%------------------------------------------------------------------------------
% File     : Otter---3.3
% Problem  : SWW189+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : otter-tptp-script %s

% Computer : n007.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Jul 27 13:22:04 EDT 2022

% Result   : Unknown 15.24s 15.17s
% Output   : None 
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SWW189+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.12  % Command  : otter-tptp-script %s
% 0.13/0.33  % Computer : n007.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Wed Jul 27 02:48:46 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 15.12/15.10  ----- Otter 3.3f, August 2004 -----
% 15.12/15.10  The process was started by sandbox2 on n007.cluster.edu,
% 15.12/15.10  Wed Jul 27 02:48:46 2022
% 15.12/15.10  The command was "./otter".  The process ID is 29288.
% 15.12/15.10  
% 15.12/15.10  set(prolog_style_variables).
% 15.12/15.10  set(auto).
% 15.12/15.10     dependent: set(auto1).
% 15.12/15.10     dependent: set(process_input).
% 15.12/15.10     dependent: clear(print_kept).
% 15.12/15.10     dependent: clear(print_new_demod).
% 15.12/15.10     dependent: clear(print_back_demod).
% 15.12/15.10     dependent: clear(print_back_sub).
% 15.12/15.10     dependent: set(control_memory).
% 15.12/15.10     dependent: assign(max_mem, 12000).
% 15.12/15.10     dependent: assign(pick_given_ratio, 4).
% 15.12/15.10     dependent: assign(stats_level, 1).
% 15.12/15.10     dependent: assign(max_seconds, 10800).
% 15.12/15.10  clear(print_given).
% 15.12/15.10  
% 15.12/15.10  formula_list(usable).
% 15.12/15.10  all A (A=A).
% 15.12/15.10  all V_g_2 V_f_2 ((all B_x (hAPP(V_f_2,B_x)=hAPP(V_g_2,B_x)))->V_f_2=V_g_2).
% 15.12/15.10  all V_x V_q V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(c_Polynomial_Opoly(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x)=c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x))).
% 15.12/15.10  all V_x V_h V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(c_Polynomial_Opoly(T_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),V_x)=hAPP(c_Polynomial_Opoly(T_a,V_p),c_Groups_Oplus__class_Oplus(T_a,V_h,V_x))).
% 15.12/15.10  all V_q_2 V_pa_2 T_a (class_Int_Oring__char__0(T_a)&class_Rings_Oidom(T_a)-> (c_Polynomial_Opoly(T_a,V_pa_2)=c_Polynomial_Opoly(T_a,V_q_2)<->V_pa_2=V_q_2)).
% 15.12/15.10  all V_c V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)=c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)).
% 15.12/15.10  all V_d V_c V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))=c_Groups_Oplus__class_Oplus(T_a,V_c,c_Groups_Oplus__class_Oplus(T_a,V_a,V_d))).
% 15.12/15.10  all V_d V_c V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_d)).
% 15.12/15.10  all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))).
% 15.12/15.10  all V_c V_b V_a T_a (class_Groups_Oab__semigroup__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))).
% 15.12/15.10  all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_b)).
% 15.12/15.10  all V_c_2 V_b_2 V_aa_2 T_a (class_Groups_Ocancel__semigroup__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_b_2)=c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_c_2)<->V_b_2=V_c_2)).
% 15.12/15.10  all V_c_2 V_aa_2 V_b_2 T_a (class_Groups_Ocancel__semigroup__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2)=c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_aa_2)<->V_b_2=V_c_2)).
% 15.12/15.10  all V_d V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))).
% 15.12/15.10  all V_c V_a V_b T_a (class_Groups_Ocancel__semigroup__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_b,V_a)=c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)->V_b=V_c)).
% 15.12/15.10  all V_c V_b V_a T_a (class_Groups_Ocancel__ab__semigroup__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)=c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)->V_b=V_c)).
% 15.12/15.10  all V_c V_b V_a T_a (class_Groups_Ocancel__semigroup__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)=c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)->V_b=V_c)).
% 15.12/15.10  all V_x V_q V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Opcompose(T_a,V_p,V_q)),V_x)=hAPP(c_Polynomial_Opoly(T_a,V_p),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x))).
% 15.12/15.10  all V_b V_n V_a T_a (class_Groups_Ocomm__monoid__add(T_a)->c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Omonom(T_a,V_a,V_n),c_Polynomial_Omonom(T_a,V_b,V_n))=c_Polynomial_Omonom(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_n)).
% 15.12/15.10  all V_q V_p T_a (class_Rings_Olinordered__idom(T_a)-> (c_Polynomial_Opos__poly(T_a,V_p)-> (c_Polynomial_Opos__poly(T_a,V_q)->c_Polynomial_Opos__poly(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q))))).
% 15.12/15.10  all V_p V_b V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Polynomial_Osmult(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_p)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_b,V_p))).
% 15.12/15.10  all V_n V_q V_p T_a (class_Groups_Ocomm__monoid__add(T_a)->hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_n)=c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n),hAPP(c_Polynomial_Ocoeff(T_a,V_q),V_n))).
% 15.12/15.10  all V_q V_b V_p V_a T_a (class_Groups_Ocomm__monoid__add(T_a)->c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,V_b,V_q))=c_Polynomial_OpCons(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q))).
% 15.12/15.10  all V_c_2 V_b_2 V_aa_2 V_f_2 T_a (c_Groups_Osemigroup(T_a,V_f_2)->hAPP(hAPP(V_f_2,hAPP(hAPP(V_f_2,V_aa_2),V_b_2)),V_c_2)=hAPP(hAPP(V_f_2,V_aa_2),hAPP(hAPP(V_f_2,V_b_2),V_c_2))).
% 15.12/15.10  all V_aa_2 V_z_2 V_f_2 T_a (c_Groups_Ocomm__monoid(T_a,V_f_2,V_z_2)->hAPP(hAPP(V_f_2,V_aa_2),V_z_2)=V_aa_2).
% 15.12/15.10  all V_h T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_h)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 15.12/15.10  all V_h_2 V_pa_2 T_a (class_Rings_Ocomm__semiring__0(T_a)-> (c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_pa_2,V_h_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))<->V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 15.12/15.10  all V_q T_a (class_Groups_Ocomm__monoid__add(T_a)->c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q)=V_q).
% 15.12/15.10  all V_p T_a (class_Groups_Ocomm__monoid__add(T_a)->c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=V_p).
% 15.12/15.10  all T_a (class_Rings_Olinordered__idom(T_a)-> -c_Polynomial_Opos__poly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 15.12/15.10  all T_a (class_Groups_Ozero(T_a)->c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 15.12/15.10  all V_n T_a (class_Groups_Ozero(T_a)->hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_n)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.12/15.10  all V_n T_a (class_Groups_Ozero(T_a)->c_Polynomial_Omonom(T_a,c_Groups_Ozero__class_Ozero(T_a),V_n)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 15.12/15.10  all V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Polynomial_Osmult(T_a,c_Groups_Ozero__class_Ozero(T_a),V_p)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 15.12/15.10  all V_q T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Polynomial_Opcompose(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 15.12/15.10  all V_x_2 T_a (class_Groups_Ozero(T_a)-> (c_Groups_Ozero__class_Ozero(T_a)=V_x_2<->V_x_2=c_Groups_Ozero__class_Ozero(T_a))).
% 15.12/15.10  all V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Polynomial_Osmult(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 15.12/15.10  all V_q_2 V_pa_2 T_a (class_Groups_Ozero(T_a)-> (V_pa_2=V_q_2<-> (all B_n (hAPP(c_Polynomial_Ocoeff(T_a,V_pa_2),B_n)=hAPP(c_Polynomial_Ocoeff(T_a,V_q_2),B_n))))).
% 15.12/15.10  all V_y_2 V_x_2 T_a (class_Groups_Ozero(T_a)-> (c_Polynomial_Ocoeff(T_a,V_x_2)=c_Polynomial_Ocoeff(T_a,V_y_2)<->V_x_2=V_y_2)).
% 15.12/15.10  all V_n_2 V_aa_2 T_a (class_Groups_Ozero(T_a)-> (c_Polynomial_Omonom(T_a,V_aa_2,V_n_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))<->V_aa_2=c_Groups_Ozero__class_Ozero(T_a))).
% 15.12/15.10  all V_pa_2 V_aa_2 T_a (class_Groups_Ozero(T_a)-> (c_Polynomial_OpCons(T_a,V_aa_2,V_pa_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))<->V_aa_2=c_Groups_Ozero__class_Ozero(T_a)&V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 15.12/15.10  all V_pa_2 V_aa_2 T_a (class_Rings_Oidom(T_a)-> (c_Polynomial_Osmult(T_a,V_aa_2,V_pa_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))<->V_aa_2=c_Groups_Ozero__class_Ozero(T_a)|V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 15.12/15.10  all V_a V_n V_m T_a (class_Groups_Ozero(T_a)-> (V_m=V_n->hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_Omonom(T_a,V_a,V_m)),V_n)=V_a)& (V_m!=V_n->hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_Omonom(T_a,V_a,V_m)),V_n)=c_Groups_Ozero__class_Ozero(T_a))).
% 15.12/15.10  all V_b_2 V_n_2 V_aa_2 T_a (class_Groups_Ozero(T_a)-> (c_Polynomial_Omonom(T_a,V_aa_2,V_n_2)=c_Polynomial_Omonom(T_a,V_b_2,V_n_2)<->V_aa_2=V_b_2)).
% 15.12/15.10  all V_q_2 V_b_2 V_pa_2 V_aa_2 T_a (class_Groups_Ozero(T_a)-> (c_Polynomial_OpCons(T_a,V_aa_2,V_pa_2)=c_Polynomial_OpCons(T_a,V_b_2,V_q_2)<->V_aa_2=V_b_2&V_pa_2=V_q_2)).
% 15.12/15.10  all V_a V_p V_c T_a (class_Rings_Ocomm__semiring__0(T_a)-> (c_Polynomial_Osmult(T_a,V_c,V_p)=c_Polynomial_OpCons(T_a,V_a,V_p)->V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 15.12/15.10  all V_a V_p V_c T_a (class_Rings_Ocomm__semiring__0(T_a)-> (c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),c_Polynomial_OpCons(T_a,V_a,V_p))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 15.12/15.10  all V_x T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.12/15.10  all V_h V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_h)=c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 15.12/15.10  all V_h V_p V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_h)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),c_Polynomial_OpCons(T_a,V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)))).
% 15.12/15.10  all V_a T_a (class_Groups_Omonoid__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=V_a).
% 15.12/15.10  all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=V_a).
% 15.12/15.10  all V_a T_a (class_Groups_Ocomm__monoid__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=V_a).
% 15.12/15.10  all V_aa_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Groups_Ozero__class_Ozero(T_a)=c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2)<->V_aa_2=c_Groups_Ozero__class_Ozero(T_a))).
% 15.12/15.10  all V_a T_a (class_Groups_Omonoid__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a).
% 15.12/15.10  all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a).
% 15.12/15.10  all V_a T_a (class_Groups_Ocomm__monoid__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a).
% 15.12/15.10  all V_aa_2 V_b_2 T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)-> (V_b_2=c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2)<->V_aa_2=c_Groups_Ozero__class_Ozero(T_a))).
% 15.12/15.10  all V_q V_p V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Polynomial_Osmult(T_a,V_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q))=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_a,V_q))).
% 15.12/15.10  all V_pa_2 T_a (class_Int_Oring__char__0(T_a)&class_Rings_Oidom(T_a)-> (c_Polynomial_Opoly(T_a,V_pa_2)=c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))<->V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 15.12/15.10  all V_r V_q V_c V_p T_a (class_Rings_Ocomm__semiring__0(T_a)-> (c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_c,V_q))=c_Polynomial_OpCons(T_a,V_r,V_q)->V_r=hAPP(c_Polynomial_Opoly(T_a,V_p),V_c)&V_q=c_Polynomial_Osynthetic__div(T_a,V_p,V_c))).
% 15.12/15.10  all V_c V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_c,c_Polynomial_Osynthetic__div(T_a,V_p,V_c)))=c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Polynomial_Osynthetic__div(T_a,V_p,V_c))).
% 15.12/15.10  all V_aa_2 V_pa_2 T_a (class_Rings_Oidom(T_a)-> (hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_aa_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Polynomial_Oorder(T_a,V_aa_2,V_pa_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.12/15.10  all V_aa_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_aa_2=c_Groups_Ozero__class_Ozero(T_a))).
% 15.12/15.10  all V_pa_2 V_aa_2 T_a V_z_2 V_f_2 T_b (class_Groups_Ozero(T_b)-> (hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2)=V_z_2->c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Polynomial_OpCons(T_b,V_aa_2,V_pa_2))=hAPP(hAPP(hAPP(V_f_2,V_aa_2),V_pa_2),c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,V_pa_2)))).
% 15.12/15.10  all V_q V_p V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Polynomial_Opcompose(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_q)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_q,c_Polynomial_Opcompose(T_a,V_p,V_q)))).
% 15.12/15.10  all V_pa_2 V_aa_2 V_f_2 V_z_2 T_a T_b (class_Groups_Ozero(T_b)->c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Polynomial_OpCons(T_b,V_aa_2,V_pa_2))=hAPP(hAPP(hAPP(V_f_2,V_aa_2),V_pa_2),c_If(T_a,c_fe_qual(V_pa_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2,c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,V_pa_2)))).
% 15.12/15.10  all V_pa_2 V_aa_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Polynomial_Opos__poly(T_a,c_Polynomial_OpCons(T_a,V_aa_2,V_pa_2))<->c_Polynomial_Opos__poly(T_a,V_pa_2)|V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))&c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2))).
% 15.12/15.10  all V_q V_a V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_OpCons(T_a,V_a,V_q))=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_p,V_q)))).
% 15.12/15.10  all V_q V_p V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p),V_q)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_q),c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_p,V_q)))).
% 15.12/15.10  all V_c V_p V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Polynomial_Osynthetic__div(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_c)=c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Polynomial_Osynthetic__div(T_a,V_p,V_c))).
% 15.12/15.10  all V_ry V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry))=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_rx),c_Groups_Otimes__class_Otimes(T_a,V_ly,V_ry))).
% 15.12/15.10  all V_ry V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry))=c_Groups_Otimes__class_Otimes(T_a,V_rx,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),V_ry))).
% 15.12/15.10  all V_ry V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry))=c_Groups_Otimes__class_Otimes(T_a,V_lx,c_Groups_Otimes__class_Otimes(T_a,V_ly,c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry)))).
% 15.12/15.10  all V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),V_rx)=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_rx),V_ly)).
% 15.12/15.10  all V_rx V_ly V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),V_rx)=c_Groups_Otimes__class_Otimes(T_a,V_lx,c_Groups_Otimes__class_Otimes(T_a,V_ly,V_rx))).
% 15.12/15.10  all V_c V_b V_a T_a (class_Groups_Oab__semigroup__mult(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c)=c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))).
% 15.12/15.10  all V_ry V_rx V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_lx,c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry))=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_rx),V_ry)).
% 15.12/15.10  all V_ry V_rx V_lx T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_lx,c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry))=c_Groups_Otimes__class_Otimes(T_a,V_rx,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ry))).
% 15.12/15.10  all V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)=c_Groups_Otimes__class_Otimes(T_a,V_b,V_a)).
% 15.12/15.10  all V_x V_q V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(c_Polynomial_Opoly(T_a,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x)=c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x))).
% 15.12/15.10  all V_n V_b V_m V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),c_Polynomial_Omonom(T_a,V_a,V_m),c_Polynomial_Omonom(T_a,V_b,V_n))=c_Polynomial_Omonom(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))).
% 15.12/15.10  all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 15.12/15.10  all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.12/15.10  all V_b V_a V_c T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))->c_Orderings_Oord__class_Oless(T_a,V_a,V_b))).
% 15.12/15.10  all V_b V_c V_a T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))->c_Orderings_Oord__class_Oless(T_a,V_a,V_b))).
% 15.12/15.10  all V_d V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))))).
% 15.12/15.10  all V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)))).
% 15.12/15.10  all V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)))).
% 15.12/15.10  all V_b_2 V_aa_2 V_c_2 T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_aa_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))<->c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2))).
% 15.12/15.10  all V_b_2 V_c_2 V_aa_2 T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))<->c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2))).
% 15.12/15.10  all V_z_2 V_x_2 V_y_2 V_w_2 T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_w_2,V_y_2),c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_z_2))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_w_2,V_z_2),c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_y_2))<->V_w_2=V_x_2|V_y_2=V_z_2)).
% 15.12/15.10  all V_b V_m V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_m),c_Groups_Otimes__class_Otimes(T_a,V_b,V_m))=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_m)).
% 15.12/15.10  all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))).
% 15.12/15.10  all V_d_2 V_c_2 V_b_2 V_aa_2 T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)-> (V_aa_2!=V_b_2&V_c_2!=V_d_2<->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_d_2))!=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_d_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_c_2)))).
% 15.12/15.10  all V_z V_y V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_x,c_Groups_Oplus__class_Oplus(T_a,V_y,V_z))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),c_Groups_Otimes__class_Otimes(T_a,V_x,V_z))).
% 15.12/15.10  all V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 15.12/15.10  all V_q T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 15.12/15.10  all V_aa_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 15.12/15.10  all V_p V_b V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Polynomial_Osmult(T_a,V_a,c_Polynomial_Osmult(T_a,V_b,V_p))=c_Polynomial_Osmult(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_p)).
% 15.12/15.10  all V_q V_p V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),V_q)=c_Polynomial_Osmult(T_a,V_a,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_p,V_q))).
% 15.12/15.10  all V_q V_a V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_a,V_q))=c_Polynomial_Osmult(T_a,V_a,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_p,V_q))).
% 15.12/15.10  all V_r V_q V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q),V_r)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_p,V_r),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_q,V_r))).
% 15.12/15.10  all V_q V_p T_a (class_Rings_Olinordered__idom(T_a)-> (c_Polynomial_Opos__poly(T_a,V_p)-> (c_Polynomial_Opos__poly(T_a,V_q)->c_Polynomial_Opos__poly(T_a,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_p,V_q))))).
% 15.12/15.10  all V_aa_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2))).
% 15.12/15.10  all V_aa_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 15.12/15.10  all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))))).
% 15.12/15.10  all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 15.12/15.10  all V_d V_c V_b V_a V_r T_a (class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)-> (V_r!=c_Groups_Ozero__class_Ozero(T_a)-> (V_a=V_b&V_c!=V_d->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_r,V_c))!=c_Groups_Oplus__class_Oplus(T_a,V_b,c_Groups_Otimes__class_Otimes(T_a,V_r,V_d))))).
% 15.12/15.10  all V_c T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Polynomial_Osynthetic__div(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_c)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 15.12/15.10  all V_p V_b V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Polynomial_Osmult(T_a,V_a,c_Polynomial_OpCons(T_a,V_b,V_p))=c_Polynomial_OpCons(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Polynomial_Osmult(T_a,V_a,V_p))).
% 15.12/15.10  all V_n V_p V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_Osmult(T_a,V_a,V_p)),V_n)=c_Groups_Otimes__class_Otimes(T_a,V_a,hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n))).
% 15.12/15.10  all V_x V_p V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Osmult(T_a,V_a,V_p)),V_x)=c_Groups_Otimes__class_Otimes(T_a,V_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))).
% 15.12/15.10  all V_n V_b V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Polynomial_Osmult(T_a,V_a,c_Polynomial_Omonom(T_a,V_b,V_n))=c_Polynomial_Omonom(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_n)).
% 15.12/15.10  all V_p V_a T_a (class_Groups_Ozero(T_a)->hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_a).
% 15.12/15.10  all V_x V_p V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),V_x)=c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_x,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)))).
% 15.12/15.10  all V_pa_2 T_a (class_Groups_Ozero(T_a)-> (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_pa_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 15.12/15.10  all V_a T_a (class_Groups_Ozero(T_a)->c_Polynomial_Omonom(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 15.12/15.10  all T_a V_z_2 V_f_2 T_b (class_Groups_Ozero(T_b)-> (hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2)=V_z_2->c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))=V_z_2)).
% 15.12/15.10  all V_y_2 V_x_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_x_2),c_Groups_Otimes__class_Otimes(T_a,V_y_2,V_y_2)))<->V_x_2!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2!=c_Groups_Ozero__class_Ozero(T_a))).
% 15.12/15.10  all V_y V_x T_a (class_Rings_Olinordered__ring(T_a)-> -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_x),c_Groups_Otimes__class_Otimes(T_a,V_y,V_y)),c_Groups_Ozero__class_Ozero(T_a))).
% 15.12/15.10  all V_y_2 V_x_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_x_2),c_Groups_Otimes__class_Otimes(T_a,V_y_2,V_y_2))=c_Groups_Ozero__class_Ozero(T_a)<->V_x_2=c_Groups_Ozero__class_Ozero(T_a)&V_y_2=c_Groups_Ozero__class_Ozero(T_a))).
% 15.12/15.10  all V_c V_b V_a T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))))).
% 15.12/15.10  all V_c V_a V_b T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))))).
% 15.12/15.10  all V_c V_a V_b T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))))).
% 15.12/15.10  all V_c V_b V_a T_a (class_Rings_Olinordered__comm__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))))).
% 15.12/15.10  all V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))))).
% 15.12/15.10  all V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))))).
% 15.12/15.10  all V_b V_a T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))))).
% 15.12/15.10  all V_y V_x T_a (class_Rings_Olinordered__idom(T_a)-> (V_x!=V_y-> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless(T_a,V_y,V_x)))).
% 15.12/15.10  all V_b V_a T_a (class_Rings_Ono__zero__divisors(T_a)-> (c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)=c_Groups_Ozero__class_Ozero(T_a)->V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a))).
% 15.12/15.10  all V_b V_a T_a (class_Rings_Ono__zero__divisors(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)!=c_Groups_Ozero__class_Ozero(T_a)))).
% 15.12/15.10  all V_b_2 V_aa_2 T_a (class_Rings_Oring__no__zero__divisors(T_a)-> (c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_aa_2=c_Groups_Ozero__class_Ozero(T_a)|V_b_2=c_Groups_Ozero__class_Ozero(T_a))).
% 15.12/15.10  all V_a T_a (class_Rings_Omult__zero(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 15.12/15.10  all V_a T_a (class_Rings_Omult__zero(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.12/15.10  all V_c V_b V_a T_a (class_Rings_Ocomm__semiring(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))).
% 15.12/15.10  all V_c V_b V_e V_a T_a (class_Rings_Osemiring(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_e),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_e),V_c))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_e),V_c)).
% 15.12/15.10  all V_a T_a (class_Rings_Olinordered__ring(T_a)-> -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_a),c_Groups_Ozero__class_Ozero(T_a))).
% 15.12/15.10  all V_b_2 V_c_2 V_aa_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_c_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)&c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2))).
% 15.12/15.10  all V_b_2 V_aa_2 V_c_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_aa_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)&c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2))).
% 15.12/15.10  all V_b_2 V_aa_2 V_c_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_aa_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))<->c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)))).
% 15.12/15.10  all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))))).
% 15.12/15.10  all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 15.12/15.10  all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_a),c_Groups_Ozero__class_Ozero(T_a))))).
% 15.12/15.10  all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)))).
% 15.12/15.10  all V_a V_b T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_b,V_a))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)))).
% 15.12/15.10  all V_b_2 V_aa_2 V_c_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_aa_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))<->c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2)))).
% 15.12/15.10  all V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 15.12/15.10  all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.12/15.10  all V_n V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)=V_m->V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.12/15.10  all V_n_2 V_m_2 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)&V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.12/15.10  all V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m).
% 15.12/15.10  all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)).
% 15.12/15.10  all V_n (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)=V_n).
% 15.12/15.10  all V_b_H V_b V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_b_H))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b_H))).
% 15.12/15.10  all V_y V_x V_xa T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_xa,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa,V_x),c_Groups_Otimes__class_Otimes(T_a,V_xa,V_y))).
% 15.12/15.10  all V_b V_a_H V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_a_H),V_b)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a_H,V_b))).
% 15.12/15.10  all V_P_2 V_n_2 V_m_2 ((c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)))-> ((V_m_2=V_n_2->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)))-> ((c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)))->hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2))))).
% 15.12/15.10  all V_t V_s (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)->V_s!=V_t).
% 15.12/15.10  all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)->V_m!=V_n).
% 15.12/15.10  all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n)).
% 15.12/15.10  all V_y V_x (V_x!=V_y-> (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x))).
% 15.12/15.10  all V_n_2 V_m_2 (V_m_2!=V_n_2<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)).
% 15.12/15.10  all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n)).
% 15.12/15.10  all V_n (V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)).
% 15.12/15.10  all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.12/15.10  all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.12/15.10  all V_n_2 (V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)).
% 15.12/15.10  all V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.12/15.10  all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_i),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_j)))).
% 15.12/15.10  all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j,V_k)))).
% 15.12/15.10  all V_n_2 V_k_2 V_m_2 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_k_2)=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2,V_k_2)<->V_m_2=V_n_2|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.12/15.10  all V_n_2 V_m_2 V_k_2 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2)=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2)<->V_m_2=V_n_2|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.12/15.10  all V_n_2 V_k_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2,V_k_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)&c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)).
% 15.12/15.10  all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)&c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)).
% 15.12/15.10  all V_n_2 V_m_2 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.12/15.10  all V_m (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.12/15.10  all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)&c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)).
% 15.12/15.10  all V_n (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.12/15.10  all V_n_2 V_k_2 V_m_2 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_k_2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2)<->V_m_2=V_n_2).
% 15.12/15.10  all V_n_2 V_m_2 V_k_2 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)<->V_m_2=V_n_2).
% 15.12/15.10  all V_k V_n V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k))).
% 15.12/15.10  all V_z V_y V_x (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,V_z))).
% 15.12/15.10  all V_n V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)).
% 15.12/15.10  all V_j V_i (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_i)).
% 15.12/15.10  all V_i V_j (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_i)).
% 15.12/15.10  all V_n V_m V_k (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_m),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_n))).
% 15.12/15.10  all V_k V_n V_m (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,V_k))).
% 15.12/15.10  all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)).
% 15.12/15.10  all V_m V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m))).
% 15.12/15.10  all V_m V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j))).
% 15.12/15.10  all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k))).
% 15.12/15.10  all V_l V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)))).
% 15.12/15.10  all V_n V_m V_l V_k (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)-> (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n))).
% 15.12/15.10  all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k)).
% 15.12/15.10  all V_b T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.12/15.10  all V_y T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.12/15.10  all V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 15.12/15.10  all V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 15.12/15.10  all V_ya V_y V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),V_ya)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_ya),c_Groups_Otimes__class_Otimes(T_a,V_y,V_ya))).
% 15.12/15.10  all V_z V_y V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))).
% 15.12/15.10  all V_y V_z V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))).
% 15.12/15.10  all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2))).
% 15.12/15.10  all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)-> (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2)=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2)<->V_m_2=V_n_2)).
% 15.12/15.10  all V_pa_2 V_aa_2 T_a (class_Groups_Ozero(T_a)->c_Polynomial_Ocoeff(T_a,c_Polynomial_OpCons(T_a,V_aa_2,V_pa_2))=c_Nat_Onat_Onat__case(T_a,V_aa_2,c_Polynomial_Ocoeff(T_a,V_pa_2))).
% 15.12/15.10  all V_pa_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Polynomial_Opos__poly(T_a,V_pa_2)<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Polynomial_Ocoeff(T_a,V_pa_2),c_Polynomial_Odegree(T_a,V_pa_2))))).
% 15.12/15.10  all V_q V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_p,V_q)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)))=c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Polynomial_Ocoeff(T_a,V_p),c_Polynomial_Odegree(T_a,V_p)),hAPP(c_Polynomial_Ocoeff(T_a,V_q),c_Polynomial_Odegree(T_a,V_q)))).
% 15.12/15.10  all V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)-> (exists B_k (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B_k)&c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,B_k)=V_j))).
% 15.12/15.10  all V_n V_m (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n)=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,V_m)).
% 15.12/15.10  all V_k V_n V_m (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n),V_k)=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,V_k))).
% 15.12/15.10  all V_h V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Polynomial_Odegree(T_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h))=c_Polynomial_Odegree(T_a,V_p)).
% 15.12/15.10  all T_a (class_Groups_Ozero(T_a)->c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.12/15.10  all V_n V_a T_a (class_Groups_Ozero(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Polynomial_Odegree(T_a,c_Polynomial_Omonom(T_a,V_a,V_n))=V_n)).
% 15.12/15.10  all V_p V_q T_a (class_Groups_Ocomm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q),c_Polynomial_Odegree(T_a,V_p))->c_Polynomial_Odegree(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q))=c_Polynomial_Odegree(T_a,V_p))).
% 15.12/15.10  all V_q V_p T_a (class_Groups_Ocomm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q))->c_Polynomial_Odegree(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q))=c_Polynomial_Odegree(T_a,V_q))).
% 15.12/15.10  all V_q V_n V_p T_a (class_Groups_Ocomm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q),V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_n)))).
% 15.12/15.10  all V_f2_2 V_f1_2 T_a (hAPP(c_Nat_Onat_Onat__case(T_a,V_f1_2,V_f2_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_f1_2).
% 15.12/15.10  all V_p V_a T_a (class_Rings_Oidom(T_a)-> (V_a=c_Groups_Ozero__class_Ozero(T_a)->c_Polynomial_Odegree(T_a,c_Polynomial_Osmult(T_a,V_a,V_p))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))& (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Polynomial_Odegree(T_a,c_Polynomial_Osmult(T_a,V_a,V_p))=c_Polynomial_Odegree(T_a,V_p))).
% 15.12/15.10  all V_n V_p T_a (class_Groups_Ozero(T_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)->hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n)=c_Groups_Ozero__class_Ozero(T_a))).
% 15.12/15.10  all V_pa_2 T_a (class_Groups_Ozero(T_a)-> (hAPP(c_Polynomial_Ocoeff(T_a,V_pa_2),c_Polynomial_Odegree(T_a,V_pa_2))=c_Groups_Ozero__class_Ozero(T_a)<->V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 15.12/15.10  all V_p T_a (class_Groups_Ozero(T_a)-> (V_p!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->hAPP(c_Polynomial_Ocoeff(T_a,V_p),c_Polynomial_Odegree(T_a,V_p))!=c_Groups_Ozero__class_Ozero(T_a))).
% 15.12/15.10  all V_a T_a (class_Groups_Ozero(T_a)->c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.12/15.10  all V_q V_p T_a (class_Rings_Oidom(T_a)-> (V_p!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))-> (V_q!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->c_Polynomial_Odegree(T_a,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_p,V_q))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q))))).
% 15.12/15.10  all V_c_2 V_pa_2 T_a (class_Rings_Ocomm__semiring__0(T_a)-> (c_Polynomial_Osynthetic__div(T_a,V_pa_2,V_c_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))<->c_Polynomial_Odegree(T_a,V_pa_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.12/15.10  all V_n_2 V_m_2 V_k_2 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2)=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2)<->V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=V_n_2).
% 15.12/15.10  all V_k V_j V_u V_i (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i,V_u),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j,V_u),V_k))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_u),V_k)).
% 15.12/15.10  all V_r_2 V_q_2 V_y_2 V_x_2 T_a (class_Fields_Ofield(T_a)-> (c_Polynomial_Opdivmod__rel(T_a,V_x_2,V_y_2,V_q_2,V_r_2)<->V_x_2=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_q_2,V_y_2),V_r_2)& (V_y_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->V_q_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))& (V_y_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->V_r_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_r_2),c_Polynomial_Odegree(T_a,V_y_2))))).
% 15.12/15.10  all V_n V_p T_a (class_Groups_Ozero(T_a)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)-> (hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n)=c_Groups_Ozero__class_Ozero(T_a)->V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)))).
% 15.12/15.10  all V_pa_2 V_aa_2 T_a (class_Groups_Ozero(T_a)->c_Polynomial_OpCons(T_a,V_aa_2,V_pa_2)=c_Polynomial_OAbs__poly(T_a,c_Nat_Onat_Onat__case(T_a,V_aa_2,c_Polynomial_Ocoeff(T_a,V_pa_2)))).
% 15.12/15.10  all V_p T_a (class_Groups_Ozero(T_a)-> (V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_p)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))& (V_p!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_p)=c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)))).
% 15.12/15.10  all V_p V_n T_a (class_Groups_Ozero(T_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Polynomial_Odegree(T_a,V_p))-> (exists B_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,B_i)&hAPP(c_Polynomial_Ocoeff(T_a,V_p),B_i)!=c_Groups_Ozero__class_Ozero(T_a))))).
% 15.12/15.10  all V_a V_p T_a (class_Groups_Ozero(T_a)-> (V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))& (V_p!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p))=c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)))).
% 15.12/15.10  all V_q V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Polynomial_Opcompose(T_a,V_p,V_q)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)))).
% 15.12/15.10  all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))).
% 15.12/15.10  all V_n c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n)).
% 15.12/15.10  all V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n).
% 15.12/15.10  all V_n c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(V_n)).
% 15.12/15.10  all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_n_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)).
% 15.12/15.10  all V_r2 V_q2 V_r1 V_q1 V_y V_x T_a (class_Fields_Ofield(T_a)-> (c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q1,V_r1)-> (c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q2,V_r2)->V_q1=V_q2&V_r1=V_r2))).
% 15.12/15.10  all V_r2 V_q2 V_r1 V_q1 V_y V_x T_a (class_Fields_Ofield(T_a)-> (c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q1,V_r1)-> (c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q2,V_r2)->V_r1=V_r2))).
% 15.12/15.10  all V_r2 V_q2 V_r1 V_q1 V_y V_x T_a (class_Fields_Ofield(T_a)-> (c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q1,V_r1)-> (c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q2,V_r2)->V_q1=V_q2))).
% 15.12/15.10  all V_m_2 V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2)).
% 15.12/15.10  all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)).
% 15.12/15.10  all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_m_2),V_n_2)<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)).
% 15.12/15.10  all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))).
% 15.12/15.10  all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)).
% 15.12/15.10  all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))<->V_n_2=V_m_2)).
% 15.12/15.10  all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)).
% 15.12/15.10  all V_y V_x (c_Nat_OSuc(V_x)=c_Nat_OSuc(V_y)->V_x=V_y).
% 15.12/15.10  all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)).
% 15.12/15.10  all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))-> (-c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)->V_m=c_Nat_OSuc(V_n))).
% 15.12/15.10  all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)->V_m=V_n)).
% 15.12/15.10  all V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j,V_k)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_k))).
% 15.12/15.10  all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))).
% 15.12/15.10  all V_n V_m (V_m=V_n->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)).
% 15.12/15.10  all V_m_2 V_n_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,V_m_2)).
% 15.12/15.10  all V_nat_H_2 V_nat_2 (c_Nat_OSuc(V_nat_2)=c_Nat_OSuc(V_nat_H_2)<->V_nat_2=V_nat_H_2).
% 15.12/15.10  all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2=c_Nat_OSuc(V_n_2)).
% 15.12/15.10  all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)).
% 15.12/15.10  all V_n_2 V_m_2 (-c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2)).
% 15.12/15.10  all V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_n).
% 15.12/15.10  all V_n (-c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n),V_n)).
% 15.12/15.10  all V_n (c_Nat_OSuc(V_n)!=V_n).
% 15.12/15.10  all V_n (V_n!=c_Nat_OSuc(V_n)).
% 15.12/15.10  all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)&c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)).
% 15.12/15.10  all V_p V_a T_a (class_Groups_Ozero(T_a)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)))).
% 15.12/15.10  all V_b V_a V_c T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b))).
% 15.12/15.10  all V_b V_c V_a T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b))).
% 15.12/15.10  all V_d V_c V_b V_a T_a (class_Groups_Oordered__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))))).
% 15.12/15.10  all V_c V_b V_a T_a (class_Groups_Oordered__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)))).
% 15.12/15.10  all V_c V_b V_a T_a (class_Groups_Oordered__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)))).
% 15.12/15.10  all V_b_2 V_aa_2 V_c_2 T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_aa_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,V_b_2))).
% 15.12/15.10  all V_b_2 V_c_2 V_aa_2 T_a (class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,V_b_2))).
% 15.12/15.10  all V_m (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(V_m)).
% 15.12/15.10  all V_nat_H (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(V_nat_H)).
% 15.12/15.10  all V_m (c_Nat_OSuc(V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.12/15.10  all V_nat_H_1 (c_Nat_OSuc(V_nat_H_1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.12/15.10  all V_m (c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(V_m)).
% 15.12/15.10  all V_m (c_Nat_OSuc(V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.12/15.10  all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)).
% 15.12/15.10  all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)).
% 15.12/15.10  all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))-> (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->V_m=V_n)).
% 15.12/15.10  all V_k V_j V_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i),V_k))).
% 15.12/15.10  all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)-> (c_Nat_OSuc(V_m)!=V_n->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n))).
% 15.12/15.10  all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))).
% 15.12/15.10  all V_m V_n (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_m))->V_m=V_n)).
% 15.12/15.10  all V_m_2 V_n_2 (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))<->V_n_2=V_m_2)).
% 15.12/15.10  all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2),c_Nat_OSuc(V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)).
% 15.12/15.10  all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2=V_n_2).
% 15.12/15.10  all V_n_2 V_m_2 (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))).
% 15.12/15.10  all V_n V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))).
% 15.12/15.10  all V_n V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))).
