TPTP Problem File: ALG391-1.p
View Solutions
- Solve Problem
%------------------------------------------------------------------------------
% File : ALG391-1 : TPTP v8.2.0. Released v4.1.0.
% Domain : General Algebra
% Problem : Fundamental theorem of algebra 0591_7
% Version : Especial.
% English :
% Refs : [Nip10] Nipkow (2010), Email to Geoff Sutcliffe
% : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% Source : [Nip10]
% Names : Fundamental_Theorem_Algebra-0591_7 [Nip10]
% Status : Unsatisfiable
% Rating : 0.15 v8.2.0, 0.14 v8.1.0, 0.16 v7.5.0, 0.21 v7.4.0, 0.24 v7.3.0, 0.08 v7.1.0, 0.00 v7.0.0, 0.20 v6.3.0, 0.09 v6.2.0, 0.10 v6.1.0, 0.21 v6.0.0, 0.20 v5.5.0, 0.35 v5.3.0, 0.28 v5.2.0, 0.25 v5.1.0, 0.35 v5.0.0, 0.36 v4.1.0
% Syntax : Number of clauses : 1282 ( 154 unt; 170 nHn; 781 RR)
% Number of literals : 3486 ( 768 equ;2056 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of predicates : 79 ( 78 usr; 0 prp; 1-5 aty)
% Number of functors : 49 ( 49 usr; 7 con; 0-4 aty)
% Number of variables : 3476 ( 225 sgn)
% SPC : CNF_UNS_RFO_SEQ_NHN
% Comments :
%------------------------------------------------------------------------------
cnf(cls_less__SucI_0,axiom,
( c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat)
| ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).
cnf(cls_Suc__lessD_0,axiom,
( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat) ) ).
cnf(cls_monom__0_0,axiom,
( ~ class_HOL_Ozero(T_a)
| c_Polynomial_Omonom(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a) = c_Polynomial_OpCons(V_a,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) ) ).
cnf(cls_mult__strict__mono_H_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
| c_HOL_Oord__class_Oless(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_Pair__eq_0,axiom,
( c_Pair(V_a,V_b,T_a,T_b) != c_Pair(V_a_H,V_b_H,T_a,T_b)
| V_a = V_a_H ) ).
cnf(cls_Pair__eq_1,axiom,
( c_Pair(V_a,V_b,T_a,T_b) != c_Pair(V_a_H,V_b_H,T_a,T_b)
| V_b = V_b_H ) ).
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_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_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_smult__pCons_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_Polynomial_Osmult(V_a,c_Polynomial_OpCons(V_b,V_p,T_a),T_a) = c_Polynomial_OpCons(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_Polynomial_Osmult(V_a,V_p,T_a),T_a) ) ).
cnf(cls_pos__poly__add_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_Polynomial_Opos__poly(c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a)
| ~ c_Polynomial_Opos__poly(V_q,T_a)
| ~ c_Polynomial_Opos__poly(V_p,T_a) ) ).
cnf(cls_le__sup__iff_1,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a) ) ).
cnf(cls_le__sup__iff_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a) ) ).
cnf(cls_le__supI2_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_lessequals(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),T_a)
| ~ c_lessequals(V_x,V_b,T_a) ) ).
cnf(cls_le__supI1_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_lessequals(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),T_a)
| ~ c_lessequals(V_x,V_a,T_a) ) ).
cnf(cls_le__supE_1,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_lessequals(V_b,V_x,T_a)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),V_x,T_a) ) ).
cnf(cls_le__supE_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_lessequals(V_a,V_x,T_a)
| ~ c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),V_x,T_a) ) ).
cnf(cls_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_Suc__n__not__n_0,axiom,
c_Suc(V_n) != V_n ).
cnf(cls_n__not__Suc__n_0,axiom,
V_n != c_Suc(V_n) ).
cnf(cls_sum__squares__eq__zero__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a) != c_HOL_Ozero__class_Ozero(T_a)
| V_y = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_sum__squares__eq__zero__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a) != c_HOL_Ozero__class_Ozero(T_a)
| V_x = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_class__ringb_Oadd__scale__eq__noteq_0,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_r,V_c,T_a),T_a) != c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_r,V_d,T_a),T_a)
| V_c = V_d
| V_r = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_prts_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| V_a = c_HOL_Oplus__class_Oplus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a,T_a),T_a) ) ).
cnf(cls_sup__eq__if_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = V_a
| c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_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__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_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_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__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_eq__poly__code_I2_J_2,axiom,
( ~ class_HOL_Ozero(T_a)
| ~ class_HOL_Oeq(T_a)
| c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(V_b,V_q,T_a),tc_Polynomial_Opoly(T_a))
| ~ c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q,tc_Polynomial_Opoly(T_a))
| ~ c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) ) ).
cnf(cls_poly__mod__mult__right_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Divides_Odiv__class_Omod(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_y,c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Odiv(V_x,V_y,tc_Polynomial_Opoly(T_a)),V_z,tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)),c_Divides_Odiv__class_Omod(V_x,V_y,tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_pos__add__strict_0,axiom,
( ~ class_Ring__and__Field_Oordered__semidom(T_a)
| c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_pCons__eq__iff_0,axiom,
( ~ class_HOL_Ozero(T_a)
| c_Polynomial_OpCons(V_a,V_p,T_a) != c_Polynomial_OpCons(V_b,V_q,T_a)
| V_a = V_b ) ).
cnf(cls_pCons__eq__iff_1,axiom,
( ~ class_HOL_Ozero(T_a)
| c_Polynomial_OpCons(V_a,V_p,T_a) != c_Polynomial_OpCons(V_b,V_q,T_a)
| V_p = V_q ) ).
cnf(cls_dvd__mult__right_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) ) ).
cnf(cls_dvd__mult__left_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) ) ).
cnf(cls_dvd__mult2_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ).
cnf(cls_dvd__mult_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a) ) ).
cnf(cls_sup__inf__distrib2_0,axiom,
( ~ class_Lattices_Odistrib__lattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),V_x,T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_y,V_x,T_a),c_Lattices_Oupper__semilattice__class_Osup(V_z,V_x,T_a),T_a) ) ).
cnf(cls_sup__inf__distrib1_0,axiom,
( ~ class_Lattices_Odistrib__lattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),c_Lattices_Oupper__semilattice__class_Osup(V_x,V_z,T_a),T_a) ) ).
cnf(cls_add__minus__cancel_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a),T_a) = V_b ) ).
cnf(cls_abs__le__D2_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ).
cnf(cls_mult__pos__neg2_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_mult__pos__neg_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_mult__neg__pos_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_mult__le__0__iff_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_mult__le__0__iff_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_mult__le__0__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_mult__le__0__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_mod__add__self2_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a) ) ).
cnf(cls_mod__add__self1_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_b,V_a,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a) ) ).
cnf(cls_abs__less__iff_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_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_inf__greatest_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a)
| ~ c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_le__inf__iff_2,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a)
| ~ c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_le__infI_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),T_a)
| ~ c_lessequals(V_x,V_b,T_a)
| ~ c_lessequals(V_x,V_a,T_a) ) ).
cnf(cls_inf__le2_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_y,T_a) ) ).
cnf(cls_inf__le1_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_x,T_a) ) ).
cnf(cls_inf__sup__ord_I2_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_y,T_a) ) ).
cnf(cls_inf__sup__ord_I1_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_x,T_a) ) ).
cnf(cls_pdivmod__rel__def_4,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_q,V_y,tc_Polynomial_Opoly(T_a)),V_r,tc_Polynomial_Opoly(T_a)),V_y,V_q,V_r,T_a)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(V_r,T_a),c_Polynomial_Odegree(V_y,T_a),tc_nat)
| V_y = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_neg__le__0__iff__le_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_neg__le__0__iff__le_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_div__mult__div__if__dvd_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_x,V_y,T_a),c_Divides_Odiv__class_Odiv(V_w,V_z,T_a),T_a) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_x,V_w,T_a),c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_w,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a) ) ).
cnf(cls_eq__poly__code_I2_J_1,axiom,
( ~ class_HOL_Ozero(T_a)
| ~ class_HOL_Oeq(T_a)
| c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q,tc_Polynomial_Opoly(T_a))
| ~ c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(V_b,V_q,T_a),tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_eq__poly__code_I2_J_0,axiom,
( ~ class_HOL_Ozero(T_a)
| ~ class_HOL_Oeq(T_a)
| c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(V_b,V_q,T_a),tc_Polynomial_Opoly(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_le__eq__neg_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_le__eq__neg_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ).
cnf(cls_minus__mult__right_0,axiom,
( ~ class_Ring__and__Field_Oring(T_a)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ).
cnf(cls_minus__mult__left_0,axiom,
( ~ class_Ring__and__Field_Oring(T_a)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) ).
cnf(cls_sgn__minus_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Osgn__class_Osgn(V_x,T_a),T_a) ) ).
cnf(cls_mult__frac__frac_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Oinverse__class_Odivide(V_z,V_w,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),c_HOL_Otimes__class_Otimes(V_y,V_w,T_a),T_a) ) ).
cnf(cls_abs__eq__mult_3,axiom,
( ~ class_Ring__and__Field_Opordered__ring__abs(T_a)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_abs__eq__mult_2,axiom,
( ~ class_Ring__and__Field_Opordered__ring__abs(T_a)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_abs__eq__mult_1,axiom,
( ~ class_Ring__and__Field_Opordered__ring__abs(T_a)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_abs__eq__mult_0,axiom,
( ~ class_Ring__and__Field_Opordered__ring__abs(T_a)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_abs__mult_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a) ) ).
cnf(cls_add__le__cancel__right_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)
| ~ c_lessequals(V_a,V_b,T_a) ) ).
cnf(cls_add__le__cancel__right_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ).
cnf(cls_add__le__cancel__left_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_lessequals(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(V_a,V_b,T_a) ) ).
cnf(cls_add__le__cancel__left_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a) ) ).
cnf(cls_add__right__mono_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a)
| c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)
| ~ c_lessequals(V_a,V_b,T_a) ) ).
cnf(cls_add__left__mono_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a)
| c_lessequals(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a)
| ~ c_lessequals(V_a,V_b,T_a) ) ).
cnf(cls_add__le__mono1_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_j,V_k,tc_nat),tc_nat)
| ~ c_lessequals(V_i,V_j,tc_nat) ) ).
cnf(cls_nat__add__left__cancel__le_0,axiom,
( c_lessequals(V_m,V_n,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat) ) ).
cnf(cls_nat__add__left__cancel__le_1,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat)
| ~ c_lessequals(V_m,V_n,tc_nat) ) ).
cnf(cls_lessI_0,axiom,
c_HOL_Oord__class_Oless(V_n,c_Suc(V_n),tc_nat) ).
cnf(cls_less__Suc__eq_2,axiom,
c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat) ).
cnf(cls_less__trans__Suc_0,axiom,
( c_HOL_Oord__class_Oless(c_Suc(V_i),V_k,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ).
cnf(cls_dvd__mult__cancel__right_1,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a),T_a) ) ).
cnf(cls_dvd__mult__cancel__left_1,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a),T_a) ) ).
cnf(cls_less__eqI_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a) ) ).
cnf(cls_less__eqI_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
| c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_le__eqI_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
| c_lessequals(V_y,V_x,T_a)
| ~ c_lessequals(V_y_H,V_x_H,T_a) ) ).
cnf(cls_le__eqI_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
| c_lessequals(V_y_H,V_x_H,T_a)
| ~ c_lessequals(V_y,V_x,T_a) ) ).
cnf(cls_zmod__simps_I2_J_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) ) ).
cnf(cls_zmod__simps_I1_J_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) ) ).
cnf(cls_inf__period_I4_J_0,axiom,
( ~ class_Ring__and__Field_Odvd(T_a)
| ~ class_Ring__and__Field_Ocomm__ring(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_x,c_HOL_Otimes__class_Otimes(V_k,V_D,T_a),T_a),V_t,T_a),T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(V_x,V_t,T_a),T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_D,T_a) ) ).
cnf(cls_inf__period_I4_J_1,axiom,
( ~ class_Ring__and__Field_Odvd(T_a)
| ~ class_Ring__and__Field_Ocomm__ring(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(V_x,V_t,T_a),T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_x,c_HOL_Otimes__class_Otimes(V_k,V_D,T_a),T_a),V_t,T_a),T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_d,V_D,T_a) ) ).
cnf(cls_add__is__1_2,axiom,
( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| V_m = c_HOL_Ozero__class_Ozero(tc_nat)
| V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
cnf(cls_add__is__1_1,axiom,
( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ).
cnf(cls_mod__div__decomp_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| V_a = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a) ) ).
cnf(cls_mod__div__equality_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a) = V_a ) ).
cnf(cls_mod__div__equality2_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a) = V_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_le__neq__implies__less_0,axiom,
( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| V_m = V_n
| ~ c_lessequals(V_m,V_n,tc_nat) ) ).
cnf(cls_le__eq__less__or__eq_0,axiom,
( V_m = V_n
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ~ c_lessequals(V_m,V_n,tc_nat) ) ).
cnf(cls_nat__less__le_2,axiom,
( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| V_m = V_n
| ~ c_lessequals(V_m,V_n,tc_nat) ) ).
cnf(cls_order__le__neq__trans_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| V_a = V_b
| ~ c_lessequals(V_a,V_b,T_a) ) ).
cnf(cls_order__neq__le__trans_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| V_a = V_b ) ).
cnf(cls_linorder__antisym__conv1_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| V_x = V_y
| ~ c_lessequals(V_x,V_y,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_linorder__antisym__conv2_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| V_x = V_y
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_xt1_I12_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| V_a = V_b ) ).
cnf(cls_xt1_I11_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| V_a = V_b
| ~ c_lessequals(V_b,V_a,T_a) ) ).
cnf(cls_divide__right__mono_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(V_a,V_b,T_a) ) ).
cnf(cls_divide__right__mono__neg_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),T_a)
| ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_a,V_b,T_a) ) ).
cnf(cls_smult__dvd__iff_4,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(V_a,V_p,T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a))
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_split__mult__pos__le_0,axiom,
( ~ class_Ring__and__Field_Opordered__ring(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_split__mult__pos__le_1,axiom,
( ~ class_Ring__and__Field_Opordered__ring(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_mult__nonpos__nonpos_0,axiom,
( ~ class_Ring__and__Field_Opordered__ring(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_zero__le__square_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_a,T_a),T_a) ) ).
cnf(cls_zero__le__mult__iff_4,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_zero__le__mult__iff_5,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_mult__nonneg__nonneg_0,axiom,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_abs__triangle__ineq2_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a),T_a) ) ).
cnf(cls_dvd__div__neg_0,axiom,
( ~ class_Divides_Oring__div(T_a)
| c_Divides_Odiv__class_Odiv(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(V_x,V_y,T_a),T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a) ) ).
cnf(cls_dvd__neg__div_0,axiom,
( ~ class_Divides_Oring__div(T_a)
| c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(V_x,V_y,T_a),T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,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_class__semiring_Osemiring__rules_I8_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ).
cnf(cls_mult__right_Oadd_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),c_HOL_Otimes__class_Otimes(V_xa,V_y,T_a),T_a) ) ).
cnf(cls_mult_Oadd__right_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oplus__class_Oplus(V_b,V_b_H,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a,V_b_H,T_a),T_a) ) ).
cnf(cls_mult__left_Oadd_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),V_ya,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_ya,T_a),c_HOL_Otimes__class_Otimes(V_y,V_ya,T_a),T_a) ) ).
cnf(cls_mult_Oadd__left_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_a_H,T_a),V_b,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a_H,V_b,T_a),T_a) ) ).
cnf(cls_mult__poly__add__left_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),V_r,tc_Polynomial_Opoly(T_a)) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_p,V_r,tc_Polynomial_Opoly(T_a)),c_HOL_Otimes__class_Otimes(V_q,V_r,tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_class__semiring_Omul__d_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a) ) ).
cnf(cls_comm__semiring__class_Odistrib_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ).
cnf(cls_coeff__minus_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_Polynomial_Ocoeff(c_HOL_Ouminus__class_Ouminus(V_p,tc_Polynomial_Opoly(T_a)),V_n,T_a) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Ocoeff(V_p,V_n,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_add__gr__0_2,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ) ).
cnf(cls_add__gr__0_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat) ) ).
cnf(cls_zero__less__double__add__iff__zero__less__single__add_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a) ) ).
cnf(cls_zero__less__double__add__iff__zero__less__single__add_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_less__supI1_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_HOL_Oord__class_Oless(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_a,T_a) ) ).
cnf(cls_less__supI2_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_HOL_Oord__class_Oless(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_b,T_a) ) ).
cnf(cls_smult__dvd__iff_2,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(V_a,V_p,T_a),V_q,tc_Polynomial_Opoly(T_a))
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_smult__dvd__iff_1,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
| V_a = c_HOL_Ozero__class_Ozero(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(V_a,V_p,T_a),V_q,tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_dvd__smult__iff_1,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_p,c_Polynomial_Osmult(V_a,V_q,T_a),tc_Polynomial_Opoly(T_a))
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_dvd__smult__iff_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,c_Polynomial_Osmult(V_a,V_q,T_a),tc_Polynomial_Opoly(T_a))
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_smult__dvd_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(V_a,V_p,T_a),V_q,tc_Polynomial_Opoly(T_a))
| V_a = c_HOL_Ozero__class_Ozero(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_dvd__smult__cancel_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
| V_a = c_HOL_Ozero__class_Ozero(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,c_Polynomial_Osmult(V_a,V_q,T_a),tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_abs__minus__commute_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),T_a) ) ).
cnf(cls_minus__divide__right_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ).
cnf(cls_minus__divide__left_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) ).
cnf(cls_zero__le__mult__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ).
cnf(cls_zero__le__mult__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ).
cnf(cls_zero__le__mult__iff_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ).
cnf(cls_zero__le__mult__iff_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ).
cnf(cls_synthetic__div__unique__lemma_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_Polynomial_Osmult(V_c,V_p,T_a) != c_Polynomial_OpCons(V_a,V_p,T_a)
| V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_sum__squares__gt__zero__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),T_a),T_a) ) ).
cnf(cls_assms_0,axiom,
( ~ class_Ring__and__Field_Oidom(t_a)
| v_sko__local__Xassms__1(v_p) != c_HOL_Ozero__class_Ozero(t_a) ) ).
cnf(cls_mod__smult__left_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Divides_Odiv__class_Omod(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_Omod(V_x,V_y,tc_Polynomial_Opoly(T_a)),T_a) ) ).
