_Int_Oint) ).
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_Oordered__semiring__strict,axiom,
class_Ring__and__Field_Oordered__semiring__strict(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__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__Ring__and__Field_Opordered__semiring,axiom,
class_Ring__and__Field_Opordered__semiring(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__OrderedGroup_Ocomm__monoid__mult,axiom,
class_OrderedGroup_Ocomm__monoid__mult(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_Odivision__ring,axiom,
class_Ring__and__Field_Odivision__ring(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__field,axiom,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom,axiom,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1,axiom,
class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__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_Ofield,axiom,
class_Ring__and__Field_Ofield(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Int_Onumber,axiom,
class_Int_Onumber(tc_RealDef_Oreal) ).
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__RealVector_Oreal__normed__div__algebra,axiom,
class_RealVector_Oreal__normed__div__algebra(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__OrderedGroup_Ocomm__monoid__mult,axiom,
class_OrderedGroup_Ocomm__monoid__mult(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__RealVector_Oreal__normed__field,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Ring__and__Field_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_Ofield,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex) ).
cnf(clsarity_Complex__Ocomplex__Int_Onumber,axiom,
class_Int_Onumber(tc_Complex_Ocomplex) ).
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_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__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__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__Ring__and__Field_Opordered__semiring,axiom,
( class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring,axiom,
( class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors,axiom,
( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oidom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semidom,axiom,
( class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1,axiom,
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0,axiom,
( class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult,axiom,
( class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult,axiom,
( class_OrderedGroup_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__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_Ozero__neq__one,axiom,
( class_Ring__and__Field_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom,axiom,
( class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono1,axiom,
( class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__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__Divides_Osemiring__div,axiom,
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ofield(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Orderings_Opreorder,axiom,
( class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Orderings_Olinorder,axiom,
( class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Orderings_Oorder,axiom,
( class_Orderings_Oorder(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Int_Oring__char__0,axiom,
( class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Int_Onumber__ring,axiom,
( class_Int_Onumber__ring(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__ring__1(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Int_Onumber,axiom,
( class_Int_Onumber(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__ring__1(T_1) ) ).
%------------------------------------------------------------------------------