% 15.12/15.10  all V_n V_m (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))).
% 15.12/15.10  all V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n).
% 15.12/15.10  all V_n_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.12/15.10  all V_n_2 V_m_2 V_k_2 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_m_2)=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_n_2)<->V_m_2=V_n_2).
% 15.12/15.10  all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|V_m=V_n->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)).
% 15.12/15.10  all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)-> (V_m!=V_n->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n))).
% 15.12/15.10  all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)).
% 15.12/15.10  all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2=V_n_2).
% 15.12/15.10  all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)&V_m_2!=V_n_2).
% 15.12/15.10  all V_y V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,V_y)).
% 15.12/15.10  all V_n V_k V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)-> -(c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)-> -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n))).
% 15.12/15.10  all V_n V_k V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)).
% 15.12/15.10  all V_n V_k V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n)).
% 15.12/15.10  all V_l V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_l)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)))).
% 15.12/15.10  all V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k))).
% 15.12/15.10  all V_m V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j))).
% 15.12/15.10  all V_m V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m))).
% 15.12/15.10  all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)).
% 15.12/15.10  all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)<-> (exists B_k (V_n_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k)))).
% 15.12/15.10  all V_m V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)).
% 15.12/15.10  all V_m V_n c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)).
% 15.12/15.10  all V_z V_y V_x (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))).
% 15.12/15.10  all V_y V_z V_x (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,V_z)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))).
% 15.12/15.10  all V_l V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_l)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j,V_l)))).
% 15.12/15.10  all V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_i),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_j))).
% 15.12/15.10  all V_k V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j,V_k))).
% 15.12/15.10  all V_m c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_m))).
% 15.12/15.10  all V_m c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_m)).
% 15.12/15.10  all V_nat_2 V_f2_2 V_f1_2 T_a (hAPP(c_Nat_Onat_Onat__case(T_a,V_f1_2,V_f2_2),c_Nat_OSuc(V_nat_2))=hAPP(V_f2_2,V_nat_2)).
% 15.12/15.10  all V_x T_a (class_Fields_Ofield(T_a)->c_Polynomial_Opdivmod__rel(T_a,V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x)).
% 15.12/15.10  all V_y T_a (class_Fields_Ofield(T_a)->c_Polynomial_Opdivmod__rel(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_y,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 15.12/15.10  all V_r_2 V_q_2 V_x_2 T_a (class_Fields_Ofield(T_a)-> (c_Polynomial_Opdivmod__rel(T_a,V_x_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q_2,V_r_2)<->V_q_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))&V_r_2=V_x_2)).
% 15.12/15.10  all V_r_2 V_q_2 V_y_2 T_a (class_Fields_Ofield(T_a)-> (c_Polynomial_Opdivmod__rel(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_y_2,V_q_2,V_r_2)<->V_q_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))&V_r_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 15.12/15.10  all V_a V_r V_q V_y V_x T_a (class_Fields_Ofield(T_a)-> (c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q,V_r)->c_Polynomial_Opdivmod__rel(T_a,c_Polynomial_Osmult(T_a,V_a,V_x),V_y,c_Polynomial_Osmult(T_a,V_a,V_q),c_Polynomial_Osmult(T_a,V_a,V_r)))).
% 15.12/15.10  all V_x_2 T_a (class_Groups_Ozero(T_a)->c_Polynomial_OAbs__poly(T_a,c_Polynomial_Ocoeff(T_a,V_x_2))=V_x_2).
% 15.12/15.10  all V_b V_a T_a (class_Rings_Oordered__cancel__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)&c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)))).
% 15.12/15.10  all V_b V_a T_a (class_Rings_Oordered__ring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)&c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)))).
% 15.12/15.10  all V_d V_c V_b V_a T_a (class_Rings_Oordered__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d))))))).
% 15.12/15.10  all V_d V_c V_b V_a T_a (class_Rings_Oordered__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d))))))).
% 15.12/15.10  all V_c V_a V_b T_a (class_Rings_Oordered__ring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))))).
% 15.12/15.10  all V_c V_a V_b T_a (class_Rings_Oordered__ring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))))).
% 15.12/15.10  all V_c V_b V_a T_a (class_Rings_Oordered__comm__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))))).
% 15.12/15.10  all V_c V_b V_a T_a (class_Rings_Oordered__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))))).
% 15.12/15.10  all V_c V_b V_a T_a (class_Rings_Oordered__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))))).
% 15.12/15.10  all V_b V_a T_a (class_Rings_Oordered__ring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))))).
% 15.12/15.10  all V_b V_a T_a (class_Rings_Oordered__cancel__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 15.12/15.10  all V_b V_a T_a (class_Rings_Oordered__cancel__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_a),c_Groups_Ozero__class_Ozero(T_a))))).
% 15.12/15.10  all V_b V_a T_a (class_Rings_Oordered__cancel__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 15.12/15.10  all V_b V_a T_a (class_Rings_Oordered__cancel__semiring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))))).
% 15.12/15.10  all V_b_2 V_aa_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)&c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2))).
% 15.12/15.10  all V_b_2 V_aa_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_b_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)&c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 15.12/15.10  all V_a T_a (class_Rings_Olinordered__ring(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_a))).
% 15.12/15.10  all V_aa_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2))).
% 15.12/15.10  all V_aa_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 15.12/15.10  all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))))).
% 15.12/15.10  all V_y_2 V_x_2 T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)-> (c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_x_2=c_Groups_Ozero__class_Ozero(T_a)&V_y_2=c_Groups_Ozero__class_Ozero(T_a))))).
% 15.12/15.10  all V_c V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))))).
% 15.12/15.10  all V_a V_b V_c T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))))).
% 15.12/15.10  all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 15.12/15.10  all V_d V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))))).
% 15.12/15.10  all V_d V_c V_b V_a T_a (class_Groups_Oordered__cancel__ab__semigroup__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))))).
% 15.12/15.10  all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)<-> (exists B_m (V_n_2=c_Nat_OSuc(B_m)))).
% 15.12/15.10  all V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))<->V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.12/15.10  all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))<->V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| (exists B_j (V_m_2=c_Nat_OSuc(B_j)&c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_n_2)))).
% 15.12/15.10  all V_n_2 V_m_2 (c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)<->V_m_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)&V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.12/15.10  all V_n_2 V_m_2 (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<->V_m_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)&V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.12/15.10  all V_n_2 V_m_2 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))<->V_m_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))&V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.12/15.10  all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)<-> (exists B_k (V_n_2=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k))))).
% 15.12/15.10  all V_m V_i c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_i))).
% 15.12/15.10  all V_m V_i c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_m))).
% 15.12/15.10  all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)).
% 15.12/15.10  all V_n V_m (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n))).
% 15.12/15.10  all V_n V_m (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n))).
% 15.12/15.10  all V_n V_p V_a T_a (class_Groups_Ozero(T_a)->hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),c_Nat_OSuc(V_n))=hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n)).
% 15.12/15.10  all V_p V_a T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Polynomial_Osmult(T_a,V_a,V_p)),c_Polynomial_Odegree(T_a,V_p))).
% 15.12/15.10  all V_q V_n V_p T_a (class_Groups_Ocomm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q),V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_n)))).
% 15.12/15.10  all V_n V_a T_a (class_Groups_Ozero(T_a)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)),V_n)).
% 15.12/15.10  all V_b V_a V_c T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)))).
% 15.12/15.10  all V_b V_c V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)))).
% 15.12/15.10  all V_b V_a V_c T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))).
% 15.12/15.10  all V_b V_a V_c T_a (class_Rings_Olinordered__semiring(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))).
% 15.12/15.10  all V_b V_c V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))).
% 15.12/15.10  all V_b V_c V_a T_a (class_Rings_Olinordered__semiring(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))).
% 15.12/15.10  all V_d V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d))))))).
% 15.12/15.10  all V_d V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d))))))).
% 15.12/15.10  all V_d V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d))))))).
% 15.12/15.10  all V_d V_c V_b V_a T_a (class_Rings_Olinordered__semiring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_d)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d))))))).
% 15.12/15.10  all V_b_2 V_aa_2 V_c_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_aa_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,V_aa_2)))).
% 15.12/15.10  all V_b_2 V_aa_2 V_c_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_aa_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,V_b_2)))).
% 15.12/15.10  all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 15.12/15.10  all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a))))).
% 15.12/15.10  all V_c V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))))).
% 15.12/15.10  all V_c V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c))))).
% 15.12/15.10  all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))))).
% 15.12/15.10  all V_b V_a T_a (class_Groups_Oordered__comm__monoid__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))))).
% 15.12/15.10  all V_y_2 V_x_2 T_a (class_Rings_Olinordered__ring__strict(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_x_2),c_Groups_Otimes__class_Otimes(T_a,V_y_2,V_y_2)),c_Groups_Ozero__class_Ozero(T_a))<->V_x_2=c_Groups_Ozero__class_Ozero(T_a)&V_y_2=c_Groups_Ozero__class_Ozero(T_a))).
% 15.12/15.10  all V_y V_x T_a (class_Rings_Olinordered__ring(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_x),c_Groups_Otimes__class_Otimes(T_a,V_y,V_y)))).
% 15.12/15.10  all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n)))).
% 15.12/15.10  all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,V_m)))).
% 15.12/15.10  all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n)))).
% 15.12/15.10  all V_n_2 V_k_2 V_m_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2,V_k_2))<-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2))).
% 15.12/15.10  all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2))<-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2))).
% 15.12/15.10  all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2))).
% 15.12/15.10  all V_r_H V_q_H V_z V_r V_q V_y V_x T_a (class_Fields_Ofield(T_a)-> (c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q,V_r)-> (c_Polynomial_Opdivmod__rel(T_a,V_q,V_z,V_q_H,V_r_H)->c_Polynomial_Opdivmod__rel(T_a,V_x,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_y,V_z),V_q_H,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_y,V_r_H),V_r))))).
% 15.12/15.10  all V_n V_p T_a (class_Groups_Ozero(T_a)-> (hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n)!=c_Groups_Ozero__class_Ozero(T_a)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,c_Polynomial_Odegree(T_a,V_p)))).
% 15.12/15.10  all V_a V_p T_a (class_Groups_Ozero(T_a)-> (V_p!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p))=c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)))).
% 15.12/15.10  all V_n V_a T_a (class_Groups_Ozero(T_a)->c_Polynomial_Omonom(T_a,V_a,c_Nat_OSuc(V_n))=c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Polynomial_Omonom(T_a,V_a,V_n))).
% 15.12/15.10  all V_q V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_p,V_q)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)))).
% 15.12/15.10  all V_a V_p T_a (class_Rings_Oidom(T_a)-> (V_p!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Oorder(T_a,V_a,V_p),c_Polynomial_Odegree(T_a,V_p)))).
% 15.12/15.10  all V_x (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))->V_x=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_x=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.12/15.10  all V_x T_a (class_Orderings_Opreorder(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_x)).
% 15.12/15.10  all V_l_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_l_2)<-> (exists B_n (V_l_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n)))).
% 15.12/15.10  all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2))).
% 15.12/15.10  all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2))).
% 15.12/15.10  all V_y V_x T_a (class_Orderings_Olinorder(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,V_y,V_x)).
% 15.12/15.10  all V_y_2 V_x_2 T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)&V_x_2!=V_y_2)).
% 15.12/15.10  all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x))).
% 15.12/15.10  all V_x_2 V_g_2 V_f_2 T_a T_b (class_Orderings_Oord(T_b)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)->c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)))).
% 15.12/15.10  all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_y)->c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_x)))).
% 15.12/15.10  all V_x V_y T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)->V_x=V_y))).
% 15.12/15.10  all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_z)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_z)))).
% 15.12/15.10  all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)->V_x=V_y))).
% 15.12/15.10  all V_c V_a V_b T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)-> (V_b=V_c->c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_a)))).
% 15.12/15.10  all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (V_b=V_c->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_c)))).
% 15.12/15.10  all V_c V_b V_a T_a (class_Orderings_Oorder(T_a)-> (V_a=V_b-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_a)))).
% 15.12/15.10  all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (V_a=V_b-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_c)))).
% 15.12/15.10  all V_x_2 V_y_2 T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)<->V_x_2=V_y_2))).
% 15.12/15.10  all V_x_2 V_g_2 V_f_2 T_a T_b (class_Orderings_Oord(T_b)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)->c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)))).
% 15.12/15.10  all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (V_x=V_y->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y))).
% 15.12/15.10  all V_y_2 V_x_2 T_a (class_Orderings_Oorder(T_a)-> (V_x_2=V_y_2<->c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)&c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2))).
% 15.12/15.10  all V_y V_x T_a (class_Orderings_Olinorder(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)).
% 15.12/15.10  all V_g_2 V_f_2 T_a T_b (class_Orderings_Oord(T_b)-> (c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)<-> (all B_x c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x))))).
% 15.12/15.10  all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> (V_x!=V_y->c_Orderings_Oord__class_Oless(T_a,V_y,V_x)))).
% 15.12/15.10  all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> -c_Orderings_Oord__class_Oless(T_a,V_y,V_x))).
% 15.12/15.10  all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_x)-> (c_Orderings_Oord__class_Oless(T_a,V_z,V_y)->c_Orderings_Oord__class_Oless(T_a,V_z,V_x)))).
% 15.12/15.10  all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_z)->c_Orderings_Oord__class_Oless(T_a,V_x,V_z)))).
% 15.12/15.10  all V_c V_a V_b T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a)-> (V_b=V_c->c_Orderings_Oord__class_Oless(T_a,V_c,V_a)))).
% 15.12/15.10  all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (V_b=V_c->c_Orderings_Oord__class_Oless(T_a,V_a,V_c)))).
% 15.12/15.10  all V_c V_b V_a T_a (class_Orderings_Oorder(T_a)-> (V_a=V_b-> (c_Orderings_Oord__class_Oless(T_a,V_c,V_b)->c_Orderings_Oord__class_Oless(T_a,V_c,V_a)))).
% 15.12/15.10  all V_c V_b V_a T_a (class_Orderings_Oord(T_a)-> (V_a=V_b-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_c)->c_Orderings_Oord__class_Oless(T_a,V_a,V_c)))).
% 15.12/15.10  all V_a V_b T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a)-> -c_Orderings_Oord__class_Oless(T_a,V_a,V_b))).
% 15.12/15.10  all V_b V_a T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> -c_Orderings_Oord__class_Oless(T_a,V_b,V_a))).
% 15.12/15.10  all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->V_y!=V_x)).
% 15.12/15.10  all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->V_x!=V_y)).
% 15.12/15.10  all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> -c_Orderings_Oord__class_Oless(T_a,V_y,V_x))).
% 15.12/15.10  all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> -c_Orderings_Oord__class_Oless(T_a,V_y,V_x))).
% 15.12/15.10  all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->V_x!=V_y)).
% 15.12/15.10  all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (V_x!=V_y-> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless(T_a,V_y,V_x)))).
% 15.12/15.10  all V_x_2 V_y_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)-> (-c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)<->V_x_2=V_y_2))).
% 15.12/15.10  all V_y V_x T_a (class_Orderings_Olinorder(T_a)->c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_y,V_x)).
% 15.12/15.10  all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)|V_x_2=V_y_2)).
% 15.12/15.10  all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (V_x_2!=V_y_2<->c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2))).
% 15.12/15.10  all V_x T_a (class_Orderings_Opreorder(T_a)-> -c_Orderings_Oord__class_Oless(T_a,V_x,V_x)).
% 15.12/15.10  all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)-> (c_Orderings_Oord__class_Oless(T_a,V_z,V_y)->c_Orderings_Oord__class_Oless(T_a,V_z,V_x)))).
% 15.12/15.10  all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_z)->c_Orderings_Oord__class_Oless(T_a,V_x,V_z)))).
% 15.12/15.10  all V_z V_x V_y T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_y)->c_Orderings_Oord__class_Oless(T_a,V_z,V_x)))).
% 15.12/15.10  all V_z V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_z)->c_Orderings_Oord__class_Oless(T_a,V_x,V_z)))).
% 15.12/15.10  all V_a V_b T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)-> (V_a!=V_b->c_Orderings_Oord__class_Oless(T_a,V_b,V_a)))).
% 15.12/15.10  all V_b V_a T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (V_a!=V_b->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))).
% 15.12/15.10  all V_y V_x T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y)).
% 15.12/15.10  all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)-> (-c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)<->V_x_2=V_y_2))).
% 15.12/15.10  all V_y V_x T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y))).
% 15.12/15.10  all V_x V_y T_a (class_Orderings_Olinorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)-> -c_Orderings_Oord__class_Oless(T_a,V_x,V_y))).
% 15.12/15.10  all V_b V_a T_a (class_Orderings_Oorder(T_a)-> (V_a!=V_b-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)->c_Orderings_Oord__class_Oless(T_a,V_b,V_a)))).
% 15.12/15.10  all V_b V_a T_a (class_Orderings_Oorder(T_a)-> (V_a!=V_b-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless(T_a,V_a,V_b)))).
% 15.12/15.10  all V_y_2 V_x_2 T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)<->V_x_2=V_y_2))).
% 15.12/15.10  all V_x V_y T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)->c_Orderings_Oord__class_Oless(T_a,V_x,V_y))).
% 15.12/15.10  all V_y V_x T_a (class_Orderings_Olinorder(T_a)-> (-c_Orderings_Oord__class_Oless(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x))).
% 15.12/15.10  all V_y_2 V_x_2 T_a (class_Orderings_Oorder(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2=V_y_2)).
% 15.12/15.10  all V_y_2 V_x_2 T_a (class_Orderings_Opreorder(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)& -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2))).
% 15.12/15.10  all V_p V_n T_a (class_Groups_Ozero(T_a)-> ((all B_i (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,B_i)->hAPP(c_Polynomial_Ocoeff(T_a,V_p),B_i)=c_Groups_Ozero__class_Ozero(T_a)))->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n))).
% 15.12/15.10  all V_v V_u V_y V_a V_x T_a (class_Rings_Olinordered__semiring__1__strict(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_y,V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)-> (c_Groups_Oplus__class_Oplus(T_a,V_u,V_v)=c_Groups_Oone__class_Oone(T_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_u,V_x),c_Groups_Otimes__class_Otimes(T_a,V_v,V_y)),V_a))))))).
% 15.12/15.10  all V_nat (c_Nat_Onat_Onat__size(c_Nat_OSuc(V_nat))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Onat_Onat__size(V_nat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))).
% 15.12/15.10  all V_n_2 V_m_2 V_u_2 V_j_2 V_i_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i_2,V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j_2,V_u_2),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2),V_u_2),V_n_2)))).
% 15.12/15.10  all V_n_2 V_m_2 V_u_2 V_i_2 V_j_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,V_i_2)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i_2,V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j_2,V_u_2),V_n_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2),V_u_2),V_m_2),V_n_2))).
% 15.12/15.10  all V_g_2 V_f_2 T_a T_b (class_Orderings_Oord(T_b)-> (c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)<->c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)& -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_g_2,V_f_2))).
% 15.12/15.10  all V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a).
% 15.12/15.10  all V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,V_a,V_a)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.12/15.10  all V_b_2 V_aa_2 T_a (class_Groups_Oab__group__add(T_a)-> (V_aa_2=V_b_2<->c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a))).
% 15.12/15.10  all V_b_2 V_aa_2 T_a (class_Groups_Ogroup__add(T_a)-> (c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_aa_2=V_b_2)).
% 15.12/15.10  all V_d_2 V_c_2 V_b_2 V_aa_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)=c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,V_b_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2,V_d_2)))).
% 15.12/15.10  all V_d_2 V_c_2 V_b_2 V_aa_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)=c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)-> (c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)<->c_Orderings_Oord__class_Oless(T_a,V_c_2,V_d_2)))).
% 15.12/15.10  all T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))=c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 15.12/15.10  all V_b_H V_b V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_b_H))=c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b_H))).
% 15.12/15.10  all V_y V_x V_xa T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_xa,c_Groups_Ominus__class_Ominus(T_a,V_x,V_y))=c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa,V_x),c_Groups_Otimes__class_Otimes(T_a,V_xa,V_y))).
% 15.12/15.11  all V_b V_a_H V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_a_H),V_b)=c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a_H,V_b))).
% 15.12/15.11  all V_ya V_y V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_y),V_ya)=c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_ya),c_Groups_Otimes__class_Otimes(T_a,V_y,V_ya))).
% 15.12/15.11  all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b)=V_a).
% 15.12/15.11  all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b)=V_a).
% 15.12/15.11  all T_a (class_Rings_Ozero__ne_q__one(T_a)->c_Groups_Ozero__class_Ozero(T_a)!=c_Groups_Oone__class_Oone(T_a)).
% 15.12/15.11  all T_a (class_Rings_Ozero__ne_q__one(T_a)->c_Groups_Oone__class_Oone(T_a)!=c_Groups_Ozero__class_Ozero(T_a)).
% 15.12/15.11  all V_n V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)-> (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_m)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->V_m=V_n)).
% 15.12/15.11  all V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.12/15.11  all V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m).
% 15.12/15.11  all V_n (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.12/15.11  all V_a T_a (class_Groups_Omonoid__mult(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a),V_a)=V_a).
% 15.12/15.11  all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a),V_a)=V_a).
% 15.12/15.11  all V_a T_a (class_Groups_Ocomm__monoid__mult(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a),V_a)=V_a).
% 15.12/15.11  all V_a T_a (class_Groups_Omonoid__mult(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oone__class_Oone(T_a))=V_a).
% 15.12/15.11  all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oone__class_Oone(T_a))=V_a).
% 15.12/15.11  all V_a T_a (class_Groups_Ocomm__monoid__mult(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oone__class_Oone(T_a))=V_a).
% 15.12/15.11  all V_n V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)).
% 15.12/15.11  all V_k V_n V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n),c_Nat_OSuc(V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_k)).
% 15.12/15.11  all V_n V_k V_j (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n),V_k)).
% 15.12/15.11  all V_l V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_l)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)))).
% 15.12/15.11  all V_n V_k V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)).
% 15.12/15.11  all V_n V_m V_k (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)).
% 15.12/15.11  all V_k V_j V_i (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k))).
% 15.12/15.11  all V_m V_n (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_n)=V_m).
% 15.12/15.11  all V_n V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_n)=V_m).
% 15.12/15.11  all V_n V_m c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m).
% 15.12/15.11  all V_l V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m))).
% 15.12/15.11  all V_l V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_l),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_l))).
% 15.12/15.11  all V_n V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_n)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i))=V_i).
% 15.12/15.11  all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_m_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_n_2)-> (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)<->V_m_2=V_n_2))).
% 15.12/15.11  all V_n V_m V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_m)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))).
% 15.12/15.11  all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_m_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_n_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)))).
% 15.12/15.11  all V_n V_m V_k (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_m),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_n))).
% 15.12/15.11  all V_k V_n V_m (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_k)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,V_k))).
% 15.12/15.11  all V_q V_b V_p V_a T_a (class_Groups_Oab__group__add(T_a)->c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,V_b,V_q))=c_Polynomial_OpCons(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q))).
% 15.12/15.11  all V_n V_q V_p T_a (class_Groups_Oab__group__add(T_a)->hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_n)=c_Groups_Ominus__class_Ominus(T_a,hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n),hAPP(c_Polynomial_Ocoeff(T_a,V_q),V_n))).
% 15.12/15.11  all V_p V_b V_a T_a (class_Rings_Ocomm__ring(T_a)->c_Polynomial_Osmult(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_p)=c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_b,V_p))).
% 15.12/15.11  all V_x V_q V_p T_a (class_Rings_Ocomm__ring(T_a)->hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x)=c_Groups_Ominus__class_Ominus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x))).
% 15.12/15.11  all V_b V_n V_a T_a (class_Groups_Oab__group__add(T_a)->c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_Omonom(T_a,V_a,V_n),c_Polynomial_Omonom(T_a,V_b,V_n))=c_Polynomial_Omonom(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_n)).
% 15.12/15.11  all V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(c_Polynomial_Opoly(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_x)=c_Groups_Oone__class_Oone(T_a)).
% 15.12/15.11  all V_d_2 V_c_2 V_b_2 V_aa_2 T_a (class_Groups_Oab__group__add(T_a)-> (c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)=c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)-> (V_aa_2=V_b_2<->V_c_2=V_d_2))).
% 15.12/15.11  all V_x_2 T_a (class_Groups_Oone(T_a)-> (c_Groups_Oone__class_Oone(T_a)=V_x_2<->V_x_2=c_Groups_Oone__class_Oone(T_a))).
% 15.12/15.11  all V_k V_j V_i (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_k),V_j)).
% 15.12/15.11  all V_n (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_n).
% 15.12/15.11  all V_n V_m (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)).
% 15.12/15.11  all V_c V_p T_a (class_Rings_Ocomm__semiring__0(T_a)->c_Polynomial_Odegree(T_a,c_Polynomial_Osynthetic__div(T_a,V_p,V_c))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Groups_Oone__class_Oone(tc_Nat_Onat))).
% 15.12/15.11  all V_n_2 V_m_2 (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2)=c_Groups_Oone__class_Oone(tc_Nat_Onat)<->V_m_2=c_Groups_Oone__class_Oone(tc_Nat_Onat)&V_n_2=c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 15.12/15.11  all V_n (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_n).
% 15.12/15.11  all V_n_2 V_m_2 (c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2)<->V_m_2=c_Groups_Oone__class_Oone(tc_Nat_Onat)&V_n_2=c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 15.12/15.11  all V_n (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n)=V_n).
% 15.12/15.11  all V_p T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Polynomial_Osmult(T_a,c_Groups_Oone__class_Oone(T_a),V_p)=V_p).
% 15.12/15.11  c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.12/15.11  all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=V_n).
% 15.12/15.11  all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->V_n=c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))).
% 15.12/15.11  all V_n V_m ((V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)=V_n)& (V_m!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)))).
% 15.12/15.11  all V_n V_m ((V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))& (V_m!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)))).
% 15.12/15.11  all V_n T_a (class_Rings_Ocomm__semiring__1(T_a)-> (V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_n)=c_Groups_Oone__class_Oone(T_a))& (V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_n)=c_Groups_Ozero__class_Ozero(T_a))).
% 15.12/15.11  all V_b_2 V_aa_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,V_b_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)))).
% 15.12/15.11  all V_b_2 V_aa_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)))).
% 15.12/15.11  all V_b V_a V_y V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_a),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_a),V_b)),c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)))).
% 15.12/15.11  all V_d_2 V_b_2 V_c_2 V_e_2 V_aa_2 T_a (class_Rings_Oring(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_e_2),V_c_2)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_d_2)<->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2),V_e_2),V_c_2)=V_d_2)).
% 15.12/15.11  all V_d_2 V_b_2 V_c_2 V_e_2 V_aa_2 T_a (class_Rings_Oring(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_e_2),V_c_2)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_d_2)<->V_c_2=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_aa_2),V_e_2),V_d_2))).
% 15.12/15.11  all T_a (class_Rings_Olinordered__semidom(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a))).
% 15.12/15.11  all T_a (class_Rings_Olinordered__semidom(T_a)-> -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a))).
% 15.12/15.11  all T_a (class_Rings_Olinordered__semidom(T_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a))).
% 15.12/15.11  all T_a (class_Rings_Olinordered__semidom(T_a)-> -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a))).
% 15.12/15.11  all V_n V_m T_a (class_Rings_Olinordered__semidom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_m)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_n)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a,V_m,V_n))))).
% 15.12/15.11  all V_a T_a (class_Rings_Olinordered__semidom(T_a)->c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a)))).
% 15.12/15.11  all V_m T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_m,V_m)=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)),V_m)).
% 15.12/15.11  all V_a V_m T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_m,c_Groups_Otimes__class_Otimes(T_a,V_a,V_m))=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a)),V_m)).
% 15.12/15.11  all V_m V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_m),V_m)=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a)),V_m)).
% 15.12/15.11  all V_m_2 V_n_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_m_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)).
% 15.12/15.11  all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m))).
% 15.12/15.11  all V_n V_m c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),c_Nat_OSuc(V_m)).
% 15.12/15.11  all V_m V_n (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.12/15.11  all V_n V_m (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.12/15.11  all V_n_2 V_m_2 (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)).
% 15.12/15.11  all V_m V_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)=c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))).
% 15.12/15.11  all V_n V_m (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=V_m).
% 15.19/15.11  all V_k_2 V_j_2 V_i_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2)).
% 15.19/15.11  all V_c V_b V_a (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_c,V_a)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_b,V_c)))).
% 15.19/15.11  all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_m_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_n_2)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))<->c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)))).
% 15.19/15.11  all V_i V_j V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i)).
% 15.19/15.11  all V_i V_j V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k)).
% 15.19/15.11  all V_i V_j V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))).
% 15.19/15.11  all V_k_2 V_j_2 V_i_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)-> (c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)=V_k_2<->V_j_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2))).
% 15.19/15.11  all V_m V_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)=V_m).
% 15.19/15.11  all V_i_2 V_j_2 V_k_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_j_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2))).
% 15.19/15.11  all V_i V_j V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)).
% 15.19/15.11  all V_m V_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=V_m).
% 15.19/15.11  all V_m V_n V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_k))).
% 15.19/15.11  all V_i_2 V_k_2 V_j_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2),V_i_2)<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2))).
% 15.19/15.11  all V_i V_j V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),V_j)).
% 15.19/15.11  c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.19/15.11  all V_n (c_Nat_OSuc(V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n)).
% 15.19/15.11  all V_n (c_Nat_OSuc(V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))).
% 15.19/15.11  all V_n V_m (V_m=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n)->V_n=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.19/15.11  all T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Polynomial_Odegree(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.19/15.11  all V_d_2 V_b_2 V_c_2 V_e_2 V_aa_2 T_a (class_Rings_Oordered__ring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_d_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2),V_e_2),V_c_2),V_d_2))).
% 15.19/15.11  all V_d_2 V_b_2 V_c_2 V_e_2 V_aa_2 T_a (class_Rings_Oordered__ring(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_d_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_aa_2),V_e_2),V_d_2)))).
% 15.19/15.11  all V_d_2 V_b_2 V_c_2 V_e_2 V_aa_2 T_a (class_Rings_Oordered__ring(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_d_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2),V_e_2),V_c_2),V_d_2))).
% 15.19/15.11  all V_d_2 V_b_2 V_c_2 V_e_2 V_aa_2 T_a (class_Rings_Oordered__ring(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_d_2))<->c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_aa_2),V_e_2),V_d_2)))).
% 15.19/15.11  all V_y V_x T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,c_Groups_Oone__class_Oone(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_y,V_x),V_x))))).
% 15.19/15.11  all V_y V_x T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,c_Groups_Oone__class_Oone(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),V_x))))).
% 15.19/15.11  all T_a (class_Rings_Olinordered__semidom(T_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)))).
% 15.19/15.11  all V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=V_n).
% 15.19/15.11  all V_i V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(V_i)),V_n)).
% 15.19/15.11  all V_b_2 V_aa_2 V_P_2 (hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))<-> -(c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2,V_b_2)& -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| (exists B_d (V_aa_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)& -hBOOL(hAPP(V_P_2,B_d)))))).
% 15.19/15.11  all V_b_2 V_aa_2 V_P_2 (hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))<-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2,V_b_2)->hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))& (all B_d (V_aa_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)->hBOOL(hAPP(V_P_2,B_d))))).
% 15.19/15.11  all V_m V_j V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_m)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_j),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m))).
% 15.19/15.11  all V_m V_j V_k (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Nat_OSuc(V_j))).
% 15.19/15.11  all V_n_2 V_m_2 V_u_2 V_i_2 V_j_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,V_i_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i_2,V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j_2,V_u_2),V_n_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2),V_u_2),V_m_2),V_n_2))).
% 15.19/15.11  all V_n V_m V_u V_i V_j (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j,V_i)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i,V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j,V_u),V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_u),V_m),V_n)).
% 15.19/15.11  all V_n_2 V_m_2 V_u_2 V_i_2 V_j_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,V_i_2)-> (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i_2,V_u_2),V_m_2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j_2,V_u_2),V_n_2)<->c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2),V_u_2),V_m_2)=V_n_2)).
% 15.19/15.11  all V_n_2 V_m_2 V_u_2 V_j_2 V_i_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i_2,V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j_2,V_u_2),V_n_2))<->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2),V_u_2),V_n_2)))).
% 15.19/15.11  all V_n V_m V_u V_j V_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)->c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i,V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j,V_u),V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_i),V_u),V_n))).
% 15.19/15.11  all V_n_2 V_m_2 V_u_2 V_j_2 V_i_2 (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)-> (c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i_2,V_u_2),V_m_2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j_2,V_u_2),V_n_2)<->V_m_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2),V_u_2),V_n_2))).
% 15.19/15.11  all V_v V_u V_y V_a V_x T_a (class_Rings_Olinordered__semiring__1(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)-> (c_Groups_Oplus__class_Oplus(T_a,V_u,V_v)=c_Groups_Oone__class_Oone(T_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_u,V_x),c_Groups_Otimes__class_Otimes(T_a,V_v,V_y)),V_a))))))).
% 15.19/15.11  all V_x T_a (class_Rings_Oring__1(T_a)->c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_x),c_Groups_Oone__class_Oone(T_a))=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Oone__class_Oone(T_a)),c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Oone__class_Oone(T_a)))).
% 15.19/15.11  all V_b V_a V_y V_x T_a (class_Rings_Oring(T_a)->c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_a),V_b))).
% 15.19/15.11  all V_p V_c T_a (class_Rings_Ocomm__ring__1(T_a)->c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_c),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),c_Polynomial_Osynthetic__div(T_a,V_p,V_c)),c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))=V_p).
% 15.19/15.11  all V_nat (c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Nat_OSuc(V_nat))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,V_nat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))).
% 15.19/15.11  all V_b_2 V_aa_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)))).
% 15.19/15.11  all V_b_2 V_aa_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_aa_2))).
% 15.19/15.11  all V_aa_2 V_b_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,V_b_2))).
% 15.19/15.11  all V_b V_a T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a)))).
% 15.19/15.11  all V_p T_a (class_Groups_Oab__group__add(T_a)->c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=V_p).
% 15.19/15.11  all V_q T_a (class_Groups_Oab__group__add(T_a)->c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q)=c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_q)).
% 15.19/15.11  all V_n (c_Nat_Osize__class_Osize(tc_Nat_Onat,V_n)=V_n).
% 15.19/15.11  all V_b V_a T_a (class_Groups_Oab__group__add(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))=c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)).
% 15.19/15.11  all V_q V_p V_a T_a (class_Rings_Ocomm__ring(T_a)->c_Polynomial_Osmult(T_a,V_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q))=c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_a,V_q))).
% 15.19/15.11  all V_p V_a T_a (class_Rings_Ocomm__ring(T_a)->c_Polynomial_Osmult(T_a,V_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p))=c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p))).
% 15.19/15.11  all V_y_2 V_x_2 T_a (class_Groups_Ogroup__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_y_2=c_Groups_Ouminus__class_Ouminus(T_a,V_x_2))).
% 15.19/15.11  all V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a))=V_a).
% 15.19/15.11  all V_b_2 V_aa_2 T_a (class_Groups_Ogroup__add(T_a)-> (V_aa_2=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)<->V_b_2=c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))).
% 15.19/15.11  all V_b_2 V_aa_2 T_a (class_Groups_Ogroup__add(T_a)-> (c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)=V_b_2<->c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)=V_aa_2)).
% 15.19/15.11  all V_b_2 V_aa_2 T_a (class_Groups_Ogroup__add(T_a)-> (c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)<->V_aa_2=V_b_2)).
% 15.19/15.11  all V_n V_a T_a (class_Groups_Oab__group__add(T_a)->c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_Omonom(T_a,V_a,V_n))=c_Polynomial_Omonom(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_n)).
% 15.19/15.11  all V_x V_p T_a (class_Rings_Ocomm__ring(T_a)->hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)),V_x)=c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))).
% 15.19/15.11  all V_p V_a T_a (class_Rings_Ocomm__ring(T_a)->c_Polynomial_Osmult(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_p)=c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p))).
% 15.19/15.11  all V_n V_p T_a (class_Groups_Oab__group__add(T_a)->hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)),V_n)=c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n))).
% 15.19/15.11  all V_p V_a T_b (class_Groups_Oab__group__add(T_b)->c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b),c_Polynomial_OpCons(T_b,V_a,V_p))=c_Polynomial_OpCons(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b),V_p))).
% 15.19/15.11  all V_p V_a T_a (class_Groups_Oab__group__add(T_a)->c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p))=c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p))).
% 15.19/15.11  all V_p T_a (class_Groups_Oab__group__add(T_a)->c_Polynomial_Odegree(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p))=c_Polynomial_Odegree(T_a,V_p)).
% 15.19/15.11  all T_a (class_Groups_Oab__group__add(T_a)->c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 15.19/15.11  all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))=V_b).
% 15.19/15.11  all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b))=V_b).
% 15.19/15.11  all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a))).
% 15.19/15.11  all V_b V_a T_a (class_Groups_Oab__group__add(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b))).
% 15.19/15.11  all V_y V_x T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x),V_y)=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y))).
% 15.19/15.11  all V_b V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))).
% 15.19/15.11  all V_x V_xa T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_xa,c_Groups_Ouminus__class_Ouminus(T_a,V_x))=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa,V_x))).
% 15.19/15.11  all V_b V_a T_a (class_RealVector_Oreal__normed__algebra(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b))=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))).