cnf(cls_eq__poly__def_1,axiom,
( ~ class_HOL_Ozero(T_a)
| ~ class_HOL_Oeq(T_a)
| c_HOL_Oeq__class_Oeq(V_x,V_x,tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_eq__class_Oeq__refl_0,axiom,
( ~ class_HOL_Oeq(T_a)
| c_HOL_Oeq__class_Oeq(V_x,V_x,T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I1_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),c_HOL_Otimes__class_Otimes(V_b,V_m,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_m,T_a) ) ).
cnf(cls_diff__frac__eq_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),c_HOL_Otimes__class_Otimes(V_w,V_y,T_a),T_a),c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a)
| V_z = c_HOL_Ozero__class_Ozero(T_a)
| V_y = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_mult_Ominus__left_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ).
cnf(cls_mult__left_Ominus_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) ) ).
cnf(cls_mult_Ominus__right_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ).
cnf(cls_mult__right_Ominus_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),T_a) ) ).
cnf(cls_square__eq__iff_1,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_b,V_b,T_a) ) ).
cnf(cls_minus__mult__minus_0,axiom,
( ~ class_Ring__and__Field_Oring(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) ) ).
cnf(cls_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_diff__pCons_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_HOL_Ominus__class_Ominus(c_Polynomial_OpCons(V_a,V_p,T_a),c_Polynomial_OpCons(V_b,V_q,T_a),tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ominus__class_Ominus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) ) ).
cnf(cls_sgn__sgn_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(V_a,T_a),T_a) = c_HOL_Osgn__class_Osgn(V_a,T_a) ) ).
cnf(cls_divide__less__eq_2,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ).
cnf(cls_divide__less__eq_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_divide__less__eq_8,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ).
cnf(cls_divide__less__eq_9,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ).
cnf(cls_less__divide__eq_2,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ).
cnf(cls_less__divide__eq_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_less__divide__eq_8,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ).
cnf(cls_less__divide__eq_9,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ).
cnf(cls_dvd__trans_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ).
cnf(cls_dvd__refl_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_a,T_a) ) ).
cnf(cls_scaleR__right_Odiff_0,axiom,
( ~ class_RealVector_Oreal__vector(T_a)
| c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ominus__class_Ominus(V_x,V_y,T_a),T_a) = c_HOL_Ominus__class_Ominus(c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),c_RealVector_OscaleR__class_OscaleR(V_a,V_y,T_a),T_a) ) ).
cnf(cls_scaleR_Odiff__right_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ominus__class_Ominus(V_b,V_b_H,T_a),T_a) = c_HOL_Ominus__class_Ominus(c_RealVector_OscaleR__class_OscaleR(V_a,V_b,T_a),c_RealVector_OscaleR__class_OscaleR(V_a,V_b_H,T_a),T_a) ) ).
cnf(cls_less__infI2_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_x,T_a) ) ).
cnf(cls_less__infI1_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_HOL_Oord__class_Oless(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_x,T_a) ) ).
cnf(cls_inf__sup__absorb_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) = V_x ) ).
cnf(cls_abs__of__nonneg_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_coeff__diff_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_Polynomial_Ocoeff(c_HOL_Ominus__class_Ominus(V_p,V_q,tc_Polynomial_Opoly(T_a)),V_n,T_a) = c_HOL_Ominus__class_Ominus(c_Polynomial_Ocoeff(V_p,V_n,T_a),c_Polynomial_Ocoeff(V_q,V_n,T_a),T_a) ) ).
cnf(cls_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_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_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_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_le__antisym_0,axiom,
( V_m = V_n
| ~ c_lessequals(V_n,V_m,tc_nat)
| ~ c_lessequals(V_m,V_n,tc_nat) ) ).
cnf(cls_nat__neq__iff_0,axiom,
( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| V_m = V_n ) ).
cnf(cls_linorder__neqE__nat_0,axiom,
( c_HOL_Oord__class_Oless(V_y,V_x,tc_nat)
| c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)
| V_x = V_y ) ).
cnf(cls_order__eq__iff_2,axiom,
( ~ class_Orderings_Oorder(T_a)
| V_x = V_y
| ~ c_lessequals(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_linorder__neqE_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| V_x = V_y ) ).
cnf(cls_order__antisym_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| V_x = V_y
| ~ c_lessequals(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_compl__eq__compl__iff_0,axiom,
( ~ class_Lattices_Oboolean__algebra(T_a)
| c_HOL_Ouminus__class_Ouminus(V_x,T_a) != c_HOL_Ouminus__class_Ouminus(V_y,T_a)
| V_x = V_y ) ).
cnf(cls_neg__equal__iff__equal_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| c_HOL_Ouminus__class_Ouminus(V_a,T_a) != c_HOL_Ouminus__class_Ouminus(V_b,T_a)
| V_a = V_b ) ).
cnf(cls_le__0__eq_0,axiom,
( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_lessequals(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ) ).
cnf(cls_eq__divide__imp_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| V_c = c_HOL_Ozero__class_Ozero(T_a)
| V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) ) ).
cnf(cls_divide__eq__imp_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| V_c = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) = V_a ) ).
cnf(cls_estimate__by__abs_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a)
| c_lessequals(V_a,c_HOL_Oplus__class_Oplus(V_c,c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) ) ).
cnf(cls_eq__divide__eq_3,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| V_a = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a)
| V_c = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_divide__eq__eq_3,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a) = V_a
| V_c = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_distrib__sup__le_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a),c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),c_Lattices_Oupper__semilattice__class_Osup(V_x,V_z,T_a),T_a),T_a) ) ).
cnf(cls_abs__le__zero__iff_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_zero__le__iff__zero__nprt_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_zero__le__iff__zero__nprt_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_abs__lattice_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a)
| c_HOL_Oabs__class_Oabs(V_a,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I15_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_ry,T_a),T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I14_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a),T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I13_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),c_HOL_Otimes__class_Otimes(V_ly,V_ry,T_a),T_a) ) ).
cnf(cls_sup__0__imp__0_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) != c_HOL_Ozero__class_Ozero(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_sum__squares__le__zero__iff_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_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_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_add__nonpos__neg_0,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_add__neg__nonpos_0,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_neg__less__iff__less_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_neg__less__iff__less_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ).
cnf(cls_abs__div__pos_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(V_x,T_a),V_y,T_a) = c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ).
cnf(cls_le__divide__eq_8,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ).
cnf(cls_divide__le__eq_8,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
| ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ).
cnf(cls_not__sum__squares__lt__zero_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_inf__left__commute_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,T_a),T_a) ) ).
cnf(cls_inf__assoc_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ).
cnf(cls_inf__sup__aci_I3_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,T_a),T_a) ) ).
cnf(cls_inf__sup__aci_I2_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ).
cnf(cls_abs__less__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ).
cnf(cls_zero__less__mult__pos2_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a) ) ).
cnf(cls_zero__less__mult__pos_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ).
cnf(cls_mult__pos__pos_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_mult__neg__neg_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_double__add__less__zero__iff__single__less__zero_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_double__add__less__zero__iff__single__less__zero_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_even__less__0__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_even__less__0__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_offset__poly__eq__0__lemma_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(V_c,V_p,T_a),c_Polynomial_OpCons(V_a,V_p,T_a),tc_Polynomial_Opoly(T_a)) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_diff__divide__distrib_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ).
cnf(cls_divide_Odiff_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(V_x,V_y,T_a),V_ya,T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Oinverse__class_Odivide(V_x,V_ya,T_a),c_HOL_Oinverse__class_Odivide(V_y,V_ya,T_a),T_a) ) ).
cnf(cls_add__nonneg__eq__0__iff_1,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
| c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)
| V_y = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_add__nonneg__eq__0__iff_0,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
| c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)
| V_x = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_add__is__0_0,axiom,
( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| V_m = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
cnf(cls_add__is__0_1,axiom,
( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_HOL_Ozero__class_Ozero(tc_nat)
| V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
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_Rational_Oordered__idom__class_Osgn__greater_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Osgn__class_Osgn(V_a,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_Rational_Oordered__idom__class_Osgn__greater_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Osgn__class_Osgn(V_a,T_a),T_a) ) ).
cnf(cls_dvd__diff_0,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_x,c_HOL_Ominus__class_Ominus(V_y,V_z,T_a),T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) ) ).
cnf(cls_abs__of__neg_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_abs__if_0,axiom,
( ~ class_Ring__and__Field_Oabs__if(T_a)
| c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_abs__if__lattice_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a)
| c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_square__eq__iff_0,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) != c_HOL_Otimes__class_Otimes(V_b,V_b,T_a)
| V_a = c_HOL_Ouminus__class_Ouminus(V_b,T_a)
| V_a = V_b ) ).
cnf(cls_mult__less__imp__less__right_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ).
cnf(cls_mult__less__imp__less__left_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ).
cnf(cls_mult__right__less__imp__less_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring(T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ).
cnf(cls_mult__left__less__imp__less_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring(T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ).
cnf(cls_mult__imp__le__div__pos_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_lessequals(V_z,c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),V_x,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ).
cnf(cls_mult__imp__div__pos__le_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),V_z,T_a)
| ~ c_lessequals(V_x,c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) ) ).
cnf(cls_le__divide__eq_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a) ) ).
cnf(cls_le__divide__eq_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ).
cnf(cls_divide__le__eq_6,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ).
cnf(cls_divide__le__eq_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ).
cnf(cls_natgb_Oadd__r0__iff_0,axiom,
( V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,tc_nat)
| V_a = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
cnf(cls_add__eq__self__zero_0,axiom,
( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != V_m
| V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
cnf(cls_synthetic__div__pCons_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_Polynomial_Osynthetic__div(c_Polynomial_OpCons(V_a,V_p,T_a),V_c,T_a) = c_Polynomial_OpCons(c_Polynomial_Opoly(V_p,V_c,T_a),c_Polynomial_Osynthetic__div(V_p,V_c,T_a),T_a) ) ).
cnf(cls_mult__sgn__abs_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(V_x,T_a),c_HOL_Oabs__class_Oabs(V_x,T_a),T_a) = V_x ) ).
cnf(cls_minus__pCons_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_HOL_Ouminus__class_Ouminus(c_Polynomial_OpCons(V_a,V_p,T_a),tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_p,tc_Polynomial_Opoly(T_a)),T_a) ) ).
cnf(cls_pdivmod__rel__def_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| V_x = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_q,V_y,tc_Polynomial_Opoly(T_a)),V_r,tc_Polynomial_Opoly(T_a))
| ~ c_Polynomial_Opdivmod__rel(V_x,V_y,V_q,V_r,T_a) ) ).
cnf(cls_sum__squares__ge__zero_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),T_a) ) ).
cnf(cls_smult__add__left_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_Polynomial_Osmult(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_p,T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(V_a,V_p,T_a),c_Polynomial_Osmult(V_b,V_p,T_a),tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_smult__add__right_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_Polynomial_Osmult(V_a,c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(V_a,V_p,T_a),c_Polynomial_Osmult(V_a,V_q,T_a),tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_dvd__mod__imp__dvd_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a) ) ).
cnf(cls_dvd__mod__iff_1,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a) ) ).
cnf(cls_dvd__mod__iff_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a) ) ).
cnf(cls_not__less__less__Suc__eq_1,axiom,
( c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)
| c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat) ) ).
cnf(cls_not__less__eq_1,axiom,
( ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat) ) ).
cnf(cls_not__less__eq_0,axiom,
( c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).
cnf(cls_smult__monom_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_Polynomial_Osmult(V_a,c_Polynomial_Omonom(V_b,V_n,T_a),T_a) = c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_n,T_a) ) ).
cnf(cls_le__SucE_0,axiom,
( V_m = c_Suc(V_n)
| c_lessequals(V_m,V_n,tc_nat)
| ~ c_lessequals(V_m,c_Suc(V_n),tc_nat) ) ).
cnf(cls_mult__less__cancel__left__disj_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ).
cnf(cls_mult__less__cancel__left__disj_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ).
cnf(cls_mult__less__cancel__right__disj_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ).
cnf(cls_mult__less__cancel__right__disj_3,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ).
cnf(cls_pprt__neg_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_x,T_a),T_a) ) ).
cnf(cls_mod__minus__eq_0,axiom,
( ~ class_Divides_Oring__div(T_a)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a),V_b,T_a) ) ).
cnf(cls_compl__sup_0,axiom,
( ~ class_Lattices_Oboolean__algebra(T_a)
| c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(V_x,T_a),c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) ) ).
cnf(cls_neg__sup__eq__inf_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ).
cnf(cls_divide__neg__neg_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_divide__pos__pos_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ).
cnf(cls_zero__less__divide__iff_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_zero__less__divide__iff_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_zero__le__pprt_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a,T_a),T_a) ) ).
cnf(cls_dvd__add_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ).
cnf(cls_abs__sgn_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Oabs__class_Oabs(V_k,T_a) = c_HOL_Otimes__class_Otimes(V_k,c_HOL_Osgn__class_Osgn(V_k,T_a),T_a) ) ).
cnf(cls_group__add__class_Odiff__0_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a) ) ).
cnf(cls_diff__poly__code_I1_J_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q,tc_Polynomial_Opoly(T_a)) = c_HOL_Ouminus__class_Ouminus(V_q,tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_offset__poly__single_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(V_a,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),V_h,T_a) = c_Polynomial_OpCons(V_a,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) ) ).
cnf(cls_add__frac__num_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),V_z,T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),T_a),V_y,T_a)
| V_y = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_add__num__frac_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oplus__class_Oplus(V_z,c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_z,V_y,T_a),T_a),V_y,T_a)
| V_y = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I20_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a) ) ).
cnf(cls_diff__def_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) ) ).
cnf(cls_class__ring_Osub__add_0,axiom,
( ~ class_Int_Onumber__ring(T_a)
| c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) ) ).
cnf(cls_diff__minus_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ).
cnf(cls_ab__diff__minus_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ).
cnf(cls_nonzero__minus__divide__divide_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a)
| V_b = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_div__dvd__div_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),c_Divides_Odiv__class_Odiv(V_c,V_a,T_a),T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ).
cnf(cls_div__dvd__div_1,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),c_Divides_Odiv__class_Odiv(V_c,V_a,T_a),T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ).
cnf(cls_dvd__minus__iff_0,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) ) ).
cnf(cls_dvd__minus__iff_1,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) ) ).
cnf(cls_minus__dvd__iff_0,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) ) ).
cnf(cls_minus__dvd__iff_1,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a) ) ).
cnf(cls_add__monom_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_HOL_Oplus__class_Oplus(c_Polynomial_Omonom(V_a,V_n,T_a),c_Polynomial_Omonom(V_b,V_n,T_a),tc_Polynomial_Opoly(T_a)) = c_Polynomial_Omonom(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_n,T_a) ) ).
cnf(cls_Rational_Oordered__idom__class_Osgn__less_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_Rational_Oordered__idom__class_Osgn__less_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Osgn__class_Osgn(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_le__infE_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_a,T_a)
| ~ c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),T_a) ) ).
cnf(cls_le__infE_1,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_b,T_a)
| ~ c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),T_a) ) ).
cnf(cls_le__infI1_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_x,T_a)
| ~ c_lessequals(V_a,V_x,T_a) ) ).
cnf(cls_le__infI2_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_x,T_a)
| ~ c_lessequals(V_b,V_x,T_a) ) ).
cnf(cls_le__inf__iff_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_y,T_a)
| ~ c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ).
cnf(cls_le__inf__iff_1,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_y,V_z,T_a),T_a) ) ).
cnf(cls_divide__strict__right__mono_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_divide__strict__right__mono__neg_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ).
cnf(cls_mod__diff__eq_0,axiom,
( ~ class_Divides_Oring__div(T_a)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ).
cnf(cls_divide__nonneg__pos_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ).
cnf(cls_divide__nonpos__neg_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_abs__leI_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a)
| ~ c_lessequals(V_a,V_b,T_a) ) ).
cnf(cls_abs__le__iff_2,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a)
| ~ c_lessequals(V_a,V_b,T_a) ) ).
cnf(cls_abs__minus__cancel_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_HOL_Oabs__class_Oabs(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Oabs__class_Oabs(V_a,T_a) ) ).
cnf(cls_nat__add__right__cancel_0,axiom,
( c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat) != c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat)
| V_m = V_n ) ).
cnf(cls_nat__add__left__cancel_0,axiom,
( c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat)
| V_m = V_n ) ).
cnf(cls_natgb_Oadd__cancel_0,axiom,
( c_HOL_Oplus__class_Oplus(V_x,V_y,tc_nat) != c_HOL_Oplus__class_Oplus(V_x,V_z,tc_nat)
| V_y = V_z ) ).
cnf(cls_class__ringb_Oadd__cancel_0,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) != c_HOL_Oplus__class_Oplus(V_x,V_z,T_a)
| V_y = V_z ) ).
cnf(cls_add__imp__eq_0,axiom,
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(T_a)
| c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)
| V_b = V_c ) ).
cnf(cls_add__left__cancel_0,axiom,
( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a)
| c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)
| V_b = V_c ) ).
cnf(cls_add__right__cancel_0,axiom,
( ~ class_OrderedGroup_Ocancel__semigroup__add(T_a)
| c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) != c_HOL_Oplus__class_Oplus(V_c,V_a,T_a)
| V_b = V_c ) ).
cnf(cls_not__square__less__zero_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_mult__le__0__iff_4,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_mult__le__0__iff_5,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_split__mult__neg__le_0,axiom,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_split__mult__neg__le_1,axiom,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_mult__nonneg__nonpos_0,axiom,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_mult__nonpos__nonneg_0,axiom,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_mult__nonneg__nonpos2_0,axiom,
( ~ class_Ring__and__Field_Opordered__cancel__semiring(T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_abs__le__zero__iff_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_add__nonneg__pos_0,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_add__pos__nonneg_0,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_mult__monom_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_HOL_Otimes__class_Otimes(c_Polynomial_Omonom(V_a,V_m,T_a),c_Polynomial_Omonom(V_b,V_n,T_a),tc_Polynomial_Opoly(T_a)) = c_Polynomial_Omonom(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),T_a) ) ).
cnf(cls_dvd__imp__mod__0_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Omod(V_b,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ).
cnf(cls_dvd__eq__mod__eq__0_1,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Omod(V_b,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ).
cnf(cls_distrib__inf__le_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,T_a),T_a),c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a),T_a) ) ).
cnf(cls_inf__sup__ord_I3_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_lessequals(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) ) ).
cnf(cls_inf__sup__ord_I4_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_lessequals(V_y,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) ) ).
cnf(cls_le__supI_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),V_x,T_a)
| ~ c_lessequals(V_b,V_x,T_a)
| ~ c_lessequals(V_a,V_x,T_a) ) ).
cnf(cls_sup__ge1_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_lessequals(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) ) ).