% 15.19/15.11  all V_b V_a T_a (class_Rings_Oring(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))=c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b))).
% 15.19/15.11  all V_b V_a T_a (class_Rings_Oring(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)).
% 15.19/15.11  all V_b V_a T_a (class_Rings_Oring(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)=c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b))).
% 15.19/15.11  all V_b V_a T_a (class_Rings_Oring(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b))=c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)).
% 15.19/15.11  all V_b_2 V_aa_2 T_a (class_Rings_Oidom(T_a)-> (c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_aa_2)=c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_b_2)<->V_aa_2=V_b_2|V_aa_2=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))).
% 15.19/15.11  all V_aa_2 V_b_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))<->c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2))).
% 15.19/15.11  all V_b_2 V_aa_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2)<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_aa_2))).
% 15.19/15.11  all V_b_2 V_aa_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))<->c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)))).
% 15.19/15.11  all V_aa_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)=V_aa_2<->V_aa_2=c_Groups_Ozero__class_Ozero(T_a))).
% 15.19/15.11  all V_aa_2 T_a (class_Groups_Ogroup__add(T_a)-> (c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_aa_2=c_Groups_Ozero__class_Ozero(T_a))).
% 15.19/15.11  all V_aa_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (V_aa_2=c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)<->V_aa_2=c_Groups_Ozero__class_Ozero(T_a))).
% 15.19/15.11  all V_aa_2 T_a (class_Groups_Ogroup__add(T_a)-> (c_Groups_Ozero__class_Ozero(T_a)=c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)<->c_Groups_Ozero__class_Ozero(T_a)=V_aa_2)).
% 15.19/15.11  all T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.11  all V_y_2 V_x_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless__e_q(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2)<->V_x_2=V_y_2|c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2)))).
% 15.19/15.11  all V_y_2 V_x_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2)<->c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2)))).
% 15.19/15.11  all V_aa_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_aa_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2))).
% 15.19/15.11  all V_aa_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2))).
% 15.19/15.11  all V_aa_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 15.19/15.11  all V_aa_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 15.19/15.11  all V_aa_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))<->c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 15.19/15.11  all V_aa_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))<->c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 15.19/15.11  all V_aa_2 T_a (class_Groups_Oordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2))).
% 15.19/15.11  all V_aa_2 T_a (class_Groups_Olinordered__ab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_aa_2)<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2))).
% 15.19/15.11  all V_b V_a T_a (class_Groups_Ogroup__add(T_a)-> (c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,V_a)=V_b)).
% 15.19/15.11  all V_a T_a (class_Groups_Oab__group__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.11  all V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.11  all V_b_2 V_aa_2 T_a (class_Groups_Ogroup__add(T_a)-> (V_aa_2=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)<->c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a))).
% 15.19/15.11  all V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.11  all V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=c_Groups_Ouminus__class_Ouminus(T_a,V_a)).
% 15.19/15.11  all V_x_2 T_a (class_Rings_Oring__1__no__zero__divisors(T_a)-> (c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_x_2)=c_Groups_Oone__class_Oone(T_a)<->V_x_2=c_Groups_Oone__class_Oone(T_a)|V_x_2=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)))).
% 15.19/15.11  all V_x T_a (class_Rings_Ocomm__ring__1(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,V_x)=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)),V_x)).
% 15.19/15.11  all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b))=c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)).
% 15.19/15.11  all V_y V_x T_a (class_Rings_Ocomm__ring__1(T_a)->c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)=c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Ouminus__class_Ouminus(T_a,V_y))).
% 15.19/15.11  all V_b V_a T_a (class_Groups_Oab__group__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)=c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b))).
% 15.19/15.11  all V_b V_a T_a (class_Groups_Ogroup__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)=c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b))).
% 15.19/15.11  all V_q V_n V_p T_a (class_Groups_Oab__group__add(T_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q),V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_n)))).
% 15.19/15.11  all V_q V_n V_p T_a (class_Groups_Oab__group__add(T_a)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q),V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_n)))).
% 15.19/15.11  all V_p T_a (class_Rings_Olinordered__idom(T_a)->V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Polynomial_Opos__poly(T_a,V_p)|c_Polynomial_Opos__poly(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p))).
% 15.19/15.11  c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.11  all V_a V_b V_r V_q V_y V_x T_a (class_Fields_Ofield(T_a)-> (c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q,V_r)-> (V_y!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))-> (V_b=c_Rings_Oinverse__class_Odivide(T_a,hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_OpCons(T_a,V_a,V_r)),c_Polynomial_Odegree(T_a,V_y)),hAPP(c_Polynomial_Ocoeff(T_a,V_y),c_Polynomial_Odegree(T_a,V_y)))->c_Polynomial_Opdivmod__rel(T_a,c_Polynomial_OpCons(T_a,V_a,V_x),V_y,c_Polynomial_OpCons(T_a,V_b,V_q),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_r),c_Polynomial_Osmult(T_a,V_b,V_y))))))).
% 15.19/15.11  all V_b V_a T_a (class_Groups_Oab__group__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b))=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))).
% 15.19/15.11  all V_d V_b V_c V_a T_a (class_Groups_Oab__group__add(T_a)->c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(T_a,V_c,V_d))).
% 15.19/15.11  all V_c V_b V_a T_a (class_Rings_Odivision__ring(T_a)->c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_c)=c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c))).
% 15.19/15.11  all V_a T_a (class_Rings_Odivision__ring(T_a)->c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Oone__class_Oone(T_a))=V_a).
% 15.19/15.11  all V_ya V_y V_x T_a (class_RealVector_Oreal__normed__field(T_a)->c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_y),V_ya)=c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_ya),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_ya))).
% 15.19/15.11  all V_y V_x T_a (class_RealVector_Oreal__normed__field(T_a)->c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x),V_y)=c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y))).
% 15.19/15.11  all V_b V_a T_a (class_Rings_Odivision__ring(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)).
% 15.19/15.11  all V_a T_a (class_Rings_Odivision__ring__inverse__zero(T_a)->c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.11  all V_a T_a (class_Rings_Odivision__ring(T_a)->c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.11  all V_y T_a (class_RealVector_Oreal__normed__field(T_a)->c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.11  all V_c V_b V_a T_a (class_Rings_Odivision__ring(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_a,c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c)).
% 15.19/15.11  all V_c V_b V_a T_a (class_Rings_Odivision__ring(T_a)->c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c))).
% 15.19/15.11  all V_ya V_y V_x T_a (class_RealVector_Oreal__normed__field(T_a)->c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),V_ya)=c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_ya),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_ya))).
% 15.19/15.11  all V_b V_a V_c T_a (class_Rings_Odivision__ring(T_a)-> (V_c!=c_Groups_Ozero__class_Ozero(T_a)-> (c_Groups_Otimes__class_Otimes(T_a,V_a,V_c)=V_b->V_a=c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)))).
% 15.19/15.11  all V_a V_b V_c T_a (class_Rings_Odivision__ring(T_a)-> (V_c!=c_Groups_Ozero__class_Ozero(T_a)-> (V_b=c_Groups_Otimes__class_Otimes(T_a,V_a,V_c)->c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)=V_a))).
% 15.19/15.11  all V_aa_2 V_b_2 V_c_2 T_a (class_Rings_Odivision__ring(T_a)-> (V_c_2!=c_Groups_Ozero__class_Ozero(T_a)-> (c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)=V_aa_2<->V_b_2=c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2)))).
% 15.19/15.11  all V_b_2 V_aa_2 V_c_2 T_a (class_Rings_Odivision__ring(T_a)-> (V_c_2!=c_Groups_Ozero__class_Ozero(T_a)-> (V_aa_2=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)<->c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2)=V_b_2))).
% 15.19/15.11  all V_h V_d V_c V_b V_a T_a (class_RealVector_Oreal__field(T_a)->c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_c,V_d)),V_h)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d),V_h)),c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c),V_h),V_d))).
% 15.19/15.11  all V_aa_2 V_b_2 T_a (class_Rings_Odivision__ring(T_a)-> (V_b_2!=c_Groups_Ozero__class_Ozero(T_a)-> (c_Rings_Oinverse__class_Odivide(T_a,V_aa_2,V_b_2)=c_Groups_Oone__class_Oone(T_a)<->V_aa_2=V_b_2))).
% 15.19/15.11  all V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a)=c_Groups_Oone__class_Oone(T_a))).
% 15.19/15.11  all V_a T_a (class_Rings_Odivision__ring__inverse__zero(T_a)-> (V_a=c_Groups_Ozero__class_Ozero(T_a)->c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a)=c_Groups_Ozero__class_Ozero(T_a))& (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a)=c_Groups_Oone__class_Oone(T_a))).
% 15.19/15.11  all V_a V_b T_a (class_Rings_Odivision__ring(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b))=c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))).
% 15.19/15.11  all V_a V_b T_a (class_Rings_Odivision__ring(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))=c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)))).
% 15.19/15.11  all V_c V_b V_a T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)))))).
% 15.19/15.11  all V_c V_a V_b T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)))))).
% 15.19/15.11  all V_aa_2 V_b_2 V_c_2 T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2)))).
% 15.19/15.11  all V_w V_z V_y V_x T_a (class_Fields_Ofield__inverse__zero(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Rings_Oinverse__class_Odivide(T_a,V_z,V_w))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_z),c_Groups_Otimes__class_Otimes(T_a,V_y,V_w))).
% 15.19/15.11  all V_b V_a T_a (class_Fields_Ofield__inverse__zero(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))=c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b))).
% 15.19/15.11  all V_b V_a T_a (class_Fields_Ofield__inverse__zero(T_a)->c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b))=c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)).
% 15.19/15.11  all V_c V_b V_a T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c))))).
% 15.19/15.11  all V_c V_b V_a T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c))))).
% 15.19/15.11  all V_b_2 V_aa_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)&c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2))).
% 15.19/15.11  all V_b_2 V_aa_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_aa_2,V_b_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)&c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 15.19/15.11  all V_b_2 V_aa_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_aa_2,V_b_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)&c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 15.19/15.11  all V_b_2 V_aa_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)&c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))&c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2))).
% 15.19/15.11  all V_y V_x T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y))))).
% 15.19/15.11  all V_y V_x T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)-> (c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a))))).
% 15.19/15.11  all V_y V_x T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)->c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a))))).
% 15.19/15.11  all V_y V_x T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y))))).
% 15.19/15.11  all V_c V_b V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)->c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c))))).
% 15.19/15.11  all V_c V_a V_b T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c))))).
% 15.19/15.11  all V_w_2 V_x_2 V_z_2 V_y_2 T_a (class_Fields_Ofield(T_a)-> (V_y_2!=c_Groups_Ozero__class_Ozero(T_a)-> (V_z_2!=c_Groups_Ozero__class_Ozero(T_a)-> (c_Rings_Oinverse__class_Odivide(T_a,V_x_2,V_y_2)=c_Rings_Oinverse__class_Odivide(T_a,V_w_2,V_z_2)<->c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_z_2)=c_Groups_Otimes__class_Otimes(T_a,V_w_2,V_y_2))))).
% 15.19/15.11  all V_b V_a V_c T_a (class_Fields_Ofield__inverse__zero(T_a)-> (V_c!=c_Groups_Ozero__class_Ozero(T_a)->c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))=c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))).
% 15.19/15.11  all V_b V_a V_c T_a (class_Fields_Ofield__inverse__zero(T_a)-> (V_c!=c_Groups_Ozero__class_Ozero(T_a)->c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))=c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))).
% 15.19/15.11  all V_aa_2 V_c_2 V_b_2 T_a (class_Fields_Ofield__inverse__zero(T_a)-> (c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)=V_aa_2<-> (V_c_2!=c_Groups_Ozero__class_Ozero(T_a)->V_b_2=c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2))& (V_c_2=c_Groups_Ozero__class_Ozero(T_a)->V_aa_2=c_Groups_Ozero__class_Ozero(T_a)))).
% 15.19/15.11  all V_c_2 V_b_2 V_aa_2 T_a (class_Fields_Ofield__inverse__zero(T_a)-> (V_aa_2=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)<-> (V_c_2!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2)=V_b_2)& (V_c_2=c_Groups_Ozero__class_Ozero(T_a)->V_aa_2=c_Groups_Ozero__class_Ozero(T_a)))).
% 15.19/15.11  all V_y V_x T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y))))).
% 15.19/15.11  all V_y V_x T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a))))).
% 15.19/15.11  all V_z V_w V_y V_x T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_w,V_z)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w))))))).
% 15.19/15.11  all V_z V_w V_y V_x T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)-> (c_Orderings_Oord__class_Oless(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_w,V_z)->c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w))))))).
% 15.19/15.11  all V_z V_w V_y V_x T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w)-> (c_Orderings_Oord__class_Oless(T_a,V_w,V_z)->c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w))))))).
% 15.19/15.11  all V_y V_x T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)-> (c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a))))).
% 15.19/15.11  all V_y V_x T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y))))).
% 15.19/15.11  all V_c_2 V_b_2 V_aa_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))<-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2))& (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)-> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2)))& (-c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)))))).
% 15.19/15.11  all V_aa_2 V_c_2 V_b_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2)<-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)->c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2)))& (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)-> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2))& (-c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2))))).
% 15.19/15.11  all V_b_2 V_aa_2 V_c_2 T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)-> (c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2)))).
% 15.19/15.11  all V_aa_2 V_b_2 V_c_2 T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)-> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2)<->c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2))))).
% 15.19/15.11  all V_z V_x V_y T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)-> (c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y))->c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z)))).
% 15.19/15.11  all V_x V_z V_y T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y),V_x)->c_Orderings_Oord__class_Oless(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y))))).
% 15.19/15.11  all V_b_2 V_aa_2 V_c_2 T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))<->c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2))))).
% 15.19/15.11  all V_aa_2 V_b_2 V_c_2 T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2)<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2)))).
% 15.19/15.11  all V_c V_a V_b T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_b,V_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))->c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)))))).
% 15.19/15.11  all V_c V_b V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))->c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)))))).
% 15.19/15.11  all V_x V_z V_y T_a (class_Fields_Ofield__inverse__zero(T_a)-> (V_y!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y)),V_y))).
% 15.19/15.11  all V_y V_x V_z T_a (class_Fields_Ofield(T_a)-> (V_z!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Oplus__class_Oplus(T_a,V_x,c_Rings_Oinverse__class_Odivide(T_a,V_y,V_z))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_z,V_x),V_y),V_z))).
% 15.19/15.11  all V_z V_x V_y T_a (class_Fields_Ofield__inverse__zero(T_a)-> (V_y!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z)=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y)),V_y))).
% 15.19/15.11  all V_y V_x V_z T_a (class_Fields_Ofield(T_a)-> (V_z!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),V_y)=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y)),V_z))).
% 15.19/15.11  all V_w V_x V_z V_y T_a (class_Fields_Ofield(T_a)-> (V_y!=c_Groups_Ozero__class_Ozero(T_a)-> (V_z!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Rings_Oinverse__class_Odivide(T_a,V_w,V_z))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_z),c_Groups_Otimes__class_Otimes(T_a,V_w,V_y)),c_Groups_Otimes__class_Otimes(T_a,V_y,V_z))))).
% 15.19/15.11  all V_y V_x V_z T_a (class_Fields_Ofield(T_a)-> (V_z!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Ominus__class_Ominus(T_a,V_x,c_Rings_Oinverse__class_Odivide(T_a,V_y,V_z))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_z,V_x),V_y),V_z))).
% 15.19/15.11  all V_y V_x V_z T_a (class_Fields_Ofield(T_a)-> (V_z!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),V_y)=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y)),V_z))).
% 15.19/15.11  all V_w V_x V_z V_y T_a (class_Fields_Ofield(T_a)-> (V_y!=c_Groups_Ozero__class_Ozero(T_a)-> (V_z!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Rings_Oinverse__class_Odivide(T_a,V_w,V_z))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_z),c_Groups_Otimes__class_Otimes(T_a,V_w,V_y)),c_Groups_Otimes__class_Otimes(T_a,V_y,V_z))))).
% 15.19/15.11  all V_b V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),V_b))).
% 15.19/15.11  all V_b V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)->c_Orderings_Oord__class_Oless(T_a,V_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)))))).
% 15.19/15.11  all V_c_2 V_b_2 V_aa_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))<-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2))& (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)-> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2)))& (-c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)))))).
% 15.19/15.11  all V_aa_2 V_c_2 V_b_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2)<-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)->c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2)))& (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)-> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2))& (-c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2))))).
% 15.19/15.11  all V_b_2 V_aa_2 V_c_2 T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2)))).
% 15.19/15.11  all V_aa_2 V_b_2 V_c_2 T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2)<->c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2))))).
% 15.19/15.11  all V_z V_x V_y T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z)))).
% 15.19/15.11  all V_x V_z V_y T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y),V_x)->c_Orderings_Oord__class_Oless__e_q(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y))))).
% 15.19/15.11  all V_b_2 V_aa_2 V_c_2 T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2))))).
% 15.19/15.11  all V_x V_a V_y T_a (class_Fields_Ofield(T_a)-> (V_y!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_x),V_y)=c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)),c_Polynomial_Osmult(T_a,c_Rings_Oinverse__class_Odivide(T_a,hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_OpCons(T_a,V_a,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y))),c_Polynomial_Odegree(T_a,V_y)),hAPP(c_Polynomial_Ocoeff(T_a,V_y),c_Polynomial_Odegree(T_a,V_y))),V_y)))).
% 15.19/15.11  all V_y_2 V_x_2 T_a (class_Lattices_Oboolean__algebra(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),c_Groups_Ouminus__class_Ouminus(T_a,V_y_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2))).
% 15.19/15.11  all V_y V_x T_a (class_Lattices_Oboolean__algebra(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_y),c_Groups_Ouminus__class_Ouminus(T_a,V_x)))).
% 15.19/15.11  all V_y V_x V_a T_a (class_Fields_Ofield(T_a)->c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_x),V_y)=c_Polynomial_Osmult(T_a,V_a,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y))).
% 15.19/15.11  all V_r V_q V_y V_x T_a (class_Fields_Ofield(T_a)-> (c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q,V_r)->c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)=V_r)).
% 15.19/15.11  all V_y V_x T_a (class_Fields_Ofield(T_a)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_x),c_Polynomial_Odegree(T_a,V_y))->c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)=V_x)).
% 15.19/15.11  all V_y V_x V_a T_a (class_Fields_Ofield(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,c_Polynomial_Osmult(T_a,V_a,V_y))=c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y))).
% 15.19/15.11  all V_y V_x T_a (class_Fields_Ofield(T_a)->c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_x),V_y)=c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y))).
% 15.19/15.11  all V_y V_x T_a (class_Fields_Ofield(T_a)->c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_y))=c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)).
% 15.19/15.11  all V_x V_y T_a (class_Fields_Ofield(T_a)-> (V_y!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)),c_Polynomial_Odegree(T_a,V_y)))).
% 15.19/15.11  all V_a T_a (class_Lattices_Oab__semigroup__idem__mult(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_a,V_a)=V_a).
% 15.19/15.11  all V_x T_a (class_Lattices_Oab__semigroup__idem__mult(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_x,V_x)=V_x).
% 15.19/15.11  all V_b V_a T_a (class_Lattices_Oab__semigroup__idem__mult(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))=c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)).
% 15.19/15.11  all V_x_2 V_B_2 V_A_2 T_b T_a (class_Groups_Ominus(T_a)->hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a),V_A_2,V_B_2),V_x_2)=c_Groups_Ominus__class_Ominus(T_a,hAPP(V_A_2,V_x_2),hAPP(V_B_2,V_x_2))).
% 15.19/15.11  all V_x T_a (class_Lattices_Oboolean__algebra(T_a)->c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x))=V_x).
% 15.19/15.11  all V_x_2 V_A_2 T_b T_a (class_Groups_Ouminus(T_a)->hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a),V_A_2),V_x_2)=c_Groups_Ouminus__class_Ouminus(T_a,hAPP(V_A_2,V_x_2))).
% 15.19/15.11  all V_y_2 V_x_2 T_a (class_Lattices_Oboolean__algebra(T_a)-> (c_Groups_Ouminus__class_Ouminus(T_a,V_x_2)=c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)<->V_x_2=V_y_2)).
% 15.19/15.11  all V_c V_b V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)),V_b)=c_Divides_Odiv__class_Omod(T_a,V_a,V_b)).
% 15.19/15.11  all V_b V_c V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)),V_b)=c_Divides_Odiv__class_Omod(T_a,V_a,V_b)).
% 15.19/15.11  all V_k V_n V_m (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n),V_k)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,V_k))).
% 15.19/15.11  all V_n V_m V_k (c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_m),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_n))).
% 15.19/15.11  all V_n V_m (c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n)).
% 15.19/15.11  all V_m V_n V_k (c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_n),V_m),V_n)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)).
% 15.19/15.11  all V_d_2 V_m_2 (c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)<-> (exists B_q (V_m_2=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_d_2,B_q)))).
% 15.19/15.11  all V_n V_m ((c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n))=V_n->c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat))& (c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n))!=V_n->c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)=c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)))).
% 15.19/15.11  all V_m (c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.19/15.11  all V_m V_n V_k (c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_n),V_m)),V_n)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)).
% 15.19/15.11  all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n),V_n)).
% 15.19/15.11  all V_n V_m c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n),V_m).
% 15.19/15.11  all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)=V_m).
% 15.19/15.11  all V_m V_n (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n),V_n)).
% 15.19/15.11  all V_n V_m (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)).
% 15.19/15.11  all V_n V_m ((c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)=V_m)& (-c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)->c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n))).
% 15.19/15.11  all V_m V_n (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)->c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)).
% 15.19/15.11  all V_k_2 V_n_2 V_P_2 (hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))<-> (V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)->hBOOL(hAPP(V_P_2,V_n_2)))& (V_k_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)-> (all B_i B_j (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_k_2)-> (V_n_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,B_i),B_j)->hBOOL(hAPP(V_P_2,B_j))))))).
% 15.19/15.11  all V_q V_b V_r V_c (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_c)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_r,V_b)->c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_b,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c)),V_r),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_b,V_c)))).
% 15.19/15.11  all V_m V_k (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_k)->c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_m)),V_k)=c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 15.19/15.11  all V_b V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_b)=c_Divides_Odiv__class_Omod(T_a,V_a,V_b)).
% 15.19/15.11  all V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.11  all V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a).
% 15.19/15.11  all V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,V_a,V_a)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.11  all V_b_H V_b V_a_H V_c V_a T_a (class_Divides_Osemiring__div(T_a)-> (c_Divides_Odiv__class_Omod(T_a,V_a,V_c)=c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)-> (c_Divides_Odiv__class_Omod(T_a,V_b,V_c)=c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)->c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_H,V_b_H),V_c)))).
% 15.19/15.11  all V_b V_c V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c)).
% 15.19/15.11  all V_b V_c V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))=c_Groups_Otimes__class_Otimes(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_c)).
% 15.19/15.11  all V_b V_a V_c T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))=c_Groups_Otimes__class_Otimes(T_a,V_c,c_Divides_Odiv__class_Omod(T_a,V_a,V_b))).
% 15.19/15.11  all V_c V_b V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c)).
% 15.19/15.11  all V_c V_b V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),V_b),V_c)).
% 15.19/15.11  all V_c V_b V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c)).
% 15.19/15.11  all V_b_H V_b V_a_H V_c V_a T_a (class_Divides_Osemiring__div(T_a)-> (c_Divides_Odiv__class_Omod(T_a,V_a,V_c)=c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)-> (c_Divides_Odiv__class_Omod(T_a,V_b,V_c)=c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)->c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_H,V_b_H),V_c)))).
% 15.19/15.11  all V_b V_c V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)).
% 15.19/15.11  all V_c V_b V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c)=c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)).
% 15.19/15.11  all V_c V_b V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c)).
% 15.19/15.11  all V_c V_b V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),V_b),V_c)).
% 15.19/15.11  all V_c V_b V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c)).
% 15.19/15.11  all V_a V_b T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_a),V_b)=c_Divides_Odiv__class_Omod(T_a,V_a,V_b)).
% 15.19/15.11  all V_b V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b)=c_Divides_Odiv__class_Omod(T_a,V_a,V_b)).
% 15.19/15.11  all V_b_H V_b V_a_H V_c V_a T_a (class_Divides_Oring__div(T_a)-> (c_Divides_Odiv__class_Omod(T_a,V_a,V_c)=c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)-> (c_Divides_Odiv__class_Omod(T_a,V_b,V_c)=c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)->c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_H,V_b_H),V_c)))).
% 15.19/15.11  all V_c V_b V_a T_a (class_Divides_Oring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c)).
% 15.19/15.11  all V_c V_b V_a T_a (class_Divides_Oring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),V_b),V_c)).
% 15.19/15.11  all V_c V_b V_a T_a (class_Divides_Oring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c)).
% 15.19/15.11  all V_a_H V_b V_a T_a (class_Divides_Oring__div(T_a)-> (c_Divides_Odiv__class_Omod(T_a,V_a,V_b)=c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b)->c_Divides_Odiv__class_Omod(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)=c_Divides_Odiv__class_Omod(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_H),V_b))).
% 15.19/15.11  all V_b V_a T_a (class_Divides_Oring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)=c_Divides_Odiv__class_Omod(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b)).
% 15.19/15.11  all V_a V_b T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_a),V_b)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.11  all V_b V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_b)=c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.11  all V_a T_a (class_Divides_Osemiring__div(T_a)->c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.11  all V_x T_a (class_Rings_Olinordered__idom(T_a)-> (V_x=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))& (V_x!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))-> (c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x)->c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x)=c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)))& (-c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x)->c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x)=c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)))))).
% 15.19/15.11  all V_y V_x T_a (class_Fields_Ofield(T_a)-> (V_x=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))&V_y=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_Opoly__gcd(T_a,V_x,V_y)),c_Polynomial_Odegree(T_a,c_Polynomial_Opoly__gcd(T_a,V_x,V_y)))=c_Groups_Ozero__class_Ozero(T_a))& (-(V_x=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))&V_y=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))->hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_Opoly__gcd(T_a,V_x,V_y)),c_Polynomial_Odegree(T_a,c_Polynomial_Opoly__gcd(T_a,V_x,V_y)))=c_Groups_Oone__class_Oone(T_a))).
% 15.19/15.11  all V_x T_a (class_RealVector_Oreal__normed__vector(T_a)->c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x))=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x))).
% 15.19/15.11  all V_y V_x T_a (class_Fields_Ofield(T_a)->c_Polynomial_Opoly__gcd(T_a,V_x,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_y))=c_Polynomial_Opoly__gcd(T_a,V_x,V_y)).
% 15.19/15.11  all V_y V_x T_a (class_Fields_Ofield(T_a)->c_Polynomial_Opoly__gcd(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_x),V_y)=c_Polynomial_Opoly__gcd(T_a,V_x,V_y)).
% 15.19/15.11  all V_aa_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Osgn__class_Osgn(T_a,V_aa_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2))).
% 15.19/15.11  all V_aa_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Osgn__class_Osgn(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 15.19/15.11  all T_a (class_RealVector_Oreal__normed__algebra__1(T_a)->c_Groups_Osgn__class_Osgn(T_a,c_Groups_Oone__class_Oone(T_a))=c_Groups_Oone__class_Oone(T_a)).
% 15.19/15.11  all T_a (class_Fields_Ofield(T_a)->c_Polynomial_Opoly__gcd(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 15.19/15.11  all V_y_2 V_x_2 T_a (class_Fields_Ofield(T_a)-> (c_Polynomial_Opoly__gcd(T_a,V_x_2,V_y_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))<->V_x_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))&V_y_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))).
% 15.19/15.11  all V_a T_a (class_Rings_Olinordered__idom(T_a)->c_Groups_Osgn__class_Osgn(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a))=c_Groups_Osgn__class_Osgn(T_a,V_a)).
% 15.19/15.11  all V_c V_b V_a T_a (class_Fields_Ofield(T_a)->c_Polynomial_Opoly__gcd(T_a,c_Polynomial_Opoly__gcd(T_a,V_a,V_b),V_c)=c_Polynomial_Opoly__gcd(T_a,V_a,c_Polynomial_Opoly__gcd(T_a,V_b,V_c))).
% 15.19/15.11  all V_c V_a V_b T_a (class_Fields_Ofield(T_a)->c_Polynomial_Opoly__gcd(T_a,V_b,c_Polynomial_Opoly__gcd(T_a,V_a,V_c))=c_Polynomial_Opoly__gcd(T_a,V_a,c_Polynomial_Opoly__gcd(T_a,V_b,V_c))).
% 15.19/15.11  all V_b V_a T_a (class_Fields_Ofield(T_a)->c_Polynomial_Opoly__gcd(T_a,V_a,V_b)=c_Polynomial_Opoly__gcd(T_a,V_b,V_a)).
% 15.19/15.11  all V_b V_a T_a (class_Rings_Olinordered__idom(T_a)->c_Groups_Osgn__class_Osgn(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a),c_Groups_Osgn__class_Osgn(T_a,V_b))).
% 15.19/15.11  all V_y V_x T_a (class_RealVector_Oreal__normed__div__algebra(T_a)->c_Groups_Osgn__class_Osgn(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y))=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x),c_Groups_Osgn__class_Osgn(T_a,V_y))).
% 15.19/15.11  all V_aa_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Groups_Osgn__class_Osgn(T_a,V_aa_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_aa_2=c_Groups_Ozero__class_Ozero(T_a))).
% 15.19/15.11  all T_a (class_Groups_Osgn__if(T_a)->c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.11  all V_x_2 T_a (class_RealVector_Oreal__normed__vector(T_a)-> (c_Groups_Osgn__class_Osgn(T_a,V_x_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_x_2=c_Groups_Ozero__class_Ozero(T_a))).
% 15.19/15.11  all T_a (class_RealVector_Oreal__normed__vector(T_a)->c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.11  all V_x T_a (class_Fields_Ofield(T_a)->c_Polynomial_Opoly__gcd(T_a,V_x,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)))=c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))).
% 15.19/15.11  all V_y T_a (class_Fields_Ofield(T_a)->c_Polynomial_Opoly__gcd(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)),V_y)=c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))).
% 15.19/15.11  all V_x V_y T_a (class_Fields_Ofield(T_a)-> (V_y!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=c_Polynomial_Opoly__gcd(T_a,V_y,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)))).
% 15.19/15.11  all V_aa_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Groups_Osgn__class_Osgn(T_a,V_aa_2)=c_Groups_Oone__class_Oone(T_a)<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2))).
% 15.19/15.11  all V_a T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Groups_Osgn__class_Osgn(T_a,V_a)=c_Groups_Oone__class_Oone(T_a))).
% 15.19/15.11  all V_a T_a (class_Rings_Olinordered__idom(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))->c_Groups_Osgn__class_Osgn(T_a,V_a)=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)))).
% 15.19/15.11  all V_aa_2 T_a (class_Rings_Olinordered__idom(T_a)-> (c_Groups_Osgn__class_Osgn(T_a,V_aa_2)=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))<->c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 15.19/15.11  all V_x T_a (class_Groups_Osgn__if(T_a)-> (V_x=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Osgn__class_Osgn(T_a,V_x)=c_Groups_Ozero__class_Ozero(T_a))& (V_x!=c_Groups_Ozero__class_Ozero(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)->c_Groups_Osgn__class_Osgn(T_a,V_x)=c_Groups_Oone__class_Oone(T_a))& (-c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)->c_Groups_Osgn__class_Osgn(T_a,V_x)=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))))).
% 15.19/15.11  all V_x V_y T_a (class_Fields_Ofield(T_a)-> (V_y=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=c_Polynomial_Osmult(T_a,c_Rings_Oinverse__class_Oinverse(T_a,hAPP(c_Polynomial_Ocoeff(T_a,V_x),c_Polynomial_Odegree(T_a,V_x))),V_x))& (V_y!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=c_Polynomial_Opoly__gcd(T_a,V_y,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)))).
% 15.19/15.11  all V_n_2 V_P_2 (-hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))-> (hBOOL(hAPP(V_P_2,V_n_2))-> (exists B_k (c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_k,V_n_2)& (all B_i (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_i,B_k)-> -hBOOL(hAPP(V_P_2,B_i))))&hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B_k,c_Groups_Oone__class_Oone(tc_Nat_Onat)))))))).
% 15.19/15.11  all V_a T_a (class_Rings_Odivision__ring(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,V_a)=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a)).
% 15.19/15.11  all V_a T_a (class_Fields_Ofield(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,V_a)=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a)).
% 15.19/15.11  all V_b V_a T_a (class_Rings_Odivision__ring(T_a)->c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)=c_Groups_Otimes__class_Otimes(T_a,V_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b))).
% 15.19/15.11  all V_b V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))=c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a))))).
% 15.19/15.11  all V_b V_a T_a (class_Rings_Odivision__ring(T_a)-> (c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)=c_Groups_Oone__class_Oone(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,V_a)=V_b)).
% 15.19/15.11  all V_a T_a (class_Rings_Odivision__ring__inverse__zero(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a))=V_a).
% 15.19/15.11  all V_b_2 V_aa_2 T_a (class_Rings_Odivision__ring__inverse__zero(T_a)-> (c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2)=c_Rings_Oinverse__class_Oinverse(T_a,V_b_2)<->V_aa_2=V_b_2)).
% 15.19/15.11  all V_b V_a T_a (class_Rings_Odivision__ring__inverse__zero(T_a)-> (c_Rings_Oinverse__class_Oinverse(T_a,V_a)=c_Rings_Oinverse__class_Oinverse(T_a,V_b)->V_a=V_b)).
% 15.19/15.11  all T_a (class_Rings_Odivision__ring__inverse__zero(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.11  all V_aa_2 T_a (class_Rings_Odivision__ring__inverse__zero(T_a)-> (c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2)=c_Groups_Ozero__class_Ozero(T_a)<->V_aa_2=c_Groups_Ozero__class_Ozero(T_a))).
% 15.19/15.11  all V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,V_a)!=c_Groups_Ozero__class_Ozero(T_a))).
% 15.19/15.11  all V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a))=V_a)).
% 15.19/15.11  all V_a T_a (class_Rings_Odivision__ring(T_a)-> (c_Rings_Oinverse__class_Oinverse(T_a,V_a)=c_Groups_Ozero__class_Ozero(T_a)->V_a=c_Groups_Ozero__class_Ozero(T_a))).
% 15.19/15.11  all V_b V_a T_a (class_Rings_Odivision__ring(T_a)-> (c_Rings_Oinverse__class_Oinverse(T_a,V_a)=c_Rings_Oinverse__class_Oinverse(T_a,V_b)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->V_a=V_b)))).
% 15.19/15.11  all T_a (class_Rings_Odivision__ring(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Oone__class_Oone(T_a))=c_Groups_Oone__class_Oone(T_a)).
% 15.19/15.11  all V_x_2 T_a (class_Fields_Ofield__inverse__zero(T_a)-> (c_Rings_Oinverse__class_Oinverse(T_a,V_x_2)=c_Groups_Oone__class_Oone(T_a)<->V_x_2=c_Groups_Oone__class_Oone(T_a))).
% 15.19/15.11  all V_b V_a T_a (class_Fields_Ofield__inverse__zero(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))=c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))).
% 15.19/15.11  all T_a (class_Fields_Ofield__inverse__zero(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.11  all V_aa_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 15.19/15.11  all V_aa_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2))<->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2))).
% 15.19/15.11  all V_b V_a T_a (class_Fields_Ofield__inverse__zero(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))=c_Rings_Oinverse__class_Odivide(T_a,V_b,V_a)).
% 15.19/15.11  all V_b V_a T_a (class_Fields_Ofield(T_a)->c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)=c_Groups_Otimes__class_Otimes(T_a,V_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b))).
% 15.19/15.11  all V_aa_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2))).
% 15.19/15.11  all V_aa_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))<->c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)))).
% 15.19/15.11  all V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)))).
% 15.19/15.11  all V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)))).
% 15.19/15.11  all V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)))).
% 15.19/15.11  all V_b V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a))))).
% 15.19/15.11  all V_b V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a))))).
% 15.19/15.11  all V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))))).
% 15.19/15.11  all V_b V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless(T_a,V_b,V_a)))).
% 15.19/15.11  all V_b V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless(T_a,V_b,V_a)))).
% 15.19/15.11  all V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a))=c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)))).
% 15.19/15.11  all V_a T_a (class_Rings_Odivision__ring__inverse__zero(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a))=c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a))).
% 15.19/15.11  all V_b V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a))))).
% 15.19/15.11  all V_b V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a))))).
% 15.19/15.11  all V_b V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)))).
% 15.19/15.11  all V_b V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))-> (c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)))).
% 15.19/15.11  all V_x_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),V_x_2))).
% 15.19/15.11  all V_b V_a T_a (class_Fields_Ofield(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),c_Rings_Oinverse__class_Oinverse(T_a,V_b))))).
% 15.19/15.11  all V_b V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),c_Rings_Oinverse__class_Oinverse(T_a,V_b))))).
% 15.19/15.11  all V_x_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)&c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oone__class_Oone(T_a)))).
% 15.19/15.11  all V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))->c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))))).
% 15.19/15.11  all V_b V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)),c_Rings_Oinverse__class_Oinverse(T_a,V_b))))).
% 15.19/15.11  all V_a T_a (class_Fields_Ofield(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),V_a)=c_Groups_Oone__class_Oone(T_a))).
% 15.19/15.11  all V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),V_a)=c_Groups_Oone__class_Oone(T_a))).
% 15.19/15.11  all V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a))=c_Groups_Oone__class_Oone(T_a))).
% 15.19/15.11  all V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Rings_Oinverse__class_Oinverse(T_a,V_a)=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a))).
% 15.19/15.11  all V_r V_q V_y V_x V_a T_a (class_Fields_Ofield(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)-> (c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q,V_r)->c_Polynomial_Opdivmod__rel(T_a,V_x,c_Polynomial_Osmult(T_a,V_a,V_y),c_Polynomial_Osmult(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),V_q),V_r)))).
% 15.19/15.11  all V_a T_a (class_Fields_Olinordered__field(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Oone__class_Oone(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))))).
% 15.19/15.11  all V_x_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))<->c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_x_2))).
% 15.19/15.11  all V_x_2 T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> (c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2))<->c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)&c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,c_Groups_Oone__class_Oone(T_a)))).
% 15.19/15.11  all V_b V_a T_a (class_Rings_Odivision__ring(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Rings_Oinverse__class_Oinverse(T_a,V_b)))))).
% 15.19/15.11  all V_h V_b V_a T_a (class_RealVector_Oreal__normed__field(T_a)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)-> (V_b!=c_Groups_Ozero__class_Ozero(T_a)->c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)),V_h)=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_h)),c_Rings_Oinverse__class_Oinverse(T_a,V_b)))))).
% 15.19/15.11  all V_x T_a (class_Fields_Ofield(T_a)->c_Polynomial_Opoly__gcd(T_a,V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=c_Polynomial_Osmult(T_a,c_Rings_Oinverse__class_Oinverse(T_a,hAPP(c_Polynomial_Ocoeff(T_a,V_x),c_Polynomial_Odegree(T_a,V_x))),V_x)).
% 15.19/15.11  all V_y V_x T_a (class_Fields_Olinordered__field__inverse__zero(T_a)-> ((all B_z (c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),B_z)-> (c_Orderings_Oord__class_Oless(T_a,B_z,c_Groups_Oone__class_Oone(T_a))->c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,B_z,V_x),V_y))))->c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y))).
% 15.19/15.11  all V_c_2 V_pa_2 T_a (class_Rings_Oidom(T_a)-> (hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_c_2)=c_Groups_Ozero__class_Ozero(T_a)<->c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_c_2),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),V_pa_2))).
% 15.19/15.11  all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))).
% 15.19/15.11  all V_y V_x T_a (class_Fields_Ofield(T_a)->c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Opoly__gcd(T_a,V_x,V_y),V_x)).
% 15.19/15.11  all V_y V_x T_a (class_Fields_Ofield(T_a)->c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Opoly__gcd(T_a,V_x,V_y),V_y)).
% 15.19/15.11  all V_y_2 V_x_2 T_a (class_Rings_Ocomm__ring__1(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,V_x_2,c_Groups_Ouminus__class_Ouminus(T_a,V_y_2))<->c_Rings_Odvd__class_Odvd(T_a,V_x_2,V_y_2))).
% 15.19/15.11  all V_y_2 V_x_2 T_a (class_Rings_Ocomm__ring__1(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),V_y_2)<->c_Rings_Odvd__class_Odvd(T_a,V_x_2,V_y_2))).
% 15.19/15.11  all V_z V_y V_x T_a (class_Rings_Ocomm__ring__1(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,V_x,V_y)-> (c_Rings_Odvd__class_Odvd(T_a,V_x,V_z)->c_Rings_Odvd__class_Odvd(T_a,V_x,c_Groups_Ominus__class_Ominus(T_a,V_y,V_z))))).
% 15.19/15.11  all V_q V_p T_a (class_Rings_Oidom(T_a)-> (hAPP(c_Polynomial_Ocoeff(T_a,V_p),c_Polynomial_Odegree(T_a,V_p))=hAPP(c_Polynomial_Ocoeff(T_a,V_q),c_Polynomial_Odegree(T_a,V_q))-> (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q)-> (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_q,V_p)->V_p=V_q)))).
% 15.19/15.11  all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Rings_Odvd__class_Odvd(T_a,c_Groups_Oone__class_Oone(T_a),V_a)).
% 15.19/15.11  all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)->V_a=c_Groups_Ozero__class_Ozero(T_a))).
% 15.19/15.11  all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c)->c_Rings_Odvd__class_Odvd(T_a,V_b,V_c))).
% 15.19/15.11  all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c)->c_Rings_Odvd__class_Odvd(T_a,V_a,V_c))).
% 15.19/15.11  all V_k V_b V_a T_a (class_Rings_Odvd(T_a)-> (V_a=c_Groups_Otimes__class_Otimes(T_a,V_b,V_k)->c_Rings_Odvd__class_Odvd(T_a,V_b,V_a))).
% 15.19/15.11  all V_d V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)-> (c_Rings_Odvd__class_Odvd(T_a,V_c,V_d)->c_Rings_Odvd__class_Odvd(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d))))).
% 15.19/15.11  all V_b V_c V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,V_a,V_c)->c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)))).
% 15.19/15.11  all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)->c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)))).
% 15.19/15.11  all V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_a))).
% 15.19/15.11  all V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))).
% 15.19/15.11  all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)-> (c_Rings_Odvd__class_Odvd(T_a,V_a,V_c)->c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))))).
% 15.19/15.11  all V_a V_q V_p T_a (class_Rings_Ocomm__semiring__1(T_a)-> (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q)->c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_a,V_q)))).
% 15.19/15.11  all V_q V_p V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),V_q)->c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q))).
% 15.19/15.11  all V_c V_b V_a T_a (class_Rings_Ocomm__semiring__1(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)-> (c_Rings_Odvd__class_Odvd(T_a,V_b,V_c)->c_Rings_Odvd__class_Odvd(T_a,V_a,V_c)))).
% 15.19/15.11  all V_a T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Rings_Odvd__class_Odvd(T_a,V_a,V_a)).
% 15.19/15.11  all V_q_2 V_pa_2 V_aa_2 T_a (class_Fields_Ofield(T_a)-> (V_aa_2!=c_Groups_Ozero__class_Ozero(T_a)-> (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_pa_2,c_Polynomial_Osmult(T_a,V_aa_2,V_q_2))<->c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_pa_2,V_q_2)))).
% 15.19/15.11  all V_a V_q V_p T_a (class_Fields_Ofield(T_a)-> (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q)-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),V_q)))).
% 15.19/15.11  all V_q V_a V_p T_a (class_Fields_Ofield(T_a)-> (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_a,V_q))-> (V_a!=c_Groups_Ozero__class_Ozero(T_a)->c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q)))).
% 15.19/15.11  all V_b_2 V_c_2 V_aa_2 T_a (class_Rings_Oidom(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_c_2))<->V_c_2=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Odvd__class_Odvd(T_a,V_aa_2,V_b_2))).
% 15.19/15.11  all V_b_2 V_aa_2 V_c_2 T_a (class_Rings_Oidom(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_aa_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))<->V_c_2=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Odvd__class_Odvd(T_a,V_aa_2,V_b_2))).
% 15.19/15.11  all V_y_2 V_x_2 V_k_2 T_a (class_Fields_Ofield(T_a)-> (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_k_2,c_Polynomial_Opoly__gcd(T_a,V_x_2,V_y_2))<->c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_k_2,V_x_2)&c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_k_2,V_y_2))).
% 15.19/15.11  all V_y V_x V_k T_a (class_Fields_Ofield(T_a)-> (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_k,V_x)-> (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_k,V_y)->c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_k,c_Polynomial_Opoly__gcd(T_a,V_x,V_y))))).
% 15.19/15.11  all V_b V_a T_a (class_Divides_Osemiring__div(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)->c_Divides_Odiv__class_Omod(T_a,V_b,V_a)=c_Groups_Ozero__class_Ozero(T_a))).
% 15.19/15.11  all V_b_2 V_aa_2 T_a (class_Divides_Osemiring__div(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,V_aa_2,V_b_2)<->c_Divides_Odiv__class_Omod(T_a,V_b_2,V_aa_2)=c_Groups_Ozero__class_Ozero(T_a))).
% 15.19/15.11  all V_n V_m V_k T_a (class_Divides_Osemiring__div(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,V_k,c_Divides_Odiv__class_Omod(T_a,V_m,V_n))-> (c_Rings_Odvd__class_Odvd(T_a,V_k,V_n)->c_Rings_Odvd__class_Odvd(T_a,V_k,V_m)))).
% 15.19/15.11  all V_n V_m V_k T_a (class_Divides_Osemiring__div(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,V_k,V_m)-> (c_Rings_Odvd__class_Odvd(T_a,V_k,V_n)->c_Rings_Odvd__class_Odvd(T_a,V_k,c_Divides_Odiv__class_Omod(T_a,V_m,V_n))))).
% 15.19/15.11  all V_a V_b V_c T_a (class_Divides_Osemiring__div(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,V_c,V_b)->c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,V_a,V_c))).
% 15.19/15.11  all V_m_2 V_n_2 V_k_2 T_a (class_Divides_Osemiring__div(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,V_k_2,V_n_2)-> (c_Rings_Odvd__class_Odvd(T_a,V_k_2,c_Divides_Odiv__class_Omod(T_a,V_m_2,V_n_2))<->c_Rings_Odvd__class_Odvd(T_a,V_k_2,V_m_2)))).
% 15.19/15.11  all V_q_2 V_pa_2 V_aa_2 T_a (class_Fields_Ofield(T_a)-> (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_aa_2,V_pa_2),V_q_2)<-> (V_aa_2=c_Groups_Ozero__class_Ozero(T_a)->V_q_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))& (V_aa_2!=c_Groups_Ozero__class_Ozero(T_a)->c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_pa_2,V_q_2)))).
% 15.19/15.11  all V_q V_p T_a (class_Rings_Oidom(T_a)-> (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q)-> (V_q!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q))))).
% 15.19/15.11  all V_pa_2 V_c_2 T_a (class_Rings_Oidom(T_a)-> (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_c_2,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),V_pa_2)<->hAPP(c_Polynomial_Opoly(T_a,V_pa_2),c_Groups_Ouminus__class_Ouminus(T_a,V_c_2))=c_Groups_Ozero__class_Ozero(T_a))).
% 15.19/15.11  all V_t_2 V_D_2 V_d_2 T_a (class_Rings_Ocomm__ring(T_a)&class_Rings_Odvd(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,V_d_2,V_D_2)-> (all B_x B_k (c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2))<->c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,c_Groups_Otimes__class_Otimes(T_a,B_k,V_D_2)),V_t_2)))))).
% 15.19/15.11  all V_t_2 V_D_2 V_d_2 T_a (class_Rings_Ocomm__ring(T_a)&class_Rings_Odvd(T_a)-> (c_Rings_Odvd__class_Odvd(T_a,V_d_2,V_D_2)-> (all B_x B_k (c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2))<->c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,c_Groups_Otimes__class_Otimes(T_a,B_k,V_D_2)),V_t_2)))))).
% 15.19/15.11  all V_k c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k).
% 15.19/15.11  all V_n V_m V_k (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_m)-> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n)->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)))).
% 15.19/15.11  all V_n V_m V_k (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))-> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_m)))).
% 15.19/15.11  all V_n V_m V_k (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))-> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_m)-> (c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n)))).
% 15.19/15.11  all V_m_2 (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))<->V_m_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.19/15.11  all V_n V_m (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)-> -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_n,V_m))).
% 15.19/15.11  all V_n_2 V_m_2 V_k_2 (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2))<->V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m_2,V_n_2)).
% 15.19/15.11  all V_m_2 (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m_2,c_Groups_Oone__class_Oone(tc_Nat_Onat))<->V_m_2=c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 15.19/15.11  all V_n_2 V_k_2 (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2))<->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k_2,V_n_2)).
% 15.19/15.11  all V_n V_k (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n)-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n))).
% 15.19/15.11  all V_n V_m V_k (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_m),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_n))-> (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m,V_n))).
% 15.19/15.11  all V_n_2 V_m_2 V_k_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)-> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2))<->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m_2,V_n_2))).
% 15.19/15.11  all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)-> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2),V_m_2)<->V_n_2=c_Groups_Oone__class_Oone(tc_Nat_Onat))).
% 15.19/15.11  all V_n_2 V_m_2 (c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)-> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2,V_m_2),V_m_2)<->V_n_2=c_Groups_Oone__class_Oone(tc_Nat_Onat))).
% 15.19/15.11  all V_l_2 V_P_2 T_a (class_Rings_Odvd(T_a)&class_Rings_Osemiring__0(T_a)-> ((exists B_x hBOOL(hAPP(V_P_2,c_Groups_Otimes__class_Otimes(T_a,V_l_2,B_x))))<-> (exists B_x (c_Rings_Odvd__class_Odvd(T_a,V_l_2,c_Groups_Oplus__class_Oplus(T_a,B_x,c_Groups_Ozero__class_Ozero(T_a)))&hBOOL(hAPP(V_P_2,B_x)))))).
% 15.19/15.11  all V_y V_x V_d T_a (class_Fields_Ofield(T_a)-> (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_x)-> (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_y)-> ((all B_k (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),B_k,V_x)-> (c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),B_k,V_y)->c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),B_k,V_d))))-> ((V_x=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))&V_y=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))=c_Groups_Ozero__class_Ozero(T_a))& (-(V_x=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))&V_y=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))->hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))=c_Groups_Oone__class_Oone(T_a))->c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=V_d))))).
% 15.19/15.11  all V_a V_p T_a (class_Rings_Oidom(T_a)-> (V_p!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))->c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),c_Polynomial_Oorder(T_a,V_a,V_p)),V_p)& -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),c_Nat_OSuc(c_Polynomial_Oorder(T_a,V_a,V_p))),V_p))).
% 15.19/15.11  all V_x c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_x).
% 15.19/15.11  all V_y V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)-> -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y))).
% 15.19/15.11  all V_z V_y V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)-> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_y)->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_x))).
% 15.19/15.11  all V_b V_a (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a)-> -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b))).
% 15.19/15.11  all V_z V_y V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)-> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_x))).
% 15.19/15.11  all V_c V_b V_a (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a)-> (V_b=V_c->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_c,V_a))).
% 15.19/15.11  all V_y V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)->V_y!=V_x).
% 15.19/15.11  all V_y V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)->V_x!=V_y).
% 15.19/15.11  all V_y V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)-> -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y))).
% 15.19/15.11  all V_y V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)).
% 15.19/15.11  all V_y V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)-> -(c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y))).
% 15.19/15.11  all V_y V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)->V_x!=V_y).
% 15.19/15.11  all V_z V_y V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)-> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_y)->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_x))).
% 15.19/15.11  all V_c V_b V_a (V_a=V_b-> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_c)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_c,V_b)->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_c,V_a))).
% 15.19/15.11  all V_z V_y V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)-> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z))).
% 15.19/15.11  all V_y V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)-> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)->V_x=V_y)).
% 15.19/15.11  all V_n V_m (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m,V_n)-> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_n,V_m)->V_m=V_n)).
% 15.19/15.11  all V_c V_b V_a (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)-> (V_b=V_c->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c))).
% 15.19/15.11  all V_c V_b V_a (V_a=V_b-> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_c)->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c))).
% 15.19/15.11  all V_b V_a (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)-> (V_a!=V_b->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a))).
% 15.19/15.11  all V_y V_x (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)|V_x=V_y).
% 15.19/15.11  all V_x_2 V_y_2 (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)-> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)<->V_x_2=V_y_2)).
% 15.19/15.11  all V_y V_x (V_x=V_y->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)).
% 15.19/15.11  all V_b V_a (V_a!=V_b-> (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a))).
% 15.19/15.11  all V_y_2 V_x_2 (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)<->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)&V_x_2!=V_y_2).
% 15.19/15.11  all V_y_2 V_x_2 (c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)<->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)& -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)|V_x_2=V_y_2).
% 15.19/15.11  all V_y_2 V_x_2 (V_x_2=V_y_2<->c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)&c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)).
% 15.19/15.11  all V_n V_p T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a),V_p,V_n)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n))).
% 15.19/15.11  all V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_x).
% 15.19/15.11  all V_q V_y V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Power_Opower__class_Opower(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),V_q)=c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_q),c_Power_Opower__class_Opower(T_a,V_y,V_q))).
% 15.19/15.11  all V_q V_p V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Power_Opower__class_Opower(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_p),V_q)=c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_p,V_q))).
% 15.19/15.11  all V_x V_n V_p T_a (class_Rings_Ocomm__semiring__1(T_a)->hAPP(c_Polynomial_Opoly(T_a,c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a),V_p,V_n)),V_x)=c_Power_Opower__class_Opower(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),V_n)).
% 15.19/15.11  all V_q V_p V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_p),c_Power_Opower__class_Opower(T_a,V_x,V_q))=c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q))).
% 15.19/15.11  all V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(T_a)).
% 15.19/15.11  all V_q V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_q),V_x)=c_Power_Opower__class_Opower(T_a,V_x,c_Nat_OSuc(V_q))).
% 15.19/15.11  all V_q V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Groups_Otimes__class_Otimes(T_a,V_x,c_Power_Opower__class_Opower(T_a,V_x,V_q))=c_Power_Opower__class_Opower(T_a,V_x,c_Nat_OSuc(V_q))).
% 15.19/15.11  all V_q V_x T_a (class_Rings_Ocomm__semiring__1(T_a)->c_Power_Opower__class_Opower(T_a,V_x,c_Nat_OSuc(V_q))=c_Groups_Otimes__class_Otimes(T_a,V_x,c_Power_Opower__class_Opower(T_a,V_x,V_q))).
% 15.19/15.11  all T_1 (class_Groups_Ocancel__comm__monoid__add(T_1)->class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1))).
% 15.19/15.11  class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex).
% 15.19/15.11  class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat).
% 15.19/15.11  all T_2 T_1 (class_Lattices_Oboolean__algebra(T_1)->class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1))).
% 15.19/15.11  all T_2 T_1 (class_Orderings_Opreorder(T_1)->class_Orderings_Opreorder(tc_fun(T_2,T_1))).
% 15.19/15.11  all T_2 T_1 (class_Orderings_Oorder(T_1)->class_Orderings_Oorder(tc_fun(T_2,T_1))).
% 15.19/15.11  all T_2 T_1 (class_Orderings_Oord(T_1)->class_Orderings_Oord(tc_fun(T_2,T_1))).
% 15.19/15.11  all T_2 T_1 (class_Groups_Ouminus(T_1)->class_Groups_Ouminus(tc_fun(T_2,T_1))).
% 15.19/15.11  all T_2 T_1 (class_Groups_Ominus(T_1)->class_Groups_Ominus(tc_fun(T_2,T_1))).
% 15.19/15.11  class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat).
% 15.19/15.11  class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat).
% 15.19/15.11  class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat).
% 15.19/15.11  class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat).
% 15.19/15.11  class_Rings_Olinordered__semiring__strict(tc_Nat_Onat).
% 15.19/15.11  class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat).
% 15.19/15.11  class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat).
% 15.19/15.11  class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat).
% 15.19/15.11  class_Rings_Oordered__cancel__semiring(tc_Nat_Onat).
% 15.19/15.11  class_Rings_Oordered__comm__semiring(tc_Nat_Onat).
% 15.19/15.11  class_Groups_Ocancel__semigroup__add(tc_Nat_Onat).
% 15.19/15.11  class_Rings_Olinordered__semiring(tc_Nat_Onat).
% 15.19/15.11  class_Rings_Olinordered__semidom(tc_Nat_Onat).
% 15.19/15.11  class_Groups_Oab__semigroup__mult(tc_Nat_Onat).
% 15.19/15.11  class_Groups_Ocomm__monoid__mult(tc_Nat_Onat).
% 15.19/15.11  class_Groups_Oab__semigroup__add(tc_Nat_Onat).
% 15.19/15.11  class_Rings_Oordered__semiring(tc_Nat_Onat).
% 15.19/15.11  class_Rings_Ono__zero__divisors(tc_Nat_Onat).
% 15.19/15.11  class_Groups_Ocomm__monoid__add(tc_Nat_Onat).
% 15.19/15.11  class_Rings_Ocomm__semiring__1(tc_Nat_Onat).
% 15.19/15.11  class_Rings_Ocomm__semiring__0(tc_Nat_Onat).
% 15.19/15.11  class_Divides_Osemiring__div(tc_Nat_Onat).
% 15.19/15.11  class_Rings_Ocomm__semiring(tc_Nat_Onat).
% 15.19/15.11  class_Rings_Ozero__ne_q__one(tc_Nat_Onat).
% 15.19/15.11  class_Orderings_Opreorder(tc_Nat_Onat).
% 15.19/15.11  class_Orderings_Olinorder(tc_Nat_Onat).
% 15.19/15.11  class_Groups_Omonoid__mult(tc_Nat_Onat).
% 15.19/15.11  class_Groups_Omonoid__add(tc_Nat_Onat).
% 15.19/15.11  class_Rings_Osemiring__0(tc_Nat_Onat).
% 15.19/15.11  class_Rings_Omult__zero(tc_Nat_Onat).
% 15.19/15.11  class_Orderings_Oorder(tc_Nat_Onat).
% 15.19/15.11  class_Rings_Osemiring(tc_Nat_Onat).
% 15.19/15.11  class_Orderings_Oord(tc_Nat_Onat).
% 15.19/15.11  class_Groups_Ominus(tc_Nat_Onat).
% 15.19/15.11  class_Groups_Ozero(tc_Nat_Onat).
% 15.19/15.11  class_Groups_Oone(tc_Nat_Onat).
% 15.19/15.11  class_Rings_Odvd(tc_Nat_Onat).
% 15.19/15.11  class_Lattices_Oboolean__algebra(tc_HOL_Obool).
% 15.19/15.11  class_Orderings_Opreorder(tc_HOL_Obool).
% 15.19/15.11  class_Orderings_Oorder(tc_HOL_Obool).
% 15.19/15.11  class_Orderings_Oord(tc_HOL_Obool).
% 15.19/15.11  class_Groups_Ouminus(tc_HOL_Obool).
% 15.19/15.11  class_Groups_Ominus(tc_HOL_Obool).
% 15.19/15.11  class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex).
% 15.19/15.11  class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex).
% 15.19/15.11  class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex).
% 15.19/15.11  class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex).
% 15.19/15.11  class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex).
% 15.19/15.11  class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex).
% 15.19/15.11  class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex).
% 15.19/15.11  class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex).
% 15.19/15.11  class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex).
% 15.19/15.11  class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex).
% 15.19/15.11  class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex).
% 15.19/15.11  class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex).
% 15.19/15.11  class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex).
% 15.19/15.11  class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex).
% 15.19/15.11  class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex).
% 15.19/15.11  class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex).
% 15.19/15.11  class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex).
% 15.19/15.11  class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex).
% 15.19/15.11  class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex).
% 15.19/15.11  class_RealVector_Oreal__field(tc_Complex_Ocomplex).
% 15.19/15.11  class_Rings_Odivision__ring(tc_Complex_Ocomplex).
% 15.19/15.12  class_Rings_Ocomm__semiring(tc_Complex_Ocomplex).
% 15.19/15.12  class_Groups_Oab__group__add(tc_Complex_Ocomplex).
% 15.19/15.12  class_Rings_Ozero__ne_q__one(tc_Complex_Ocomplex).
% 15.19/15.12  class_Groups_Omonoid__mult(tc_Complex_Ocomplex).
% 15.19/15.12  class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex).
% 15.19/15.12  class_Groups_Omonoid__add(tc_Complex_Ocomplex).
% 15.19/15.12  class_Rings_Osemiring__0(tc_Complex_Ocomplex).
% 15.19/15.12  class_Groups_Ogroup__add(tc_Complex_Ocomplex).
% 15.19/15.12  class_Rings_Omult__zero(tc_Complex_Ocomplex).
% 15.19/15.12  class_Rings_Ocomm__ring(tc_Complex_Ocomplex).
% 15.19/15.12  class_Int_Oring__char__0(tc_Complex_Ocomplex).
% 15.19/15.12  class_Rings_Osemiring(tc_Complex_Ocomplex).
% 15.19/15.12  class_Groups_Ouminus(tc_Complex_Ocomplex).
% 15.19/15.12  class_Rings_Oring__1(tc_Complex_Ocomplex).
% 15.19/15.12  class_Groups_Ominus(tc_Complex_Ocomplex).
% 15.19/15.12  class_Fields_Ofield(tc_Complex_Ocomplex).
% 15.19/15.12  class_Groups_Ozero(tc_Complex_Ocomplex).
% 15.19/15.12  class_Rings_Oring(tc_Complex_Ocomplex).
% 15.19/15.12  class_Rings_Oidom(tc_Complex_Ocomplex).
% 15.19/15.12  class_Groups_Oone(tc_Complex_Ocomplex).
% 15.19/15.12  class_Rings_Odvd(tc_Complex_Ocomplex).
% 15.19/15.12  all T_1 (class_Rings_Oidom(T_1)->class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Groups_Ocancel__comm__monoid__add(T_1)->class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Oidom(T_1)->class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Oidom(T_1)->class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Groups_Ocancel__comm__monoid__add(T_1)->class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Groups_Ocomm__monoid__add(T_1)->class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Oordered__semiring(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Oidom(T_1)->class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Groups_Ocomm__monoid__add(T_1)->class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Fields_Ofield(T_1)->class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Groups_Oab__group__add(T_1)->class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Rings_Ozero__ne_q__one(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Ocomm__ring__1(T_1)->class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Groups_Ocomm__monoid__add(T_1)->class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Groups_Oab__group__add(T_1)->class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Fields_Ofield(T_1)->class_Divides_Oring__div(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Ocomm__ring(T_1)->class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Orderings_Oorder(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Ocomm__semiring__0(T_1)->class_Rings_Osemiring(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Orderings_Oord(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Groups_Oab__group__add(T_1)->class_Groups_Ouminus(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Olinordered__idom(T_1)->class_Groups_Osgn__if(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Ocomm__ring__1(T_1)->class_Rings_Oring__1(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Groups_Oab__group__add(T_1)->class_Groups_Ominus(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Groups_Ozero(T_1)->class_Groups_Ozero(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Ocomm__ring(T_1)->class_Rings_Oring(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Oidom(T_1)->class_Rings_Oidom(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Groups_Oone(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all T_1 (class_Rings_Ocomm__semiring__1(T_1)->class_Rings_Odvd(tc_Polynomial_Opoly(T_1))).
% 15.19/15.12  all V_y_2 V_x_2 (-hBOOL(c_fe_qual(V_x_2,V_y_2))|V_x_2=V_y_2).
% 15.19/15.12  all V_y_2 V_x_2 (V_x_2!=V_y_2|hBOOL(c_fe_qual(V_x_2,V_y_2))).
% 15.19/15.12  -(exists B_q (c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,B_q)=c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_p)& (all B_x (hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,B_q),B_x)=hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a,B_x)))))).
% 15.19/15.12  end_of_list.
% 15.19/15.12  
% 15.19/15.12  -------> usable clausifies to:
% 15.19/15.12  
% 15.19/15.12  list(usable).
% 15.19/15.12  0 [] A=A.
% 15.19/15.12  0 [] hAPP(V_f_2,$f1(V_g_2,V_f_2))!=hAPP(V_g_2,$f1(V_g_2,V_f_2))|V_f_2=V_g_2.
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(c_Polynomial_Opoly(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x)=c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(c_Polynomial_Opoly(T_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),V_x)=hAPP(c_Polynomial_Opoly(T_a,V_p),c_Groups_Oplus__class_Oplus(T_a,V_h,V_x)).
% 15.19/15.12  0 [] -class_Int_Oring__char__0(T_a)| -class_Rings_Oidom(T_a)|c_Polynomial_Opoly(T_a,V_pa_2)!=c_Polynomial_Opoly(T_a,V_q_2)|V_pa_2=V_q_2.
% 15.19/15.12  0 [] -class_Int_Oring__char__0(T_a)| -class_Rings_Oidom(T_a)|c_Polynomial_Opoly(T_a,V_pa_2)=c_Polynomial_Opoly(T_a,V_q_2)|V_pa_2!=V_q_2.
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)=c_Groups_Oplus__class_Oplus(T_a,V_c,V_a).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))=c_Groups_Oplus__class_Oplus(T_a,V_c,c_Groups_Oplus__class_Oplus(T_a,V_a,V_d)).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_d).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)).
% 15.19/15.12  0 [] -class_Groups_Oab__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_b).
% 15.19/15.12  0 [] -class_Groups_Ocancel__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_b_2)!=c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_c_2)|V_b_2=V_c_2.
% 15.19/15.12  0 [] -class_Groups_Ocancel__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_b_2)=c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_c_2)|V_b_2!=V_c_2.
% 15.19/15.12  0 [] -class_Groups_Ocancel__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2)!=c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_aa_2)|V_b_2=V_c_2.
% 15.19/15.12  0 [] -class_Groups_Ocancel__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2)=c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_aa_2)|V_b_2!=V_c_2.
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)).
% 15.19/15.12  0 [] -class_Groups_Ocancel__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_b,V_a)!=c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)|V_b=V_c.
% 15.19/15.12  0 [] -class_Groups_Ocancel__ab__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)!=c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)|V_b=V_c.
% 15.19/15.12  0 [] -class_Groups_Ocancel__semigroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)!=c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)|V_b=V_c.
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Opcompose(T_a,V_p,V_q)),V_x)=hAPP(c_Polynomial_Opoly(T_a,V_p),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)).
% 15.19/15.12  0 [] -class_Groups_Ocomm__monoid__add(T_a)|c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Omonom(T_a,V_a,V_n),c_Polynomial_Omonom(T_a,V_b,V_n))=c_Polynomial_Omonom(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_n).
% 15.19/15.12  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Polynomial_Opos__poly(T_a,V_p)| -c_Polynomial_Opos__poly(T_a,V_q)|c_Polynomial_Opos__poly(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Polynomial_Osmult(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_p)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_b,V_p)).
% 15.19/15.12  0 [] -class_Groups_Ocomm__monoid__add(T_a)|hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_n)=c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n),hAPP(c_Polynomial_Ocoeff(T_a,V_q),V_n)).
% 15.19/15.12  0 [] -class_Groups_Ocomm__monoid__add(T_a)|c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,V_b,V_q))=c_Polynomial_OpCons(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)).
% 15.19/15.12  0 [] -c_Groups_Osemigroup(T_a,V_f_2)|hAPP(hAPP(V_f_2,hAPP(hAPP(V_f_2,V_aa_2),V_b_2)),V_c_2)=hAPP(hAPP(V_f_2,V_aa_2),hAPP(hAPP(V_f_2,V_b_2),V_c_2)).
% 15.19/15.12  0 [] -c_Groups_Ocomm__monoid(T_a,V_f_2,V_z_2)|hAPP(hAPP(V_f_2,V_aa_2),V_z_2)=V_aa_2.
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_h)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_pa_2,V_h_2)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_pa_2,V_h_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_pa_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.12  0 [] -class_Groups_Ocomm__monoid__add(T_a)|c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q)=V_q.
% 15.19/15.12  0 [] -class_Groups_Ocomm__monoid__add(T_a)|c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=V_p.
% 15.19/15.12  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Polynomial_Opos__poly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 15.19/15.12  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.12  0 [] -class_Groups_Ozero(T_a)|hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_n)=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.12  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_Omonom(T_a,c_Groups_Ozero__class_Ozero(T_a),V_n)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Polynomial_Osmult(T_a,c_Groups_Ozero__class_Ozero(T_a),V_p)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Polynomial_Opcompose(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.12  0 [] -class_Groups_Ozero(T_a)|c_Groups_Ozero__class_Ozero(T_a)!=V_x_2|V_x_2=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.12  0 [] -class_Groups_Ozero(T_a)|c_Groups_Ozero__class_Ozero(T_a)=V_x_2|V_x_2!=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Polynomial_Osmult(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.12  0 [] -class_Groups_Ozero(T_a)|V_pa_2!=V_q_2|hAPP(c_Polynomial_Ocoeff(T_a,V_pa_2),B_n)=hAPP(c_Polynomial_Ocoeff(T_a,V_q_2),B_n).
% 15.19/15.12  0 [] -class_Groups_Ozero(T_a)|V_pa_2=V_q_2|hAPP(c_Polynomial_Ocoeff(T_a,V_pa_2),$f2(V_q_2,V_pa_2,T_a))!=hAPP(c_Polynomial_Ocoeff(T_a,V_q_2),$f2(V_q_2,V_pa_2,T_a)).
% 15.19/15.12  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_Ocoeff(T_a,V_x_2)!=c_Polynomial_Ocoeff(T_a,V_y_2)|V_x_2=V_y_2.
% 15.19/15.12  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_Ocoeff(T_a,V_x_2)=c_Polynomial_Ocoeff(T_a,V_y_2)|V_x_2!=V_y_2.
% 15.19/15.12  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_Omonom(T_a,V_aa_2,V_n_2)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_aa_2=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.12  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_Omonom(T_a,V_aa_2,V_n_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_aa_2!=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.12  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_OpCons(T_a,V_aa_2,V_pa_2)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_aa_2=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.12  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_OpCons(T_a,V_aa_2,V_pa_2)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.12  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_OpCons(T_a,V_aa_2,V_pa_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_aa_2!=c_Groups_Ozero__class_Ozero(T_a)|V_pa_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.12  0 [] -class_Rings_Oidom(T_a)|c_Polynomial_Osmult(T_a,V_aa_2,V_pa_2)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_aa_2=c_Groups_Ozero__class_Ozero(T_a)|V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.12  0 [] -class_Rings_Oidom(T_a)|c_Polynomial_Osmult(T_a,V_aa_2,V_pa_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_aa_2!=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.12  0 [] -class_Rings_Oidom(T_a)|c_Polynomial_Osmult(T_a,V_aa_2,V_pa_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_pa_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.12  0 [] -class_Groups_Ozero(T_a)|V_m!=V_n|hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_Omonom(T_a,V_a,V_m)),V_n)=V_a.
% 15.19/15.12  0 [] -class_Groups_Ozero(T_a)|V_m=V_n|hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_Omonom(T_a,V_a,V_m)),V_n)=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.12  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_Omonom(T_a,V_aa_2,V_n_2)!=c_Polynomial_Omonom(T_a,V_b_2,V_n_2)|V_aa_2=V_b_2.
% 15.19/15.12  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_Omonom(T_a,V_aa_2,V_n_2)=c_Polynomial_Omonom(T_a,V_b_2,V_n_2)|V_aa_2!=V_b_2.
% 15.19/15.12  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_OpCons(T_a,V_aa_2,V_pa_2)!=c_Polynomial_OpCons(T_a,V_b_2,V_q_2)|V_aa_2=V_b_2.
% 15.19/15.12  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_OpCons(T_a,V_aa_2,V_pa_2)!=c_Polynomial_OpCons(T_a,V_b_2,V_q_2)|V_pa_2=V_q_2.
% 15.19/15.12  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_OpCons(T_a,V_aa_2,V_pa_2)=c_Polynomial_OpCons(T_a,V_b_2,V_q_2)|V_aa_2!=V_b_2|V_pa_2!=V_q_2.
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Polynomial_Osmult(T_a,V_c,V_p)!=c_Polynomial_OpCons(T_a,V_a,V_p)|V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_c,V_p),c_Polynomial_OpCons(T_a,V_a,V_p))!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x)=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_h)=c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_h)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_h,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h)),c_Polynomial_OpCons(T_a,V_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h))).
% 15.19/15.12  0 [] -class_Groups_Omonoid__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=V_a.
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=V_a.
% 15.19/15.12  0 [] -class_Groups_Ocomm__monoid__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=V_a.
% 15.19/15.12  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Ozero__class_Ozero(T_a)!=c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2)|V_aa_2=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.12  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Ozero__class_Ozero(T_a)=c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2)|V_aa_2!=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.12  0 [] -class_Groups_Omonoid__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a.
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a.
% 15.19/15.12  0 [] -class_Groups_Ocomm__monoid__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a.
% 15.19/15.12  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_b_2!=c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2)|V_aa_2=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.12  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_b_2=c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_aa_2)|V_aa_2!=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Polynomial_Osmult(T_a,V_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q))=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_a,V_q)).
% 15.19/15.12  0 [] -class_Int_Oring__char__0(T_a)| -class_Rings_Oidom(T_a)|c_Polynomial_Opoly(T_a,V_pa_2)!=c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))|V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.12  0 [] -class_Int_Oring__char__0(T_a)| -class_Rings_Oidom(T_a)|c_Polynomial_Opoly(T_a,V_pa_2)=c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))|V_pa_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_c,V_q))!=c_Polynomial_OpCons(T_a,V_r,V_q)|V_r=hAPP(c_Polynomial_Opoly(T_a,V_p),V_c).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_c,V_q))!=c_Polynomial_OpCons(T_a,V_r,V_q)|V_q=c_Polynomial_Osynthetic__div(T_a,V_p,V_c).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_c,c_Polynomial_Osynthetic__div(T_a,V_p,V_c)))=c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Polynomial_Osynthetic__div(T_a,V_p,V_c)).