cnf(cls_sup__ge2_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_lessequals(V_y,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) ) ).
cnf(cls_sup__least_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),V_x,T_a)
| ~ c_lessequals(V_z,V_x,T_a)
| ~ c_lessequals(V_y,V_x,T_a) ) ).
cnf(cls_le__sup__iff_2,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_lessequals(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_z,T_a) ) ).
cnf(cls_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_add__Suc__shift_0,axiom,
c_HOL_Oplus__class_Oplus(c_Suc(V_m),V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_m,c_Suc(V_n),tc_nat) ).
cnf(cls_pos__poly__total_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_Polynomial_Opos__poly(c_HOL_Ouminus__class_Ouminus(V_p,tc_Polynomial_Opoly(T_a)),T_a)
| c_Polynomial_Opos__poly(V_p,T_a)
| V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_one__is__add_3,axiom,
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)
| V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
cnf(cls_one__is__add_0,axiom,
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)
| V_m = c_HOL_Ozero__class_Ozero(tc_nat)
| V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ).
cnf(cls_coeff__add_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_Polynomial_Ocoeff(c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),V_n,T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Ocoeff(V_p,V_n,T_a),c_Polynomial_Ocoeff(V_q,V_n,T_a),T_a) ) ).
cnf(cls_minus__monom_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_HOL_Ouminus__class_Ouminus(c_Polynomial_Omonom(V_a,V_n,T_a),tc_Polynomial_Opoly(T_a)) = c_Polynomial_Omonom(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_n,T_a) ) ).
cnf(cls_one__is__add_5,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ).
cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_c,T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ).
cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_HOL_Oplus__class_Oplus(V_a,c_Lattices_Olower__semilattice__class_Oinf(V_b,V_c,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) ) ).
cnf(cls_add__inf__distrib__left_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(T_a)
| c_HOL_Oplus__class_Oplus(V_a,c_Lattices_Olower__semilattice__class_Oinf(V_b,V_c,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) ) ).
cnf(cls_add__inf__distrib__right_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add__meet(T_a)
| c_HOL_Oplus__class_Oplus(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),V_c,T_a) = c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ).
cnf(cls_neg__0__le__iff__le_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ).
cnf(cls_neg__0__le__iff__le_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
| ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_dvd__mod_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a) ) ).
cnf(cls_le__add__iff2_1,axiom,
( ~ class_Ring__and__Field_Opordered__ring(T_a)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)
| ~ c_lessequals(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a) ) ).
cnf(cls_le__add__iff2_0,axiom,
( ~ class_Ring__and__Field_Opordered__ring(T_a)
| c_lessequals(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a) ) ).
cnf(cls_le__add__iff1_1,axiom,
( ~ class_Ring__and__Field_Opordered__ring(T_a)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a) ) ).
cnf(cls_le__add__iff1_0,axiom,
( ~ class_Ring__and__Field_Opordered__ring(T_a)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a) ) ).
cnf(cls_divide__le__0__iff_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_divide__le__0__iff_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_termination__basic__simps_I1_J_0,axiom,
( c_HOL_Oord__class_Oless(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) ) ).
cnf(cls_termination__basic__simps_I2_J_0,axiom,
( c_HOL_Oord__class_Oless(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(V_x,V_z,tc_nat) ) ).
cnf(cls_add__lessD1_0,axiom,
( c_HOL_Oord__class_Oless(V_i,V_k,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_k,tc_nat) ) ).
cnf(cls_trans__less__add1_0,axiom,
( c_HOL_Oord__class_Oless(V_i,c_HOL_Oplus__class_Oplus(V_j,V_m,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ).
cnf(cls_trans__less__add2_0,axiom,
( c_HOL_Oord__class_Oless(V_i,c_HOL_Oplus__class_Oplus(V_m,V_j,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ).
cnf(cls_add__eq__inf__sup_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),T_a) ) ).
cnf(cls_Suc__leI_0,axiom,
( c_lessequals(c_Suc(V_m),V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).
cnf(cls_Suc__le__eq_0,axiom,
( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ~ c_lessequals(c_Suc(V_m),V_n,tc_nat) ) ).
cnf(cls_less__eq__Suc__le_0,axiom,
( c_lessequals(c_Suc(V_n),V_m,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ) ).
cnf(cls_less__eq__Suc__le_1,axiom,
( c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)
| ~ c_lessequals(c_Suc(V_n),V_m,tc_nat) ) ).
cnf(cls_eq__poly__code_I4_J_2,axiom,
( ~ class_HOL_Ozero(T_a)
| ~ class_HOL_Oeq(T_a)
| c_HOL_Oeq__class_Oeq(c_Polynomial_OpCons(V_a,V_p,T_a),c_Polynomial_OpCons(V_b,V_q,T_a),tc_Polynomial_Opoly(T_a))
| ~ c_HOL_Oeq__class_Oeq(V_p,V_q,tc_Polynomial_Opoly(T_a))
| ~ c_HOL_Oeq__class_Oeq(V_a,V_b,T_a) ) ).
cnf(cls_add__increasing2_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_add__increasing_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_lessequals(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
| ~ c_lessequals(V_b,V_c,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_scaleR__minus__right_0,axiom,
( ~ class_RealVector_Oreal__vector(T_a)
| c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),T_a) ) ).
cnf(cls_scaleR_Ominus__right_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_RealVector_OscaleR__class_OscaleR(V_a,V_b,T_a),T_a) ) ).
cnf(cls_abs__minus__le__zero_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Oabs__class_Oabs(V_a,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_less__add__Suc1_0,axiom,
c_HOL_Oord__class_Oless(V_i,c_Suc(c_HOL_Oplus__class_Oplus(V_i,V_m,tc_nat)),tc_nat) ).
cnf(cls_less__add__Suc2_0,axiom,
c_HOL_Oord__class_Oless(V_i,c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_i,tc_nat)),tc_nat) ).
cnf(cls_less__iff__Suc__add_1,axiom,
c_HOL_Oord__class_Oless(V_m,c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_x,tc_nat)),tc_nat) ).
cnf(cls_eq__add__iff2_1,axiom,
( ~ class_Ring__and__Field_Oring(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a) ) ).
cnf(cls_nat_Osimps_I2_J_0,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_nat_H) ).
cnf(cls_Zero__neq__Suc_0,axiom,
c_HOL_Ozero__class_Ozero(tc_nat) != c_Suc(V_m) ).
cnf(cls_div__add_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),V_z,T_a) = c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(V_x,V_z,T_a),c_Divides_Odiv__class_Odiv(V_y,V_z,T_a),T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_y,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_z,V_x,T_a) ) ).
cnf(cls_neg__le__iff__le_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ).
cnf(cls_le__imp__neg__le_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
| ~ c_lessequals(V_a,V_b,T_a) ) ).
cnf(cls_poly__offset__poly_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_Polynomial_Opoly(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),V_x,T_a) = c_Polynomial_Opoly(V_p,c_HOL_Oplus__class_Oplus(V_h,V_x,T_a),T_a) ) ).
cnf(cls_abs__le__mult_0,axiom,
( ~ class_Ring__and__Field_Olordered__ring(T_a)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a) ) ).
cnf(cls_abs__le__D1_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ).
cnf(cls_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_zmod__simps_I4_J_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) ) ).
cnf(cls_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_divide__left__mono__neg_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_c,V_a,T_a),c_HOL_Oinverse__class_Odivide(V_c,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ c_lessequals(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_a,V_b,T_a) ) ).
cnf(cls_divide__left__mono_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_c,V_a,T_a),c_HOL_Oinverse__class_Odivide(V_c,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(V_b,V_a,T_a) ) ).
cnf(cls_exp__diff_0,axiom,
( ~ class_SEQ_Obanach(T_a)
| ~ class_RealVector_Oreal__normed__field(T_a)
| c_Transcendental_Oexp(c_HOL_Ominus__class_Ominus(V_x,V_y,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_Transcendental_Oexp(V_x,T_a),c_Transcendental_Oexp(V_y,T_a),T_a) ) ).
cnf(cls_dvd__triv__right_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a) ) ).
cnf(cls_dvd__triv__left_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ).
cnf(cls_dvdI_0,axiom,
( ~ class_Ring__and__Field_Odvd(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_b,c_HOL_Otimes__class_Otimes(V_b,V_k,T_a),T_a) ) ).
cnf(cls_abs__prts_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a)
| c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ominus__class_Ominus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a,T_a),T_a) ) ).
cnf(cls_pdivmod__rel_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Polynomial_Opdivmod__rel(V_x,V_y,c_Divides_Odiv__class_Odiv(V_x,V_y,tc_Polynomial_Opoly(T_a)),c_Divides_Odiv__class_Omod(V_x,V_y,tc_Polynomial_Opoly(T_a)),T_a) ) ).
cnf(cls_frac__less2_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_x,V_z,T_a),c_HOL_Oinverse__class_Odivide(V_y,V_w,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_w,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_w,T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ).
cnf(cls_add__is__1_4,axiom,
c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ).
cnf(cls_smult__dvd__cancel_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a))
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(V_a,V_p,T_a),V_q,tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_dvd__smult_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_p,c_Polynomial_Osmult(V_a,V_q,T_a),tc_Polynomial_Opoly(T_a))
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_mod__pCons_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Divides_Odiv__class_Omod(c_Polynomial_OpCons(V_a,V_x,T_a),V_y,tc_Polynomial_Opoly(T_a)) = c_HOL_Ominus__class_Ominus(c_Polynomial_OpCons(V_a,c_Divides_Odiv__class_Omod(V_x,V_y,tc_Polynomial_Opoly(T_a)),T_a),c_Polynomial_Osmult(c_HOL_Oinverse__class_Odivide(c_Polynomial_Ocoeff(c_Polynomial_OpCons(V_a,c_Divides_Odiv__class_Omod(V_x,V_y,tc_Polynomial_Opoly(T_a)),T_a),c_Polynomial_Odegree(V_y,T_a),T_a),c_Polynomial_Ocoeff(V_y,c_Polynomial_Odegree(V_y,T_a),T_a),T_a),V_y,T_a),tc_Polynomial_Opoly(T_a))
| V_y = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_nonzero__minus__divide__right_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a)
| V_b = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_neg__less__0__iff__less_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_neg__less__0__iff__less_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_class__ringb_Oadd__mul__solve_1,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) ) ).
cnf(cls_class__ringb_Onoteq__reduce_1,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_c,T_a),c_HOL_Otimes__class_Otimes(V_x,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_d,T_a),c_HOL_Otimes__class_Otimes(V_x,V_c,T_a),T_a) ) ).
cnf(cls_less__Suc0_0,axiom,
( V_n = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ) ).
cnf(cls_abs__triangle__ineq3_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a),T_a) ) ).
cnf(cls_poly__gcd__left__commute_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Polynomial_Opoly__gcd(V_x,c_Polynomial_Opoly__gcd(V_y,V_z,T_a),T_a) = c_Polynomial_Opoly__gcd(V_y,c_Polynomial_Opoly__gcd(V_x,V_z,T_a),T_a) ) ).
cnf(cls_poly__gcd__assoc_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Polynomial_Opoly__gcd(c_Polynomial_Opoly__gcd(V_x,V_y,T_a),V_z,T_a) = c_Polynomial_Opoly__gcd(V_x,c_Polynomial_Opoly__gcd(V_y,V_z,T_a),T_a) ) ).
cnf(cls_abs__mult__less_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),c_HOL_Otimes__class_Otimes(V_c,V_d,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_b,T_a),V_d,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_c,T_a) ) ).
cnf(cls_degree__monom__le_0,axiom,
( ~ class_HOL_Ozero(T_a)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_Omonom(V_a,V_n,T_a),T_a),V_n,tc_nat) ) ).
cnf(cls_diff__add__cancel_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_b,T_a) = V_a ) ).
cnf(cls_offset__poly__pCons_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_Polynomial_OpCons(V_a,V_p,T_a),V_h,T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),T_a),c_Polynomial_OpCons(V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),T_a),tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_inf__sup__distrib2_0,axiom,
( ~ class_Lattices_Odistrib__lattice(T_a)
| c_Lattices_Olower__semilattice__class_Oinf(c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),V_x,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_y,V_x,T_a),c_Lattices_Olower__semilattice__class_Oinf(V_z,V_x,T_a),T_a) ) ).
cnf(cls_inf__sup__distrib1_0,axiom,
( ~ class_Lattices_Odistrib__lattice(T_a)
| c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),c_Lattices_Olower__semilattice__class_Oinf(V_x,V_z,T_a),T_a) ) ).
cnf(cls_poly__gcd__minus__right_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Polynomial_Opoly__gcd(V_x,c_HOL_Ouminus__class_Ouminus(V_y,tc_Polynomial_Opoly(T_a)),T_a) = c_Polynomial_Opoly__gcd(V_x,V_y,T_a) ) ).
cnf(cls_poly__gcd__minus__left_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Polynomial_Opoly__gcd(c_HOL_Ouminus__class_Ouminus(V_x,tc_Polynomial_Opoly(T_a)),V_y,T_a) = c_Polynomial_Opoly__gcd(V_x,V_y,T_a) ) ).
cnf(cls_add__nonneg__eq__0__iff_2,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_class__semiring_Omul__c_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Otimes__class_Otimes(V_x,V_y,T_a) = c_HOL_Otimes__class_Otimes(V_y,V_x,T_a) ) ).
cnf(cls_add__is__0_2,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = c_HOL_Ozero__class_Ozero(tc_nat) ).
cnf(cls_class__semiring_Osemiring__rules_I7_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) = c_HOL_Otimes__class_Otimes(V_b,V_a,T_a) ) ).
cnf(cls_mod__add__eq_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ).
cnf(cls_add__sup__distrib__right_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add__join(T_a)
| c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),V_c,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ).
cnf(cls_add__sup__distrib__left_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add__join(T_a)
| c_HOL_Oplus__class_Oplus(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_b,V_c,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) ) ).
cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I4_J_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_HOL_Oplus__class_Oplus(V_a,c_Lattices_Oupper__semilattice__class_Osup(V_b,V_c,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) ) ).
cnf(cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I3_J_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_HOL_Oplus__class_Oplus(c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a),V_c,T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ).
cnf(cls_sup__idem_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_x,V_x,T_a) = V_x ) ).
cnf(cls_xt1_I10_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
cnf(cls_order__less__trans_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_coeff__smult_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_Polynomial_Ocoeff(c_Polynomial_Osmult(V_a,V_p,T_a),V_n,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_Polynomial_Ocoeff(V_p,V_n,T_a),T_a) ) ).
cnf(cls_coeff__monom_1,axiom,
( ~ class_HOL_Ozero(T_a)
| c_Polynomial_Ocoeff(c_Polynomial_Omonom(V_a,V_m,T_a),V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| V_m = V_n ) ).
cnf(cls_comm__monoid__add_Omult__left__commute_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a) ) ).
cnf(cls_comm__monoid__add_Omult__assoc_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ).
cnf(cls_class__semiring_Oadd__a_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),V_z,T_a) ) ).
cnf(cls_nat__add__assoc_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),V_k,tc_nat) = c_HOL_Oplus__class_Oplus(V_m,c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat),tc_nat) ).
cnf(cls_nat__add__left__commute_0,axiom,
c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(V_y,c_HOL_Oplus__class_Oplus(V_x,V_z,tc_nat),tc_nat) ).
cnf(cls_add__cancel__21_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_y,c_HOL_Oplus__class_Oplus(V_x,V_z,T_a),T_a) ) ).
cnf(cls_ab__semigroup__add__class_Oadd__ac_I1_J_0,axiom,
( ~ class_OrderedGroup_Oab__semigroup__add(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I25_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_d,T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I23_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_b,T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I22_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_c,c_HOL_Oplus__class_Oplus(V_a,V_d,T_a),T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I21_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ).
cnf(cls_add__gr__0_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) ) ).
cnf(cls_abs__triangle__ineq_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a) ) ).
cnf(cls_termination__basic__simps_I3_J_0,axiom,
( c_lessequals(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat)
| ~ c_lessequals(V_x,V_y,tc_nat) ) ).
cnf(cls_termination__basic__simps_I4_J_0,axiom,
( c_lessequals(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat)
| ~ c_lessequals(V_x,V_z,tc_nat) ) ).
cnf(cls_add__leE_0,axiom,
( c_lessequals(V_m,V_n,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat),V_n,tc_nat) ) ).
cnf(cls_add__leE_1,axiom,
( c_lessequals(V_k,V_n,tc_nat)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat),V_n,tc_nat) ) ).
cnf(cls_trans__le__add1_0,axiom,
( c_lessequals(V_i,c_HOL_Oplus__class_Oplus(V_j,V_m,tc_nat),tc_nat)
| ~ c_lessequals(V_i,V_j,tc_nat) ) ).
cnf(cls_mult_OscaleR__left_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(V_r,V_a,T_a),V_b,T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ).
cnf(cls_mult__left_OscaleR_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(V_r,V_x,T_a),V_y,T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) ) ).
cnf(cls_mult_OscaleR__right_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_HOL_Otimes__class_Otimes(V_a,c_RealVector_OscaleR__class_OscaleR(V_r,V_b,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) ) ).
cnf(cls_mult__right_OscaleR_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_HOL_Otimes__class_Otimes(V_xa,c_RealVector_OscaleR__class_OscaleR(V_r,V_x,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),T_a) ) ).
cnf(cls_mult__scaleR__left_0,axiom,
( ~ class_RealVector_Oreal__algebra(T_a)
| c_HOL_Otimes__class_Otimes(c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),V_y,T_a) = c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) ) ).
cnf(cls_mult__scaleR__right_0,axiom,
( ~ class_RealVector_Oreal__algebra(T_a)
| c_HOL_Otimes__class_Otimes(V_x,c_RealVector_OscaleR__class_OscaleR(V_a,V_y,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) ) ).
cnf(cls_nonzero__abs__divide_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a)
| V_b = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_coeff__monom_0,axiom,
( ~ class_HOL_Ozero(T_a)
| c_Polynomial_Ocoeff(c_Polynomial_Omonom(V_a,V_x,T_a),V_x,T_a) = V_a ) ).
cnf(cls_mod__diff__left__eq_0,axiom,
( ~ class_Divides_Oring__div(T_a)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) ) ).
cnf(cls_mod__diff__right__eq_0,axiom,
( ~ class_Divides_Oring__div(T_a)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ).
cnf(cls_mult__exp__exp_0,axiom,
( ~ class_SEQ_Obanach(T_a)
| ~ class_RealVector_Oreal__normed__field(T_a)
| c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(V_x,T_a),c_Transcendental_Oexp(V_y,T_a),T_a) = c_Transcendental_Oexp(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),T_a) ) ).