% 15.19/15.12  0 [] -class_Rings_Oidom(T_a)|hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_aa_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Polynomial_Oorder(T_a,V_aa_2,V_pa_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.12  0 [] -class_Rings_Oidom(T_a)|hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_aa_2)=c_Groups_Ozero__class_Ozero(T_a)|V_pa_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.12  0 [] -class_Rings_Oidom(T_a)|hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_aa_2)=c_Groups_Ozero__class_Ozero(T_a)|c_Polynomial_Oorder(T_a,V_aa_2,V_pa_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.12  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_aa_2=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.12  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2)=c_Groups_Ozero__class_Ozero(T_a)|V_aa_2!=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.12  0 [] -class_Groups_Ozero(T_b)|hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2)!=V_z_2|c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Polynomial_OpCons(T_b,V_aa_2,V_pa_2))=hAPP(hAPP(hAPP(V_f_2,V_aa_2),V_pa_2),c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,V_pa_2)).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Polynomial_Opcompose(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_q)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_q,c_Polynomial_Opcompose(T_a,V_p,V_q))).
% 15.19/15.12  0 [] -class_Groups_Ozero(T_b)|c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Polynomial_OpCons(T_b,V_aa_2,V_pa_2))=hAPP(hAPP(hAPP(V_f_2,V_aa_2),V_pa_2),c_If(T_a,c_fe_qual(V_pa_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2,c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,V_pa_2))).
% 15.19/15.12  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Polynomial_Opos__poly(T_a,c_Polynomial_OpCons(T_a,V_aa_2,V_pa_2))|c_Polynomial_Opos__poly(T_a,V_pa_2)|V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.12  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Polynomial_Opos__poly(T_a,c_Polynomial_OpCons(T_a,V_aa_2,V_pa_2))|c_Polynomial_Opos__poly(T_a,V_pa_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 15.19/15.12  0 [] -class_Rings_Olinordered__idom(T_a)|c_Polynomial_Opos__poly(T_a,c_Polynomial_OpCons(T_a,V_aa_2,V_pa_2))| -c_Polynomial_Opos__poly(T_a,V_pa_2).
% 15.19/15.12  0 [] -class_Rings_Olinordered__idom(T_a)|c_Polynomial_Opos__poly(T_a,c_Polynomial_OpCons(T_a,V_aa_2,V_pa_2))|V_pa_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_OpCons(T_a,V_a,V_q))=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_p,V_q))).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p),V_q)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_q),c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_p,V_q))).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Polynomial_Osynthetic__div(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_c)=c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Polynomial_Osynthetic__div(T_a,V_p,V_c)).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry))=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_rx),c_Groups_Otimes__class_Otimes(T_a,V_ly,V_ry)).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry))=c_Groups_Otimes__class_Otimes(T_a,V_rx,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),V_ry)).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry))=c_Groups_Otimes__class_Otimes(T_a,V_lx,c_Groups_Otimes__class_Otimes(T_a,V_ly,c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry))).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),V_rx)=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_rx),V_ly).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ly),V_rx)=c_Groups_Otimes__class_Otimes(T_a,V_lx,c_Groups_Otimes__class_Otimes(T_a,V_ly,V_rx)).
% 15.19/15.12  0 [] -class_Groups_Oab__semigroup__mult(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c)=c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_lx,c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry))=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_rx),V_ry).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_lx,c_Groups_Otimes__class_Otimes(T_a,V_rx,V_ry))=c_Groups_Otimes__class_Otimes(T_a,V_rx,c_Groups_Otimes__class_Otimes(T_a,V_lx,V_ry)).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)=c_Groups_Otimes__class_Otimes(T_a,V_b,V_a).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(c_Polynomial_Opoly(T_a,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x)=c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),c_Polynomial_Omonom(T_a,V_a,V_m),c_Polynomial_Omonom(T_a,V_b,V_n))=c_Polynomial_Omonom(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.12  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 15.19/15.12  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 15.19/15.12  0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_c,V_d)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)).
% 15.19/15.12  0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)).
% 15.19/15.12  0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)).
% 15.19/15.12  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_aa_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))|c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2).
% 15.19/15.12  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_aa_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2).
% 15.19/15.12  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))|c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2).
% 15.19/15.12  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2).
% 15.19/15.12  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_w_2,V_y_2),c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_z_2))!=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_w_2,V_z_2),c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_y_2))|V_w_2=V_x_2|V_y_2=V_z_2.
% 15.19/15.12  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_w_2,V_y_2),c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_z_2))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_w_2,V_z_2),c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_y_2))|V_w_2!=V_x_2.
% 15.19/15.12  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_w_2,V_y_2),c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_z_2))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_w_2,V_z_2),c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_y_2))|V_y_2!=V_z_2.
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_m),c_Groups_Otimes__class_Otimes(T_a,V_b,V_m))=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_m).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)).
% 15.19/15.12  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_aa_2=V_b_2|V_c_2=V_d_2|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_d_2))!=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_d_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_c_2)).
% 15.19/15.12  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_aa_2!=V_b_2|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_d_2))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_d_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_c_2)).
% 15.19/15.12  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_c_2!=V_d_2|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_d_2))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_d_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_c_2)).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_x,c_Groups_Oplus__class_Oplus(T_a,V_y,V_z))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),c_Groups_Otimes__class_Otimes(T_a,V_x,V_z)).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.12  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.12  0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Polynomial_Osmult(T_a,V_a,c_Polynomial_Osmult(T_a,V_b,V_p))=c_Polynomial_Osmult(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_p).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),V_q)=c_Polynomial_Osmult(T_a,V_a,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_p,V_q)).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_a,V_q))=c_Polynomial_Osmult(T_a,V_a,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_p,V_q)).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q),V_r)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_p,V_r),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_q,V_r)).
% 15.19/15.12  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Polynomial_Opos__poly(T_a,V_p)| -c_Polynomial_Opos__poly(T_a,V_q)|c_Polynomial_Opos__poly(T_a,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_p,V_q)).
% 15.19/15.12  0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 15.19/15.12  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 15.19/15.12  0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.12  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.12  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)).
% 15.19/15.12  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.12  0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)|V_r=c_Groups_Ozero__class_Ozero(T_a)|V_a!=V_b|V_c=V_d|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_r,V_c))!=c_Groups_Oplus__class_Oplus(T_a,V_b,c_Groups_Otimes__class_Otimes(T_a,V_r,V_d)).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Polynomial_Osynthetic__div(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_c)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Polynomial_Osmult(T_a,V_a,c_Polynomial_OpCons(T_a,V_b,V_p))=c_Polynomial_OpCons(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Polynomial_Osmult(T_a,V_a,V_p)).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_Osmult(T_a,V_a,V_p)),V_n)=c_Groups_Otimes__class_Otimes(T_a,V_a,hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n)).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Osmult(T_a,V_a,V_p)),V_x)=c_Groups_Otimes__class_Otimes(T_a,V_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Polynomial_Osmult(T_a,V_a,c_Polynomial_Omonom(T_a,V_b,V_n))=c_Polynomial_Omonom(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_n).
% 15.19/15.12  0 [] -class_Groups_Ozero(T_a)|hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_a.
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),V_x)=c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_x,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))).
% 15.19/15.12  0 [] -class_Groups_Ozero(T_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_pa_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.12  0 [] -class_Groups_Ozero(T_a)|c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_pa_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_pa_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.12  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_Omonom(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 15.19/15.12  0 [] -class_Groups_Ozero(T_b)|hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2)!=V_z_2|c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b)))=V_z_2.
% 15.19/15.12  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_x_2),c_Groups_Otimes__class_Otimes(T_a,V_y_2,V_y_2)))|V_x_2!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2!=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.12  0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_x_2),c_Groups_Otimes__class_Otimes(T_a,V_y_2,V_y_2)))|V_x_2=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.12  0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_x_2),c_Groups_Otimes__class_Otimes(T_a,V_y_2,V_y_2)))|V_y_2=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.12  0 [] -class_Rings_Olinordered__ring(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_x),c_Groups_Otimes__class_Otimes(T_a,V_y,V_y)),c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.12  0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_x_2),c_Groups_Otimes__class_Otimes(T_a,V_y_2,V_y_2))!=c_Groups_Ozero__class_Ozero(T_a)|V_x_2=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.12  0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_x_2),c_Groups_Otimes__class_Otimes(T_a,V_y_2,V_y_2))!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.12  0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_x_2),c_Groups_Otimes__class_Otimes(T_a,V_y_2,V_y_2))=c_Groups_Ozero__class_Ozero(T_a)|V_x_2!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2!=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.12  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)).
% 15.19/15.12  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)).
% 15.19/15.12  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)).
% 15.19/15.12  0 [] -class_Rings_Olinordered__comm__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)).
% 15.19/15.12  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)).
% 15.19/15.12  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)).
% 15.19/15.12  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)).
% 15.19/15.12  0 [] -class_Rings_Olinordered__idom(T_a)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 15.19/15.12  0 [] -class_Rings_Ono__zero__divisors(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)!=c_Groups_Ozero__class_Ozero(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.12  0 [] -class_Rings_Ono__zero__divisors(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)!=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.12  0 [] -class_Rings_Oring__no__zero__divisors(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_b_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_aa_2=c_Groups_Ozero__class_Ozero(T_a)|V_b_2=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.12  0 [] -class_Rings_Oring__no__zero__divisors(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a)|V_aa_2!=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.12  0 [] -class_Rings_Oring__no__zero__divisors(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a)|V_b_2!=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.12  0 [] -class_Rings_Omult__zero(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.12  0 [] -class_Rings_Omult__zero(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.12  0 [] -class_Rings_Ocomm__semiring(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)).
% 15.19/15.12  0 [] -class_Rings_Osemiring(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_e),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_e),V_c))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_e),V_c).
% 15.19/15.12  0 [] -class_Rings_Olinordered__ring(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_a),c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.12  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_c_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.12  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_c_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2).
% 15.19/15.12  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_c_2))|c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.12  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_c_2))|c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2).
% 15.19/15.12  0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_c_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2).
% 15.19/15.12  0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_c_2))| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2).
% 15.19/15.12  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_aa_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.12  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_aa_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2).
% 15.19/15.12  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_aa_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))|c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.12  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_aa_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))|c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2).
% 15.19/15.12  0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_aa_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2).
% 15.19/15.12  0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_aa_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2).
% 15.19/15.12  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_aa_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))|c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2).
% 15.19/15.12  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_aa_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2).
% 15.19/15.12  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)).
% 15.19/15.12  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.12  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_a),c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.12  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b).
% 15.19/15.12  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_b,V_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b).
% 15.19/15.12  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_aa_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))|c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2).
% 15.19/15.12  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_aa_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))| -c_Orderings_Oord__class_Oless(T_a,V_b_2,V_aa_2).
% 15.19/15.12  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.12  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.19/15.12  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)!=V_m|V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.12  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.12  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.12  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.12  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m.
% 15.19/15.12  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 15.19/15.12  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2).
% 15.19/15.12  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 15.19/15.12  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)=V_n.
% 15.19/15.12  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_b_H))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b_H)).
% 15.19/15.12  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_xa,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa,V_x),c_Groups_Otimes__class_Otimes(T_a,V_xa,V_y)).
% 15.19/15.12  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_a_H),V_b)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a_H,V_b)).
% 15.19/15.12  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2=V_n_2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)|hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)).
% 15.19/15.12  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)|V_s!=V_t.
% 15.19/15.12  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)|V_m!=V_n.
% 15.19/15.12  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n).
% 15.19/15.12  0 [] V_x=V_y|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x).
% 15.19/15.12  0 [] V_m_2=V_n_2|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2).
% 15.19/15.12  0 [] V_m_2!=V_n_2| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.12  0 [] V_m_2!=V_n_2| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2).
% 15.19/15.12  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n).
% 15.19/15.12  0 [] V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n).
% 15.19/15.12  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.12  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.19/15.12  0 [] V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 15.19/15.12  0 [] V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 15.19/15.12  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.19/15.12  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_i),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_j)).
% 15.19/15.12  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j,V_k)).
% 15.19/15.12  0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_k_2)!=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2,V_k_2)|V_m_2=V_n_2|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.12  0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_k_2)=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2,V_k_2)|V_m_2!=V_n_2.
% 15.19/15.12  0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_k_2)=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2,V_k_2)|V_k_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.12  0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2)!=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2)|V_m_2=V_n_2|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.12  0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2)=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2)|V_m_2!=V_n_2.
% 15.19/15.12  0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2)=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2)|V_k_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.12  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2,V_k_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2).
% 15.19/15.12  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2,V_k_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.12  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2,V_k_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.12  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2).
% 15.19/15.12  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.12  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.12  0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.12  0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.12  0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.12  0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.12  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2).
% 15.19/15.12  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 15.19/15.12  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2).
% 15.19/15.13  0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.13  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_k_2)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2)|V_m_2=V_n_2.
% 15.19/15.13  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_k_2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2)|V_m_2!=V_n_2.
% 15.19/15.13  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)|V_m_2=V_n_2.
% 15.19/15.13  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)|V_m_2!=V_n_2.
% 15.19/15.13  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k)).
% 15.19/15.13  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_x,V_z)).
% 15.19/15.13  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_i).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_i).
% 15.19/15.13  0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_m),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_n)).
% 15.19/15.13  0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,V_k)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_k,V_l)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_l)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_k).
% 15.19/15.13  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),V_ya)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_ya),c_Groups_Otimes__class_Otimes(T_a,V_y,V_ya)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)|c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2)!=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2)|V_m_2=V_n_2.
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)|c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2)=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2)|V_m_2!=V_n_2.
% 15.19/15.13  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_Ocoeff(T_a,c_Polynomial_OpCons(T_a,V_aa_2,V_pa_2))=c_Nat_Onat_Onat__case(T_a,V_aa_2,c_Polynomial_Ocoeff(T_a,V_pa_2)).
% 15.19/15.13  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Polynomial_Opos__poly(T_a,V_pa_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Polynomial_Ocoeff(T_a,V_pa_2),c_Polynomial_Odegree(T_a,V_pa_2))).
% 15.19/15.13  0 [] -class_Rings_Olinordered__idom(T_a)|c_Polynomial_Opos__poly(T_a,V_pa_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(c_Polynomial_Ocoeff(T_a,V_pa_2),c_Polynomial_Odegree(T_a,V_pa_2))).
% 15.19/15.13  0 [] -class_Rings_Ocomm__semiring__0(T_a)|hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_p,V_q)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)))=c_Groups_Otimes__class_Otimes(T_a,hAPP(c_Polynomial_Ocoeff(T_a,V_p),c_Polynomial_Odegree(T_a,V_p)),hAPP(c_Polynomial_Ocoeff(T_a,V_q),c_Polynomial_Odegree(T_a,V_q))).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),$f3(V_j,V_i)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,$f3(V_j,V_i))=V_j.
% 15.19/15.13  0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n)=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,V_m).
% 15.19/15.13  0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n),V_k)=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,V_k)).
% 15.19/15.13  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Polynomial_Odegree(T_a,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(T_a,V_p,V_h))=c_Polynomial_Odegree(T_a,V_p).
% 15.19/15.13  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_Odegree(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.13  0 [] -class_Groups_Ozero(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Polynomial_Odegree(T_a,c_Polynomial_Omonom(T_a,V_a,V_n))=V_n.
% 15.19/15.13  0 [] -class_Groups_Ocomm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q),c_Polynomial_Odegree(T_a,V_p))|c_Polynomial_Odegree(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q))=c_Polynomial_Odegree(T_a,V_p).
% 15.19/15.13  0 [] -class_Groups_Ocomm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q))|c_Polynomial_Odegree(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q))=c_Polynomial_Odegree(T_a,V_q).
% 15.19/15.13  0 [] -class_Groups_Ocomm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q),V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_n).
% 15.19/15.13  0 [] hAPP(c_Nat_Onat_Onat__case(T_a,V_f1_2,V_f2_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_f1_2.
% 15.19/15.13  0 [] -class_Rings_Oidom(T_a)|V_a!=c_Groups_Ozero__class_Ozero(T_a)|c_Polynomial_Odegree(T_a,c_Polynomial_Osmult(T_a,V_a,V_p))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.13  0 [] -class_Rings_Oidom(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Polynomial_Odegree(T_a,c_Polynomial_Osmult(T_a,V_a,V_p))=c_Polynomial_Odegree(T_a,V_p).
% 15.19/15.13  0 [] -class_Groups_Ozero(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)|hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n)=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_Groups_Ozero(T_a)|hAPP(c_Polynomial_Ocoeff(T_a,V_pa_2),c_Polynomial_Odegree(T_a,V_pa_2))!=c_Groups_Ozero__class_Ozero(T_a)|V_pa_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.13  0 [] -class_Groups_Ozero(T_a)|hAPP(c_Polynomial_Ocoeff(T_a,V_pa_2),c_Polynomial_Odegree(T_a,V_pa_2))=c_Groups_Ozero__class_Ozero(T_a)|V_pa_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.13  0 [] -class_Groups_Ozero(T_a)|V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|hAPP(c_Polynomial_Ocoeff(T_a,V_p),c_Polynomial_Odegree(T_a,V_p))!=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.13  0 [] -class_Rings_Oidom(T_a)|V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_q=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Polynomial_Odegree(T_a,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_p,V_q))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)).
% 15.19/15.13  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Polynomial_Osynthetic__div(T_a,V_pa_2,V_c_2)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Polynomial_Odegree(T_a,V_pa_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.13  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Polynomial_Osynthetic__div(T_a,V_pa_2,V_c_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Polynomial_Odegree(T_a,V_pa_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.13  0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2)!=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2)|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=V_n_2.
% 15.19/15.13  0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2)=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2)|V_k_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.13  0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2)=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2)|V_m_2!=V_n_2.
% 15.19/15.13  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i,V_u),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j,V_u),V_k))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_u),V_k).
% 15.19/15.13  0 [] -class_Fields_Ofield(T_a)| -c_Polynomial_Opdivmod__rel(T_a,V_x_2,V_y_2,V_q_2,V_r_2)|V_x_2=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_q_2,V_y_2),V_r_2).
% 15.19/15.13  0 [] -class_Fields_Ofield(T_a)| -c_Polynomial_Opdivmod__rel(T_a,V_x_2,V_y_2,V_q_2,V_r_2)|V_y_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_q_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.13  0 [] -class_Fields_Ofield(T_a)| -c_Polynomial_Opdivmod__rel(T_a,V_x_2,V_y_2,V_q_2,V_r_2)|V_y_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_r_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_r_2),c_Polynomial_Odegree(T_a,V_y_2)).
% 15.19/15.13  0 [] -class_Fields_Ofield(T_a)|c_Polynomial_Opdivmod__rel(T_a,V_x_2,V_y_2,V_q_2,V_r_2)|V_x_2!=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_q_2,V_y_2),V_r_2)|V_y_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_r_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.13  0 [] -class_Fields_Ofield(T_a)|c_Polynomial_Opdivmod__rel(T_a,V_x_2,V_y_2,V_q_2,V_r_2)|V_x_2!=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_q_2,V_y_2),V_r_2)|V_y_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_r_2),c_Polynomial_Odegree(T_a,V_y_2)).
% 15.19/15.13  0 [] -class_Fields_Ofield(T_a)|c_Polynomial_Opdivmod__rel(T_a,V_x_2,V_y_2,V_q_2,V_r_2)|V_x_2!=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_q_2,V_y_2),V_r_2)|V_q_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_y_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.13  0 [] -class_Fields_Ofield(T_a)|c_Polynomial_Opdivmod__rel(T_a,V_x_2,V_y_2,V_q_2,V_r_2)|V_x_2!=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_q_2,V_y_2),V_r_2)|V_q_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_r_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.13  0 [] -class_Fields_Ofield(T_a)|c_Polynomial_Opdivmod__rel(T_a,V_x_2,V_y_2,V_q_2,V_r_2)|V_x_2!=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_q_2,V_y_2),V_r_2)|V_q_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_r_2),c_Polynomial_Odegree(T_a,V_y_2)).
% 15.19/15.13  0 [] -class_Groups_Ozero(T_a)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)|hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n)!=c_Groups_Ozero__class_Ozero(T_a)|V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n).
% 15.19/15.13  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_OpCons(T_a,V_aa_2,V_pa_2)=c_Polynomial_OAbs__poly(T_a,c_Nat_Onat_Onat__case(T_a,V_aa_2,c_Polynomial_Ocoeff(T_a,V_pa_2))).
% 15.19/15.13  0 [] -class_Groups_Ozero(T_a)|V_p!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_p)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.13  0 [] -class_Groups_Ozero(T_a)|V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(T_a,V_p)=c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)).
% 15.19/15.13  0 [] -class_Groups_Ozero(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Polynomial_Odegree(T_a,V_p))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,$f4(V_p,V_n,T_a)).
% 15.19/15.13  0 [] -class_Groups_Ozero(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Polynomial_Odegree(T_a,V_p))|hAPP(c_Polynomial_Ocoeff(T_a,V_p),$f4(V_p,V_n,T_a))!=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_Groups_Ozero(T_a)|V_p!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.13  0 [] -class_Groups_Ozero(T_a)|V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p))=c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)).
% 15.19/15.13  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Polynomial_Opcompose(T_a,V_p,V_q)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q))).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n)).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(V_n)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_n_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.13  0 [] -class_Fields_Ofield(T_a)| -c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q1,V_r1)| -c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q2,V_r2)|V_q1=V_q2.
% 15.19/15.13  0 [] -class_Fields_Ofield(T_a)| -c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q1,V_r1)| -c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q2,V_r2)|V_r1=V_r2.
% 15.19/15.13  0 [] -class_Fields_Ofield(T_a)| -c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q1,V_r1)| -c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q2,V_r2)|V_r1=V_r2.
% 15.19/15.13  0 [] -class_Fields_Ofield(T_a)| -c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q1,V_r1)| -c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q2,V_r2)|V_q1=V_q2.
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_m_2),V_n_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_m_2),V_n_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))|V_n_2=V_m_2.
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))|V_n_2!=V_m_2.
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 15.19/15.13  0 [] c_Nat_OSuc(V_x)!=c_Nat_OSuc(V_y)|V_x=V_y.
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|V_m=c_Nat_OSuc(V_n).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)|V_m=V_n.
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j,V_k)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_k).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)).
% 15.19/15.13  0 [] V_m!=V_n|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,V_m_2).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_m_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,V_m_2).
% 15.19/15.13  0 [] c_Nat_OSuc(V_nat_2)!=c_Nat_OSuc(V_nat_H_2)|V_nat_2=V_nat_H_2.
% 15.19/15.13  0 [] c_Nat_OSuc(V_nat_2)=c_Nat_OSuc(V_nat_H_2)|V_nat_2!=V_nat_H_2.
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2=c_Nat_OSuc(V_n_2).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))|V_m_2!=c_Nat_OSuc(V_n_2).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_m_2).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_n).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(V_n),V_n).
% 15.19/15.13  0 [] c_Nat_OSuc(V_n)!=V_n.
% 15.19/15.13  0 [] V_n!=c_Nat_OSuc(V_n).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2).
% 15.19/15.13  0 [] -class_Groups_Ozero(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p))).
% 15.19/15.13  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b).
% 15.19/15.13  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b).
% 15.19/15.13  0 [] -class_Groups_Oordered__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)).
% 15.19/15.13  0 [] -class_Groups_Oordered__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_a),c_Groups_Oplus__class_Oplus(T_a,V_c,V_b)).
% 15.19/15.13  0 [] -class_Groups_Oordered__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)).
% 15.19/15.13  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_aa_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,V_b_2).
% 15.19/15.13  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_aa_2),c_Groups_Oplus__class_Oplus(T_a,V_c_2,V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,V_b_2).
% 15.19/15.13  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,V_b_2).
% 15.19/15.13  0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_c_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_c_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,V_b_2).
% 15.19/15.13  0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(V_m).
% 15.19/15.13  0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(V_nat_H).
% 15.19/15.13  0 [] c_Nat_OSuc(V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.13  0 [] c_Nat_OSuc(V_nat_H_1)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.13  0 [] c_Groups_Ozero__class_Ozero(tc_Nat_Onat)!=c_Nat_OSuc(V_m).
% 15.19/15.13  0 [] c_Nat_OSuc(V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|V_m=V_n.
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i),V_k).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Nat_OSuc(V_m)=V_n|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_m))|V_m=V_n.
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))|V_n_2=V_m_2.
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_m_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2))|V_n_2!=V_m_2.
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2),c_Nat_OSuc(V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m_2),c_Nat_OSuc(V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2=V_n_2.
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))|V_m_2!=V_n_2.
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_m_2)).
% 15.19/15.13  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)).
% 15.19/15.13  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)).
% 15.19/15.13  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.13  0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_m_2)!=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_n_2)|V_m_2=V_n_2.
% 15.19/15.13  0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_m_2)=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_n_2)|V_m_2!=V_n_2.
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 15.19/15.13  0 [] V_m!=V_n|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|V_m=V_n|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2=V_n_2.
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2!=V_n_2.
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2!=V_n_2.
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2=V_n_2.
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,V_y).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_l)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_l)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_j)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_m)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)|V_n_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,$f5(V_n_2,V_m_2)).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2)|V_n_2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m)).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,V_z)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_l)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j,V_l)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_i),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_j)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j,V_k)).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_m))).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_m)).
% 15.19/15.13  0 [] hAPP(c_Nat_Onat_Onat__case(T_a,V_f1_2,V_f2_2),c_Nat_OSuc(V_nat_2))=hAPP(V_f2_2,V_nat_2).
% 15.19/15.13  0 [] -class_Fields_Ofield(T_a)|c_Polynomial_Opdivmod__rel(T_a,V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x).
% 15.19/15.13  0 [] -class_Fields_Ofield(T_a)|c_Polynomial_Opdivmod__rel(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_y,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 15.19/15.13  0 [] -class_Fields_Ofield(T_a)| -c_Polynomial_Opdivmod__rel(T_a,V_x_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q_2,V_r_2)|V_q_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.13  0 [] -class_Fields_Ofield(T_a)| -c_Polynomial_Opdivmod__rel(T_a,V_x_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q_2,V_r_2)|V_r_2=V_x_2.
% 15.19/15.13  0 [] -class_Fields_Ofield(T_a)|c_Polynomial_Opdivmod__rel(T_a,V_x_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q_2,V_r_2)|V_q_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_r_2!=V_x_2.
% 15.19/15.13  0 [] -class_Fields_Ofield(T_a)| -c_Polynomial_Opdivmod__rel(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_y_2,V_q_2,V_r_2)|V_q_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.13  0 [] -class_Fields_Ofield(T_a)| -c_Polynomial_Opdivmod__rel(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_y_2,V_q_2,V_r_2)|V_r_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.13  0 [] -class_Fields_Ofield(T_a)|c_Polynomial_Opdivmod__rel(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_y_2,V_q_2,V_r_2)|V_q_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_r_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.13  0 [] -class_Fields_Ofield(T_a)| -c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q,V_r)|c_Polynomial_Opdivmod__rel(T_a,c_Polynomial_Osmult(T_a,V_a,V_x),V_y,c_Polynomial_Osmult(T_a,V_a,V_q),c_Polynomial_Osmult(T_a,V_a,V_r)).
% 15.19/15.13  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_OAbs__poly(T_a,c_Polynomial_Ocoeff(T_a,V_x_2))=V_x_2.
% 15.19/15.13  0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)).
% 15.19/15.13  0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)).
% 15.19/15.13  0 [] -class_Rings_Oordered__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d)).
% 15.19/15.13  0 [] -class_Rings_Oordered__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d)).
% 15.19/15.13  0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)).
% 15.19/15.13  0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)).
% 15.19/15.13  0 [] -class_Rings_Oordered__comm__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)).
% 15.19/15.13  0 [] -class_Rings_Oordered__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)).
% 15.19/15.13  0 [] -class_Rings_Oordered__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)).
% 15.19/15.13  0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)).
% 15.19/15.13  0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_a),c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Rings_Oordered__cancel__semiring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)).
% 15.19/15.13  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2).
% 15.19/15.13  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2).
% 15.19/15.13  0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2).
% 15.19/15.13  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2).
% 15.19/15.13  0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Rings_Olinordered__ring(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_a)).
% 15.19/15.13  0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 15.19/15.13  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 15.19/15.13  0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)).
% 15.19/15.13  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)|c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_x_2=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)|c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)|c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2)=c_Groups_Ozero__class_Ozero(T_a)|V_x_2!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2!=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)).
% 15.19/15.13  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)).
% 15.19/15.13  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)).
% 15.19/15.13  0 [] -class_Groups_Oordered__cancel__ab__semigroup__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_c,V_d)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)|V_n_2=c_Nat_OSuc($f6(V_n_2)).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)|V_n_2!=c_Nat_OSuc(B_m).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=c_Nat_OSuc($f7(V_n_2,V_m_2)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f7(V_n_2,V_m_2),V_n_2).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))|V_m_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Nat_OSuc(V_n_2))|V_m_2!=c_Nat_OSuc(B_j)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_n_2).
% 15.19/15.13  0 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.13  0 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.19/15.13  0 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.13  0 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.19/15.13  0 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.13  0 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.19/15.13  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.13  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.19/15.13  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.13  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.19/15.13  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.13  0 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,V_n_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.19/15.13  0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.19/15.13  0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.19/15.13  0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_m_2!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|V_n_2!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_n_2=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,$f8(V_n_2,V_m_2))).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2)|V_n_2!=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m_2,B_k)).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_i))).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_m))).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_k_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.13  0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n)).
% 15.19/15.13  0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n)).
% 15.19/15.13  0 [] -class_Groups_Ozero(T_a)|hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),c_Nat_OSuc(V_n))=hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n).
% 15.19/15.13  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Polynomial_Osmult(T_a,V_a,V_p)),c_Polynomial_Odegree(T_a,V_p)).
% 15.19/15.13  0 [] -class_Groups_Ocomm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q),V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_n).
% 15.19/15.13  0 [] -class_Groups_Ozero(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Polynomial_Omonom(T_a,V_a,V_n)),V_n).
% 15.19/15.13  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b).
% 15.19/15.13  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b).
% 15.19/15.13  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 15.19/15.13  0 [] -class_Rings_Olinordered__semiring(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 15.19/15.13  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 15.19/15.13  0 [] -class_Rings_Olinordered__semiring(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 15.19/15.13  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_c,V_d)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d)).
% 15.19/15.13  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_d)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d)).
% 15.19/15.13  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_c,V_d)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d)).
% 15.19/15.13  0 [] -class_Rings_Olinordered__semiring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_c,V_d)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d)).
% 15.19/15.13  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_aa_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,V_aa_2).
% 15.19/15.13  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_aa_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,V_aa_2).
% 15.19/15.13  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_aa_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,V_b_2).
% 15.19/15.13  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_aa_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,V_b_2).
% 15.19/15.13  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)).
% 15.19/15.13  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)).
% 15.19/15.13  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)).
% 15.19/15.13  0 [] -class_Groups_Oordered__comm__monoid__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)).
% 15.19/15.13  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_x_2),c_Groups_Otimes__class_Otimes(T_a,V_y_2,V_y_2)),c_Groups_Ozero__class_Ozero(T_a))|V_x_2=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_Rings_Olinordered__ring__strict(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_x_2),c_Groups_Otimes__class_Otimes(T_a,V_y_2,V_y_2)),c_Groups_Ozero__class_Ozero(T_a))|V_y_2=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_Rings_Olinordered__ring__strict(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_x_2),c_Groups_Otimes__class_Otimes(T_a,V_y_2,V_y_2)),c_Groups_Ozero__class_Ozero(T_a))|V_x_2!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2!=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_Rings_Olinordered__ring(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_x),c_Groups_Otimes__class_Otimes(T_a,V_y,V_y))).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,V_m)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2,V_k_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2,V_k_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2,V_k_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.13  0 [] -class_Fields_Ofield(T_a)| -c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q,V_r)| -c_Polynomial_Opdivmod__rel(T_a,V_q,V_z,V_q_H,V_r_H)|c_Polynomial_Opdivmod__rel(T_a,V_x,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_y,V_z),V_q_H,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_y,V_r_H),V_r)).
% 15.19/15.13  0 [] -class_Groups_Ozero(T_a)|hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n)=c_Groups_Ozero__class_Ozero(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,c_Polynomial_Odegree(T_a,V_p)).
% 15.19/15.13  0 [] -class_Groups_Ozero(T_a)|V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Polynomial_Odegree(T_a,c_Polynomial_OpCons(T_a,V_a,V_p))=c_Nat_OSuc(c_Polynomial_Odegree(T_a,V_p)).
% 15.19/15.13  0 [] -class_Groups_Ozero(T_a)|c_Polynomial_Omonom(T_a,V_a,c_Nat_OSuc(V_n))=c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Polynomial_Omonom(T_a,V_a,V_n)).
% 15.19/15.13  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),V_p,V_q)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q))).
% 15.19/15.13  0 [] -class_Rings_Oidom(T_a)|V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Oorder(T_a,V_a,V_p),c_Polynomial_Odegree(T_a,V_p)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|V_x=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_x=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.19/15.13  0 [] -class_Orderings_Opreorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_x).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_l_2)|V_l_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,$f9(V_l_2,V_k_2)).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_l_2)|V_l_2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,B_n).
% 15.19/15.13  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2).
% 15.19/15.13  0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2).
% 15.19/15.13  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2).
% 15.19/15.13  0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2).
% 15.19/15.13  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 15.19/15.13  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2).
% 15.19/15.13  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 15.19/15.13  0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|V_x_2=V_y_2.
% 15.19/15.13  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x).
% 15.19/15.13  0 [] -class_Orderings_Oord(T_b)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)|c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)).
% 15.19/15.13  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_x).
% 15.19/15.13  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|V_x=V_y.
% 15.19/15.13  0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_z)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_z).
% 15.19/15.13  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)|V_x=V_y.
% 15.19/15.13  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)|V_b!=V_c|c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_a).
% 15.19/15.13  0 [] -class_Orderings_Oord(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)|V_b!=V_c|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_c).
% 15.19/15.13  0 [] -class_Orderings_Oorder(T_a)|V_a!=V_b| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,V_c,V_a).
% 15.19/15.13  0 [] -class_Orderings_Oord(T_a)|V_a!=V_b| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_c).
% 15.19/15.13  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|V_x_2=V_y_2.
% 15.19/15.13  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 15.19/15.13  0 [] -class_Orderings_Oord(T_b)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)|c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_2)).
% 15.19/15.13  0 [] -class_Orderings_Opreorder(T_a)|V_x!=V_y|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y).
% 15.19/15.13  0 [] -class_Orderings_Oorder(T_a)|V_x_2!=V_y_2|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2).
% 15.19/15.13  0 [] -class_Orderings_Oorder(T_a)|V_x_2!=V_y_2|c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2).
% 15.19/15.13  0 [] -class_Orderings_Oorder(T_a)|V_x_2=V_y_2| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2).
% 15.19/15.13  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x).
% 15.19/15.13  0 [] -class_Orderings_Oord(T_b)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)|c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x)).
% 15.19/15.13  0 [] -class_Orderings_Oord(T_b)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)| -c_Orderings_Oord__class_Oless__e_q(T_b,hAPP(V_f_2,$f10(V_g_2,V_f_2,T_a,T_b)),hAPP(V_g_2,$f10(V_g_2,V_f_2,T_a,T_b))).
% 15.19/15.13  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 15.19/15.13  0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 15.19/15.13  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless(T_a,V_z,V_y)|c_Orderings_Oord__class_Oless(T_a,V_z,V_x).
% 15.19/15.13  0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_z)|c_Orderings_Oord__class_Oless(T_a,V_x,V_z).
% 15.19/15.13  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)|V_b!=V_c|c_Orderings_Oord__class_Oless(T_a,V_c,V_a).
% 15.19/15.13  0 [] -class_Orderings_Oord(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)|V_b!=V_c|c_Orderings_Oord__class_Oless(T_a,V_a,V_c).
% 15.19/15.13  0 [] -class_Orderings_Oorder(T_a)|V_a!=V_b| -c_Orderings_Oord__class_Oless(T_a,V_c,V_b)|c_Orderings_Oord__class_Oless(T_a,V_c,V_a).
% 15.19/15.13  0 [] -class_Orderings_Oord(T_a)|V_a!=V_b| -c_Orderings_Oord__class_Oless(T_a,V_b,V_c)|c_Orderings_Oord__class_Oless(T_a,V_a,V_c).
% 15.19/15.13  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 15.19/15.13  0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a).
% 15.19/15.13  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_y!=V_x.
% 15.19/15.13  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x!=V_y.
% 15.19/15.13  0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 15.19/15.13  0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 15.19/15.13  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x!=V_y.
% 15.19/15.13  0 [] -class_Orderings_Olinorder(T_a)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 15.19/15.13  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2=V_y_2.
% 15.19/15.13  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 15.19/15.13  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y|c_Orderings_Oord__class_Oless(T_a,V_y,V_x).
% 15.19/15.13  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)|V_x_2=V_y_2.
% 15.19/15.13  0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2).
% 15.19/15.13  0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 15.19/15.13  0 [] -class_Orderings_Olinorder(T_a)|V_x_2=V_y_2|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2).
% 15.19/15.13  0 [] -class_Orderings_Olinorder(T_a)|V_x_2!=V_y_2| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2).
% 15.19/15.13  0 [] -class_Orderings_Olinorder(T_a)|V_x_2!=V_y_2| -c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2).
% 15.19/15.13  0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_x).
% 15.19/15.13  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless(T_a,V_z,V_y)|c_Orderings_Oord__class_Oless(T_a,V_z,V_x).
% 15.19/15.13  0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_z)|c_Orderings_Oord__class_Oless(T_a,V_x,V_z).
% 15.19/15.13  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_z,V_y)|c_Orderings_Oord__class_Oless(T_a,V_z,V_x).
% 15.19/15.13  0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_z)|c_Orderings_Oord__class_Oless(T_a,V_x,V_z).
% 15.19/15.13  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)|V_a=V_b|c_Orderings_Oord__class_Oless(T_a,V_b,V_a).
% 15.19/15.13  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)|V_a=V_b|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 15.19/15.13  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|V_x=V_y.
% 15.19/15.13  0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2=V_y_2.
% 15.19/15.13  0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 15.19/15.13  0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y).
% 15.19/15.13  0 [] -class_Orderings_Olinorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y).
% 15.19/15.13  0 [] -class_Orderings_Oorder(T_a)|V_a=V_b| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)|c_Orderings_Oord__class_Oless(T_a,V_b,V_a).
% 15.19/15.13  0 [] -class_Orderings_Oorder(T_a)|V_a=V_b| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless(T_a,V_a,V_b).
% 15.19/15.13  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|V_x_2=V_y_2.
% 15.19/15.13  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 15.19/15.13  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y).
% 15.19/15.13  0 [] -class_Orderings_Olinorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_x).
% 15.19/15.13  0 [] -class_Orderings_Oorder(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|V_x_2=V_y_2.
% 15.19/15.13  0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2).
% 15.19/15.13  0 [] -class_Orderings_Oorder(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 15.19/15.13  0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2).
% 15.19/15.13  0 [] -class_Orderings_Opreorder(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2).
% 15.19/15.13  0 [] -class_Orderings_Opreorder(T_a)|c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,V_y_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2).
% 15.19/15.13  0 [] -class_Groups_Ozero(T_a)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,$f11(V_p,V_n,T_a))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n).
% 15.19/15.13  0 [] -class_Groups_Ozero(T_a)|hAPP(c_Polynomial_Ocoeff(T_a,V_p),$f11(V_p,V_n,T_a))!=c_Groups_Ozero__class_Ozero(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n).
% 15.19/15.13  0 [] -class_Rings_Olinordered__semiring__1__strict(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_a)| -c_Orderings_Oord__class_Oless(T_a,V_y,V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)|c_Groups_Oplus__class_Oplus(T_a,V_u,V_v)!=c_Groups_Oone__class_Oone(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_u,V_x),c_Groups_Otimes__class_Otimes(T_a,V_v,V_y)),V_a).
% 15.19/15.13  0 [] c_Nat_Onat_Onat__size(c_Nat_OSuc(V_nat))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Onat_Onat__size(V_nat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i_2,V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j_2,V_u_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2),V_u_2),V_n_2)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i_2,V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j_2,V_u_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2),V_u_2),V_n_2)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,V_i_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i_2,V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j_2,V_u_2),V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2),V_u_2),V_m_2),V_n_2).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,V_i_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i_2,V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j_2,V_u_2),V_n_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2),V_u_2),V_m_2),V_n_2).
% 15.19/15.13  0 [] -class_Orderings_Oord(T_b)| -c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2).
% 15.19/15.13  0 [] -class_Orderings_Oord(T_b)| -c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_g_2,V_f_2).
% 15.19/15.13  0 [] -class_Orderings_Oord(T_b)|c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_f_2,V_g_2)|c_Orderings_Oord__class_Oless__e_q(tc_fun(T_a,T_b),V_g_2,V_f_2).
% 15.19/15.13  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a.
% 15.19/15.13  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a,V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_Groups_Oab__group__add(T_a)|V_aa_2!=V_b_2|c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_Groups_Oab__group__add(T_a)|V_aa_2=V_b_2|c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)!=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_aa_2=V_b_2.
% 15.19/15.13  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a)|V_aa_2!=V_b_2.
% 15.19/15.13  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)!=c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2,V_d_2).
% 15.19/15.13  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)!=c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2,V_d_2).
% 15.19/15.13  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)!=c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,V_d_2).
% 15.19/15.13  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)!=c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)|c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,V_d_2).
% 15.19/15.13  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))=c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))).
% 15.19/15.13  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_b_H))=c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b_H)).
% 15.19/15.13  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_xa,c_Groups_Ominus__class_Ominus(T_a,V_x,V_y))=c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa,V_x),c_Groups_Otimes__class_Otimes(T_a,V_xa,V_y)).
% 15.19/15.13  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_a_H),V_b)=c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_a_H,V_b)).
% 15.19/15.13  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_y),V_ya)=c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_ya),c_Groups_Otimes__class_Otimes(T_a,V_y,V_ya)).
% 15.19/15.13  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_b)=V_a.
% 15.19/15.13  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b)=V_a.
% 15.19/15.13  0 [] -class_Rings_Ozero__ne_q__one(T_a)|c_Groups_Ozero__class_Ozero(T_a)!=c_Groups_Oone__class_Oone(T_a).
% 15.19/15.13  0 [] -class_Rings_Ozero__ne_q__one(T_a)|c_Groups_Oone__class_Oone(T_a)!=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_m)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m=V_n.
% 15.19/15.13  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_m)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.13  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=V_m.
% 15.19/15.13  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.13  0 [] -class_Groups_Omonoid__mult(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a),V_a)=V_a.
% 15.19/15.13  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a),V_a)=V_a.
% 15.19/15.13  0 [] -class_Groups_Ocomm__monoid__mult(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oone__class_Oone(T_a),V_a)=V_a.
% 15.19/15.13  0 [] -class_Groups_Omonoid__mult(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oone__class_Oone(T_a))=V_a.
% 15.19/15.13  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oone__class_Oone(T_a))=V_a.
% 15.19/15.13  0 [] -class_Groups_Ocomm__monoid__mult(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Oone__class_Oone(T_a))=V_a.
% 15.19/15.13  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n).
% 15.19/15.13  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n),c_Nat_OSuc(V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_k).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n),V_k).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_l)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)).
% 15.19/15.13  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n).
% 15.19/15.13  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n).
% 15.19/15.13  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_k)).
% 15.19/15.13  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_n)=V_m.
% 15.19/15.13  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n),V_n)=V_m.
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_l),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_l)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_n)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i))=V_i.
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_m_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_n_2)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)!=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)|V_m_2=V_n_2.
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_m_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_n_2)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)|V_m_2!=V_n_2.
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_m)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_m_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_n_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_m_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_n_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.13  0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_m),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_n)).
% 15.19/15.13  0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_k)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,V_k)).
% 15.19/15.13  0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,V_b,V_q))=c_Polynomial_OpCons(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)).
% 15.19/15.13  0 [] -class_Groups_Oab__group__add(T_a)|hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_n)=c_Groups_Ominus__class_Ominus(T_a,hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n),hAPP(c_Polynomial_Ocoeff(T_a,V_q),V_n)).
% 15.19/15.13  0 [] -class_Rings_Ocomm__ring(T_a)|c_Polynomial_Osmult(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_p)=c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_b,V_p)).
% 15.19/15.13  0 [] -class_Rings_Ocomm__ring(T_a)|hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x)=c_Groups_Ominus__class_Ominus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)).
% 15.19/15.13  0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_Omonom(T_a,V_a,V_n),c_Polynomial_Omonom(T_a,V_b,V_n))=c_Polynomial_Omonom(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_n).
% 15.19/15.13  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(c_Polynomial_Opoly(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_x)=c_Groups_Oone__class_Oone(T_a).
% 15.19/15.13  0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)!=c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)|V_aa_2!=V_b_2|V_c_2=V_d_2.
% 15.19/15.13  0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2)!=c_Groups_Ominus__class_Ominus(T_a,V_c_2,V_d_2)|V_aa_2=V_b_2|V_c_2!=V_d_2.
% 15.19/15.13  0 [] -class_Groups_Oone(T_a)|c_Groups_Oone__class_Oone(T_a)!=V_x_2|V_x_2=c_Groups_Oone__class_Oone(T_a).
% 15.19/15.13  0 [] -class_Groups_Oone(T_a)|c_Groups_Oone__class_Oone(T_a)=V_x_2|V_x_2!=c_Groups_Oone__class_Oone(T_a).
% 15.19/15.13  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_k)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_k),V_j).
% 15.19/15.13  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_n.
% 15.19/15.13  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n).
% 15.19/15.13  0 [] -class_Rings_Ocomm__semiring__0(T_a)|c_Polynomial_Odegree(T_a,c_Polynomial_Osynthetic__div(T_a,V_p,V_c))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 15.19/15.13  0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_m_2=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.19/15.13  0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_n_2=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.19/15.13  0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_m_2!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_n_2!=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.19/15.13  0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_n.
% 15.19/15.13  0 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)!=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.19/15.13  0 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)!=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2)|V_n_2=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.19/15.13  0 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2)|V_m_2!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_n_2!=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.19/15.13  0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n)=V_n.
% 15.19/15.13  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Polynomial_Osmult(T_a,c_Groups_Oone__class_Oone(T_a),V_p)=V_p.
% 15.19/15.13  0 [] c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=V_n.
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|V_n=c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))).
% 15.19/15.13  0 [] V_m!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)=V_n.
% 15.19/15.13  0 [] V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)).
% 15.19/15.13  0 [] V_m!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.13  0 [] V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)).
% 15.19/15.13  0 [] -class_Rings_Ocomm__semiring__1(T_a)|V_n!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_n)=c_Groups_Oone__class_Oone(T_a).
% 15.19/15.13  0 [] -class_Rings_Ocomm__semiring__1(T_a)|V_n=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_n)=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_a),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_a),V_b)),c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ominus__class_Ominus(T_a,V_y,V_b))).
% 15.19/15.13  0 [] -class_Rings_Oring(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_e_2),V_c_2)!=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_d_2)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2),V_e_2),V_c_2)=V_d_2.
% 15.19/15.13  0 [] -class_Rings_Oring(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_e_2),V_c_2)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_d_2)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2),V_e_2),V_c_2)!=V_d_2.
% 15.19/15.13  0 [] -class_Rings_Oring(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_e_2),V_c_2)!=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_d_2)|V_c_2=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_aa_2),V_e_2),V_d_2).
% 15.19/15.13  0 [] -class_Rings_Oring(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_e_2),V_c_2)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_d_2)|V_c_2!=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_aa_2),V_e_2),V_d_2).
% 15.19/15.13  0 [] -class_Rings_Olinordered__semidom(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)).
% 15.19/15.13  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Rings_Olinordered__semidom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oone__class_Oone(T_a)).
% 15.19/15.13  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Rings_Olinordered__semidom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_m)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_n)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a,V_m,V_n)).
% 15.19/15.13  0 [] -class_Rings_Olinordered__semidom(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))).
% 15.19/15.13  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_m,V_m)=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)),V_m).
% 15.19/15.13  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_m,c_Groups_Otimes__class_Otimes(T_a,V_a,V_m))=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a)),V_m).
% 15.19/15.13  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_m),V_m)=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a)),V_m).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_m_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_m_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),c_Nat_OSuc(V_m)).
% 15.19/15.13  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,V_n)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.13  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_n_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.13  0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_n_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)=c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=V_m.
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_c,V_a)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_b,V_c)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_m_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_n_2)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_m_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_n_2)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k),V_i)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_j,V_i),V_k).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)!=V_k_2|V_j_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)=V_k_2|V_j_2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_i_2).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n)=V_m.
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_j_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k_2,V_j_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j),V_k).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))=V_m.
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,V_m),V_k)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2),V_i_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2)).
% 15.19/15.13  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2),V_i_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_k),V_j).
% 15.19/15.13  0 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.19/15.13  0 [] c_Nat_OSuc(V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_n).
% 15.19/15.13  0 [] c_Nat_OSuc(V_n)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 15.19/15.13  0 [] V_m!=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n)|V_n=c_Groups_Oone__class_Oone(tc_Nat_Onat)|V_m=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.13  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Polynomial_Odegree(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.13  0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_d_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2),V_e_2),V_c_2),V_d_2).
% 15.19/15.13  0 [] -class_Rings_Oordered__ring(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_d_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2),V_e_2),V_c_2),V_d_2).
% 15.19/15.13  0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_d_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_aa_2),V_e_2),V_d_2)).
% 15.19/15.13  0 [] -class_Rings_Oordered__ring(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_d_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_aa_2),V_e_2),V_d_2)).
% 15.19/15.13  0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_d_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2),V_e_2),V_c_2),V_d_2).
% 15.19/15.13  0 [] -class_Rings_Oordered__ring(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_d_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_aa_2,V_b_2),V_e_2),V_c_2),V_d_2).
% 15.19/15.13  0 [] -class_Rings_Oordered__ring(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_d_2))|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_aa_2),V_e_2),V_d_2)).
% 15.19/15.13  0 [] -class_Rings_Oordered__ring(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_e_2),V_d_2))| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b_2,V_aa_2),V_e_2),V_d_2)).
% 15.19/15.13  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_y,V_x),V_x).
% 15.19/15.13  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),V_x).
% 15.19/15.13  0 [] -class_Rings_Olinordered__semidom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=V_n.
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(V_i)),V_n).
% 15.19/15.13  0 [] -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2,V_b_2)|hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.19/15.13  0 [] -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))|V_aa_2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)|hBOOL(hAPP(V_P_2,B_d)).
% 15.19/15.13  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2,V_b_2)|V_aa_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,$f12(V_b_2,V_aa_2,V_P_2)).
% 15.19/15.13  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2,V_b_2)| -hBOOL(hAPP(V_P_2,$f12(V_b_2,V_aa_2,V_P_2))).
% 15.19/15.13  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_aa_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,$f12(V_b_2,V_aa_2,V_P_2)).
% 15.19/15.13  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,$f12(V_b_2,V_aa_2,V_P_2))).
% 15.19/15.13  0 [] -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2,V_b_2)|hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.19/15.13  0 [] -hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))|V_aa_2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)|hBOOL(hAPP(V_P_2,B_d)).
% 15.19/15.13  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2,V_b_2)|V_aa_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,$f13(V_b_2,V_aa_2,V_P_2)).
% 15.19/15.13  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_aa_2,V_b_2)| -hBOOL(hAPP(V_P_2,$f13(V_b_2,V_aa_2,V_P_2))).
% 15.19/15.13  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_aa_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,$f13(V_b_2,V_aa_2,V_P_2)).
% 15.19/15.13  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_aa_2,V_b_2)))| -hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,$f13(V_b_2,V_aa_2,V_P_2))).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)),V_m)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_j),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k,V_m)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_j)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_k)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_k),c_Nat_OSuc(V_j)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,V_i_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i_2,V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j_2,V_u_2),V_n_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2),V_u_2),V_m_2),V_n_2).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,V_i_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i_2,V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j_2,V_u_2),V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2),V_u_2),V_m_2),V_n_2).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j,V_i)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i,V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j,V_u),V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j),V_u),V_m),V_n).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,V_i_2)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i_2,V_u_2),V_m_2)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j_2,V_u_2),V_n_2)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2),V_u_2),V_m_2)=V_n_2.
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_j_2,V_i_2)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i_2,V_u_2),V_m_2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j_2,V_u_2),V_n_2)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2),V_u_2),V_m_2)!=V_n_2.
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i_2,V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j_2,V_u_2),V_n_2))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2),V_u_2),V_n_2)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i_2,V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j_2,V_u_2),V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2),V_u_2),V_n_2)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i,V_j)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i,V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j,V_u),V_n))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_i),V_u),V_n)).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i_2,V_u_2),V_m_2)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j_2,V_u_2),V_n_2)|V_m_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2),V_u_2),V_n_2).
% 15.19/15.13  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_i_2,V_j_2)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_i_2,V_u_2),V_m_2)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_j_2,V_u_2),V_n_2)|V_m_2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2),V_u_2),V_n_2).
% 15.19/15.13  0 [] -class_Rings_Olinordered__semiring__1(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y,V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)|c_Groups_Oplus__class_Oplus(T_a,V_u,V_v)!=c_Groups_Oone__class_Oone(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_u,V_x),c_Groups_Otimes__class_Otimes(T_a,V_v,V_y)),V_a).
% 15.19/15.13  0 [] -class_Rings_Oring__1(T_a)|c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_x),c_Groups_Oone__class_Oone(T_a))=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Oone__class_Oone(T_a)),c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))).
% 15.19/15.13  0 [] -class_Rings_Oring(T_a)|c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_a),V_b)).
% 15.19/15.13  0 [] -class_Rings_Ocomm__ring__1(T_a)|c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_c),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),c_Polynomial_Osynthetic__div(T_a,V_p,V_c)),c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))=V_p.
% 15.19/15.13  0 [] c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Nat_OSuc(V_nat))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,V_nat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.19/15.13  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)).
% 15.19/15.13  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)).
% 15.19/15.13  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_aa_2).
% 15.19/15.13  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_aa_2).
% 15.19/15.13  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,V_b_2).
% 15.19/15.13  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,V_b_2).
% 15.19/15.13  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a)).
% 15.19/15.13  0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=V_p.
% 15.19/15.13  0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q)=c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_q).
% 15.19/15.13  0 [] c_Nat_Osize__class_Osize(tc_Nat_Onat,V_n)=V_n.
% 15.19/15.13  0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))=c_Groups_Ominus__class_Ominus(T_a,V_b,V_a).
% 15.19/15.13  0 [] -class_Rings_Ocomm__ring(T_a)|c_Polynomial_Osmult(T_a,V_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q))=c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),c_Polynomial_Osmult(T_a,V_a,V_q)).
% 15.19/15.13  0 [] -class_Rings_Ocomm__ring(T_a)|c_Polynomial_Osmult(T_a,V_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p))=c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p)).
% 15.19/15.13  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_y_2=c_Groups_Ouminus__class_Ouminus(T_a,V_x_2).
% 15.19/15.13  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2)=c_Groups_Ozero__class_Ozero(T_a)|V_y_2!=c_Groups_Ouminus__class_Ouminus(T_a,V_x_2).
% 15.19/15.13  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a))=V_a.
% 15.19/15.13  0 [] -class_Groups_Ogroup__add(T_a)|V_aa_2!=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)|V_b_2=c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2).
% 15.19/15.13  0 [] -class_Groups_Ogroup__add(T_a)|V_aa_2=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)|V_b_2!=c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2).
% 15.19/15.13  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)!=V_b_2|c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)=V_aa_2.
% 15.19/15.13  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)=V_b_2|c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)!=V_aa_2.
% 15.19/15.13  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)!=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)|V_aa_2=V_b_2.
% 15.19/15.13  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)|V_aa_2!=V_b_2.
% 15.19/15.13  0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_Omonom(T_a,V_a,V_n))=c_Polynomial_Omonom(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_n).
% 15.19/15.13  0 [] -class_Rings_Ocomm__ring(T_a)|hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)),V_x)=c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)).
% 15.19/15.13  0 [] -class_Rings_Ocomm__ring(T_a)|c_Polynomial_Osmult(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_p)=c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p)).
% 15.19/15.13  0 [] -class_Groups_Oab__group__add(T_a)|hAPP(c_Polynomial_Ocoeff(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)),V_n)=c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Polynomial_Ocoeff(T_a,V_p),V_n)).
% 15.19/15.13  0 [] -class_Groups_Oab__group__add(T_b)|c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b),c_Polynomial_OpCons(T_b,V_a,V_p))=c_Polynomial_OpCons(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b),V_p)).
% 15.19/15.13  0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p))=c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)).
% 15.19/15.13  0 [] -class_Groups_Oab__group__add(T_a)|c_Polynomial_Odegree(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p))=c_Polynomial_Odegree(T_a,V_p).
% 15.19/15.13  0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.13  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))=V_b.
% 15.19/15.13  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b))=V_b.
% 15.19/15.13  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a)).
% 15.19/15.13  0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)).
% 15.19/15.13  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x),V_y)=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y)).
% 15.19/15.13  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)).
% 15.19/15.13  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_xa,c_Groups_Ouminus__class_Ouminus(T_a,V_x))=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_xa,V_x)).
% 15.19/15.13  0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b))=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)).
% 15.19/15.13  0 [] -class_Rings_Oring(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))=c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)).
% 15.19/15.13  0 [] -class_Rings_Oring(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b).
% 15.19/15.13  0 [] -class_Rings_Oring(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)=c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)).
% 15.19/15.13  0 [] -class_Rings_Oring(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b))=c_Groups_Otimes__class_Otimes(T_a,V_a,V_b).
% 15.19/15.13  0 [] -class_Rings_Oidom(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_aa_2)!=c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_b_2)|V_aa_2=V_b_2|V_aa_2=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2).
% 15.19/15.13  0 [] -class_Rings_Oidom(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_aa_2)=c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_b_2)|V_aa_2!=V_b_2.
% 15.19/15.13  0 [] -class_Rings_Oidom(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_aa_2)=c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_b_2)|V_aa_2!=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2).
% 15.19/15.13  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))|c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2).
% 15.19/15.13  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,V_b_2).
% 15.19/15.13  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_aa_2).
% 15.19/15.13  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_aa_2).
% 15.19/15.13  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))|c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)).
% 15.19/15.13  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))| -c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)).
% 15.19/15.13  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)!=V_aa_2|V_aa_2=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)=V_aa_2|V_aa_2!=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_aa_2=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)=c_Groups_Ozero__class_Ozero(T_a)|V_aa_2!=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|V_aa_2!=c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)|V_aa_2=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|V_aa_2=c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)|V_aa_2!=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ozero__class_Ozero(T_a)!=c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)|c_Groups_Ozero__class_Ozero(T_a)=V_aa_2.
% 15.19/15.13  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ozero__class_Ozero(T_a)=c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2)|c_Groups_Ozero__class_Ozero(T_a)!=V_aa_2.
% 15.19/15.13  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless__e_q(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2)|V_x_2=V_y_2|c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2)).
% 15.19/15.13  0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2)|V_x_2!=V_y_2.
% 15.19/15.13  0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2)| -c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2)).
% 15.19/15.13  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2)|c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2)).
% 15.19/15.13  0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2)| -c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2)).
% 15.19/15.13  0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_aa_2)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 15.19/15.13  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_aa_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 15.19/15.13  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 15.19/15.13  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 15.19/15.13  0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))|c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))|c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2))| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Groups_Oordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 15.19/15.13  0 [] -class_Groups_Oordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 15.19/15.13  0 [] -class_Groups_Olinordered__ab__group__add(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_aa_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 15.19/15.13  0 [] -class_Groups_Olinordered__ab__group__add(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_aa_2),V_aa_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 15.19/15.13  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)!=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_a)=V_b.
% 15.19/15.13  0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_Groups_Ogroup__add(T_a)|V_aa_2!=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)|c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_b_2)=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_Groups_Ogroup__add(T_a)|V_aa_2=c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)|c_Groups_Oplus__class_Oplus(T_a,V_aa_2,V_b_2)!=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a))=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=c_Groups_Ouminus__class_Ouminus(T_a,V_a).
% 15.19/15.13  0 [] -class_Rings_Oring__1__no__zero__divisors(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_x_2)!=c_Groups_Oone__class_Oone(T_a)|V_x_2=c_Groups_Oone__class_Oone(T_a)|V_x_2=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)).
% 15.19/15.13  0 [] -class_Rings_Oring__1__no__zero__divisors(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_x_2)=c_Groups_Oone__class_Oone(T_a)|V_x_2!=c_Groups_Oone__class_Oone(T_a).
% 15.19/15.13  0 [] -class_Rings_Oring__1__no__zero__divisors(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_x_2)=c_Groups_Oone__class_Oone(T_a)|V_x_2!=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)).
% 15.19/15.13  0 [] -class_Rings_Ocomm__ring__1(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_x)=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)),V_x).
% 15.19/15.13  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b))=c_Groups_Oplus__class_Oplus(T_a,V_a,V_b).
% 15.19/15.13  0 [] -class_Rings_Ocomm__ring__1(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)=c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Ouminus__class_Ouminus(T_a,V_y)).
% 15.19/15.13  0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)=c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)).
% 15.19/15.13  0 [] -class_Groups_Ogroup__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)=c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)).
% 15.19/15.13  0 [] -class_Groups_Oab__group__add(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q),V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_n).
% 15.19/15.13  0 [] -class_Groups_Oab__group__add(T_a)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_q),V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_n).
% 15.19/15.13  0 [] -class_Rings_Olinordered__idom(T_a)|V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Polynomial_Opos__poly(T_a,V_p)|c_Polynomial_Opos__poly(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)).
% 15.19/15.13  0 [] c_Nat_Osize__class_Osize(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.13  0 [] -class_Fields_Ofield(T_a)| -c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q,V_r)|V_y=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_b!=c_Rings_Oinverse__class_Odivide(T_a,hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_OpCons(T_a,V_a,V_r)),c_Polynomial_Odegree(T_a,V_y)),hAPP(c_Polynomial_Ocoeff(T_a,V_y),c_Polynomial_Odegree(T_a,V_y)))|c_Polynomial_Opdivmod__rel(T_a,c_Polynomial_OpCons(T_a,V_a,V_x),V_y,c_Polynomial_OpCons(T_a,V_b,V_q),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_r),c_Polynomial_Osmult(T_a,V_b,V_y))).
% 15.19/15.13  0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b))=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)).
% 15.19/15.13  0 [] -class_Groups_Oab__group__add(T_a)|c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d))=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(T_a,V_c,V_d)).
% 15.19/15.13  0 [] -class_Rings_Odivision__ring(T_a)|c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_c)=c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)).
% 15.19/15.13  0 [] -class_Rings_Odivision__ring(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Oone__class_Oone(T_a))=V_a.
% 15.19/15.13  0 [] -class_RealVector_Oreal__normed__field(T_a)|c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,V_y),V_ya)=c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_ya),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_ya)).
% 15.19/15.13  0 [] -class_RealVector_Oreal__normed__field(T_a)|c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x),V_y)=c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)).
% 15.19/15.13  0 [] -class_Rings_Odivision__ring(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b).
% 15.19/15.13  0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_Rings_Odivision__ring(T_a)|c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_RealVector_Oreal__normed__field(T_a)|c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_Rings_Odivision__ring(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a,c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c).
% 15.19/15.13  0 [] -class_Rings_Odivision__ring(T_a)|c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)).
% 15.19/15.13  0 [] -class_RealVector_Oreal__normed__field(T_a)|c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,V_y),V_ya)=c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_ya),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_ya)).
% 15.19/15.13  0 [] -class_Rings_Odivision__ring(T_a)|V_c=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a,V_c)!=V_b|V_a=c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c).
% 15.19/15.13  0 [] -class_Rings_Odivision__ring(T_a)|V_c=c_Groups_Ozero__class_Ozero(T_a)|V_b!=c_Groups_Otimes__class_Otimes(T_a,V_a,V_c)|c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)=V_a.
% 15.19/15.13  0 [] -class_Rings_Odivision__ring(T_a)|V_c_2=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)!=V_aa_2|V_b_2=c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2).
% 15.19/15.13  0 [] -class_Rings_Odivision__ring(T_a)|V_c_2=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)=V_aa_2|V_b_2!=c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2).
% 15.19/15.13  0 [] -class_Rings_Odivision__ring(T_a)|V_c_2=c_Groups_Ozero__class_Ozero(T_a)|V_aa_2!=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)|c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2)=V_b_2.
% 15.19/15.13  0 [] -class_Rings_Odivision__ring(T_a)|V_c_2=c_Groups_Ozero__class_Ozero(T_a)|V_aa_2=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)|c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2)!=V_b_2.
% 15.19/15.13  0 [] -class_RealVector_Oreal__field(T_a)|c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),c_Groups_Otimes__class_Otimes(T_a,V_c,V_d)),V_h)=c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d),V_h)),c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c),V_h),V_d)).
% 15.19/15.13  0 [] -class_Rings_Odivision__ring(T_a)|V_b_2=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_aa_2,V_b_2)!=c_Groups_Oone__class_Oone(T_a)|V_aa_2=V_b_2.
% 15.19/15.13  0 [] -class_Rings_Odivision__ring(T_a)|V_b_2=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_aa_2,V_b_2)=c_Groups_Oone__class_Oone(T_a)|V_aa_2!=V_b_2.
% 15.19/15.13  0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a)=c_Groups_Oone__class_Oone(T_a).
% 15.19/15.13  0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|V_a!=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_a,V_a)=c_Groups_Oone__class_Oone(T_a).
% 15.19/15.13  0 [] -class_Rings_Odivision__ring(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b))=c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b).
% 15.19/15.13  0 [] -class_Rings_Odivision__ring(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))=c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2).
% 15.19/15.13  0 [] -class_Fields_Ofield__inverse__zero(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Rings_Oinverse__class_Odivide(T_a,V_z,V_w))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_z),c_Groups_Otimes__class_Otimes(T_a,V_y,V_w)).
% 15.19/15.13  0 [] -class_Fields_Ofield__inverse__zero(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))=c_Rings_Oinverse__class_Odivide(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)).
% 15.19/15.13  0 [] -class_Fields_Ofield__inverse__zero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b))=c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_aa_2,V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_aa_2,V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_aa_2,V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_aa_2,V_b_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_aa_2,V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_aa_2,V_b_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_aa_2,V_b_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)|c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_aa_2,V_b_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)|c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_aa_2,V_b_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_aa_2,V_b_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_aa_2,V_b_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_aa_2,V_b_2))| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)|c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_aa_2,V_b_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b_2).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)| -c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_c),c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)).
% 15.19/15.13  0 [] -class_Fields_Ofield(T_a)|V_y_2=c_Groups_Ozero__class_Ozero(T_a)|V_z_2=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_x_2,V_y_2)!=c_Rings_Oinverse__class_Odivide(T_a,V_w_2,V_z_2)|c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_z_2)=c_Groups_Otimes__class_Otimes(T_a,V_w_2,V_y_2).
% 15.19/15.13  0 [] -class_Fields_Ofield(T_a)|V_y_2=c_Groups_Ozero__class_Ozero(T_a)|V_z_2=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_x_2,V_y_2)=c_Rings_Oinverse__class_Odivide(T_a,V_w_2,V_z_2)|c_Groups_Otimes__class_Otimes(T_a,V_x_2,V_z_2)!=c_Groups_Otimes__class_Otimes(T_a,V_w_2,V_y_2).
% 15.19/15.13  0 [] -class_Fields_Ofield__inverse__zero(T_a)|V_c=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))=c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b).
% 15.19/15.13  0 [] -class_Fields_Ofield__inverse__zero(T_a)|V_c=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))=c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b).
% 15.19/15.13  0 [] -class_Fields_Ofield__inverse__zero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)!=V_aa_2|V_c_2=c_Groups_Ozero__class_Ozero(T_a)|V_b_2=c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2).
% 15.19/15.13  0 [] -class_Fields_Ofield__inverse__zero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)!=V_aa_2|V_c_2!=c_Groups_Ozero__class_Ozero(T_a)|V_aa_2=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_Fields_Ofield__inverse__zero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)=V_aa_2|V_c_2!=c_Groups_Ozero__class_Ozero(T_a)|V_aa_2!=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_Fields_Ofield__inverse__zero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)=V_aa_2|V_b_2!=c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2)|V_c_2=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_Fields_Ofield__inverse__zero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)=V_aa_2|V_b_2!=c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2)|V_aa_2!=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_Fields_Ofield__inverse__zero(T_a)|V_aa_2!=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)|V_c_2=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2)=V_b_2.
% 15.19/15.13  0 [] -class_Fields_Ofield__inverse__zero(T_a)|V_aa_2!=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)|V_c_2!=c_Groups_Ozero__class_Ozero(T_a)|V_aa_2=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_Fields_Ofield__inverse__zero(T_a)|V_aa_2=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)|V_c_2!=c_Groups_Ozero__class_Ozero(T_a)|V_aa_2!=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_Fields_Ofield__inverse__zero(T_a)|V_aa_2=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)|c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2)!=V_b_2|V_c_2=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_Fields_Ofield__inverse__zero(T_a)|V_aa_2=c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)|c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2)!=V_b_2|V_aa_2!=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_w,V_z)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)| -c_Orderings_Oord__class_Oless(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_w,V_z)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_w)| -c_Orderings_Oord__class_Oless(T_a,V_w,V_z)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),c_Rings_Oinverse__class_Odivide(T_a,V_y,V_w)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)| -c_Orderings_Oord__class_Oless(T_a,V_y,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2))| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2))| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2))| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2))| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2))|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2)|c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2)| -c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)| -c_Orderings_Oord__class_Oless(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y))|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y),V_x)|c_Orderings_Oord__class_Oless(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))|c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))| -c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_b,V_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_c,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)).
% 15.19/15.13  0 [] -class_Fields_Ofield__inverse__zero(T_a)|V_y=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y)),V_y).
% 15.19/15.13  0 [] -class_Fields_Ofield(T_a)|V_z=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Oplus__class_Oplus(T_a,V_x,c_Rings_Oinverse__class_Odivide(T_a,V_y,V_z))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_z,V_x),V_y),V_z).
% 15.19/15.13  0 [] -class_Fields_Ofield__inverse__zero(T_a)|V_y=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z)=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y)),V_y).
% 15.19/15.13  0 [] -class_Fields_Ofield(T_a)|V_z=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),V_y)=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y)),V_z).
% 15.19/15.13  0 [] -class_Fields_Ofield(T_a)|V_y=c_Groups_Ozero__class_Ozero(T_a)|V_z=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Rings_Oinverse__class_Odivide(T_a,V_w,V_z))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_z),c_Groups_Otimes__class_Otimes(T_a,V_w,V_y)),c_Groups_Otimes__class_Otimes(T_a,V_y,V_z)).
% 15.19/15.13  0 [] -class_Fields_Ofield(T_a)|V_z=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Ominus__class_Ominus(T_a,V_x,c_Rings_Oinverse__class_Odivide(T_a,V_y,V_z))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_z,V_x),V_y),V_z).
% 15.19/15.13  0 [] -class_Fields_Ofield(T_a)|V_z=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),V_y)=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y)),V_z).
% 15.19/15.13  0 [] -class_Fields_Ofield(T_a)|V_y=c_Groups_Ozero__class_Ozero(T_a)|V_z=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Rings_Oinverse__class_Odivide(T_a,V_w,V_z))=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_z),c_Groups_Otimes__class_Otimes(T_a,V_w,V_y)),c_Groups_Otimes__class_Otimes(T_a,V_y,V_z)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),V_b).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)|c_Orderings_Oord__class_Oless(T_a,V_a,c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a)))).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2))| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2))| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2)).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 15.19/15.13  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2))|c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),V_b_2).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2)).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_aa_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2)).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,V_z,V_y),V_x)|c_Orderings_Oord__class_Oless__e_q(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2)).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_b_2,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2)).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)|V_y=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_x),V_y)=c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)),c_Polynomial_Osmult(T_a,c_Rings_Oinverse__class_Odivide(T_a,hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_OpCons(T_a,V_a,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y))),c_Polynomial_Odegree(T_a,V_y)),hAPP(c_Polynomial_Ocoeff(T_a,V_y),c_Polynomial_Odegree(T_a,V_y))),V_y)).
% 15.19/15.14  0 [] -class_Lattices_Oboolean__algebra(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),c_Groups_Ouminus__class_Ouminus(T_a,V_y_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2).
% 15.19/15.14  0 [] -class_Lattices_Oboolean__algebra(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),c_Groups_Ouminus__class_Ouminus(T_a,V_y_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_y_2,V_x_2).
% 15.19/15.14  0 [] -class_Lattices_Oboolean__algebra(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_y),c_Groups_Ouminus__class_Ouminus(T_a,V_x)).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)|c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_x),V_y)=c_Polynomial_Osmult(T_a,V_a,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)| -c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q,V_r)|c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)=V_r.
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_x),c_Polynomial_Odegree(T_a,V_y))|c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)=V_x.
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,c_Polynomial_Osmult(T_a,V_a,V_y))=c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)|c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_x),V_y)=c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)|c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_y))=c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)|V_y=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)),c_Polynomial_Odegree(T_a,V_y)).
% 15.19/15.14  0 [] -class_Lattices_Oab__semigroup__idem__mult(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a,V_a)=V_a.
% 15.19/15.14  0 [] -class_Lattices_Oab__semigroup__idem__mult(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_x,V_x)=V_x.
% 15.19/15.14  0 [] -class_Lattices_Oab__semigroup__idem__mult(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))=c_Groups_Otimes__class_Otimes(T_a,V_a,V_b).
% 15.19/15.14  0 [] -class_Groups_Ominus(T_a)|hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a),V_A_2,V_B_2),V_x_2)=c_Groups_Ominus__class_Ominus(T_a,hAPP(V_A_2,V_x_2),hAPP(V_B_2,V_x_2)).
% 15.19/15.14  0 [] -class_Lattices_Oboolean__algebra(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x))=V_x.
% 15.19/15.14  0 [] -class_Groups_Ouminus(T_a)|hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a),V_A_2),V_x_2)=c_Groups_Ouminus__class_Ouminus(T_a,hAPP(V_A_2,V_x_2)).
% 15.19/15.14  0 [] -class_Lattices_Oboolean__algebra(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_x_2)!=c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)|V_x_2=V_y_2.
% 15.19/15.14  0 [] -class_Lattices_Oboolean__algebra(T_a)|c_Groups_Ouminus__class_Ouminus(T_a,V_x_2)=c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)|V_x_2!=V_y_2.
% 15.19/15.14  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)),V_b)=c_Divides_Odiv__class_Omod(T_a,V_a,V_b).
% 15.19/15.14  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_b)),V_b)=c_Divides_Odiv__class_Omod(T_a,V_a,V_b).