cnf(cls_add__cancel__21_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) != c_HOL_Oplus__class_Oplus(V_y,V_u,T_a)
| c_HOL_Oplus__class_Oplus(V_x,V_z,T_a) = V_u ) ).
cnf(cls_mult__le__prts_0,axiom,
( ~ class_Ring__and__Field_Olordered__ring(T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a2,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_b2,T_a),T_a),c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a1,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_b2,T_a),T_a),T_a),c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a2,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_b1,T_a),T_a),T_a),c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a1,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_b1,T_a),T_a),T_a),T_a)
| ~ c_lessequals(V_b,V_b2,T_a)
| ~ c_lessequals(V_b1,V_b,T_a)
| ~ c_lessequals(V_a,V_a2,T_a)
| ~ c_lessequals(V_a1,V_a,T_a) ) ).
cnf(cls_pos__poly__mult_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_Polynomial_Opos__poly(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a)
| ~ c_Polynomial_Opos__poly(V_q,T_a)
| ~ c_Polynomial_Opos__poly(V_p,T_a) ) ).
cnf(cls_gr__implies__not0_0,axiom,
~ c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ).
cnf(cls_not__less0_0,axiom,
~ c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ).
cnf(cls_psize__def_0,axiom,
( ~ class_HOL_Ozero(T_a)
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
cnf(cls_nprt__neg_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_x,T_a),T_a) ) ).
cnf(cls_le__zero__iff__pprt__id_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a,T_a) = V_a
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_le__zero__iff__pprt__id_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a,T_a) != V_a
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_mod__smult__right_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Divides_Odiv__class_Omod(V_x,c_Polynomial_Osmult(V_a,V_y,T_a),tc_Polynomial_Opoly(T_a)) = c_Divides_Odiv__class_Omod(V_x,V_y,tc_Polynomial_Opoly(T_a))
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_add__nonneg__nonneg_0,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_pos__poly__pCons_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| c_Polynomial_Opos__poly(V_p,T_a)
| ~ c_Polynomial_Opos__poly(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) ) ).
cnf(cls_pdivmod__rel__def_6,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_y,tc_Polynomial_Opoly(T_a)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)),V_y,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) ) ).
cnf(cls_pdivmod__rel__def_5,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)),V_r,tc_Polynomial_Opoly(T_a)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_r,T_a) ) ).
cnf(cls_less__Suc__eq__le_1,axiom,
( c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat)
| ~ c_lessequals(V_m,V_n,tc_nat) ) ).
cnf(cls_less__Suc__eq__le_0,axiom,
( c_lessequals(V_m,V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat) ) ).
cnf(cls_le__less__Suc__eq_1,axiom,
( ~ c_lessequals(V_x,V_x,tc_nat)
| c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat) ) ).
cnf(cls_degree__pCons__le_0,axiom,
( ~ class_HOL_Ozero(T_a)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a),c_Suc(c_Polynomial_Odegree(V_p,T_a)),tc_nat) ) ).
cnf(cls_divide_OscaleR_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| c_HOL_Oinverse__class_Odivide(c_RealVector_OscaleR__class_OscaleR(V_r,V_x,T_a),V_y,T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) ) ).
cnf(cls_add__le__mono_0,axiom,
( c_lessequals(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_j,V_l,tc_nat),tc_nat)
| ~ c_lessequals(V_k,V_l,tc_nat)
| ~ c_lessequals(V_i,V_j,tc_nat) ) ).
cnf(cls_add__mono_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(T_a)
| c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a)
| ~ c_lessequals(V_c,V_d,T_a)
| ~ c_lessequals(V_a,V_b,T_a) ) ).
cnf(cls_sup__eq__if_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_inf__0__imp__0_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_Lattices_Olower__semilattice__class_Oinf(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) != c_HOL_Ozero__class_Ozero(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_zero__le__double__add__iff__zero__le__single__add_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a) ) ).
cnf(cls_zero__le__double__add__iff__zero__le__single__add_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_pos__poly__pCons_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| c_Polynomial_Opos__poly(V_p,T_a)
| ~ c_Polynomial_Opos__poly(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) ) ).
cnf(cls_pcompose__pCons_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_Polynomial_Opcompose(c_Polynomial_OpCons(V_a,V_p,T_a),V_q,T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_OpCons(V_a,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),c_HOL_Otimes__class_Otimes(V_q,c_Polynomial_Opcompose(V_p,V_q,T_a),tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_DERIV__mult__lemma_0,axiom,
( ~ class_RealVector_Oreal__field(T_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_c,V_d,T_a),T_a),V_h,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(V_b,V_d,T_a),V_h,T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(V_a,V_c,T_a),V_h,T_a),V_d,T_a),T_a) ) ).
cnf(cls_mod__mod__trivial_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a) ) ).
cnf(cls_abs__diff__triangle__ineq_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a),T_a),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_a,V_c,T_a),T_a),c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_b,V_d,T_a),T_a),T_a),T_a) ) ).
cnf(cls_add__strict__increasing_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
| ~ c_lessequals(V_b,V_c,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_smult__minus__left_0,axiom,
( ~ class_Ring__and__Field_Ocomm__ring(T_a)
| c_Polynomial_Osmult(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_p,T_a) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(V_a,V_p,T_a),tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_smult__minus__right_0,axiom,
( ~ class_Ring__and__Field_Ocomm__ring(T_a)
| c_Polynomial_Osmult(V_a,c_HOL_Ouminus__class_Ouminus(V_p,tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Osmult(V_a,V_p,T_a),tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_le__minus__self__iff_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ).
cnf(cls_le__minus__self__iff_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
| ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_minus__le__self__iff_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) ) ).
cnf(cls_minus__le__self__iff_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_less__eq__neg__nonpos_0,axiom,
( ~ class_OrderedGroup_Oordered__ab__group__add(T_a)
| c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ).
cnf(cls_less__eq__neg__nonpos_1,axiom,
( ~ class_OrderedGroup_Oordered__ab__group__add(T_a)
| c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
| ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_neg__less__eq__nonneg_0,axiom,
( ~ class_OrderedGroup_Oordered__ab__group__add(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) ) ).
cnf(cls_neg__less__eq__nonneg_1,axiom,
( ~ class_OrderedGroup_Oordered__ab__group__add(T_a)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_eq__add__iff1_1,axiom,
( ~ class_Ring__and__Field_Oring(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),T_a) ) ).
cnf(cls_dvd__mult__cancel__left_2,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ).
cnf(cls_dvd__mult__cancel__right_2,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ).
cnf(cls_coeff__pCons__Suc_0,axiom,
( ~ class_HOL_Ozero(T_a)
| c_Polynomial_Ocoeff(c_Polynomial_OpCons(V_a,V_p,T_a),c_Suc(V_n),T_a) = c_Polynomial_Ocoeff(V_p,V_n,T_a) ) ).
cnf(cls_eq__poly__code_I4_J_0,axiom,
( ~ class_HOL_Ozero(T_a)
| ~ class_HOL_Oeq(T_a)
| c_HOL_Oeq__class_Oeq(V_a,V_b,T_a)
| ~ c_HOL_Oeq__class_Oeq(c_Polynomial_OpCons(V_a,V_p,T_a),c_Polynomial_OpCons(V_b,V_q,T_a),tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_eq__poly__code_I4_J_1,axiom,
( ~ class_HOL_Ozero(T_a)
| ~ class_HOL_Oeq(T_a)
| c_HOL_Oeq__class_Oeq(V_p,V_q,tc_Polynomial_Opoly(T_a))
| ~ c_HOL_Oeq__class_Oeq(c_Polynomial_OpCons(V_a,V_p,T_a),c_Polynomial_OpCons(V_b,V_q,T_a),tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_abs__idempotent_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) = c_HOL_Oabs__class_Oabs(V_a,T_a) ) ).
cnf(cls_add__Suc_0,axiom,
c_HOL_Oplus__class_Oplus(c_Suc(V_m),V_n,tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)) ).
cnf(cls_add__Suc__right_0,axiom,
c_HOL_Oplus__class_Oplus(V_m,c_Suc(V_n),tc_nat) = c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)) ).
cnf(cls_eq__add__iff1_0,axiom,
( ~ class_Ring__and__Field_Oring(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) = V_d ) ).
cnf(cls_eq__add__iff2_0,axiom,
( ~ class_Ring__and__Field_Oring(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a)
| V_c = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a) ) ).
cnf(cls_div__mod__equality_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) ) ).
cnf(cls_div__mod__equality2_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) ) ).
cnf(cls_zero__less__abs__iff_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_poly__mult_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_Polynomial_Opoly(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_HOL_Otimes__class_Otimes(c_Polynomial_Opoly(V_p,V_x,T_a),c_Polynomial_Opoly(V_q,V_x,T_a),T_a) ) ).
cnf(cls_dvd__poly__gcd__iff_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_k,V_x,tc_Polynomial_Opoly(T_a))
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Polynomial_Opoly__gcd(V_x,V_y,T_a),tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_dvd__poly__gcd__iff_1,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_k,V_y,tc_Polynomial_Opoly(T_a))
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Polynomial_Opoly__gcd(V_x,V_y,T_a),tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_poly__add_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_Polynomial_Opoly(c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Opoly(V_p,V_x,T_a),c_Polynomial_Opoly(V_q,V_x,T_a),T_a) ) ).
cnf(cls_le__zero__iff__zero__pprt_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_le__zero__iff__zero__pprt_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_psize__eq__0__iff_0,axiom,
( ~ class_HOL_Ozero(T_a)
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_nat)
| V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_scaleR_OscaleR__right_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_RealVector_OscaleR__class_OscaleR(V_a,c_RealVector_OscaleR__class_OscaleR(V_r,V_b,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,c_RealVector_OscaleR__class_OscaleR(V_a,V_b,T_a),T_a) ) ).
cnf(cls_scaleR__left__commute_0,axiom,
( ~ class_RealVector_Oreal__vector(T_a)
| c_RealVector_OscaleR__class_OscaleR(V_a,c_RealVector_OscaleR__class_OscaleR(V_b,V_x,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_b,c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),T_a) ) ).
cnf(cls_scaleR__right_OscaleR_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_RealVector_OscaleR__class_OscaleR(V_ra,c_RealVector_OscaleR__class_OscaleR(V_r,V_x,T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_r,c_RealVector_OscaleR__class_OscaleR(V_ra,V_x,T_a),T_a) ) ).
cnf(cls_mult__ge__prts_0,axiom,
( ~ class_Ring__and__Field_Olordered__ring(T_a)
| c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a1,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_b2,T_a),T_a),c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a2,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_b2,T_a),T_a),T_a),c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a1,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_b1,T_a),T_a),T_a),c_HOL_Otimes__class_Otimes(c_OrderedGroup_Olordered__ab__group__add__class_Opprt(V_a2,T_a),c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_b1,T_a),T_a),T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ c_lessequals(V_b,V_b2,T_a)
| ~ c_lessequals(V_b1,V_b,T_a)
| ~ c_lessequals(V_a,V_a2,T_a)
| ~ c_lessequals(V_a1,V_a,T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I24_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Oplus__class_Oplus(V_a,V_c,T_a) = c_HOL_Oplus__class_Oplus(V_c,V_a,T_a) ) ).
cnf(cls_less__add__eq__less_0,axiom,
( c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat) != c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).
cnf(cls_nat__add__commute_0,axiom,
c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) = c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat) ).
cnf(cls_class__semiring_Oadd__c_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Oplus__class_Oplus(V_x,V_y,T_a) = c_HOL_Oplus__class_Oplus(V_y,V_x,T_a) ) ).
cnf(cls_comm__monoid__add_Omult__commute_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) = c_HOL_Oplus__class_Oplus(V_b,V_a,T_a) ) ).
cnf(cls_divide__le__0__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_divide__le__0__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_divide__le__0__iff_2,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_divide__le__0__iff_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_mod__div__trivial_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_mod__minus__cong_0,axiom,
( ~ class_Divides_Oring__div(T_a)
| c_Divides_Odiv__class_Omod(V_a,V_b,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_b,T_a)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(V_a_H,T_a),V_b,T_a) ) ).
cnf(cls_nprt__le__zero_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_lessequals(c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_mod__mult__eq_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ).
cnf(cls_pos__poly__def_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_Polynomial_Opos__poly(V_p,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Polynomial_Ocoeff(V_p,c_Polynomial_Odegree(V_p,T_a),T_a),T_a) ) ).
cnf(cls_pos__poly__def_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Polynomial_Ocoeff(V_p,c_Polynomial_Odegree(V_p,T_a),T_a),T_a)
| ~ c_Polynomial_Opos__poly(V_p,T_a) ) ).
cnf(cls_div__mult__self1_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a),V_b,T_a) = c_HOL_Oplus__class_Oplus(V_c,c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),T_a)
| V_b = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_div__mult__self2_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a),V_b,T_a) = c_HOL_Oplus__class_Oplus(V_c,c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),T_a)
| V_b = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_divide__less__eq_1,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ).
cnf(cls_divide__less__eq_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_divide__less__eq_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_divide__less__eq_7,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ).
cnf(cls_less__divide__eq_1,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ).
cnf(cls_less__divide__eq_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_trans__le__add2_0,axiom,
( c_lessequals(V_i,c_HOL_Oplus__class_Oplus(V_m,V_j,tc_nat),tc_nat)
| ~ c_lessequals(V_i,V_j,tc_nat) ) ).
cnf(cls_poly__div__minus__right_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Divides_Odiv__class_Odiv(V_x,c_HOL_Ouminus__class_Ouminus(V_y,tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(V_x,V_y,tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_poly__div__minus__left_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Divides_Odiv__class_Odiv(c_HOL_Ouminus__class_Ouminus(V_x,tc_Polynomial_Opoly(T_a)),V_y,tc_Polynomial_Opoly(T_a)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Odiv(V_x,V_y,tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_less__le__not__le_1,axiom,
( ~ class_Orderings_Opreorder(T_a)
| ~ c_lessequals(V_y,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_not__leE_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| c_lessequals(V_y,V_x,T_a) ) ).
cnf(cls_linorder__antisym__conv2_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_lessequals(V_x,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).
cnf(cls_linorder__antisym__conv1_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_x,T_a)
| c_lessequals(V_x,V_x,T_a) ) ).
cnf(cls_linorder__not__less_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_lessequals(V_y,V_x,T_a) ) ).
cnf(cls_linorder__not__less_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_linorder__not__le_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_linorder__not__le_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_lessequals(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
cnf(cls_mod__add__right__eq_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ).
cnf(cls_mod__add__left__eq_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) ) ).
cnf(cls_zero__le__divide__iff_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ).
cnf(cls_zero__le__divide__iff_2,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ).
cnf(cls_zero__le__divide__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ).
cnf(cls_zero__le__divide__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) ) ).
cnf(cls_add__strict__increasing2_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_c,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_eq__eqI_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) != c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)
| V_x_H = V_y_H ) ).
cnf(cls_eq__eqI_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_HOL_Ominus__class_Ominus(V_xa,V_y,T_a) != c_HOL_Ominus__class_Ominus(V_x,V_x,T_a)
| V_xa = V_y ) ).
cnf(cls_mod__poly__eq_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Divides_Odiv__class_Omod(V_x,V_y,tc_Polynomial_Opoly(T_a)) = V_r
| ~ c_Polynomial_Opdivmod__rel(V_x,V_y,V_q,V_r,T_a) ) ).
cnf(cls_diff__eq_0,axiom,
( ~ class_Lattices_Oboolean__algebra(T_a)
| c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) ) ).
cnf(cls_mult__right__le__imp__le_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
| c_lessequals(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ).
cnf(cls_mult__left__le__imp__le_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
| c_lessequals(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ).
cnf(cls_mult__le__cancel__left__pos_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ c_lessequals(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_mult__le__cancel__left__pos_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_mult__le__cancel__left__neg_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ c_lessequals(V_b,V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_mult__le__cancel__left__neg_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_lessequals(V_b,V_a,T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_nat__lt__two__imp__zero__or__one_0,axiom,
( V_x = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| V_x = c_HOL_Ozero__class_Ozero(tc_nat)
| ~ c_HOL_Oord__class_Oless(V_x,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat) ) ).
cnf(cls_sup__left__commute_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_z,T_a),T_a) ) ).
cnf(cls_sup__assoc_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) ) ).
cnf(cls_inf__sup__aci_I7_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_z,T_a),T_a) ) ).
cnf(cls_inf__sup__aci_I6_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),V_z,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_y,V_z,T_a),T_a) ) ).
cnf(cls_minus__divide__divide_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a) ) ).
cnf(cls_divide_Ominus_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(V_x,T_a),V_y,T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),T_a) ) ).
cnf(cls_mult_Oprod__diff__prod_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_x,V_a,T_a),c_HOL_Ominus__class_Ominus(V_y,V_b,T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_x,V_a,T_a),V_b,T_a),T_a),c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ominus__class_Ominus(V_y,V_b,T_a),T_a),T_a) ) ).
cnf(cls_poly__minus_0,axiom,
( ~ class_Ring__and__Field_Ocomm__ring(T_a)
| c_Polynomial_Opoly(c_HOL_Ouminus__class_Ouminus(V_p,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_HOL_Ouminus__class_Ouminus(c_Polynomial_Opoly(V_p,V_x,T_a),T_a) ) ).
cnf(cls_inf__absorb2_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_y
| ~ c_lessequals(V_y,V_x,T_a) ) ).
cnf(cls_le__iff__inf_1,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) != V_x
| c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_le__iff__inf_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = V_x
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_gr0__conv__Suc_1,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_x),tc_nat) ).
cnf(cls_zero__less__Suc_0,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat) ).
cnf(cls_inf__commute_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,V_x,T_a) ) ).
cnf(cls_inf__sup__aci_I1_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_y,V_x,T_a) ) ).
cnf(cls_combine__common__factor_0,axiom,
( ~ class_Ring__and__Field_Osemiring(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_c,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_e,T_a),V_c,T_a) ) ).
cnf(cls_eq__neg__iff__add__eq__0_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_ab__left__minus_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_right__minus_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_left__minus_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_add__neg__neg_0,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_sum__squares__le__zero__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| V_y = c_HOL_Ozero__class_Ozero(T_a)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_sum__squares__le__zero__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| V_x = c_HOL_Ozero__class_Ozero(T_a)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_mult__right_Odiff_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Ominus__class_Ominus(V_x,V_y,T_a),T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),c_HOL_Otimes__class_Otimes(V_xa,V_y,T_a),T_a) ) ).
cnf(cls_mult_Odiff__right_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ominus__class_Ominus(V_b,V_b_H,T_a),T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a,V_b_H,T_a),T_a) ) ).
cnf(cls_mult_Odiff__left_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_a_H,T_a),V_b,T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a_H,V_b,T_a),T_a) ) ).
cnf(cls_mult__left_Odiff_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_x,V_y,T_a),V_ya,T_a) = c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_x,V_ya,T_a),c_HOL_Otimes__class_Otimes(V_y,V_ya,T_a),T_a) ) ).
cnf(cls_Deriv_Oadd__diff__add_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ominus__class_Ominus(V_c,V_d,T_a),T_a) ) ).
cnf(cls_le0_0,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) ).
cnf(cls_dvd__div__mult_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),V_c,T_a) = c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),V_a,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ).
cnf(cls_Suc__lessI_0,axiom,
( c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat)
| c_Suc(V_m) = V_n
| ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).
cnf(cls_not__less__eq__eq_0,axiom,
( c_lessequals(c_Suc(V_n),V_m,tc_nat)
| c_lessequals(V_m,V_n,tc_nat) ) ).
cnf(cls_not__less__eq__eq_1,axiom,
( ~ c_lessequals(V_m,V_n,tc_nat)
| ~ c_lessequals(c_Suc(V_n),V_m,tc_nat) ) ).
cnf(cls_pos__poly__pCons_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_Polynomial_Opos__poly(c_Polynomial_OpCons(V_a,V_p,T_a),T_a)
| ~ c_Polynomial_Opos__poly(V_p,T_a) ) ).
cnf(cls_coeff__mult__degree__sum_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_Polynomial_Ocoeff(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat),T_a) = c_HOL_Otimes__class_Otimes(c_Polynomial_Ocoeff(V_p,c_Polynomial_Odegree(V_p,T_a),T_a),c_Polynomial_Ocoeff(V_q,c_Polynomial_Odegree(V_q,T_a),T_a),T_a) ) ).
cnf(cls_abs__diff__less__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_r,T_a),V_x,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_x,V_a,T_a),T_a),V_r,T_a) ) ).
cnf(cls_pdivmod__rel__pCons_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| V_y = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ c_Polynomial_Opdivmod__rel(V_x,V_y,V_q,V_r,T_a)
| c_Polynomial_Opdivmod__rel(c_Polynomial_OpCons(V_a,V_x,T_a),V_y,c_Polynomial_OpCons(c_HOL_Oinverse__class_Odivide(c_Polynomial_Ocoeff(c_Polynomial_OpCons(V_a,V_r,T_a),c_Polynomial_Odegree(V_y,T_a),T_a),c_Polynomial_Ocoeff(V_y,c_Polynomial_Odegree(V_y,T_a),T_a),T_a),V_q,T_a),c_HOL_Ominus__class_Ominus(c_Polynomial_OpCons(V_a,V_r,T_a),c_Polynomial_Osmult(c_HOL_Oinverse__class_Odivide(c_Polynomial_Ocoeff(c_Polynomial_OpCons(V_a,V_r,T_a),c_Polynomial_Odegree(V_y,T_a),T_a),c_Polynomial_Ocoeff(V_y,c_Polynomial_Odegree(V_y,T_a),T_a),T_a),V_y,T_a),tc_Polynomial_Opoly(T_a)),T_a) ) ).
cnf(cls_abs__divide_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a) ) ).
cnf(cls_abs__of__pos_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_mod__mult__right__eq_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a) ) ).
cnf(cls_mod__mult__left__eq_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a) ) ).
cnf(cls_add__is__1_0,axiom,
( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| V_m = c_HOL_Ozero__class_Ozero(tc_nat)
| V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ).
cnf(cls_add__is__1_3,axiom,
( c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat) != c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
cnf(cls_sum__squares__gt__zero__iff_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),T_a)
| V_y = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_sum__squares__gt__zero__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),T_a)
| V_x = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_scaleR__right_Oadd_0,axiom,
( ~ class_RealVector_Oreal__vector(T_a)
| c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a),c_RealVector_OscaleR__class_OscaleR(V_a,V_y,T_a),T_a) ) ).
cnf(cls_scaleR_Oadd__right_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Oplus__class_Oplus(V_b,V_b_H,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_RealVector_OscaleR__class_OscaleR(V_a,V_b,T_a),c_RealVector_OscaleR__class_OscaleR(V_a,V_b_H,T_a),T_a) ) ).
cnf(cls_inf__eq__neg__sup_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a),T_a) ) ).
cnf(cls_sup__commute_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,V_x,T_a) ) ).
cnf(cls_inf__sup__aci_I5_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_y,V_x,T_a) ) ).
cnf(cls_neg__inf__eq__sup_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(V_a,V_b,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ).
cnf(cls_compl__inf_0,axiom,
( ~ class_Lattices_Oboolean__algebra(T_a)
| c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(c_HOL_Ouminus__class_Ouminus(V_x,T_a),c_HOL_Ouminus__class_Ouminus(V_y,T_a),T_a) ) ).
cnf(cls_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_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_pos__poly__pCons_3,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_Polynomial_Opos__poly(c_Polynomial_OpCons(V_a,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_pdivmod__rel__mult_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Polynomial_Opdivmod__rel(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,tc_Polynomial_Opoly(T_a)),V_q_H,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_y,V_r_H,tc_Polynomial_Opoly(T_a)),V_r,tc_Polynomial_Opoly(T_a)),T_a)
| ~ c_Polynomial_Opdivmod__rel(V_q,V_z,V_q_H,V_r_H,T_a)
| ~ c_Polynomial_Opdivmod__rel(V_x,V_y,V_q,V_r,T_a) ) ).
cnf(cls_add__cancel__end_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) != V_y
| V_x = c_HOL_Ouminus__class_Ouminus(V_z,T_a) ) ).
cnf(cls_mult__divide__mult__cancel__right_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a)
| V_c = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_mult__divide__mult__cancel__left_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) = c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a)
| V_c = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_le__Suc__eq_2,axiom,
c_lessequals(c_Suc(V_n),c_Suc(V_n),tc_nat) ).
cnf(cls_sup__left__idem_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) ) ).
cnf(cls_inf__sup__aci_I8_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a),T_a) = c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) ) ).
cnf(cls_exp__add_0,axiom,
( ~ class_SEQ_Obanach(T_a)
| ~ class_RealVector_Oreal__normed__field(T_a)
| c_Transcendental_Oexp(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_Transcendental_Oexp(V_x,T_a),c_Transcendental_Oexp(V_y,T_a),T_a) ) ).
cnf(cls_mult__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__smult__right_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_HOL_Otimes__class_Otimes(V_p,c_Polynomial_Osmult(V_a,V_q,T_a),tc_Polynomial_Opoly(T_a)) = c_Polynomial_Osmult(V_a,c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) ) ).
cnf(cls_mult__smult__left_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_HOL_Otimes__class_Otimes(c_Polynomial_Osmult(V_a,V_p,T_a),V_q,tc_Polynomial_Opoly(T_a)) = c_Polynomial_Osmult(V_a,c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) ) ).
cnf(cls_dvd__mult__div__cancel_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),T_a) = V_b
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ).
cnf(cls_dvd__div__mult__self_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),V_a,T_a) = V_b
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_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_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_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_nat_Oinject_0,axiom,
( c_Suc(V_nat) != c_Suc(V_nat_H)
| V_nat = V_nat_H ) ).
cnf(cls_Suc__inject_0,axiom,
( c_Suc(V_x) != c_Suc(V_y)
| V_x = V_y ) ).
cnf(cls_abs__ge__minus__self_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ) ).
cnf(cls_add__pCons_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_HOL_Oplus__class_Oplus(c_Polynomial_OpCons(V_a,V_p,T_a),c_Polynomial_OpCons(V_b,V_q,T_a),tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) ) ).
cnf(cls_abs__ge__self_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_lessequals(V_a,c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ) ).
cnf(cls_less__add__iff1_0,axiom,
( ~ class_Ring__and__Field_Opordered__ring(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a) ) ).
cnf(cls_less__add__iff1_1,axiom,
( ~ class_Ring__and__Field_Opordered__ring(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a) ) ).
cnf(cls_less__add__iff2_0,axiom,
( ~ class_Ring__and__Field_Opordered__ring(T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a) ) ).
cnf(cls_less__add__iff2_1,axiom,
( ~ class_Ring__and__Field_Opordered__ring(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a) ) ).
cnf(cls_pdivmod__rel__def_7,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_y,tc_Polynomial_Opoly(T_a)),V_r,tc_Polynomial_Opoly(T_a)),V_y,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_r,T_a)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(V_r,T_a),c_Polynomial_Odegree(V_y,T_a),tc_nat) ) ).
cnf(cls_eq__divide__eq_4,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a),V_c,T_a) ) ).
cnf(cls_mod__add__cong_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a)
| c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a_H,V_b_H,T_a),V_c,T_a) ) ).
cnf(cls_less__Suc0_1,axiom,
c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) ).
cnf(cls_one__is__add_2,axiom,
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)
| V_m = c_HOL_Ozero__class_Ozero(tc_nat)
| V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
cnf(cls_one__is__add_1,axiom,
( c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) != c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)
| V_n = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))
| V_m = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ) ).
cnf(cls_smult__diff__left_0,axiom,
( ~ class_Ring__and__Field_Ocomm__ring(T_a)
| c_Polynomial_Osmult(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_p,T_a) = c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(V_a,V_p,T_a),c_Polynomial_Osmult(V_b,V_p,T_a),tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_smult__diff__right_0,axiom,
( ~ class_Ring__and__Field_Ocomm__ring(T_a)
| c_Polynomial_Osmult(V_a,c_HOL_Ominus__class_Ominus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ominus__class_Ominus(c_Polynomial_Osmult(V_a,V_p,T_a),c_Polynomial_Osmult(V_a,V_q,T_a),tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_minus__unique_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Ouminus__class_Ouminus(V_a,T_a) = V_b ) ).
cnf(cls_eq__neg__iff__add__eq__0_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| V_a = c_HOL_Ouminus__class_Ouminus(V_b,T_a) ) ).
cnf(cls_abs__less__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),V_b,T_a) ) ).
cnf(cls_class__ringb_Onoteq__reduce_0,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_d,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| V_c = V_d
| V_a = V_b ) ).
cnf(cls_class__ringb_Oadd__mul__solve_0,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_w,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a) != c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_w,V_z,T_a),c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a)
| V_y = V_z
| V_w = V_x ) ).
cnf(cls_abs__mult__self_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_a,V_a,T_a) ) ).
cnf(cls_not__less__less__Suc__eq_0,axiom,
( V_n = V_m
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)
| c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ) ).
cnf(cls_less__antisym_0,axiom,
( V_m = V_n
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)
| c_HOL_Oord__class_Oless(V_n,V_m,tc_nat) ) ).
cnf(cls_less__SucE_0,axiom,
( V_m = V_n
| c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat) ) ).
cnf(cls_mod__mult__cong_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a)
| c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a_H,V_b_H,T_a),V_c,T_a) ) ).
cnf(cls_add__frac__eq_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a),T_a) = c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),c_HOL_Otimes__class_Otimes(V_w,V_y,T_a),T_a),c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a)
| V_z = c_HOL_Ozero__class_Ozero(T_a)
| V_y = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_divide__eq__eq_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| V_b = c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a)
| V_c = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_eq__divide__eq_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a) = V_b
| V_c = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_degree__mult__le_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_lessequals(c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a),c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat),tc_nat) ) ).
cnf(cls_eq__poly__code_I3_J_0,axiom,
( ~ class_HOL_Ozero(T_a)
| ~ class_HOL_Oeq(T_a)
| c_HOL_Oeq__class_Oeq(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oeq__class_Oeq(c_Polynomial_OpCons(V_a,V_p,T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_eq__poly__code_I3_J_1,axiom,
( ~ class_HOL_Ozero(T_a)
| ~ class_HOL_Oeq(T_a)
| c_HOL_Oeq__class_Oeq(V_p,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a))
| ~ c_HOL_Oeq__class_Oeq(c_Polynomial_OpCons(V_a,V_p,T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_mult__pCons__left_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_HOL_Otimes__class_Otimes(c_Polynomial_OpCons(V_a,V_p,T_a),V_q,tc_Polynomial_Opoly(T_a)) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(V_a,V_q,T_a),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a),tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_mult__pCons__right_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_HOL_Otimes__class_Otimes(V_p,c_Polynomial_OpCons(V_a,V_q,T_a),tc_Polynomial_Opoly(T_a)) = c_HOL_Oplus__class_Oplus(c_Polynomial_Osmult(V_a,V_p,T_a),c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a),tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_synthetic__div__unique_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_HOL_Oplus__class_Oplus(V_p,c_Polynomial_Osmult(V_c,V_q,T_a),tc_Polynomial_Opoly(T_a)) != c_Polynomial_OpCons(V_r,V_q,T_a)
| V_r = c_Polynomial_Opoly(V_p,V_c,T_a) ) ).
cnf(cls_abs__mult__pos_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_y,T_a),V_x,T_a) = c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_y,V_x,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ).
cnf(cls_abs__dvd__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(V_m,T_a),V_k,T_a) ) ).
cnf(cls_abs__dvd__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(V_m,T_a),V_k,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a) ) ).
cnf(cls_dvd__abs__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,c_HOL_Oabs__class_Oabs(V_k,T_a),T_a) ) ).
cnf(cls_dvd__abs__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_m,c_HOL_Oabs__class_Oabs(V_k,T_a),T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a) ) ).
cnf(cls_one__is__add_4,axiom,
c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) = c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ).
cnf(cls_linorder__neq__iff_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).
cnf(cls_order__less__le_1,axiom,
( ~ class_Orderings_Oorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).
cnf(cls_less__not__refl_0,axiom,
~ c_HOL_Oord__class_Oless(V_n,V_n,tc_nat) ).
cnf(cls_nat__less__le_1,axiom,
~ c_HOL_Oord__class_Oless(V_x,V_x,tc_nat) ).
cnf(cls_order__less__irrefl_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_x,T_a) ) ).
cnf(cls_less__le__not__le_2,axiom,
( ~ class_Orderings_Opreorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| c_lessequals(V_y,V_x,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_sup__inf__absorb_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a) = V_x ) ).
cnf(cls_add__pos__pos_0,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_le__Suc__ex__iff_1,axiom,
c_lessequals(V_k,c_HOL_Oplus__class_Oplus(V_k,V_x,tc_nat),tc_nat) ).
cnf(cls_le__iff__add_1,axiom,
c_lessequals(V_m,c_HOL_Oplus__class_Oplus(V_m,V_x,tc_nat),tc_nat) ).
cnf(cls_le__add2_0,axiom,
c_lessequals(V_n,c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat) ).
cnf(cls_le__add1_0,axiom,
c_lessequals(V_n,c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),tc_nat) ).
cnf(cls_degree__diff__le_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_lessequals(c_Polynomial_Odegree(c_HOL_Ominus__class_Ominus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a),V_n,tc_nat)
| ~ c_lessequals(c_Polynomial_Odegree(V_q,T_a),V_n,tc_nat)
| ~ c_lessequals(c_Polynomial_Odegree(V_p,T_a),V_n,tc_nat) ) ).
cnf(cls_eq__poly__code_I3_J_2,axiom,
( ~ class_HOL_Ozero(T_a)
| ~ class_HOL_Oeq(T_a)
| c_HOL_Oeq__class_Oeq(c_Polynomial_OpCons(V_a,V_p,T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a))
| ~ c_HOL_Oeq__class_Oeq(V_p,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a))
| ~ c_HOL_Oeq__class_Oeq(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_mod__diff__cong_0,axiom,
( ~ class_Divides_Oring__div(T_a)
| c_Divides_Odiv__class_Omod(V_b,V_c,T_a) != c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a)
| c_Divides_Odiv__class_Omod(V_a,V_c,T_a) != c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a)
| c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a_H,V_b_H,T_a),V_c,T_a) ) ).
cnf(cls_le__iff__diff__le__0_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_a,V_b,T_a) ) ).
cnf(cls_le__iff__diff__le__0_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,V_b,T_a)
| ~ c_lessequals(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_add__less__mono_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_j,V_l,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ).
cnf(cls_add__strict__mono_0,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_order__le__less_1,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_nat__less__le_0,axiom,
( c_lessequals(V_m,V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).