% 15.19/15.14  0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n),V_k)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_k),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,V_k)).
% 15.19/15.14  0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n))=c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_m),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_n)).
% 15.19/15.14  0 [] c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)),V_n).
% 15.19/15.14  0 [] c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_n),V_m),V_n)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n).
% 15.19/15.14  0 [] c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_d_2,$f14(V_d_2,V_m_2)).
% 15.19/15.14  0 [] c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_m_2!=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_d_2,B_q).
% 15.19/15.14  0 [] c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n))!=V_n|c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.14  0 [] c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n))=V_n|c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)=c_Nat_OSuc(c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)).
% 15.19/15.14  0 [] c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.14  0 [] c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_n),V_m)),V_n)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n).
% 15.19/15.14  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n),V_n).
% 15.19/15.14  0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n),V_m).
% 15.19/15.14  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)=V_m.
% 15.19/15.14  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n),V_n).
% 15.19/15.14  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n).
% 15.19/15.14  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)=V_m.
% 15.19/15.14  0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)|c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n).
% 15.19/15.14  0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)|c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)=c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_n).
% 15.19/15.14  0 [] -hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))|V_k_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hBOOL(hAPP(V_P_2,V_n_2)).
% 15.19/15.14  0 [] -hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_k_2)|V_n_2!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,B_i),B_j)|hBOOL(hAPP(V_P_2,B_j)).
% 15.19/15.14  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f15(V_k_2,V_n_2,V_P_2),V_k_2).
% 15.19/15.14  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|V_n_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,$f16(V_k_2,V_n_2,V_P_2)),$f15(V_k_2,V_n_2,V_P_2)).
% 15.19/15.14  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -hBOOL(hAPP(V_P_2,$f15(V_k_2,V_n_2,V_P_2))).
% 15.19/15.14  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,V_n_2))|V_k_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.14  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f15(V_k_2,V_n_2,V_P_2),V_k_2).
% 15.19/15.14  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,V_n_2))|V_n_2=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,$f16(V_k_2,V_n_2,V_P_2)),$f15(V_k_2,V_n_2,V_P_2)).
% 15.19/15.14  0 [] hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))| -hBOOL(hAPP(V_P_2,V_n_2))| -hBOOL(hAPP(V_P_2,$f15(V_k_2,V_n_2,V_P_2))).
% 15.19/15.14  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_c)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_r,V_b)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_b,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_q,V_c)),V_r),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_b,V_c)).
% 15.19/15.14  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_k)|c_Divides_Odiv__class_Omod(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_m)),V_k)=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.19/15.14  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_b)=c_Divides_Odiv__class_Omod(T_a,V_a,V_b).
% 15.19/15.14  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.14  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))=V_a.
% 15.19/15.14  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,V_a,V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.14  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,V_a,V_c)!=c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)|c_Divides_Odiv__class_Omod(T_a,V_b,V_c)!=c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)|c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a_H,V_b_H),V_c).
% 15.19/15.14  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c).
% 15.19/15.14  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_c))=c_Groups_Otimes__class_Otimes(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_c).
% 15.19/15.14  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c,V_a),c_Groups_Otimes__class_Otimes(T_a,V_c,V_b))=c_Groups_Otimes__class_Otimes(T_a,V_c,c_Divides_Odiv__class_Omod(T_a,V_a,V_b)).
% 15.19/15.14  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c).
% 15.19/15.14  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),V_b),V_c).
% 15.19/15.14  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c).
% 15.19/15.14  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,V_a,V_c)!=c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)|c_Divides_Odiv__class_Omod(T_a,V_b,V_c)!=c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)|c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_H,V_b_H),V_c).
% 15.19/15.14  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c).
% 15.19/15.14  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c)=c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c).
% 15.19/15.14  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c).
% 15.19/15.14  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),V_b),V_c).
% 15.19/15.14  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c).
% 15.19/15.14  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_a),V_b)=c_Divides_Odiv__class_Omod(T_a,V_a,V_b).
% 15.19/15.14  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_b)=c_Divides_Odiv__class_Omod(T_a,V_a,V_b).
% 15.19/15.14  0 [] -class_Divides_Oring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,V_a,V_c)!=c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)|c_Divides_Odiv__class_Omod(T_a,V_b,V_c)!=c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)|c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_H,V_b_H),V_c).
% 15.19/15.14  0 [] -class_Divides_Oring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c).
% 15.19/15.14  0 [] -class_Divides_Oring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_c),V_b),V_c).
% 15.19/15.14  0 [] -class_Divides_Oring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,c_Divides_Odiv__class_Omod(T_a,V_b,V_c)),V_c).
% 15.19/15.14  0 [] -class_Divides_Oring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,V_a,V_b)!=c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b)|c_Divides_Odiv__class_Omod(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)=c_Divides_Odiv__class_Omod(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_H),V_b).
% 15.19/15.14  0 [] -class_Divides_Oring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)=c_Divides_Odiv__class_Omod(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b)),V_b).
% 15.19/15.14  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_a),V_b)=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.14  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_b)=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.14  0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_a)|V_x!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_a)|V_x=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))| -c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x)|c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x)=c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_a)|V_x=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x)|c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x)=c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)|V_x!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_y!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_Opoly__gcd(T_a,V_x,V_y)),c_Polynomial_Odegree(T_a,c_Polynomial_Opoly__gcd(T_a,V_x,V_y)))=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)|V_x=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_Opoly__gcd(T_a,V_x,V_y)),c_Polynomial_Odegree(T_a,c_Polynomial_Opoly__gcd(T_a,V_x,V_y)))=c_Groups_Oone__class_Oone(T_a).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)|V_y=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|hAPP(c_Polynomial_Ocoeff(T_a,c_Polynomial_Opoly__gcd(T_a,V_x,V_y)),c_Polynomial_Odegree(T_a,c_Polynomial_Opoly__gcd(T_a,V_x,V_y)))=c_Groups_Oone__class_Oone(T_a).
% 15.19/15.14  0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x))=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)|c_Polynomial_Opoly__gcd(T_a,V_x,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_y))=c_Polynomial_Opoly__gcd(T_a,V_x,V_y).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)|c_Polynomial_Opoly__gcd(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_x),V_y)=c_Polynomial_Opoly__gcd(T_a,V_x,V_y).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Osgn__class_Osgn(T_a,V_aa_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Osgn__class_Osgn(T_a,V_aa_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Osgn__class_Osgn(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Osgn__class_Osgn(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.14  0 [] -class_RealVector_Oreal__normed__algebra__1(T_a)|c_Groups_Osgn__class_Osgn(T_a,c_Groups_Oone__class_Oone(T_a))=c_Groups_Oone__class_Oone(T_a).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)|c_Polynomial_Opoly__gcd(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)|c_Polynomial_Opoly__gcd(T_a,V_x_2,V_y_2)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_x_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)|c_Polynomial_Opoly__gcd(T_a,V_x_2,V_y_2)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_y_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)|c_Polynomial_Opoly__gcd(T_a,V_x_2,V_y_2)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_x_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_y_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Osgn__class_Osgn(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a))=c_Groups_Osgn__class_Osgn(T_a,V_a).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)|c_Polynomial_Opoly__gcd(T_a,c_Polynomial_Opoly__gcd(T_a,V_a,V_b),V_c)=c_Polynomial_Opoly__gcd(T_a,V_a,c_Polynomial_Opoly__gcd(T_a,V_b,V_c)).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)|c_Polynomial_Opoly__gcd(T_a,V_b,c_Polynomial_Opoly__gcd(T_a,V_a,V_c))=c_Polynomial_Opoly__gcd(T_a,V_a,c_Polynomial_Opoly__gcd(T_a,V_b,V_c)).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)|c_Polynomial_Opoly__gcd(T_a,V_a,V_b)=c_Polynomial_Opoly__gcd(T_a,V_b,V_a).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Osgn__class_Osgn(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a),c_Groups_Osgn__class_Osgn(T_a,V_b)).
% 15.19/15.14  0 [] -class_RealVector_Oreal__normed__div__algebra(T_a)|c_Groups_Osgn__class_Osgn(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y))=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x),c_Groups_Osgn__class_Osgn(T_a,V_y)).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_aa_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_aa_2=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_aa_2)=c_Groups_Ozero__class_Ozero(T_a)|V_aa_2!=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.14  0 [] -class_Groups_Osgn__if(T_a)|c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.14  0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_x_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_x_2=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.14  0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_x_2)=c_Groups_Ozero__class_Ozero(T_a)|V_x_2!=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.14  0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)|c_Polynomial_Opoly__gcd(T_a,V_x,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)))=c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)|c_Polynomial_Opoly__gcd(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)),V_y)=c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)|V_y=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=c_Polynomial_Opoly__gcd(T_a,V_y,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_aa_2)!=c_Groups_Oone__class_Oone(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_aa_2)=c_Groups_Oone__class_Oone(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Groups_Osgn__class_Osgn(T_a,V_a)=c_Groups_Oone__class_Oone(T_a).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))|c_Groups_Osgn__class_Osgn(T_a,V_a)=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_aa_2)!=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_aa_2)=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.14  0 [] -class_Groups_Osgn__if(T_a)|V_x!=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Osgn__class_Osgn(T_a,V_x)=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.14  0 [] -class_Groups_Osgn__if(T_a)|V_x=c_Groups_Ozero__class_Ozero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)|c_Groups_Osgn__class_Osgn(T_a,V_x)=c_Groups_Oone__class_Oone(T_a).
% 15.19/15.14  0 [] -class_Groups_Osgn__if(T_a)|V_x=c_Groups_Ozero__class_Ozero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)|c_Groups_Osgn__class_Osgn(T_a,V_x)=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)|V_y!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=c_Polynomial_Osmult(T_a,c_Rings_Oinverse__class_Oinverse(T_a,hAPP(c_Polynomial_Ocoeff(T_a,V_x),c_Polynomial_Odegree(T_a,V_x))),V_x).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)|V_y=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=c_Polynomial_Opoly__gcd(T_a,V_y,c_Divides_Odiv__class_Omod(tc_Polynomial_Opoly(T_a),V_x,V_y)).
% 15.19/15.14  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,V_n_2))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f17(V_n_2,V_P_2),V_n_2).
% 15.19/15.14  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,V_n_2))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B_i,$f17(V_n_2,V_P_2))| -hBOOL(hAPP(V_P_2,B_i)).
% 15.19/15.14  0 [] hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(V_P_2,V_n_2))|hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,$f17(V_n_2,V_P_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))).
% 15.19/15.14  0 [] -class_Rings_Odivision__ring(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,V_a)=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,V_a)=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a).
% 15.19/15.14  0 [] -class_Rings_Odivision__ring(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)=c_Groups_Otimes__class_Otimes(T_a,V_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b)).
% 15.19/15.14  0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))=c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)).
% 15.19/15.14  0 [] -class_Rings_Odivision__ring(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)!=c_Groups_Oone__class_Oone(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,V_a)=V_b.
% 15.19/15.14  0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a))=V_a.
% 15.19/15.14  0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2)!=c_Rings_Oinverse__class_Oinverse(T_a,V_b_2)|V_aa_2=V_b_2.
% 15.19/15.14  0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2)=c_Rings_Oinverse__class_Oinverse(T_a,V_b_2)|V_aa_2!=V_b_2.
% 15.19/15.14  0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,V_a)!=c_Rings_Oinverse__class_Oinverse(T_a,V_b)|V_a=V_b.
% 15.19/15.14  0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.14  0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2)!=c_Groups_Ozero__class_Ozero(T_a)|V_aa_2=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.14  0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2)=c_Groups_Ozero__class_Ozero(T_a)|V_aa_2!=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.14  0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,V_a)!=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.14  0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a))=V_a.
% 15.19/15.14  0 [] -class_Rings_Odivision__ring(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,V_a)!=c_Groups_Ozero__class_Ozero(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.14  0 [] -class_Rings_Odivision__ring(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,V_a)!=c_Rings_Oinverse__class_Oinverse(T_a,V_b)|V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|V_a=V_b.
% 15.19/15.14  0 [] -class_Rings_Odivision__ring(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Oone__class_Oone(T_a))=c_Groups_Oone__class_Oone(T_a).
% 15.19/15.14  0 [] -class_Fields_Ofield__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,V_x_2)!=c_Groups_Oone__class_Oone(T_a)|V_x_2=c_Groups_Oone__class_Oone(T_a).
% 15.19/15.14  0 [] -class_Fields_Ofield__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,V_x_2)=c_Groups_Oone__class_Oone(T_a)|V_x_2!=c_Groups_Oone__class_Oone(T_a).
% 15.19/15.14  0 [] -class_Fields_Ofield__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b))=c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)).
% 15.19/15.14  0 [] -class_Fields_Ofield__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ozero__class_Ozero(T_a))=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 15.19/15.14  0 [] -class_Fields_Ofield__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b))=c_Rings_Oinverse__class_Odivide(T_a,V_b,V_a).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)|c_Rings_Oinverse__class_Odivide(T_a,V_a,V_b)=c_Groups_Otimes__class_Otimes(T_a,V_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b)).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_aa_2).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_aa_2),c_Groups_Ozero__class_Ozero(T_a))| -c_Orderings_Oord__class_Oless(T_a,V_aa_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a))|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ozero__class_Ozero(T_a))|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless(T_a,V_b,V_a).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,V_b,V_a).
% 15.19/15.14  0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a))=c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)).
% 15.19/15.14  0 [] -class_Rings_Odivision__ring__inverse__zero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a))=c_Groups_Ouminus__class_Ouminus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a)).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,V_b)| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))| -c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_b,V_a).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),V_x_2).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),V_x_2).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Rings_Oinverse__class_Oinverse(T_a,V_a)),c_Rings_Oinverse__class_Oinverse(T_a,V_b)).
% 15.19/15.14  0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),c_Rings_Oinverse__class_Oinverse(T_a,V_b)).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2))|c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oone__class_Oone(T_a)).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)| -c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oone__class_Oone(T_a)).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)).
% 15.19/15.14  0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))=c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)),c_Rings_Oinverse__class_Oinverse(T_a,V_b)).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),V_a)=c_Groups_Oone__class_Oone(T_a).
% 15.19/15.14  0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),V_a)=c_Groups_Oone__class_Oone(T_a).
% 15.19/15.14  0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a))=c_Groups_Oone__class_Oone(T_a).
% 15.19/15.14  0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Oinverse(T_a,V_a)=c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),V_a).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)| -c_Polynomial_Opdivmod__rel(T_a,V_x,V_y,V_q,V_r)|c_Polynomial_Opdivmod__rel(T_a,V_x,c_Polynomial_Osmult(T_a,V_a,V_y),c_Polynomial_Osmult(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),V_q),V_r).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_a,c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_a)).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_x_2).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_x_2),c_Groups_Oone__class_Oone(T_a))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_x_2).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2))|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2))|c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,c_Groups_Oone__class_Oone(T_a)).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Oone__class_Oone(T_a),c_Rings_Oinverse__class_Oinverse(T_a,V_x_2))| -c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)| -c_Orderings_Oord__class_Oless__e_q(T_a,V_x_2,c_Groups_Oone__class_Oone(T_a)).
% 15.19/15.14  0 [] -class_Rings_Odivision__ring(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b))=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)),c_Rings_Oinverse__class_Oinverse(T_a,V_b))).
% 15.19/15.14  0 [] -class_RealVector_Oreal__normed__field(T_a)|V_a=c_Groups_Ozero__class_Ozero(T_a)|V_b=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Oinverse(T_a,V_b)),V_h)=c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Groups_Otimes__class_Otimes(T_a,c_Rings_Oinverse__class_Oinverse(T_a,V_a),c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),V_h)),c_Rings_Oinverse__class_Oinverse(T_a,V_b))).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)|c_Polynomial_Opoly__gcd(T_a,V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))=c_Polynomial_Osmult(T_a,c_Rings_Oinverse__class_Oinverse(T_a,hAPP(c_Polynomial_Ocoeff(T_a,V_x),c_Polynomial_Odegree(T_a,V_x))),V_x).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),$f18(V_y,V_x,T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)|c_Orderings_Oord__class_Oless(T_a,$f18(V_y,V_x,T_a),c_Groups_Oone__class_Oone(T_a))|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y).
% 15.19/15.14  0 [] -class_Fields_Olinordered__field__inverse__zero(T_a)| -c_Orderings_Oord__class_Oless__e_q(T_a,c_Groups_Otimes__class_Otimes(T_a,$f18(V_y,V_x,T_a),V_x),V_y)|c_Orderings_Oord__class_Oless__e_q(T_a,V_x,V_y).
% 15.19/15.14  0 [] -class_Rings_Oidom(T_a)|hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_c_2)!=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_c_2),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),V_pa_2).
% 15.19/15.14  0 [] -class_Rings_Oidom(T_a)|hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_c_2)=c_Groups_Ozero__class_Ozero(T_a)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_c_2),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),V_pa_2).
% 15.19/15.14  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Opoly__gcd(T_a,V_x,V_y),V_x).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Opoly__gcd(T_a,V_x,V_y),V_y).
% 15.19/15.14  0 [] -class_Rings_Ocomm__ring__1(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_x_2,c_Groups_Ouminus__class_Ouminus(T_a,V_y_2))|c_Rings_Odvd__class_Odvd(T_a,V_x_2,V_y_2).
% 15.19/15.14  0 [] -class_Rings_Ocomm__ring__1(T_a)|c_Rings_Odvd__class_Odvd(T_a,V_x_2,c_Groups_Ouminus__class_Ouminus(T_a,V_y_2))| -c_Rings_Odvd__class_Odvd(T_a,V_x_2,V_y_2).
% 15.19/15.14  0 [] -class_Rings_Ocomm__ring__1(T_a)| -c_Rings_Odvd__class_Odvd(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),V_y_2)|c_Rings_Odvd__class_Odvd(T_a,V_x_2,V_y_2).
% 15.19/15.14  0 [] -class_Rings_Ocomm__ring__1(T_a)|c_Rings_Odvd__class_Odvd(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),V_y_2)| -c_Rings_Odvd__class_Odvd(T_a,V_x_2,V_y_2).
% 15.19/15.14  0 [] -class_Rings_Ocomm__ring__1(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_x,V_y)| -c_Rings_Odvd__class_Odvd(T_a,V_x,V_z)|c_Rings_Odvd__class_Odvd(T_a,V_x,c_Groups_Ominus__class_Ominus(T_a,V_y,V_z)).
% 15.19/15.14  0 [] -class_Rings_Oidom(T_a)|hAPP(c_Polynomial_Ocoeff(T_a,V_p),c_Polynomial_Odegree(T_a,V_p))!=hAPP(c_Polynomial_Ocoeff(T_a,V_q),c_Polynomial_Odegree(T_a,V_q))| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_q,V_p)|V_p=V_q.
% 15.19/15.14  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Rings_Odvd__class_Odvd(T_a,c_Groups_Oone__class_Oone(T_a),V_a).
% 15.19/15.14  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -c_Rings_Odvd__class_Odvd(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)|V_a=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.14  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -c_Rings_Odvd__class_Odvd(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c)|c_Rings_Odvd__class_Odvd(T_a,V_b,V_c).
% 15.19/15.14  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -c_Rings_Odvd__class_Odvd(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b),V_c)|c_Rings_Odvd__class_Odvd(T_a,V_a,V_c).
% 15.19/15.14  0 [] -class_Rings_Odvd(T_a)|V_a!=c_Groups_Otimes__class_Otimes(T_a,V_b,V_k)|c_Rings_Odvd__class_Odvd(T_a,V_b,V_a).
% 15.19/15.14  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)| -c_Rings_Odvd__class_Odvd(T_a,V_c,V_d)|c_Rings_Odvd__class_Odvd(T_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_c),c_Groups_Otimes__class_Otimes(T_a,V_b,V_d)).
% 15.19/15.14  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_a,V_c)|c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)).
% 15.19/15.14  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)|c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_c)).
% 15.19/15.14  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_b,V_a)).
% 15.19/15.14  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Otimes__class_Otimes(T_a,V_a,V_b)).
% 15.19/15.14  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)| -c_Rings_Odvd__class_Odvd(T_a,V_a,V_c)|c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)).
% 15.19/15.14  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_a,V_q)).
% 15.19/15.14  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),V_q)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q).
% 15.19/15.14  0 [] -class_Rings_Ocomm__semiring__1(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)| -c_Rings_Odvd__class_Odvd(T_a,V_b,V_c)|c_Rings_Odvd__class_Odvd(T_a,V_a,V_c).
% 15.19/15.14  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Rings_Odvd__class_Odvd(T_a,V_a,V_a).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)|V_aa_2=c_Groups_Ozero__class_Ozero(T_a)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_pa_2,c_Polynomial_Osmult(T_a,V_aa_2,V_q_2))|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_pa_2,V_q_2).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)|V_aa_2=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_pa_2,c_Polynomial_Osmult(T_a,V_aa_2,V_q_2))| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_pa_2,V_q_2).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q)|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_a,V_p),V_q).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,c_Polynomial_Osmult(T_a,V_a,V_q))|V_a=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q).
% 15.19/15.14  0 [] -class_Rings_Oidom(T_a)| -c_Rings_Odvd__class_Odvd(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_c_2))|V_c_2=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Odvd__class_Odvd(T_a,V_aa_2,V_b_2).
% 15.19/15.14  0 [] -class_Rings_Oidom(T_a)|c_Rings_Odvd__class_Odvd(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_c_2))|V_c_2!=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.14  0 [] -class_Rings_Oidom(T_a)|c_Rings_Odvd__class_Odvd(T_a,c_Groups_Otimes__class_Otimes(T_a,V_aa_2,V_c_2),c_Groups_Otimes__class_Otimes(T_a,V_b_2,V_c_2))| -c_Rings_Odvd__class_Odvd(T_a,V_aa_2,V_b_2).
% 15.19/15.14  0 [] -class_Rings_Oidom(T_a)| -c_Rings_Odvd__class_Odvd(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_aa_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))|V_c_2=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Odvd__class_Odvd(T_a,V_aa_2,V_b_2).
% 15.19/15.14  0 [] -class_Rings_Oidom(T_a)|c_Rings_Odvd__class_Odvd(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_aa_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))|V_c_2!=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.14  0 [] -class_Rings_Oidom(T_a)|c_Rings_Odvd__class_Odvd(T_a,c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_aa_2),c_Groups_Otimes__class_Otimes(T_a,V_c_2,V_b_2))| -c_Rings_Odvd__class_Odvd(T_a,V_aa_2,V_b_2).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_k_2,c_Polynomial_Opoly__gcd(T_a,V_x_2,V_y_2))|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_k_2,V_x_2).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_k_2,c_Polynomial_Opoly__gcd(T_a,V_x_2,V_y_2))|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_k_2,V_y_2).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_k_2,c_Polynomial_Opoly__gcd(T_a,V_x_2,V_y_2))| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_k_2,V_x_2)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_k_2,V_y_2).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_k,V_x)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_k,V_y)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_k,c_Polynomial_Opoly__gcd(T_a,V_x,V_y)).
% 15.19/15.14  0 [] -class_Divides_Osemiring__div(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)|c_Divides_Odiv__class_Omod(T_a,V_b,V_a)=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.14  0 [] -class_Divides_Osemiring__div(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_aa_2,V_b_2)|c_Divides_Odiv__class_Omod(T_a,V_b_2,V_aa_2)=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.14  0 [] -class_Divides_Osemiring__div(T_a)|c_Rings_Odvd__class_Odvd(T_a,V_aa_2,V_b_2)|c_Divides_Odiv__class_Omod(T_a,V_b_2,V_aa_2)!=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.14  0 [] -class_Divides_Osemiring__div(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_k,c_Divides_Odiv__class_Omod(T_a,V_m,V_n))| -c_Rings_Odvd__class_Odvd(T_a,V_k,V_n)|c_Rings_Odvd__class_Odvd(T_a,V_k,V_m).
% 15.19/15.14  0 [] -class_Divides_Osemiring__div(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_k,V_m)| -c_Rings_Odvd__class_Odvd(T_a,V_k,V_n)|c_Rings_Odvd__class_Odvd(T_a,V_k,c_Divides_Odiv__class_Omod(T_a,V_m,V_n)).
% 15.19/15.14  0 [] -class_Divides_Osemiring__div(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_c,V_b)|c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_c)=c_Divides_Odiv__class_Omod(T_a,V_a,V_c).
% 15.19/15.14  0 [] -class_Divides_Osemiring__div(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_k_2,V_n_2)| -c_Rings_Odvd__class_Odvd(T_a,V_k_2,c_Divides_Odiv__class_Omod(T_a,V_m_2,V_n_2))|c_Rings_Odvd__class_Odvd(T_a,V_k_2,V_m_2).
% 15.19/15.14  0 [] -class_Divides_Osemiring__div(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_k_2,V_n_2)|c_Rings_Odvd__class_Odvd(T_a,V_k_2,c_Divides_Odiv__class_Omod(T_a,V_m_2,V_n_2))| -c_Rings_Odvd__class_Odvd(T_a,V_k_2,V_m_2).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_aa_2,V_pa_2),V_q_2)|V_aa_2!=c_Groups_Ozero__class_Ozero(T_a)|V_q_2=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_aa_2,V_pa_2),V_q_2)|V_aa_2=c_Groups_Ozero__class_Ozero(T_a)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_pa_2,V_q_2).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_aa_2,V_pa_2),V_q_2)|V_aa_2=c_Groups_Ozero__class_Ozero(T_a)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_pa_2,V_q_2).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_aa_2,V_pa_2),V_q_2)|V_q_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_aa_2!=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_Osmult(T_a,V_aa_2,V_pa_2),V_q_2)|V_q_2!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_pa_2,V_q_2).
% 15.19/15.14  0 [] -class_Rings_Oidom(T_a)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_p,V_q)|V_q=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),c_Polynomial_Odegree(T_a,V_q)).
% 15.19/15.14  0 [] -class_Rings_Oidom(T_a)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_c_2,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),V_pa_2)|hAPP(c_Polynomial_Opoly(T_a,V_pa_2),c_Groups_Ouminus__class_Ouminus(T_a,V_c_2))=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.14  0 [] -class_Rings_Oidom(T_a)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_c_2,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),V_pa_2)|hAPP(c_Polynomial_Opoly(T_a,V_pa_2),c_Groups_Ouminus__class_Ouminus(T_a,V_c_2))!=c_Groups_Ozero__class_Ozero(T_a).
% 15.19/15.14  0 [] -class_Rings_Ocomm__ring(T_a)| -class_Rings_Odvd(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_d_2,V_D_2)| -c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2))|c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,c_Groups_Otimes__class_Otimes(T_a,B_k,V_D_2)),V_t_2)).
% 15.19/15.14  0 [] -class_Rings_Ocomm__ring(T_a)| -class_Rings_Odvd(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_d_2,V_D_2)|c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2))| -c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,c_Groups_Otimes__class_Otimes(T_a,B_k,V_D_2)),V_t_2)).
% 15.19/15.14  0 [] -class_Rings_Ocomm__ring(T_a)| -class_Rings_Odvd(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_d_2,V_D_2)| -c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2))|c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,c_Groups_Otimes__class_Otimes(T_a,B_k,V_D_2)),V_t_2)).
% 15.19/15.14  0 [] -class_Rings_Ocomm__ring(T_a)| -class_Rings_Odvd(T_a)| -c_Rings_Odvd__class_Odvd(T_a,V_d_2,V_D_2)|c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2))| -c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,c_Groups_Otimes__class_Otimes(T_a,B_k,V_D_2)),V_t_2)).
% 15.19/15.14  0 [] c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k).
% 15.19/15.14  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_m)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)).
% 15.19/15.14  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_m).
% 15.19/15.14  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_m)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_n,V_m)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n).
% 15.19/15.14  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_m_2=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.19/15.14  0 [] c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|V_m_2!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.19/15.14  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_n,V_m).
% 15.19/15.14  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2))|V_k_2=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.14  0 [] c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2))|V_k_2!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.14  0 [] c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2))| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.14  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m_2,c_Groups_Oone__class_Oone(tc_Nat_Onat))|V_m_2=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.19/15.14  0 [] c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m_2,c_Groups_Oone__class_Oone(tc_Nat_Onat))|V_m_2!=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.19/15.14  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2))|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k_2,V_n_2).
% 15.19/15.14  0 [] c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2))| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k_2,V_n_2).
% 15.19/15.14  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,V_k,V_n).
% 15.19/15.14  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_m),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k,V_n))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m,V_n).
% 15.19/15.14  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2))|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.14  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_m_2),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_k_2,V_n_2))| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m_2,V_n_2).
% 15.19/15.14  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2),V_m_2)|V_n_2=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.19/15.14  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m_2,V_n_2),V_m_2)|V_n_2!=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.19/15.14  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2,V_m_2),V_m_2)|V_n_2=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.19/15.14  0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m_2)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n_2,V_m_2),V_m_2)|V_n_2!=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.19/15.14  0 [] -class_Rings_Odvd(T_a)| -class_Rings_Osemiring__0(T_a)| -hBOOL(hAPP(V_P_2,c_Groups_Otimes__class_Otimes(T_a,V_l_2,B_x)))|c_Rings_Odvd__class_Odvd(T_a,V_l_2,c_Groups_Oplus__class_Oplus(T_a,$f19(V_l_2,V_P_2,T_a),c_Groups_Ozero__class_Ozero(T_a))).
% 15.19/15.14  0 [] -class_Rings_Odvd(T_a)| -class_Rings_Osemiring__0(T_a)| -hBOOL(hAPP(V_P_2,c_Groups_Otimes__class_Otimes(T_a,V_l_2,B_x)))|hBOOL(hAPP(V_P_2,$f19(V_l_2,V_P_2,T_a))).
% 15.19/15.14  0 [] -class_Rings_Odvd(T_a)| -class_Rings_Osemiring__0(T_a)|hBOOL(hAPP(V_P_2,c_Groups_Otimes__class_Otimes(T_a,V_l_2,$f20(V_l_2,V_P_2,T_a))))| -c_Rings_Odvd__class_Odvd(T_a,V_l_2,c_Groups_Oplus__class_Oplus(T_a,X1,c_Groups_Ozero__class_Ozero(T_a)))| -hBOOL(hAPP(V_P_2,X1)).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_x)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_y)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),$f21(V_y,V_x,V_d,T_a),V_x)|V_x=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))!=c_Groups_Oone__class_Oone(T_a)|c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=V_d.
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_x)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_y)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),$f21(V_y,V_x,V_d,T_a),V_x)|V_y=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))!=c_Groups_Oone__class_Oone(T_a)|c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=V_d.
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_x)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_y)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),$f21(V_y,V_x,V_d,T_a),V_x)|hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))!=c_Groups_Ozero__class_Ozero(T_a)|V_x!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_y!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=V_d.
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_x)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_y)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),$f21(V_y,V_x,V_d,T_a),V_x)|hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))!=c_Groups_Ozero__class_Ozero(T_a)|hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))!=c_Groups_Oone__class_Oone(T_a)|c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=V_d.
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_x)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_y)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),$f21(V_y,V_x,V_d,T_a),V_y)|V_x=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))!=c_Groups_Oone__class_Oone(T_a)|c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=V_d.
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_x)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_y)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),$f21(V_y,V_x,V_d,T_a),V_y)|V_y=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))!=c_Groups_Oone__class_Oone(T_a)|c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=V_d.
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_x)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_y)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),$f21(V_y,V_x,V_d,T_a),V_y)|hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))!=c_Groups_Ozero__class_Ozero(T_a)|V_x!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_y!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=V_d.
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_x)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_y)|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),$f21(V_y,V_x,V_d,T_a),V_y)|hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))!=c_Groups_Ozero__class_Ozero(T_a)|hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))!=c_Groups_Oone__class_Oone(T_a)|c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=V_d.
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_x)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_y)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),$f21(V_y,V_x,V_d,T_a),V_d)|V_x=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))!=c_Groups_Oone__class_Oone(T_a)|c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=V_d.
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_x)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_y)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),$f21(V_y,V_x,V_d,T_a),V_d)|V_y=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))!=c_Groups_Oone__class_Oone(T_a)|c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=V_d.
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_x)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_y)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),$f21(V_y,V_x,V_d,T_a),V_d)|hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))!=c_Groups_Ozero__class_Ozero(T_a)|V_x!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|V_y!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=V_d.
% 15.19/15.14  0 [] -class_Fields_Ofield(T_a)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_x)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),V_d,V_y)| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),$f21(V_y,V_x,V_d,T_a),V_d)|hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))!=c_Groups_Ozero__class_Ozero(T_a)|hAPP(c_Polynomial_Ocoeff(T_a,V_d),c_Polynomial_Odegree(T_a,V_d))!=c_Groups_Oone__class_Oone(T_a)|c_Polynomial_Opoly__gcd(T_a,V_x,V_y)=V_d.
% 15.19/15.14  0 [] -class_Rings_Oidom(T_a)|V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))|c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),c_Polynomial_Oorder(T_a,V_a,V_p)),V_p).
% 15.19/15.14  0 [] -class_Rings_Oidom(T_a)|V_p=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))| -c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),c_Nat_OSuc(c_Polynomial_Oorder(T_a,V_a,V_p))),V_p).
% 15.19/15.14  0 [] c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_x).
% 15.19/15.14  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_y)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z).
% 15.19/15.14  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_y)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_x).
% 15.19/15.14  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z).
% 15.19/15.14  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_x).
% 15.19/15.14  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a)|V_b!=V_c|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c).
% 15.19/15.14  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a)|V_b!=V_c| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_c,V_a).
% 15.19/15.14  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)|V_y!=V_x.
% 15.19/15.14  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)|V_x!=V_y.
% 15.19/15.14  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)|V_x!=V_y.
% 15.19/15.14  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_y)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z).
% 15.19/15.14  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_y)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_x).
% 15.19/15.14  0 [] V_a!=V_b| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_c)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_c,V_b)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c).
% 15.19/15.14  0 [] V_a!=V_b| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_c)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_c,V_b)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_c,V_a).
% 15.19/15.14  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z).
% 15.19/15.14  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)|V_x=V_y.
% 15.19/15.14  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m,V_n)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_n,V_m)|V_m=V_n.
% 15.19/15.14  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)|V_b!=V_c|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c).
% 15.19/15.14  0 [] V_a!=V_b| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_c)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c).
% 15.19/15.14  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)|V_a=V_b| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a).
% 15.19/15.14  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)|V_x=V_y.
% 15.19/15.14  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)|V_x_2=V_y_2.
% 15.19/15.14  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 15.19/15.14  0 [] V_x!=V_y|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y).
% 15.19/15.14  0 [] V_a=V_b| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a).
% 15.19/15.14  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)|V_x_2!=V_y_2.
% 15.19/15.14  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)|V_x_2=V_y_2.
% 15.19/15.14  0 [] -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)|V_x_2=V_y_2.
% 15.19/15.14  0 [] c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)|V_x_2!=V_y_2.
% 15.19/15.14  0 [] V_x_2!=V_y_2|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2).
% 15.19/15.14  0 [] V_x_2!=V_y_2|c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2).
% 15.19/15.14  0 [] V_x_2=V_y_2| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)| -c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2).
% 15.19/15.14  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(T_a,c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a),V_p,V_n)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Polynomial_Odegree(T_a,V_p),V_n)).
% 15.19/15.14  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Oone__class_Oone(tc_Nat_Onat))=V_x.
% 15.19/15.14  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Power_Opower__class_Opower(T_a,c_Groups_Otimes__class_Otimes(T_a,V_x,V_y),V_q)=c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_q),c_Power_Opower__class_Opower(T_a,V_y,V_q)).
% 15.19/15.14  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Power_Opower__class_Opower(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_p),V_q)=c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_p,V_q)).
% 15.19/15.14  0 [] -class_Rings_Ocomm__semiring__1(T_a)|hAPP(c_Polynomial_Opoly(T_a,c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a),V_p,V_n)),V_x)=c_Power_Opower__class_Opower(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),V_n).
% 15.19/15.14  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_p),c_Power_Opower__class_Opower(T_a,V_x,V_q))=c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)).
% 15.19/15.14  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Power_Opower__class_Opower(T_a,V_x,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oone__class_Oone(T_a).
% 15.19/15.14  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Otimes__class_Otimes(T_a,c_Power_Opower__class_Opower(T_a,V_x,V_q),V_x)=c_Power_Opower__class_Opower(T_a,V_x,c_Nat_OSuc(V_q)).
% 15.19/15.14  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Groups_Otimes__class_Otimes(T_a,V_x,c_Power_Opower__class_Opower(T_a,V_x,V_q))=c_Power_Opower__class_Opower(T_a,V_x,c_Nat_OSuc(V_q)).
% 15.19/15.14  0 [] -class_Rings_Ocomm__semiring__1(T_a)|c_Power_Opower__class_Opower(T_a,V_x,c_Nat_OSuc(V_q))=c_Groups_Otimes__class_Otimes(T_a,V_x,c_Power_Opower__class_Opower(T_a,V_x,V_q)).
% 15.19/15.14  0 [] -class_Groups_Ocancel__comm__monoid__add(T_1)|class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat).
% 15.19/15.14  0 [] -class_Lattices_Oboolean__algebra(T_1)|class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)).
% 15.19/15.14  0 [] -class_Orderings_Opreorder(T_1)|class_Orderings_Opreorder(tc_fun(T_2,T_1)).
% 15.19/15.14  0 [] -class_Orderings_Oorder(T_1)|class_Orderings_Oorder(tc_fun(T_2,T_1)).