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_termination__basic__simps_I5_J_0,axiom,
( c_lessequals(V_x,V_y,tc_nat)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,tc_nat) ) ).
cnf(cls_le__iff__sup_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = V_y
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_le__iff__sup_1,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) != V_y
| c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_sup__absorb1_0,axiom,
( ~ class_Lattices_Oupper__semilattice(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_x,V_y,T_a) = V_x
| ~ c_lessequals(V_y,V_x,T_a) ) ).
cnf(cls_add__cancel__end_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_z,T_a),c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a) = V_y ) ).
cnf(cls_minus__add__cancel_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a) = V_b ) ).
cnf(cls_zero__le__divide__iff_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_zero__le__divide__iff_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_poly__mod__minus__right_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Divides_Odiv__class_Omod(V_x,c_HOL_Ouminus__class_Ouminus(V_y,tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) = c_Divides_Odiv__class_Omod(V_x,V_y,tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_Suc__neq__Zero_0,axiom,
c_Suc(V_m) != c_HOL_Ozero__class_Ozero(tc_nat) ).
cnf(cls_nat_Osimps_I3_J_0,axiom,
c_Suc(V_nat_H) != c_HOL_Ozero__class_Ozero(tc_nat) ).
cnf(cls_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_eq__poly__def_0,axiom,
( ~ class_HOL_Ozero(T_a)
| ~ class_HOL_Oeq(T_a)
| V_p = V_q
| ~ c_HOL_Oeq__class_Oeq(V_p,V_q,tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_eq__equals_0,axiom,
( ~ class_HOL_Oeq(T_a)
| V_x = V_y
| ~ c_HOL_Oeq__class_Oeq(V_x,V_y,T_a) ) ).
cnf(cls_coeff__pCons__0_0,axiom,
( ~ class_HOL_Ozero(T_a)
| c_Polynomial_Ocoeff(c_Polynomial_OpCons(V_a,V_p,T_a),c_HOL_Ozero__class_Ozero(tc_nat),T_a) = V_a ) ).
cnf(cls_less__iff__diff__less__0_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_less__iff__diff__less__0_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_abs__not__less__zero_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_nz_0,axiom,
( ~ class_Ring__and__Field_Oidom(t_a)
| v_sko__local__Xnz__1(v_p) != c_HOL_Ozero__class_Ozero(t_a) ) ).
cnf(cls_divide__strict__left__mono_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_c,V_a,T_a),c_HOL_Oinverse__class_Odivide(V_c,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ).
cnf(cls_divide__strict__left__mono__neg_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_c,V_a,T_a),c_HOL_Oinverse__class_Odivide(V_c,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_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_gr0I_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)
| V_n = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
cnf(cls_poly__gcd__commute_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Polynomial_Opoly__gcd(V_x,V_y,T_a) = c_Polynomial_Opoly__gcd(V_y,V_x,T_a) ) ).
cnf(cls_minus__mult__commute_0,axiom,
( ~ class_Ring__and__Field_Oring(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) = c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ).
cnf(cls_neq0__conv_1,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ).
cnf(cls_abs__triangle__ineq4_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_lessequals(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a),c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a) ) ).
cnf(cls_le__SucI_0,axiom,
( c_lessequals(V_m,c_Suc(V_n),tc_nat)
| ~ c_lessequals(V_m,V_n,tc_nat) ) ).
cnf(cls_Suc__leD_0,axiom,
( c_lessequals(V_m,V_n,tc_nat)
| ~ c_lessequals(c_Suc(V_m),V_n,tc_nat) ) ).
cnf(cls_poly__gcd__dvd2_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(V_x,V_y,T_a),V_y,tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_poly__gcd__dvd1_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Opoly__gcd(V_x,V_y,T_a),V_x,tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_dvd__poly__gcd__iff_2,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Polynomial_Opoly__gcd(V_x,V_y,T_a),tc_Polynomial_Opoly(T_a))
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_y,tc_Polynomial_Opoly(T_a))
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_x,tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_poly__diff_0,axiom,
( ~ class_Ring__and__Field_Ocomm__ring(T_a)
| c_Polynomial_Opoly(c_HOL_Ominus__class_Ominus(V_p,V_q,tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_HOL_Ominus__class_Ominus(c_Polynomial_Opoly(V_p,V_x,T_a),c_Polynomial_Opoly(V_q,V_x,T_a),T_a) ) ).
cnf(cls_abs__of__nonpos_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_HOL_Oabs__class_Oabs(V_a,T_a) = c_HOL_Ouminus__class_Ouminus(V_a,T_a)
| ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_mult__strict__left__mono__comm_0,axiom,
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_mult__less__cancel__right__disj_5,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_mult__less__cancel__right__disj_4,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_mult__strict__right__mono_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_mult__strict__right__mono__neg_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ).
cnf(cls_mult__less__cancel__left__disj_5,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_mult__less__cancel__left__disj_4,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_mult__strict__left__mono_0,axiom,
( ~ class_Ring__and__Field_Oordered__semiring__strict(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_mult__strict__left__mono__neg_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ).
cnf(cls_mult__less__cancel__left__pos_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_mult__less__cancel__left__pos_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_mult__less__cancel__left__neg_1,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_mult__less__cancel__left__neg_0,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_diff__minus__eq__add_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| c_HOL_Ominus__class_Ominus(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Oplus__class_Oplus(V_a,V_b,T_a) ) ).
cnf(cls_mod__mult__self2_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a) ) ).
cnf(cls_mod__mult__self1_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a),V_b,T_a) = c_Divides_Odiv__class_Omod(V_a,V_b,T_a) ) ).
cnf(cls_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_dvd__mult__cancel__right_0,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| V_c = c_HOL_Ozero__class_Ozero(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) ) ).
cnf(cls_dvd__mult__cancel__left_0,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)
| V_c = c_HOL_Ozero__class_Ozero(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) ) ).
cnf(cls_natgb_Oadd__r0__iff_1,axiom,
V_x = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ).
cnf(cls_Nat_Oadd__0__right_0,axiom,
c_HOL_Oplus__class_Oplus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) = V_m ).
cnf(cls_plus__nat_Oadd__0_0,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat) = V_n ).
cnf(cls_degree__diff__less_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(c_HOL_Ominus__class_Ominus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a),V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(V_q,T_a),V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(V_p,T_a),V_n,tc_nat) ) ).
cnf(cls_synthetic__div__correct_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_HOL_Oplus__class_Oplus(V_p,c_Polynomial_Osmult(V_c,c_Polynomial_Osynthetic__div(V_p,V_c,T_a),T_a),tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(c_Polynomial_Opoly(V_p,V_c,T_a),c_Polynomial_Osynthetic__div(V_p,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_le__divide__eq_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_le__divide__eq_2,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ).
cnf(cls_divide__le__eq_9,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
| ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a) ) ).
cnf(cls_divide__le__eq_3,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_divide__le__eq_2,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)
| c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ).
cnf(cls_id__apply_0,axiom,
c_Fun_Oid(V_x,T_a) = V_x ).
cnf(cls_add__diff__cancel_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a) = V_a ) ).
cnf(cls_add__divide__distrib_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_a,V_c,T_a),c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ).
cnf(cls_divide_Oadd_0,axiom,
( ~ class_RealVector_Oreal__normed__field(T_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),V_ya,T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oinverse__class_Odivide(V_x,V_ya,T_a),c_HOL_Oinverse__class_Odivide(V_y,V_ya,T_a),T_a) ) ).
cnf(cls_abs__diff__less__iff_2,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_x,V_a,T_a),T_a),V_r,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Oplus__class_Oplus(V_a,V_r,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_r,T_a),V_x,T_a) ) ).
cnf(cls_minus__equation__iff_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = V_b ) ).
cnf(cls_equation__minus__iff_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| V_a = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ).
cnf(cls_equation__minus__iff_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| V_b = c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ).
cnf(cls_double__compl_0,axiom,
( ~ class_Lattices_Oboolean__algebra(T_a)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_x,T_a),T_a) = V_x ) ).
cnf(cls_minus__minus_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) = V_a ) ).
cnf(cls_minus__diff__eq_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) = c_HOL_Ominus__class_Ominus(V_b,V_a,T_a) ) ).
cnf(cls_add__less__le__mono_0,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a)
| ~ c_lessequals(V_c,V_d,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_add__le__less__mono_0,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,V_d,T_a)
| ~ c_lessequals(V_a,V_b,T_a) ) ).
cnf(cls_Suc__mono_0,axiom,
( c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat)
| ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).
cnf(cls_Suc__less__eq_0,axiom,
( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat) ) ).
cnf(cls_less__Suc__eq__0__disj_3,axiom,
( c_HOL_Oord__class_Oless(c_Suc(V_x),c_Suc(V_n),tc_nat)
| ~ c_HOL_Oord__class_Oless(V_x,V_n,tc_nat) ) ).
cnf(cls_minus__less__iff_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a) ) ).
cnf(cls_minus__less__iff_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) ).
cnf(cls_less__minus__iff_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ).
cnf(cls_less__minus__iff_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_HOL_Oord__class_Oless(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ).
cnf(cls_minus__le__iff_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a) ) ).
cnf(cls_minus__le__iff_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(c_HOL_Ouminus__class_Ouminus(V_b,T_a),V_a,T_a)
| ~ c_lessequals(c_HOL_Ouminus__class_Ouminus(V_a,T_a),V_b,T_a) ) ).
cnf(cls_le__minus__iff_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ).
cnf(cls_le__minus__iff_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_b,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
| ~ c_lessequals(V_a,c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ).
cnf(cls_eq__divide__eq_2,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_scaleR__cancel__right_0,axiom,
( ~ class_RealVector_Oreal__vector(T_a)
| c_RealVector_OscaleR__class_OscaleR(V_a,V_x,T_a) != c_RealVector_OscaleR__class_OscaleR(V_b,V_x,T_a)
| V_x = c_HOL_Ozero__class_Ozero(T_a)
| V_a = V_b ) ).
cnf(cls_scaleR__cancel__right_1,axiom,
( ~ class_RealVector_Oreal__vector(T_a)
| c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_RealVector_OscaleR__class_OscaleR(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_abs__eq__0_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_HOL_Oabs__class_Oabs(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_neg__equal__zero_1,axiom,
( ~ class_OrderedGroup_Oordered__ab__group__add(T_a)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_minus__zero_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_neg__0__equal__iff__equal_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| c_HOL_Ozero__class_Ozero(T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_sgn__0__0_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_sgn0_0,axiom,
( ~ class_Ring__and__Field_Osgn__if(T_a)
| c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_sgn__zero_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_mult__eq__0__iff_2,axiom,
( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a)
| c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_mult__eq__0__iff_1,axiom,
( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_mult__zero__right_0,axiom,
( ~ class_Ring__and__Field_Omult__zero(T_a)
| c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_mult__zero__left_0,axiom,
( ~ class_Ring__and__Field_Omult__zero(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_class__semiring_Omul__0_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_mult__right_Ozero_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_HOL_Otimes__class_Otimes(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_mult_Ozero__right_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_mult_Ozero__left_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_mult__left_Ozero_0,axiom,
( ~ class_RealVector_Oreal__normed__algebra(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I10_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_class__semiring_Osemiring__rules_I9_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_dvd__0__right_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_mod__self_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Omod(V_a,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_mod__by__0_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Omod(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ).
cnf(cls_dvd__0__left_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_divide__self__if_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_neg__equal__zero_0,axiom,
( ~ class_OrderedGroup_Oordered__ab__group__add(T_a)
| c_HOL_Ouminus__class_Ouminus(V_a,T_a) != V_a
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_nprt__0_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_OrderedGroup_Olordered__ab__group__add__class_Onprt(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_neg__equal__0__iff__equal_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| c_HOL_Ouminus__class_Ouminus(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_mult__eq__0__iff_0,axiom,
( ~ class_Ring__and__Field_Oring__no__zero__divisors(T_a)
| c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| V_b = c_HOL_Ozero__class_Ozero(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_no__zero__divisors_0,axiom,
( ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| V_b = c_HOL_Ozero__class_Ozero(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_no__zero__divirors__neq0_0,axiom,
( ~ class_Ring__and__Field_Ono__zero__divisors(T_a)
| c_HOL_Otimes__class_Otimes(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a)
| V_b = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_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_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_double__eq__0__iff_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_HOL_Oplus__class_Oplus(V_a,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_eq__iff__diff__eq__0_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_right__minus__eq_1,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_diff__0__right_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| c_HOL_Ominus__class_Ominus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ).
cnf(cls_diff__self_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| c_HOL_Ominus__class_Ominus(V_a,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_class__ringb_Osubr0__iff_1,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| c_HOL_Ominus__class_Ominus(V_x,V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_class__ringb_Oadd__r0__iff_0,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| V_x != c_HOL_Oplus__class_Oplus(V_x,V_a,T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_pprt__0_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_OrderedGroup_Olordered__ab__group__add__class_Opprt(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_mod__0_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_double__eq__0__iff_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_poly__gcd__greatest_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Polynomial_Opoly__gcd(V_x,V_y,T_a),tc_Polynomial_Opoly(T_a))
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_y,tc_Polynomial_Opoly(T_a))
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_k,V_x,tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_poly__gcd__code_1,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Polynomial_Opoly__gcd(V_x,V_y,T_a) = c_Polynomial_Opoly__gcd(V_y,c_Divides_Odiv__class_Omod(V_x,V_y,tc_Polynomial_Opoly(T_a)),T_a)
| V_y = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_Suc__n__not__le__n_0,axiom,
~ c_lessequals(c_Suc(V_n),V_n,tc_nat) ).
cnf(cls_inf__sup__aci_I4_J_0,axiom,
( ~ class_Lattices_Olattice(T_a)
| c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) ) ).
cnf(cls_inf__left__idem_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_Lattices_Olower__semilattice__class_Oinf(V_x,c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a),T_a) = c_Lattices_Olower__semilattice__class_Oinf(V_x,V_y,T_a) ) ).
cnf(cls_zero__le__iff__nprt__id_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a,T_a) = V_a
| ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_zero__le__iff__nprt__id_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_OrderedGroup_Olordered__ab__group__add__class_Onprt(V_a,T_a) != V_a
| c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_mod__mod__cancel_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_c,T_a) = c_Divides_Odiv__class_Omod(V_a,V_c,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_c,V_b,T_a) ) ).
cnf(cls_synthetic__div__unique_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_HOL_Oplus__class_Oplus(V_p,c_Polynomial_Osmult(V_c,V_q,T_a),tc_Polynomial_Opoly(T_a)) != c_Polynomial_OpCons(V_r,V_q,T_a)
| V_q = c_Polynomial_Osynthetic__div(V_p,V_c,T_a) ) ).
cnf(cls_poly__dvd__antisym_0,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| c_Polynomial_Ocoeff(V_p,c_Polynomial_Odegree(V_p,T_a),T_a) != c_Polynomial_Ocoeff(V_q,c_Polynomial_Odegree(V_q,T_a),T_a)
| V_p = V_q
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_q,V_p,tc_Polynomial_Opoly(T_a))
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_double__add__le__zero__iff__single__add__le__zero_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_double__add__le__zero__iff__single__add__le__zero_1,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_abs__if__lattice_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ class_OrderedGroup_Olordered__ab__group__add__abs(T_a)
| c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a
| c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_abs__if_1,axiom,
( ~ class_Ring__and__Field_Oabs__if(T_a)
| c_HOL_Oabs__class_Oabs(V_a,T_a) = V_a
| c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_not__add__less2_0,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_j,V_i,tc_nat),V_i,tc_nat) ).
cnf(cls_not__add__less1_0,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_i,tc_nat) ).
cnf(cls_Lim_Ominus__diff__minus_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) = c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),T_a) ) ).
cnf(cls_poly__div__mult__right_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Divides_Odiv__class_Odiv(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) = c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(V_x,V_y,tc_Polynomial_Opoly(T_a)),V_z,tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_mult__dvd__mono_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_c,V_d,T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a) ) ).
cnf(cls_diff__monom_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_HOL_Ominus__class_Ominus(c_Polynomial_Omonom(V_a,V_n,T_a),c_Polynomial_Omonom(V_b,V_n,T_a),tc_Polynomial_Opoly(T_a)) = c_Polynomial_Omonom(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_n,T_a) ) ).
cnf(cls_degree__add__le_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_lessequals(c_Polynomial_Odegree(c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a),V_n,tc_nat)
| ~ c_lessequals(c_Polynomial_Odegree(V_q,T_a),V_n,tc_nat)
| ~ c_lessequals(c_Polynomial_Odegree(V_p,T_a),V_n,tc_nat) ) ).
cnf(cls_le__0__eq_1,axiom,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat) ).
cnf(cls_abs__add__abs_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_HOL_Oabs__class_Oabs(c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a) ) ).
cnf(cls_divide__le__eq_1,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a) ) ).
cnf(cls_divide__le__eq_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_b,T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_le__divide__eq_1,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)
| ~ c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a) ) ).
cnf(cls_le__divide__eq_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_lessequals(V_a,c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a) ) ).
cnf(cls_inf__idem_0,axiom,
( ~ class_Lattices_Olower__semilattice(T_a)
| c_Lattices_Olower__semilattice__class_Oinf(V_x,V_x,T_a) = V_x ) ).
cnf(cls_zero__less__abs__iff_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(T_a),T_a),T_a) ) ).
cnf(cls_divide__neg__pos_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_divide__pos__neg_0,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_y,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) ) ).
cnf(cls_divide__less__0__iff_4,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) ) ).
cnf(cls_divide__less__0__iff_5,axiom,
( ~ class_Ring__and__Field_Oordered__field(T_a)
| ~ class_Ring__and__Field_Odivision__by__zero(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_add__less__mono1_0,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_j,V_k,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(V_i,V_j,tc_nat) ) ).
cnf(cls_nat__add__left__cancel__less_0,axiom,
( c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat) ) ).
cnf(cls_nat__add__left__cancel__less_1,axiom,
( c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat)
| ~ c_HOL_Oord__class_Oless(V_m,V_n,tc_nat) ) ).
cnf(cls_add__less__cancel__left_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a) ) ).
cnf(cls_add__less__cancel__left_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_add__strict__left__mono_0,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_add__less__cancel__right_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ).
cnf(cls_add__less__cancel__right_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_add__strict__right__mono_0,axiom,
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_order__eq__refl_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| c_lessequals(V_x,V_x,T_a) ) ).
cnf(cls_order__eq__iff_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_x,V_x,T_a) ) ).
cnf(cls_eq__imp__le_0,axiom,
c_lessequals(V_x,V_x,tc_nat) ).
cnf(cls_le__trans_0,axiom,
( c_lessequals(V_i,V_k,tc_nat)
| ~ c_lessequals(V_j,V_k,tc_nat)
| ~ c_lessequals(V_i,V_j,tc_nat) ) ).
cnf(cls_le__refl_0,axiom,
c_lessequals(V_n,V_n,tc_nat) ).
cnf(cls_order__le__less__trans_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_order__less__le__trans_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| c_HOL_Oord__class_Oless(V_x,V_z,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_le__add__right__mono_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_lessequals(V_a,c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a)
| ~ c_lessequals(V_c,V_d,T_a)
| ~ c_lessequals(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a) ) ).
cnf(cls_order__trans_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| c_lessequals(V_x,V_z,T_a)
| ~ c_lessequals(V_y,V_z,T_a)
| ~ c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_add__nonpos__nonpos_0,axiom,
( ~ class_OrderedGroup_Opordered__comm__monoid__add(T_a)
| c_lessequals(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_lessequals(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_xt1_I8_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_z,V_y,T_a)
| ~ c_lessequals(V_y,V_x,T_a) ) ).
cnf(cls_xt1_I7_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_HOL_Oord__class_Oless(V_z,V_x,T_a)
| ~ c_lessequals(V_z,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
cnf(cls_xt1_I6_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| c_lessequals(V_z,V_x,T_a)
| ~ c_lessequals(V_z,V_y,T_a)
| ~ c_lessequals(V_y,V_x,T_a) ) ).
cnf(cls_mod__poly__less_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Divides_Odiv__class_Omod(V_x,V_y,tc_Polynomial_Opoly(T_a)) = V_x
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(V_x,T_a),c_Polynomial_Odegree(V_y,T_a),tc_nat) ) ).
cnf(cls_add__is__1_5,axiom,
c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat) = c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)) ).
cnf(cls_poly__pCons_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_Polynomial_Opoly(c_Polynomial_OpCons(V_a,V_p,T_a),V_x,T_a) = c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_x,c_Polynomial_Opoly(V_p,V_x,T_a),T_a),T_a) ) ).
cnf(cls_mod__mult__self1__is__0_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_mod__mult__self2__is__0_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_b,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_le__less__Suc__eq_0,axiom,
( V_n = V_m
| ~ c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)
| ~ c_lessequals(V_m,V_n,tc_nat) ) ).
cnf(cls_semiring__div__class_Omod__div__equality_H_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a),T_a) = V_a ) ).
cnf(cls_degree__add__eq__left_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_Polynomial_Odegree(c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_Polynomial_Odegree(V_p,T_a)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(V_q,T_a),c_Polynomial_Odegree(V_p,T_a),tc_nat) ) ).
cnf(cls_degree__add__eq__right_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_Polynomial_Odegree(c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_Polynomial_Odegree(V_q,T_a)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat) ) ).
cnf(cls_sum__squares__eq__zero__iff_2,axiom,
( ~ class_Ring__and__Field_Oordered__ring__strict(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_pdivmod__rel__def_3,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| V_y = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| c_Polynomial_Opdivmod__rel(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_q,V_y,tc_Polynomial_Opoly(T_a)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)),V_y,V_q,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(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_monom__Suc_0,axiom,
( ~ class_HOL_Ozero(T_a)
| c_Polynomial_Omonom(V_a,c_Suc(V_n),T_a) = c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_Polynomial_Omonom(V_a,V_n,T_a),T_a) ) ).
cnf(cls_abs__diff__less__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Oord__class_Oless(V_x,c_HOL_Oplus__class_Oplus(V_a,V_r,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Oabs__class_Oabs(c_HOL_Ominus__class_Ominus(V_x,V_a,T_a),T_a),V_r,T_a) ) ).
cnf(cls_degree__add__less_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(c_HOL_Oplus__class_Oplus(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a),V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(V_q,T_a),V_n,tc_nat)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(V_p,T_a),V_n,tc_nat) ) ).
cnf(cls_sup__eq__neg__inf_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(T_a)
| c_Lattices_Oupper__semilattice__class_Osup(V_a,V_b,T_a) = c_HOL_Ouminus__class_Ouminus(c_Lattices_Olower__semilattice__class_Oinf(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a),T_a) ) ).
cnf(cls_neg__0__less__iff__less_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ).
cnf(cls_neg__0__less__iff__less_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add(T_a)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_frac__eq__eq_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) != c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a)
| V_z = c_HOL_Ozero__class_Ozero(T_a)
| V_y = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Otimes__class_Otimes(V_x,V_z,T_a) = c_HOL_Otimes__class_Otimes(V_w,V_y,T_a) ) ).
cnf(cls_frac__eq__eq_1,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_HOL_Otimes__class_Otimes(V_x,V_z,T_a) != c_HOL_Otimes__class_Otimes(V_w,V_y,T_a)
| V_z = c_HOL_Ozero__class_Ozero(T_a)
| V_y = c_HOL_Ozero__class_Ozero(T_a)
| c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a) = c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a) ) ).
cnf(cls_poly__mod__minus__left_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Divides_Odiv__class_Omod(c_HOL_Ouminus__class_Ouminus(V_x,tc_Polynomial_Opoly(T_a)),V_y,tc_Polynomial_Opoly(T_a)) = c_HOL_Ouminus__class_Ouminus(c_Divides_Odiv__class_Omod(V_x,V_y,tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_sgn__mult_0,axiom,
( ~ class_RealVector_Oreal__normed__div__algebra(T_a)
| c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(V_x,T_a),c_HOL_Osgn__class_Osgn(V_y,T_a),T_a) ) ).
cnf(cls_sgn__times_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(V_a,T_a),c_HOL_Osgn__class_Osgn(V_b,T_a),T_a) ) ).
cnf(cls_mod__mult__mult1_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a) = c_HOL_Otimes__class_Otimes(V_c,c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a) ) ).
cnf(cls_mod__mult__mult2_0,axiom,
( ~ class_Divides_Osemiring__div(T_a)
| c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a) = c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_c,T_a) ) ).
cnf(cls_less__minus__self__iff_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ).
cnf(cls_less__minus__self__iff_1,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Oord__class_Oless(V_a,c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a)
| ~ c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_abs__ge__zero_0,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_lessequals(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a) ) ).
cnf(cls_Suc__le__mono_1,axiom,
( c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat)
| ~ c_lessequals(V_n,V_m,tc_nat) ) ).
cnf(cls_Suc__le__mono_0,axiom,
( c_lessequals(V_n,V_m,tc_nat)
| ~ c_lessequals(c_Suc(V_n),c_Suc(V_m),tc_nat) ) ).
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_monom__eq__iff_0,axiom,
( ~ class_HOL_Ozero(T_a)
| c_Polynomial_Omonom(V_a,V_n,T_a) != c_Polynomial_Omonom(V_b,V_n,T_a)
| V_a = V_b ) ).
cnf(cls_dvd__if__abs__eq_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Oabs__class_Oabs(V_l,T_a) != c_HOL_Oabs__class_Oabs(V_k,T_a)
| c_Ring__and__Field_Odvd__class_Odvd(V_l,V_k,T_a) ) ).
cnf(cls_minus__add_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_b,T_a),c_HOL_Ouminus__class_Ouminus(V_a,T_a),T_a) ) ).
cnf(cls_minus__add__distrib_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a) = c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(V_a,T_a),c_HOL_Ouminus__class_Ouminus(V_b,T_a),T_a) ) ).
cnf(cls_degree__smult__le_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_lessequals(c_Polynomial_Odegree(c_Polynomial_Osmult(V_a,V_p,T_a),T_a),c_Polynomial_Odegree(V_p,T_a),tc_nat) ) ).
cnf(cls_order__less__asym_H_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a) ) ).
cnf(cls_order__less__asym_0,axiom,
( ~ class_Orderings_Opreorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a) ) ).
cnf(cls_linorder__linear_0,axiom,
( ~ class_Orderings_Olinorder(T_a)
| c_lessequals(V_y,V_x,T_a)
| c_lessequals(V_x,V_y,T_a) ) ).
cnf(cls_nat__le__linear_0,axiom,
( c_lessequals(V_n,V_m,tc_nat)
| c_lessequals(V_m,V_n,tc_nat) ) ).
cnf(cls_not__less__iff__gr__or__eq_1,axiom,
( ~ class_Orderings_Olinorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_x,V_y,T_a)
| ~ c_HOL_Oord__class_Oless(V_y,V_x,T_a) ) ).
cnf(cls_xt1_I9_J_0,axiom,
( ~ class_Orderings_Oorder(T_a)
| ~ c_HOL_Oord__class_Oless(V_a,V_b,T_a)
| ~ c_HOL_Oord__class_Oless(V_b,V_a,T_a) ) ).
cnf(cls_abs__eq__0_1,axiom,
( ~ class_OrderedGroup_Opordered__ab__group__add__abs(T_a)
| c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_neg__0__equal__iff__equal_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| c_HOL_Ozero__class_Ozero(T_a) != c_HOL_Ouminus__class_Ouminus(V_a,T_a)
| c_HOL_Ozero__class_Ozero(T_a) = V_a ) ).
cnf(cls_scaleR_Ozero__right_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_scaleR__eq__0__iff_2,axiom,
( ~ class_RealVector_Oreal__vector(T_a)
| c_RealVector_OscaleR__class_OscaleR(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_eq__iff__diff__eq__0_1,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| V_a = V_b ) ).
cnf(cls_right__minus__eq_0,axiom,
( ~ class_OrderedGroup_Ogroup__add(T_a)
| c_HOL_Ominus__class_Ominus(V_a,V_b,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| V_a = V_b ) ).
cnf(cls_class__ringb_Osubr0__iff_0,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| c_HOL_Ominus__class_Ominus(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| V_x = V_y ) ).
cnf(cls_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_sgn__0__0_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Osgn__class_Osgn(V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_sgn__zero__iff_0,axiom,
( ~ class_RealVector_Oreal__normed__vector(T_a)
| c_HOL_Osgn__class_Osgn(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| V_x = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_exp__not__eq__zero_0,axiom,
( ~ class_SEQ_Obanach(T_a)
| ~ class_RealVector_Oreal__normed__field(T_a)
| c_Transcendental_Oexp(V_x,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_monoid__add__class_Oadd__0__right_0,axiom,
( ~ class_OrderedGroup_Omonoid__add(T_a)
| c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ).
cnf(cls_add__0__left_0,axiom,
( ~ class_OrderedGroup_Omonoid__add(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a ) ).
cnf(cls_comm__monoid__add_Omult__1__right_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ).
cnf(cls_class__ringb_Oadd__r0__iff_1,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| ~ class_Int_Onumber__ring(T_a)
| V_x = c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a) ) ).
cnf(cls_class__semiring_Oadd__0_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a) = V_x ) ).
cnf(cls_comm__monoid__add_Omult__1_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a ) ).
cnf(cls_class__semiring_Osemiring__rules_I6_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a) = V_a ) ).
cnf(cls_class__semiring_Osemiring__rules_I5_J_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a) = V_a ) ).
cnf(cls_smult__dvd__iff_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(T_a),V_p,T_a),V_q,tc_Polynomial_Opoly(T_a))
| V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_synthetic__divmod__0_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_Polynomial_Osynthetic__divmod(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_c,T_a) = c_Pair(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_HOL_Ozero__class_Ozero(T_a),tc_Polynomial_Opoly(T_a),T_a) ) ).
cnf(cls_smult__dvd__iff_3,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Ring__and__Field_Odvd__class_Odvd(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(T_a),V_p,T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_le__degree_0,axiom,
( ~ class_HOL_Ozero(T_a)
| c_lessequals(V_n,c_Polynomial_Odegree(V_p,T_a),tc_nat)
| c_Polynomial_Ocoeff(V_p,V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_coeff__eq__0_0,axiom,
( ~ class_HOL_Ozero(T_a)
| c_Polynomial_Ocoeff(V_p,V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(V_p,T_a),V_n,tc_nat) ) ).
cnf(cls_degree__smult__eq_0,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| c_Polynomial_Odegree(c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(T_a),V_p,T_a),T_a) = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
cnf(cls_pprt__def__raw_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(t_a)
| c_OrderedGroup_Olordered__ab__group__add__class_Opprt(v_x,t_a) = c_Lattices_Oupper__semilattice__class_Osup(v_x,c_HOL_Ozero__class_Ozero(t_a),t_a) ) ).
cnf(cls_nprt__def__raw_0,axiom,
( ~ class_OrderedGroup_Olordered__ab__group__add(t_a)
| c_OrderedGroup_Olordered__ab__group__add__class_Onprt(v_x,t_a) = c_Lattices_Olower__semilattice__class_Oinf(v_x,c_HOL_Ozero__class_Ozero(t_a),t_a) ) ).
cnf(cls_eq__zero__or__degree__less_0,axiom,
( ~ class_HOL_Ozero(T_a)
| c_Polynomial_Ocoeff(V_p,V_n,T_a) != c_HOL_Ozero__class_Ozero(T_a)
| ~ c_lessequals(c_Polynomial_Odegree(V_p,T_a),V_n,tc_nat)
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(V_p,T_a),V_n,tc_nat)
| V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_assms_1,axiom,
( ~ class_Ring__and__Field_Oidom(t_a)
| c_Polynomial_Opoly(v_p,v_sko__local__Xassms__1(v_p),t_a) != c_HOL_Ozero__class_Ozero(t_a) ) ).
cnf(cls_order__root_2,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| c_Polynomial_Opoly(V_p,V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a)
| c_Polynomial_Oorder(V_a,V_p,T_a) = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
cnf(cls_nz_1,axiom,
( ~ class_Ring__and__Field_Oidom(t_a)
| c_Polynomial_Opoly(v_p,v_sko__local__Xnz__1(v_p),t_a) != c_HOL_Ozero__class_Ozero(t_a) ) ).
cnf(cls_smult__0__right_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_Polynomial_Osmult(V_a,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_smult__eq__0__iff_2,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| c_Polynomial_Osmult(V_a,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_minus__poly__code_I1_J_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_synthetic__div__0_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_Polynomial_Osynthetic__div(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_c,T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_sgn__poly__def_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_mult__poly__0__right_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_HOL_Otimes__class_Otimes(V_p,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_mult__poly__0__left_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q,tc_Polynomial_Opoly(T_a)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_pCons__eq__0__iff_1,axiom,
( ~ class_HOL_Ozero(T_a)
| c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_pdivmod__rel__by__0_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Polynomial_Opdivmod__rel(V_x,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x,T_a) ) ).
cnf(cls_offset__poly__eq__0__iff_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_pdivmod__rel__0_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_y,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) ) ).
cnf(cls_eq__poly__code_I1_J_0,axiom,
( ~ class_HOL_Ozero(T_a)
| ~ class_HOL_Oeq(T_a)
| c_HOL_Oeq__class_Oeq(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_poly__gcd__zero__iff_1,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Polynomial_Opoly__gcd(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| V_y = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_poly__gcd__zero__iff_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Polynomial_Opoly__gcd(V_x,V_y,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| V_x = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_pdivmod__rel__by__0__iff_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ c_Polynomial_Opdivmod__rel(V_x,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q,V_r,T_a) ) ).
cnf(cls_pdivmod__rel__0__iff_1,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| V_r = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_y,V_q,V_r,T_a) ) ).
cnf(cls_pdivmod__rel__0__iff_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ c_Polynomial_Opdivmod__rel(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_y,V_q,V_r,T_a) ) ).
cnf(cls_pdivmod__rel__def_1,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| ~ c_Polynomial_Opdivmod__rel(V_x,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q,V_r,T_a)
| V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_pdivmod__rel__by__0__iff_1,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| V_r = V_x
| ~ c_Polynomial_Opdivmod__rel(V_x,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q,V_r,T_a) ) ).
cnf(cls_poly__gcd__0__0_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_not__pos__poly__0_0,axiom,
( ~ class_Ring__and__Field_Oordered__idom(T_a)
| ~ c_Polynomial_Opos__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) ) ).
cnf(cls_diff__poly__code_I2_J_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_HOL_Ominus__class_Ominus(V_p,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) = V_p ) ).
cnf(cls_offset__poly__0_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_h,T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_pcompose__0_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_Polynomial_Opcompose(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q,T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_add__poly__code_I1_J_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q,tc_Polynomial_Opoly(T_a)) = V_q ) ).
cnf(cls_add__poly__code_I2_J_0,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(T_a)
| c_HOL_Oplus__class_Oplus(V_p,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),tc_Polynomial_Opoly(T_a)) = V_p ) ).
cnf(cls_synthetic__div__eq__0__iff_1,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_Polynomial_Odegree(V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_nat)
| c_Polynomial_Osynthetic__div(V_p,V_c,T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_synthetic__div__eq__0__iff_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_Polynomial_Osynthetic__div(V_p,V_c,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| c_Polynomial_Odegree(V_p,T_a) = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
cnf(cls_pdivmod__rel__def_2,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(V_r,T_a),c_Polynomial_Odegree(V_y,T_a),tc_nat)
| V_r = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| V_y = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ c_Polynomial_Opdivmod__rel(V_x,V_y,V_q,V_r,T_a) ) ).
cnf(cls_dvd__imp__degree__le_0,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| c_lessequals(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat)
| V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ c_Ring__and__Field_Odvd__class_Odvd(V_p,V_q,tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_degree__mult__eq_0,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| c_Polynomial_Odegree(c_HOL_Otimes__class_Otimes(V_p,V_q,tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Oplus__class_Oplus(c_Polynomial_Odegree(V_p,T_a),c_Polynomial_Odegree(V_q,T_a),tc_nat)
| V_q = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_degree__pCons__0_0,axiom,
( ~ class_HOL_Ozero(T_a)
| c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a) = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
cnf(cls_div__poly__less_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Divides_Odiv__class_Odiv(V_x,V_y,tc_Polynomial_Opoly(T_a)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ c_HOL_Oord__class_Oless(c_Polynomial_Odegree(V_x,T_a),c_Polynomial_Odegree(V_y,T_a),tc_nat) ) ).
cnf(cls_psize__def_1,axiom,
( ~ class_HOL_Ozero(T_a)
| c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(V_p,T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a))
| V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_order__degree_0,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| c_lessequals(c_Polynomial_Oorder(V_a,V_p,T_a),c_Polynomial_Odegree(V_p,T_a),tc_nat)
| V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_degree__pCons__eq_0,axiom,
( ~ class_HOL_Ozero(T_a)
| c_Polynomial_Odegree(c_Polynomial_OpCons(V_a,V_p,T_a),T_a) = c_Suc(c_Polynomial_Odegree(V_p,T_a))
| V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_degree__mod__less_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_HOL_Oord__class_Oless(c_Polynomial_Odegree(c_Divides_Odiv__class_Omod(V_x,V_y,tc_Polynomial_Opoly(T_a)),T_a),c_Polynomial_Odegree(V_y,T_a),tc_nat)
| c_Divides_Odiv__class_Omod(V_x,V_y,tc_Polynomial_Opoly(T_a)) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| V_y = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_degree__minus_0,axiom,
( ~ class_OrderedGroup_Oab__group__add(T_a)
| c_Polynomial_Odegree(c_HOL_Ouminus__class_Ouminus(V_p,tc_Polynomial_Opoly(T_a)),T_a) = c_Polynomial_Odegree(V_p,T_a) ) ).
cnf(cls_degree__offset__poly_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_Polynomial_Odegree(c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(V_p,V_h,T_a),T_a) = c_Polynomial_Odegree(V_p,T_a) ) ).
cnf(cls_id__def_0,axiom,
c_Fun_Oid(v_x,t_a) = v_x ).
cnf(cls_poly__pcompose_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_Polynomial_Opoly(c_Polynomial_Opcompose(V_p,V_q,T_a),V_x,T_a) = c_Polynomial_Opoly(V_p,c_Polynomial_Opoly(V_q,V_x,T_a),T_a) ) ).
cnf(cls_poly__gcd__monic_0,axiom,
( ~ class_Ring__and__Field_Ofield(T_a)
| c_Polynomial_Ocoeff(c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),c_Polynomial_Odegree(c_Polynomial_Opoly__gcd(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_order__root_0,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| c_Polynomial_Oorder(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_nat)
| V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| c_Polynomial_Opoly(V_p,V_a,T_a) != c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_smult__0__left_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(T_a),V_p,T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_smult__eq__0__iff_1,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| c_Polynomial_Osmult(c_HOL_Ozero__class_Ozero(T_a),V_p,T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_pCons__eq__0__iff_0,axiom,
( ~ class_HOL_Ozero(T_a)
| c_Polynomial_OpCons(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_smult__eq__0__iff_0,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| c_Polynomial_Osmult(V_a,V_p,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_pCons__0__0_0,axiom,
( ~ class_HOL_Ozero(T_a)
| c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_monom__eq__0__iff_0,axiom,
( ~ class_HOL_Ozero(T_a)
| c_Polynomial_Omonom(V_a,V_n,T_a) != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_monom__eq__0_0,axiom,
( ~ class_HOL_Ozero(T_a)
| c_Polynomial_Omonom(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a) = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_coeff__0_0,axiom,
( ~ class_HOL_Ozero(T_a)
| c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_n,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_degree__monom__eq_0,axiom,
( ~ class_HOL_Ozero(T_a)
| c_Polynomial_Odegree(c_Polynomial_Omonom(V_a,V_n,T_a),T_a) = V_n
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_degree__smult__eq_1,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| c_Polynomial_Odegree(c_Polynomial_Osmult(V_a,V_p,T_a),T_a) = c_Polynomial_Odegree(V_p,T_a)
| V_a = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_degree__0_0,axiom,
( ~ class_HOL_Ozero(T_a)
| c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a) = c_HOL_Ozero__class_Ozero(tc_nat) ) ).
cnf(cls_pCons_I2_J_1,axiom,
( ~ class_Ring__and__Field_Oidom(t_a)
| c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,t_a),v_sko__local__XpCons__2__1(v_c____,v_cs____),t_a) != c_HOL_Ozero__class_Ozero(t_a) ) ).
cnf(cls_pCons_Oprems_1,axiom,
( ~ class_Ring__and__Field_Oidom(t_a)
| c_Polynomial_Opoly(c_Polynomial_OpCons(v_c____,v_cs____,t_a),v_sko__local__XpCons__Xprems__1(v_c____,v_cs____),t_a) != c_HOL_Ozero__class_Ozero(t_a) ) ).
cnf(cls_leading__coeff__0__iff_1,axiom,
( ~ class_HOL_Ozero(T_a)
| c_Polynomial_Ocoeff(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_Polynomial_Odegree(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),T_a),T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_leading__coeff__0__iff_0,axiom,
( ~ class_HOL_Ozero(T_a)
| c_Polynomial_Ocoeff(V_p,c_Polynomial_Odegree(V_p,T_a),T_a) != c_HOL_Ozero__class_Ozero(T_a)
| V_p = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ).
cnf(cls_pCons_I1_J_0,axiom,
( ~ class_Ring__and__Field_Oidom(t_a)
| v_sko__local__XpCons__1__2(v_cs____) != c_HOL_Ozero__class_Ozero(t_a)
| c_Polynomial_Opoly(v_cs____,V_z,t_a) = c_HOL_Ozero__class_Ozero(t_a)
| V_z = c_HOL_Ozero__class_Ozero(t_a) ) ).
cnf(cls_pCons_Ohyps_0,axiom,
( ~ class_Ring__and__Field_Oidom(t_a)
| v_sko__local__XpCons__Xhyps__2(v_cs____) != c_HOL_Ozero__class_Ozero(t_a)
| c_Polynomial_Opoly(v_cs____,V_z,t_a) = c_HOL_Ozero__class_Ozero(t_a)
| V_z = c_HOL_Ozero__class_Ozero(t_a) ) ).
cnf(cls_pCons_Oprems_0,axiom,
( ~ class_Ring__and__Field_Oidom(t_a)
| v_sko__local__XpCons__Xprems__1(v_c____,v_cs____) != c_HOL_Ozero__class_Ozero(t_a) ) ).
cnf(cls_pCons_I2_J_0,axiom,
( ~ class_Ring__and__Field_Oidom(t_a)
| v_sko__local__XpCons__2__1(v_c____,v_cs____) != c_HOL_Ozero__class_Ozero(t_a) ) ).
cnf(cls_calculation_0,axiom,
( ~ class_Ring__and__Field_Oidom(t_a)
| v_sko__unknown__thm__ro4__2(v_c____,v_cs____) != c_HOL_Ozero__class_Ozero(t_a)
| v_c____ != c_HOL_Ozero__class_Ozero(t_a) ) ).
cnf(cls_poly__0_0,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(T_a)
| c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_order__root_1,axiom,
( ~ class_Ring__and__Field_Oidom(T_a)
| c_Polynomial_Opoly(c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_a,T_a) = c_HOL_Ozero__class_Ozero(T_a) ) ).
cnf(cls_c0_0,axiom,
( ~ class_Ring__and__Field_Oidom(t_a)
| v_c____ != c_HOL_Ozero__class_Ozero(t_a) ) ).
cnf(tfree_tcs,negated_conjecture,
class_Ring__and__Field_Oidom(t_a) ).
cnf(cls_conjecture_0,negated_conjecture,
v_cs____ != c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ).
cnf(cls_conjecture_1,negated_conjecture,
( hAPP(v_x,V_xa) != c_HOL_Ozero__class_Ozero(t_a)
| c_Polynomial_Odegree(V_xa,t_a) != c_Polynomial_Odegree(v_cs____,t_a)
| V_xa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ).
cnf(cls_conjecture_2,negated_conjecture,
( c_Polynomial_Opoly(v_cs____,hAPP(v_x,V_xa),t_a) != c_Polynomial_Opoly(V_xa,hAPP(v_x,V_xa),t_a)
| c_Polynomial_Odegree(V_xa,t_a) != c_Polynomial_Odegree(v_cs____,t_a)
| V_xa = c_HOL_Ozero__class_Ozero(tc_Polynomial_Opoly(t_a)) ) ).
cnf(clsrel_Ring__and__Field_Oidom_Ring__and__Field_Oring__no__zero__divisors,axiom,
( ~ class_Ring__and__Field_Oidom(T)
| class_Ring__and__Field_Oring__no__zero__divisors(T) ) ).
cnf(clsrel_Ring__and__Field_Oidom_OrderedGroup_Ocancel__ab__semigroup__add,axiom,
( ~ class_Ring__and__Field_Oidom(T)
| class_OrderedGroup_Ocancel__ab__semigroup__add(T) ) ).
cnf(clsrel_Ring__and__Field_Oidom_OrderedGroup_Ocancel__semigroup__add,axiom,
( ~ class_Ring__and__Field_Oidom(T)
| class_OrderedGroup_Ocancel__semigroup__add(T) ) ).
cnf(clsrel_Ring__and__Field_Oidom_Ring__and__Field_Ono__zero__divisors,axiom,
( ~ class_Ring__and__Field_Oidom(T)
| class_Ring__and__Field_Ono__zero__divisors(T) ) ).
cnf(clsrel_Ring__and__Field_Oidom_Ring__and__Field_Ocomm__semiring__1,axiom,
( ~ class_Ring__and__Field_Oidom(T)
| class_Ring__and__Field_Ocomm__semiring__1(T) ) ).
cnf(clsrel_Ring__and__Field_Oidom_Ring__and__Field_Ocomm__semiring__0,axiom,
( ~ class_Ring__and__Field_Oidom(T)
| class_Ring__and__Field_Ocomm__semiring__0(T) ) ).
cnf(clsrel_Ring__and__Field_Oidom_OrderedGroup_Oab__semigroup__mult,axiom,
( ~ class_Ring__and__Field_Oidom(T)
| class_OrderedGroup_Oab__semigroup__mult(T) ) ).
cnf(clsrel_Ring__and__Field_Oidom_OrderedGroup_Oab__semigroup__add,axiom,
( ~ class_Ring__and__Field_Oidom(T)
| class_OrderedGroup_Oab__semigroup__add(T) ) ).
cnf(clsrel_Ring__and__Field_Oidom_Ring__and__Field_Ocomm__semiring,axiom,
( ~ class_Ring__and__Field_Oidom(T)
| class_Ring__and__Field_Ocomm__semiring(T) ) ).
cnf(clsrel_Ring__and__Field_Oidom_OrderedGroup_Ocomm__monoid__add,axiom,
( ~ class_Ring__and__Field_Oidom(T)
| class_OrderedGroup_Ocomm__monoid__add(T) ) ).
cnf(clsrel_Ring__and__Field_Oidom_Ring__and__Field_Ocomm__ring__1,axiom,
( ~ class_Ring__and__Field_Oidom(T)
| class_Ring__and__Field_Ocomm__ring__1(T) ) ).
cnf(clsrel_Ring__and__Field_Oidom_OrderedGroup_Oab__group__add,axiom,
( ~ class_Ring__and__Field_Oidom(T)
| class_OrderedGroup_Oab__group__add(T) ) ).
cnf(clsrel_Ring__and__Field_Oidom_Ring__and__Field_Omult__zero,axiom,
( ~ class_Ring__and__Field_Oidom(T)
| class_Ring__and__Field_Omult__zero(T) ) ).
cnf(clsrel_Ring__and__Field_Oidom_Ring__and__Field_Ocomm__ring,axiom,
( ~ class_Ring__and__Field_Oidom(T)
| class_Ring__and__Field_Ocomm__ring(T) ) ).
cnf(clsrel_Ring__and__Field_Oidom_Ring__and__Field_Osemiring,axiom,
( ~ class_Ring__and__Field_Oidom(T)
| class_Ring__and__Field_Osemiring(T) ) ).
cnf(clsrel_Ring__and__Field_Oidom_OrderedGroup_Omonoid__add,axiom,
( ~ class_Ring__and__Field_Oidom(T)
| class_OrderedGroup_Omonoid__add(T) ) ).
cnf(clsrel_Ring__and__Field_Oidom_OrderedGroup_Ogroup__add,axiom,
( ~ class_Ring__and__Field_Oidom(T)
| class_OrderedGroup_Ogroup__add(T) ) ).
cnf(clsrel_Ring__and__Field_Oidom_Ring__and__Field_Oring,axiom,
( ~ class_Ring__and__Field_Oidom(T)
| class_Ring__and__Field_Oring(T) ) ).
cnf(clsrel_Ring__and__Field_Oidom_Ring__and__Field_Odvd,axiom,
( ~ class_Ring__and__Field_Oidom(T)
| class_Ring__and__Field_Odvd(T) ) ).
cnf(clsrel_Ring__and__Field_Oidom_HOL_Ozero,axiom,
( ~ class_Ring__and__Field_Oidom(T)
| class_HOL_Ozero(T) ) ).
cnf(clsrel_Ring__and__Field_Oidom_OrderedGroup_Ocancel__comm__monoid__add,axiom,
( ~ class_Ring__and__Field_Oidom(T)
| class_OrderedGroup_Ocancel__comm__monoid__add(T) ) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__comm__monoid__add,axiom,
( class_OrderedGroup_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(T_1) ) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__comm__monoid__add,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_RealDef_Oreal) ).
cnf(clsarity_nat__OrderedGroup_Ocancel__comm__monoid__add,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_nat) ).
cnf(clsarity_prod__HOL_Oeq,axiom,
class_HOL_Oeq(tc_prod(T_2,T_1)) ).
cnf(clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Opordered__cancel__semiring,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Oordered__semiring__strict,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Opordered__comm__monoid__add,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Ocancel__semigroup__add,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Opordered__semiring,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Oordered__semiring,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Ono__zero__divisors,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Oordered__semidom,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring__0,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Oab__semigroup__mult,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Oab__semigroup__add,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Ocomm__semiring,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat) ).
cnf(clsarity_nat__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_nat) ).
cnf(clsarity_nat__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Omult__mono1,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Omult__zero,axiom,
class_Ring__and__Field_Omult__zero(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Omult__mono,axiom,
class_Ring__and__Field_Omult__mono(tc_nat) ).
cnf(clsarity_nat__Lattices_Odistrib__lattice,axiom,
class_Lattices_Odistrib__lattice(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Osemiring,axiom,
class_Ring__and__Field_Osemiring(tc_nat) ).
cnf(clsarity_nat__OrderedGroup_Omonoid__add,axiom,
class_OrderedGroup_Omonoid__add(tc_nat) ).
cnf(clsarity_nat__Divides_Osemiring__div,axiom,
class_Divides_Osemiring__div(tc_nat) ).
cnf(clsarity_nat__Ring__and__Field_Odvd,axiom,
class_Ring__and__Field_Odvd(tc_nat) ).
cnf(clsarity_nat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_nat) ).
cnf(clsarity_nat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_nat) ).
cnf(clsarity_nat__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_nat) ).
cnf(clsarity_nat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_nat) ).
cnf(clsarity_nat__HOL_Ozero,axiom,
class_HOL_Ozero(tc_nat) ).
cnf(clsarity_nat__HOL_Oeq,axiom,
class_HOL_Oeq(tc_nat) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__meet,axiom,
class_OrderedGroup_Olordered__ab__group__add__meet(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__join,axiom,
class_OrderedGroup_Olordered__ab__group__add__join(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs,axiom,
class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add,axiom,
class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring,axiom,
class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring__abs,axiom,
class_Ring__and__Field_Opordered__ring__abs(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring,axiom,
class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom,axiom,
class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__0,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring,axiom,
class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field,axiom,
class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring,axiom,
class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__RealVector_Oreal__normed__field,axiom,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom,axiom,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring__1,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Lattices_Oupper__semilattice,axiom,
class_Lattices_Oupper__semilattice(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Lattices_Olower__semilattice,axiom,
class_Lattices_Olower__semilattice(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1,axiom,
class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add,axiom,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero,axiom,
class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono,axiom,
class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring,axiom,
class_Ring__and__Field_Ocomm__ring(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Lattices_Odistrib__lattice,axiom,
class_Lattices_Odistrib__lattice(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Osemiring,axiom,
class_Ring__and__Field_Osemiring(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__RealVector_Oreal__algebra,axiom,
class_RealVector_Oreal__algebra(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add,axiom,
class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__RealVector_Oreal__vector,axiom,
class_RealVector_Oreal__vector(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Osgn__if,axiom,
class_Ring__and__Field_Osgn__if(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if,axiom,
class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__RealVector_Oreal__field,axiom,
class_RealVector_Oreal__field(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Ofield,axiom,
class_Ring__and__Field_Ofield(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oring,axiom,
class_Ring__and__Field_Oring(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Oidom,axiom,
class_Ring__and__Field_Oidom(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Ring__and__Field_Odvd,axiom,
class_Ring__and__Field_Odvd(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Lattices_Olattice,axiom,
class_Lattices_Olattice(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__Int_Onumber__ring,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__SEQ_Obanach,axiom,
class_SEQ_Obanach(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__HOL_Ozero,axiom,
class_HOL_Ozero(tc_RealDef_Oreal) ).
cnf(clsarity_RealDef__Oreal__HOL_Oeq,axiom,
class_HOL_Oeq(tc_RealDef_Oreal) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__cancel__ab__semigroup__add,axiom,
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add__imp__le,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__comm__semiring__strict,axiom,
( class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__cancel__semiring,axiom,
( class_Ring__and__Field_Opordered__cancel__semiring(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring__strict,axiom,
( class_Ring__and__Field_Oordered__semiring__strict(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add,axiom,
( class_OrderedGroup_Opordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add__abs,axiom,
( class_OrderedGroup_Opordered__ab__group__add__abs(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__comm__monoid__add,axiom,
( class_OrderedGroup_Opordered__comm__monoid__add(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors,axiom,
( class_Ring__and__Field_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oidom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add,axiom,
( class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict,axiom,
( class_Ring__and__Field_Oordered__ring__strict(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add,axiom,
( class_OrderedGroup_Opordered__ab__group__add(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add,axiom,
( class_OrderedGroup_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add,axiom,
( class_OrderedGroup_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1))
| ~ class_OrderedGroup_Ocancel__comm__monoid__add(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__semiring,axiom,
( class_Ring__and__Field_Opordered__semiring(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring__abs,axiom,
( class_Ring__and__Field_Opordered__ring__abs(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring,axiom,
( class_Ring__and__Field_Oordered__semiring(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors,axiom,
( class_Ring__and__Field_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oidom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semidom,axiom,
( class_Ring__and__Field_Oordered__semidom(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1,axiom,
( class_Ring__and__Field_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0,axiom,
( class_Ring__and__Field_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult,axiom,
( class_OrderedGroup_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add,axiom,
( class_OrderedGroup_Oab__semigroup__add(tc_Polynomial_Opoly(T_1))
| ~ class_OrderedGroup_Ocomm__monoid__add(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring,axiom,
( class_Ring__and__Field_Opordered__ring(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring,axiom,
( class_Ring__and__Field_Ocomm__semiring(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__add,axiom,
( class_OrderedGroup_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1))
| ~ class_OrderedGroup_Ocomm__monoid__add(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom,axiom,
( class_Ring__and__Field_Oordered__idom(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1,axiom,
( class_Ring__and__Field_Ocomm__ring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__ring__1(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono1,axiom,
( class_Ring__and__Field_Omult__mono1(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add,axiom,
( class_OrderedGroup_Oab__group__add(tc_Polynomial_Opoly(T_1))
| ~ class_OrderedGroup_Oab__group__add(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero,axiom,
( class_Ring__and__Field_Omult__zero(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono,axiom,
( class_Ring__and__Field_Omult__mono(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring,axiom,
( class_Ring__and__Field_Ocomm__ring(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__ring(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring,axiom,
( class_Ring__and__Field_Osemiring(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__0(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add,axiom,
( class_OrderedGroup_Omonoid__add(tc_Polynomial_Opoly(T_1))
| ~ class_OrderedGroup_Ocomm__monoid__add(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add,axiom,
( class_OrderedGroup_Ogroup__add(tc_Polynomial_Opoly(T_1))
| ~ class_OrderedGroup_Oab__group__add(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Osgn__if,axiom,
( class_Ring__and__Field_Osgn__if(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oabs__if,axiom,
( class_Ring__and__Field_Oabs__if(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Divides_Osemiring__div,axiom,
( class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ofield(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oring,axiom,
( class_Ring__and__Field_Oring(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__ring(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Oidom,axiom,
( class_Ring__and__Field_Oidom(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oidom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Ring__and__Field_Odvd,axiom,
( class_Ring__and__Field_Odvd(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__semiring__1(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__Divides_Oring__div,axiom,
( class_Divides_Oring__div(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ofield(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Orderings_Oorder,axiom,
( class_Orderings_Oorder(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Oordered__idom(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__Int_Onumber__ring,axiom,
( class_Int_Onumber__ring(tc_Polynomial_Opoly(T_1))
| ~ class_Ring__and__Field_Ocomm__ring__1(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__HOL_Ozero,axiom,
( class_HOL_Ozero(tc_Polynomial_Opoly(T_1))
| ~ class_HOL_Ozero(T_1) ) ).
cnf(clsarity_Polynomial__Opoly__HOL_Oeq,axiom,
( class_HOL_Oeq(tc_Polynomial_Opoly(T_1))
| ~ class_HOL_Ozero(T_1)
| ~ class_HOL_Oeq(T_1) ) ).
%------------------------------------------------------------------------------