% 15.19/15.14  0 [] -class_Orderings_Oord(T_1)|class_Orderings_Oord(tc_fun(T_2,T_1)).
% 15.19/15.14  0 [] -class_Groups_Ouminus(T_1)|class_Groups_Ouminus(tc_fun(T_2,T_1)).
% 15.19/15.14  0 [] -class_Groups_Ominus(T_1)|class_Groups_Ominus(tc_fun(T_2,T_1)).
% 15.19/15.14  0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat).
% 15.19/15.14  0 [] class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat).
% 15.19/15.14  0 [] class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat).
% 15.19/15.14  0 [] class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat).
% 15.19/15.14  0 [] class_Rings_Olinordered__semiring__strict(tc_Nat_Onat).
% 15.19/15.14  0 [] class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat).
% 15.19/15.14  0 [] class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat).
% 15.19/15.14  0 [] class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat).
% 15.19/15.14  0 [] class_Rings_Oordered__cancel__semiring(tc_Nat_Onat).
% 15.19/15.14  0 [] class_Rings_Oordered__comm__semiring(tc_Nat_Onat).
% 15.19/15.14  0 [] class_Groups_Ocancel__semigroup__add(tc_Nat_Onat).
% 15.19/15.14  0 [] class_Rings_Olinordered__semiring(tc_Nat_Onat).
% 15.19/15.14  0 [] class_Rings_Olinordered__semidom(tc_Nat_Onat).
% 15.19/15.14  0 [] class_Groups_Oab__semigroup__mult(tc_Nat_Onat).
% 15.19/15.14  0 [] class_Groups_Ocomm__monoid__mult(tc_Nat_Onat).
% 15.19/15.14  0 [] class_Groups_Oab__semigroup__add(tc_Nat_Onat).
% 15.19/15.14  0 [] class_Rings_Oordered__semiring(tc_Nat_Onat).
% 15.19/15.14  0 [] class_Rings_Ono__zero__divisors(tc_Nat_Onat).
% 15.19/15.14  0 [] class_Groups_Ocomm__monoid__add(tc_Nat_Onat).
% 15.19/15.14  0 [] class_Rings_Ocomm__semiring__1(tc_Nat_Onat).
% 15.19/15.14  0 [] class_Rings_Ocomm__semiring__0(tc_Nat_Onat).
% 15.19/15.14  0 [] class_Divides_Osemiring__div(tc_Nat_Onat).
% 15.19/15.14  0 [] class_Rings_Ocomm__semiring(tc_Nat_Onat).
% 15.19/15.14  0 [] class_Rings_Ozero__ne_q__one(tc_Nat_Onat).
% 15.19/15.14  0 [] class_Orderings_Opreorder(tc_Nat_Onat).
% 15.19/15.14  0 [] class_Orderings_Olinorder(tc_Nat_Onat).
% 15.19/15.14  0 [] class_Groups_Omonoid__mult(tc_Nat_Onat).
% 15.19/15.14  0 [] class_Groups_Omonoid__add(tc_Nat_Onat).
% 15.19/15.14  0 [] class_Rings_Osemiring__0(tc_Nat_Onat).
% 15.19/15.14  0 [] class_Rings_Omult__zero(tc_Nat_Onat).
% 15.19/15.14  0 [] class_Orderings_Oorder(tc_Nat_Onat).
% 15.19/15.14  0 [] class_Rings_Osemiring(tc_Nat_Onat).
% 15.19/15.14  0 [] class_Orderings_Oord(tc_Nat_Onat).
% 15.19/15.14  0 [] class_Groups_Ominus(tc_Nat_Onat).
% 15.19/15.14  0 [] class_Groups_Ozero(tc_Nat_Onat).
% 15.19/15.14  0 [] class_Groups_Oone(tc_Nat_Onat).
% 15.19/15.14  0 [] class_Rings_Odvd(tc_Nat_Onat).
% 15.19/15.14  0 [] class_Lattices_Oboolean__algebra(tc_HOL_Obool).
% 15.19/15.14  0 [] class_Orderings_Opreorder(tc_HOL_Obool).
% 15.19/15.14  0 [] class_Orderings_Oorder(tc_HOL_Obool).
% 15.19/15.14  0 [] class_Orderings_Oord(tc_HOL_Obool).
% 15.19/15.14  0 [] class_Groups_Ouminus(tc_HOL_Obool).
% 15.19/15.14  0 [] class_Groups_Ominus(tc_HOL_Obool).
% 15.19/15.14  0 [] class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_RealVector_Oreal__field(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_Rings_Odivision__ring(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_Rings_Ocomm__semiring(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_Groups_Oab__group__add(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_Rings_Ozero__ne_q__one(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_Groups_Omonoid__mult(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_Groups_Omonoid__add(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_Rings_Osemiring__0(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_Groups_Ogroup__add(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_Rings_Omult__zero(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_Rings_Ocomm__ring(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_Int_Oring__char__0(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_Rings_Osemiring(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_Groups_Ouminus(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_Rings_Oring__1(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_Groups_Ominus(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_Fields_Ofield(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_Groups_Ozero(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_Rings_Oring(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_Rings_Oidom(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_Groups_Oone(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] class_Rings_Odvd(tc_Complex_Ocomplex).
% 15.19/15.14  0 [] -class_Rings_Oidom(T_1)|class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Groups_Ocancel__comm__monoid__add(T_1)|class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Oidom(T_1)|class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Oidom(T_1)|class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Groups_Ocancel__comm__monoid__add(T_1)|class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Groups_Ocomm__monoid__add(T_1)|class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Oordered__semiring(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Oidom(T_1)|class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Groups_Ocomm__monoid__add(T_1)|class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_1)|class_Divides_Osemiring__div(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Groups_Oab__group__add(T_1)|class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Rings_Ozero__ne_q__one(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_1)|class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_1)|class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_1)|class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Ocomm__ring__1(T_1)|class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Groups_Ocomm__monoid__add(T_1)|class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Groups_Oab__group__add(T_1)|class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Fields_Ofield(T_1)|class_Divides_Oring__div(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Ocomm__ring(T_1)|class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_1)|class_Orderings_Oorder(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_1)|class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Ocomm__semiring__0(T_1)|class_Rings_Osemiring(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_1)|class_Orderings_Oord(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Groups_Oab__group__add(T_1)|class_Groups_Ouminus(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Olinordered__idom(T_1)|class_Groups_Osgn__if(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Ocomm__ring__1(T_1)|class_Rings_Oring__1(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Groups_Oab__group__add(T_1)|class_Groups_Ominus(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Groups_Ozero(T_1)|class_Groups_Ozero(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Ocomm__ring(T_1)|class_Rings_Oring(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Oidom(T_1)|class_Rings_Oidom(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Groups_Oone(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -class_Rings_Ocomm__semiring__1(T_1)|class_Rings_Odvd(tc_Polynomial_Opoly(T_1)).
% 15.19/15.14  0 [] -hBOOL(c_fe_qual(V_x_2,V_y_2))|V_x_2=V_y_2.
% 15.19/15.14  0 [] V_x_2!=V_y_2|hBOOL(c_fe_qual(V_x_2,V_y_2)).
% 15.19/15.14  0 [] c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,B_q)!=c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(tc_Complex_Ocomplex,v_p)|hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,B_q),$f22(B_q))!=hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_p),c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_a,$f22(B_q))).
% 15.19/15.14  end_of_list.
% 15.19/15.14  
% 15.19/15.14  SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=8.
% 15.19/15.14  
% 15.19/15.14  This ia a non-Horn set with equality.  The strategy will be
% 15.19/15.14  Knuth-Bendix, ordered hyper_res, factoring, and unit
% 15.19/15.14  deletion, with positive clauses in sos and nonpositive
% 15.19/15.14  clauses in usable.
% 15.19/15.14  
% 15.19/15.14     dependent: set(knuth_bendix).
% 15.19/15.14     dependent: set(anl_eq).
% 15.19/15.14     dependent: set(para_from).
% 15.19/15.14     dependent: set(para_into).
% 15.19/15.14     dependent: clear(para_from_right).
% 15.19/15.14     dependent: clear(para_into_right).
% 15.19/15.14     dependent: set(para_from_vars).
% 15.19/15.14     dependent: set(eq_units_both_ways).
% 15.19/15.14     dependent: set(dynamic_demod_all).
% 15.19/15.14     dependent: set(dynamic_demod).
% 15.19/15.14     dependent: set(order_eq).
% 15.19/15.14     dependent: set(back_demod).
% 15.19/15.14     dependent: set(lrpo).
% 15.19/15.14     dependent: set(hyper_res).
% 15.19/15.14     dependent: set(unit_deletion).
% 15.19/15.14     dependent: set(factor).
% 15.19/15.14  
% 15.19/15.14  ------------> process usable:
% 15.19/15.14  ** KEPT (pick-wt=14): 1 [] hAPP(A,$f1(B,A))!=hAPP(B,$f1(B,A))|A=B.
% 15.19/15.14  ** KEPT (pick-wt=24): 2 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(c_Polynomial_Opoly(A,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C)),D)=c_Groups_Oplus__class_Oplus(A,hAPP(c_Polynomial_Opoly(A,B),D),hAPP(c_Polynomial_Opoly(A,C),D)).
% 15.19/15.14  ** KEPT (pick-wt=19): 3 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(c_Polynomial_Opoly(A,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(A,B,C)),D)=hAPP(c_Polynomial_Opoly(A,B),c_Groups_Oplus__class_Oplus(A,C,D)).
% 15.19/15.14  ** KEPT (pick-wt=14): 4 [] -class_Int_Oring__char__0(A)| -class_Rings_Oidom(A)|c_Polynomial_Opoly(A,B)!=c_Polynomial_Opoly(A,C)|B=C.
% 15.19/15.14  ** KEPT (pick-wt=14): 5 [] -class_Int_Oring__char__0(A)| -class_Rings_Oidom(A)|c_Polynomial_Opoly(A,B)=c_Polynomial_Opoly(A,C)|B!=C.
% 15.19/15.14  ** KEPT (pick-wt=11): 6 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,B,C)=c_Groups_Oplus__class_Oplus(A,C,B).
% 15.19/15.14  ** KEPT (pick-wt=17): 7 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oplus__class_Oplus(A,C,D))=c_Groups_Oplus__class_Oplus(A,C,c_Groups_Oplus__class_Oplus(A,B,D)).
% 15.19/15.14  ** KEPT (pick-wt=17): 9 [copy,8,flip.2] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,C),D)=c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oplus__class_Oplus(A,C,D)).
% 15.19/15.14    Following clause subsumed by 9 during input processing: 0 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,C),D)=c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oplus__class_Oplus(A,C,D)).
% 15.19/15.14  ** KEPT (pick-wt=17): 10 [] -class_Groups_Oab__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,C),D)=c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oplus__class_Oplus(A,C,D)).
% 15.19/15.14  ** KEPT (pick-wt=17): 11 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,C),D)=c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,D),C).
% 15.19/15.14  ** KEPT (pick-wt=14): 12 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Oplus__class_Oplus(A,B,D)|C=D.
% 15.19/15.14  ** KEPT (pick-wt=14): 13 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)=c_Groups_Oplus__class_Oplus(A,B,D)|C!=D.
% 15.19/15.14  ** KEPT (pick-wt=14): 14 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Oplus__class_Oplus(A,D,C)|B=D.
% 15.19/15.14  ** KEPT (pick-wt=14): 15 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)=c_Groups_Oplus__class_Oplus(A,D,C)|B!=D.
% 15.19/15.14  ** KEPT (pick-wt=23): 16 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,E))=c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)).
% 15.19/15.14    Following clause subsumed by 14 during input processing: 0 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Oplus__class_Oplus(A,D,C)|B=D.
% 15.19/15.14  ** KEPT (pick-wt=14): 17 [] -class_Groups_Ocancel__ab__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Oplus__class_Oplus(A,B,D)|C=D.
% 15.19/15.14    Following clause subsumed by 12 during input processing: 0 [] -class_Groups_Ocancel__semigroup__add(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Oplus__class_Oplus(A,B,D)|C=D.
% 15.19/15.14  ** KEPT (pick-wt=20): 18 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(c_Polynomial_Opoly(A,c_Polynomial_Opcompose(A,B,C)),D)=hAPP(c_Polynomial_Opoly(A,B),hAPP(c_Polynomial_Opoly(A,C),D)).
% 15.19/15.14  ** KEPT (pick-wt=21): 19 [] -class_Groups_Ocomm__monoid__add(A)|c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Polynomial_Omonom(A,B,C),c_Polynomial_Omonom(A,D,C))=c_Polynomial_Omonom(A,c_Groups_Oplus__class_Oplus(A,B,D),C).
% 15.19/15.14  ** KEPT (pick-wt=15): 20 [] -class_Rings_Olinordered__idom(A)| -c_Polynomial_Opos__poly(A,B)| -c_Polynomial_Opos__poly(A,C)|c_Polynomial_Opos__poly(A,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C)).
% 15.19/15.14  ** KEPT (pick-wt=21): 21 [] -class_Rings_Ocomm__semiring__0(A)|c_Polynomial_Osmult(A,c_Groups_Oplus__class_Oplus(A,B,C),D)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Polynomial_Osmult(A,B,D),c_Polynomial_Osmult(A,C,D)).
% 15.19/15.14  ** KEPT (pick-wt=24): 22 [] -class_Groups_Ocomm__monoid__add(A)|hAPP(c_Polynomial_Ocoeff(A,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C)),D)=c_Groups_Oplus__class_Oplus(A,hAPP(c_Polynomial_Ocoeff(A,B),D),hAPP(c_Polynomial_Ocoeff(A,C),D)).
% 15.19/15.14  ** KEPT (pick-wt=25): 24 [copy,23,flip.2] -class_Groups_Ocomm__monoid__add(A)|c_Polynomial_OpCons(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),D,E))=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Polynomial_OpCons(A,B,D),c_Polynomial_OpCons(A,C,E)).
% 15.19/15.14  ** KEPT (pick-wt=22): 25 [] -c_Groups_Osemigroup(A,B)|hAPP(hAPP(B,hAPP(hAPP(B,C),D)),E)=hAPP(hAPP(B,C),hAPP(hAPP(B,D),E)).
% 15.19/15.14  ** KEPT (pick-wt=11): 26 [] -c_Groups_Ocomm__monoid(A,B,C)|hAPP(hAPP(B,D),C)=D.
% 15.19/15.14  ** KEPT (pick-wt=12): 27 [] -class_Rings_Ocomm__semiring__0(A)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.19/15.14  ** KEPT (pick-wt=15): 28 [] -class_Rings_Ocomm__semiring__0(A)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(A,B,C)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.19/15.14  ** KEPT (pick-wt=15): 29 [] -class_Rings_Ocomm__semiring__0(A)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(A,B,C)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|B!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.19/15.14  ** KEPT (pick-wt=11): 30 [] -class_Groups_Ocomm__monoid__add(A)|c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B)=B.
% 15.19/15.14  ** KEPT (pick-wt=11): 31 [] -class_Groups_Ocomm__monoid__add(A)|c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))=B.
% 15.19/15.14  ** KEPT (pick-wt=7): 32 [] -class_Rings_Olinordered__idom(A)| -c_Polynomial_Opos__poly(A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))).
% 15.19/15.14  ** KEPT (pick-wt=13): 33 [] -class_Groups_Ozero(A)|c_Polynomial_OpCons(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.19/15.14  ** KEPT (pick-wt=12): 34 [] -class_Groups_Ozero(A)|hAPP(c_Polynomial_Ocoeff(A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.14  ** KEPT (pick-wt=11): 35 [] -class_Groups_Ozero(A)|c_Polynomial_Omonom(A,c_Groups_Ozero__class_Ozero(A),B)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.19/15.14  ** KEPT (pick-wt=11): 36 [] -class_Rings_Ocomm__semiring__0(A)|c_Polynomial_Osmult(A,c_Groups_Ozero__class_Ozero(A),B)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.19/15.14  ** KEPT (pick-wt=12): 37 [] -class_Rings_Ocomm__semiring__0(A)|c_Polynomial_Opcompose(A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.19/15.14  ** KEPT (pick-wt=10): 38 [] -class_Groups_Ozero(A)|c_Groups_Ozero__class_Ozero(A)!=B|B=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.14  ** KEPT (pick-wt=10): 39 [] -class_Groups_Ozero(A)|c_Groups_Ozero__class_Ozero(A)=B|B!=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.14  ** KEPT (pick-wt=12): 40 [] -class_Rings_Ocomm__semiring__0(A)|c_Polynomial_Osmult(A,B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.19/15.14  ** KEPT (pick-wt=16): 41 [] -class_Groups_Ozero(A)|B!=C|hAPP(c_Polynomial_Ocoeff(A,B),D)=hAPP(c_Polynomial_Ocoeff(A,C),D).
% 15.19/15.14  ** KEPT (pick-wt=22): 42 [] -class_Groups_Ozero(A)|B=C|hAPP(c_Polynomial_Ocoeff(A,B),$f2(C,B,A))!=hAPP(c_Polynomial_Ocoeff(A,C),$f2(C,B,A)).
% 15.19/15.14  ** KEPT (pick-wt=12): 43 [] -class_Groups_Ozero(A)|c_Polynomial_Ocoeff(A,B)!=c_Polynomial_Ocoeff(A,C)|B=C.
% 15.19/15.14  ** KEPT (pick-wt=12): 44 [] -class_Groups_Ozero(A)|c_Polynomial_Ocoeff(A,B)=c_Polynomial_Ocoeff(A,C)|B!=C.
% 15.19/15.14  ** KEPT (pick-wt=14): 45 [] -class_Groups_Ozero(A)|c_Polynomial_Omonom(A,B,C)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|B=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.14  ** KEPT (pick-wt=14): 46 [] -class_Groups_Ozero(A)|c_Polynomial_Omonom(A,B,C)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|B!=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.14  ** KEPT (pick-wt=14): 47 [] -class_Groups_Ozero(A)|c_Polynomial_OpCons(A,B,C)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|B=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.14  ** KEPT (pick-wt=15): 48 [] -class_Groups_Ozero(A)|c_Polynomial_OpCons(A,B,C)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|C=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.19/15.14  ** KEPT (pick-wt=19): 49 [] -class_Groups_Ozero(A)|c_Polynomial_OpCons(A,B,C)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|B!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.19/15.14  ** KEPT (pick-wt=19): 50 [] -class_Rings_Oidom(A)|c_Polynomial_Osmult(A,B,C)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|B=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.19/15.14  ** KEPT (pick-wt=14): 51 [] -class_Rings_Oidom(A)|c_Polynomial_Osmult(A,B,C)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|B!=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.14  ** KEPT (pick-wt=15): 52 [] -class_Rings_Oidom(A)|c_Polynomial_Osmult(A,B,C)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|C!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.19/15.14  ** KEPT (pick-wt=15): 53 [] -class_Groups_Ozero(A)|B!=C|hAPP(c_Polynomial_Ocoeff(A,c_Polynomial_Omonom(A,D,B)),C)=D.
% 15.19/15.14  ** KEPT (pick-wt=16): 54 [] -class_Groups_Ozero(A)|B=C|hAPP(c_Polynomial_Ocoeff(A,c_Polynomial_Omonom(A,D,B)),C)=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.14  ** KEPT (pick-wt=14): 55 [] -class_Groups_Ozero(A)|c_Polynomial_Omonom(A,B,C)!=c_Polynomial_Omonom(A,D,C)|B=D.
% 15.19/15.14  ** KEPT (pick-wt=14): 56 [] -class_Groups_Ozero(A)|c_Polynomial_Omonom(A,B,C)=c_Polynomial_Omonom(A,D,C)|B!=D.
% 15.19/15.14  ** KEPT (pick-wt=14): 57 [] -class_Groups_Ozero(A)|c_Polynomial_OpCons(A,B,C)!=c_Polynomial_OpCons(A,D,E)|B=D.
% 15.19/15.14  ** KEPT (pick-wt=14): 58 [] -class_Groups_Ozero(A)|c_Polynomial_OpCons(A,B,C)!=c_Polynomial_OpCons(A,D,E)|C=E.
% 15.19/15.14  ** KEPT (pick-wt=17): 59 [] -class_Groups_Ozero(A)|c_Polynomial_OpCons(A,B,C)=c_Polynomial_OpCons(A,D,E)|B!=D|C!=E.
% 15.19/15.14  ** KEPT (pick-wt=16): 60 [] -class_Rings_Ocomm__semiring__0(A)|c_Polynomial_Osmult(A,B,C)!=c_Polynomial_OpCons(A,D,C)|C=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.19/15.14  ** KEPT (pick-wt=22): 61 [] -class_Rings_Ocomm__semiring__0(A)|c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Polynomial_Osmult(A,B,C),c_Polynomial_OpCons(A,D,C))!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|C=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.19/15.14  ** KEPT (pick-wt=12): 62 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(c_Polynomial_Opoly(A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),B)=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.14  ** KEPT (pick-wt=18): 63 [] -class_Rings_Ocomm__semiring__0(A)|c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(A,c_Polynomial_OpCons(A,B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)=c_Polynomial_OpCons(A,B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))).
% 15.19/15.14  ** KEPT (pick-wt=27): 65 [copy,64,flip.2] -class_Rings_Ocomm__semiring__0(A)|c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Polynomial_Osmult(A,B,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(A,C,B)),c_Polynomial_OpCons(A,D,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(A,C,B)))=c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(A,c_Polynomial_OpCons(A,D,C),B).
% 15.19/15.14  ** KEPT (pick-wt=9): 66 [] -class_Groups_Omonoid__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ozero__class_Ozero(A),B)=B.
% 15.19/15.14  ** KEPT (pick-wt=9): 67 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ozero__class_Ozero(A),B)=B.
% 15.19/15.14  ** KEPT (pick-wt=9): 68 [] -class_Groups_Ocomm__monoid__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ozero__class_Ozero(A),B)=B.
% 15.19/15.14  ** KEPT (pick-wt=13): 69 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ozero__class_Ozero(A)!=c_Groups_Oplus__class_Oplus(A,B,B)|B=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.14  ** KEPT (pick-wt=13): 70 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Ozero__class_Ozero(A)=c_Groups_Oplus__class_Oplus(A,B,B)|B!=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.14  ** KEPT (pick-wt=9): 71 [] -class_Groups_Omonoid__add(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ozero__class_Ozero(A))=B.
% 15.19/15.14  ** KEPT (pick-wt=9): 72 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ozero__class_Ozero(A))=B.
% 15.19/15.14  ** KEPT (pick-wt=9): 73 [] -class_Groups_Ocomm__monoid__add(A)|c_Groups_Oplus__class_Oplus(A,B,c_Groups_Ozero__class_Ozero(A))=B.
% 15.19/15.14  ** KEPT (pick-wt=12): 75 [copy,74,flip.2] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|c_Groups_Oplus__class_Oplus(A,B,C)!=B|C=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.14  ** KEPT (pick-wt=12): 77 [copy,76,flip.2] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|c_Groups_Oplus__class_Oplus(A,B,C)=B|C!=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.14  ** KEPT (pick-wt=22): 78 [] -class_Rings_Ocomm__semiring__0(A)|c_Polynomial_Osmult(A,B,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),C,D))=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Polynomial_Osmult(A,B,C),c_Polynomial_Osmult(A,B,D)).
% 15.19/15.14    Following clause subsumed by 4 during input processing: 0 [] -class_Int_Oring__char__0(A)| -class_Rings_Oidom(A)|c_Polynomial_Opoly(A,B)!=c_Polynomial_Opoly(A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.19/15.14    Following clause subsumed by 5 during input processing: 0 [] -class_Int_Oring__char__0(A)| -class_Rings_Oidom(A)|c_Polynomial_Opoly(A,B)=c_Polynomial_Opoly(A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))|B!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.19/15.14  ** KEPT (pick-wt=22): 79 [] -class_Rings_Ocomm__semiring__0(A)|c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,c_Polynomial_Osmult(A,C,D))!=c_Polynomial_OpCons(A,E,D)|E=hAPP(c_Polynomial_Opoly(A,B),C).
% 15.19/15.14  ** KEPT (pick-wt=21): 80 [] -class_Rings_Ocomm__semiring__0(A)|c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,c_Polynomial_Osmult(A,C,D))!=c_Polynomial_OpCons(A,E,D)|D=c_Polynomial_Osynthetic__div(A,B,C).
% 15.19/15.14  ** KEPT (pick-wt=25): 81 [] -class_Rings_Ocomm__semiring__0(A)|c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,c_Polynomial_Osmult(A,C,c_Polynomial_Osynthetic__div(A,B,C)))=c_Polynomial_OpCons(A,hAPP(c_Polynomial_Opoly(A,B),C),c_Polynomial_Osynthetic__div(A,B,C)).
% 15.19/15.14  ** KEPT (pick-wt=22): 82 [] -class_Rings_Oidom(A)|hAPP(c_Polynomial_Opoly(A,B),C)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|c_Polynomial_Oorder(A,C,B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.14  ** KEPT (pick-wt=15): 83 [] -class_Rings_Oidom(A)|hAPP(c_Polynomial_Opoly(A,B),C)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.19/15.14  ** KEPT (pick-wt=17): 84 [] -class_Rings_Oidom(A)|hAPP(c_Polynomial_Opoly(A,B),C)=c_Groups_Ozero__class_Ozero(A)|c_Polynomial_Oorder(A,C,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.14  ** KEPT (pick-wt=13): 85 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Oplus__class_Oplus(A,B,B)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.14  ** KEPT (pick-wt=13): 86 [] -class_Groups_Olinordered__ab__group__add(A)|c_Groups_Oplus__class_Oplus(A,B,B)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.14  ** KEPT (pick-wt=36): 88 [copy,87,flip.3] -class_Groups_Ozero(A)|hAPP(hAPP(hAPP(B,c_Groups_Ozero__class_Ozero(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)!=C|hAPP(hAPP(hAPP(B,D),E),c_Polynomial_Opoly__rec(F,A,C,B,E))=c_Polynomial_Opoly__rec(F,A,C,B,c_Polynomial_OpCons(A,D,E)).
% 15.19/15.14  ** KEPT (pick-wt=27): 89 [] -class_Rings_Ocomm__semiring__0(A)|c_Polynomial_Opcompose(A,c_Polynomial_OpCons(A,B,C),D)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Polynomial_OpCons(A,B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),D,c_Polynomial_Opcompose(A,C,D))).
% 15.19/15.14  ** KEPT (pick-wt=32): 91 [copy,90,flip.2] -class_Groups_Ozero(A)|hAPP(hAPP(hAPP(B,C),D),c_If(E,c_fe_qual(D,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),F,c_Polynomial_Opoly__rec(E,A,F,B,D)))=c_Polynomial_Opoly__rec(E,A,F,B,c_Polynomial_OpCons(A,C,D)).
% 15.19/15.14  ** KEPT (pick-wt=16): 92 [] -class_Rings_Olinordered__idom(A)| -c_Polynomial_Opos__poly(A,c_Polynomial_OpCons(A,B,C))|c_Polynomial_Opos__poly(A,C)|C=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.19/15.14  ** KEPT (pick-wt=16): 93 [] -class_Rings_Olinordered__idom(A)| -c_Polynomial_Opos__poly(A,c_Polynomial_OpCons(A,B,C))|c_Polynomial_Opos__poly(A,C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 15.19/15.14  ** KEPT (pick-wt=11): 94 [] -class_Rings_Olinordered__idom(A)|c_Polynomial_Opos__poly(A,c_Polynomial_OpCons(A,B,C))| -c_Polynomial_Opos__poly(A,C).
% 15.19/15.14  ** KEPT (pick-wt=18): 95 [] -class_Rings_Olinordered__idom(A)|c_Polynomial_Opos__poly(A,c_Polynomial_OpCons(A,B,C))|C!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 15.19/15.14  ** KEPT (pick-wt=27): 96 [] -class_Rings_Ocomm__semiring__0(A)|c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,c_Polynomial_OpCons(A,C,D))=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Polynomial_Osmult(A,C,B),c_Polynomial_OpCons(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,D))).
% 15.19/15.14  ** KEPT (pick-wt=27): 97 [] -class_Rings_Ocomm__semiring__0(A)|c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),c_Polynomial_OpCons(A,B,C),D)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Polynomial_Osmult(A,B,D),c_Polynomial_OpCons(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,D))).
% 15.19/15.14  ** KEPT (pick-wt=21): 98 [] -class_Rings_Ocomm__semiring__0(A)|c_Polynomial_Osynthetic__div(A,c_Polynomial_OpCons(A,B,C),D)=c_Polynomial_OpCons(A,hAPP(c_Polynomial_Opoly(A,C),D),c_Polynomial_Osynthetic__div(A,C,D)).
% 15.19/15.14  ** KEPT (pick-wt=23): 99 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Otimes__class_Otimes(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,E))=c_Groups_Otimes__class_Otimes(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,E)).
% 15.19/15.14  ** KEPT (pick-wt=23): 100 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Otimes__class_Otimes(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,E))=c_Groups_Otimes__class_Otimes(A,D,c_Groups_Otimes__class_Otimes(A,c_Groups_Otimes__class_Otimes(A,B,C),E)).
% 15.19/15.14  ** KEPT (pick-wt=23): 101 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Otimes__class_Otimes(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,E))=c_Groups_Otimes__class_Otimes(A,B,c_Groups_Otimes__class_Otimes(A,C,c_Groups_Otimes__class_Otimes(A,D,E))).
% 15.19/15.14  ** KEPT (pick-wt=17): 102 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Otimes__class_Otimes(A,c_Groups_Otimes__class_Otimes(A,B,C),D)=c_Groups_Otimes__class_Otimes(A,c_Groups_Otimes__class_Otimes(A,B,D),C).
% 15.19/15.14  ** KEPT (pick-wt=17): 103 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Otimes__class_Otimes(A,c_Groups_Otimes__class_Otimes(A,B,C),D)=c_Groups_Otimes__class_Otimes(A,B,c_Groups_Otimes__class_Otimes(A,C,D)).
% 15.19/15.14  ** KEPT (pick-wt=17): 104 [] -class_Groups_Oab__semigroup__mult(A)|c_Groups_Otimes__class_Otimes(A,c_Groups_Otimes__class_Otimes(A,B,C),D)=c_Groups_Otimes__class_Otimes(A,B,c_Groups_Otimes__class_Otimes(A,C,D)).
% 15.19/15.14    Following clause subsumed by 103 during input processing: 0 [flip.2] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Otimes__class_Otimes(A,c_Groups_Otimes__class_Otimes(A,B,C),D)=c_Groups_Otimes__class_Otimes(A,B,c_Groups_Otimes__class_Otimes(A,C,D)).
% 15.19/15.14  ** KEPT (pick-wt=17): 105 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Otimes__class_Otimes(A,B,c_Groups_Otimes__class_Otimes(A,C,D))=c_Groups_Otimes__class_Otimes(A,C,c_Groups_Otimes__class_Otimes(A,B,D)).
% 15.19/15.14  ** KEPT (pick-wt=11): 106 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Otimes__class_Otimes(A,B,C)=c_Groups_Otimes__class_Otimes(A,C,B).
% 15.19/15.14  ** KEPT (pick-wt=24): 107 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(c_Polynomial_Opoly(A,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C)),D)=c_Groups_Otimes__class_Otimes(A,hAPP(c_Polynomial_Opoly(A,B),D),hAPP(c_Polynomial_Opoly(A,C),D)).
% 15.19/15.14  ** KEPT (pick-wt=24): 108 [] -class_Rings_Ocomm__semiring__0(A)|c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),c_Polynomial_Omonom(A,B,C),c_Polynomial_Omonom(A,D,E))=c_Polynomial_Omonom(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,E)).
% 15.19/15.14  ** KEPT (pick-wt=10): 109 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Otimes__class_Otimes(A,B,c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.14  ** KEPT (pick-wt=10): 110 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Otimes__class_Otimes(A,c_Groups_Ozero__class_Ozero(A),B)=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.14  ** KEPT (pick-wt=16): 111 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D))|c_Orderings_Oord__class_Oless(A,C,D).
% 15.19/15.14  ** KEPT (pick-wt=16): 112 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C))|c_Orderings_Oord__class_Oless(A,B,D).
% 15.19/15.14  ** KEPT (pick-wt=20): 113 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,E)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)).
% 15.19/15.14  ** KEPT (pick-wt=16): 114 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,D,B),c_Groups_Oplus__class_Oplus(A,D,C)).
% 15.19/15.14  ** KEPT (pick-wt=16): 115 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,D)).
% 15.19/15.14    Following clause subsumed by 111 during input processing: 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D))|c_Orderings_Oord__class_Oless(A,C,D).
% 15.19/15.14  ** KEPT (pick-wt=16): 116 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D))| -c_Orderings_Oord__class_Oless(A,C,D).
% 15.19/15.14    Following clause subsumed by 112 during input processing: 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C))|c_Orderings_Oord__class_Oless(A,B,D).
% 15.19/15.14  ** KEPT (pick-wt=16): 117 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C))| -c_Orderings_Oord__class_Oless(A,B,D).
% 15.19/15.15  ** KEPT (pick-wt=29): 118 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,E))!=c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,E),c_Groups_Otimes__class_Otimes(A,D,C))|B=D|C=E.
% 15.19/15.15  ** KEPT (pick-wt=26): 119 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,E))=c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,E),c_Groups_Otimes__class_Otimes(A,D,C))|B!=D.
% 15.19/15.15  ** KEPT (pick-wt=26): 120 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,E))=c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,E),c_Groups_Otimes__class_Otimes(A,D,C))|C!=E.
% 15.19/15.15  ** KEPT (pick-wt=20): 122 [copy,121,flip.2] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,C),D)=c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,D)).
% 15.19/15.15    Following clause subsumed by 122 during input processing: 0 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,C),D)=c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,D)).
% 15.19/15.15    Following clause subsumed by 118 during input processing: 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|B=C|D=E|c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,E))!=c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,E),c_Groups_Otimes__class_Otimes(A,C,D)).
% 15.19/15.15    Following clause subsumed by 119 during input processing: 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|B!=C|c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,E))=c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,E),c_Groups_Otimes__class_Otimes(A,C,D)).
% 15.19/15.15    Following clause subsumed by 120 during input processing: 0 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|B!=C|c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,D,B),c_Groups_Otimes__class_Otimes(A,E,C))=c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,D,C),c_Groups_Otimes__class_Otimes(A,E,B)).
% 15.19/15.15  ** KEPT (pick-wt=20): 123 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Otimes__class_Otimes(A,B,c_Groups_Oplus__class_Oplus(A,C,D))=c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)).
% 15.19/15.15  ** KEPT (pick-wt=13): 124 [] -class_Rings_Ocomm__semiring__0(A)|c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.19/15.15  ** KEPT (pick-wt=13): 125 [] -class_Rings_Ocomm__semiring__0(A)|c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.19/15.15  ** KEPT (pick-wt=15): 126 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 15.19/15.15  ** KEPT (pick-wt=15): 127 [] -class_Rings_Olinordered__idom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 15.19/15.15  ** KEPT (pick-wt=17): 129 [copy,128,flip.2] -class_Rings_Ocomm__semiring__0(A)|c_Polynomial_Osmult(A,c_Groups_Otimes__class_Otimes(A,B,C),D)=c_Polynomial_Osmult(A,B,c_Polynomial_Osmult(A,C,D)).
% 15.19/15.15  ** KEPT (pick-wt=19): 131 [copy,130,flip.2] -class_Rings_Ocomm__semiring__0(A)|c_Polynomial_Osmult(A,B,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,D))=c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),c_Polynomial_Osmult(A,B,C),D).
% 15.19/15.15  ** KEPT (pick-wt=19): 133 [copy,132,flip.2] -class_Rings_Ocomm__semiring__0(A)|c_Polynomial_Osmult(A,B,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,D))=c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,c_Polynomial_Osmult(A,B,D)).
% 15.19/15.15  ** KEPT (pick-wt=25): 134 [] -class_Rings_Ocomm__semiring__0(A)|c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C),D)=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,D),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,D)).
% 15.19/15.15  ** KEPT (pick-wt=15): 135 [] -class_Rings_Olinordered__idom(A)| -c_Polynomial_Opos__poly(A,B)| -c_Polynomial_Opos__poly(A,C)|c_Polynomial_Opos__poly(A,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C)).
% 15.19/15.15  ** KEPT (pick-wt=15): 136 [] -class_Groups_Olinordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,B))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 15.19/15.15  ** KEPT (pick-wt=15): 137 [] -class_Groups_Olinordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,B))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 15.19/15.15  ** KEPT (pick-wt=15): 138 [] -class_Groups_Olinordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 15.19/15.15  ** KEPT (pick-wt=15): 139 [] -class_Groups_Olinordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 15.19/15.15  ** KEPT (pick-wt=20): 140 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,C)).
% 15.19/15.15  ** KEPT (pick-wt=20): 141 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Ozero__class_Ozero(A)).
% 15.19/15.15  ** KEPT (pick-wt=27): 142 [] -class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(A)|B=c_Groups_Ozero__class_Ozero(A)|C!=D|E=F|c_Groups_Oplus__class_Oplus(A,C,c_Groups_Otimes__class_Otimes(A,B,E))!=c_Groups_Oplus__class_Oplus(A,D,c_Groups_Otimes__class_Otimes(A,B,F)).
% 15.19/15.15  ** KEPT (pick-wt=12): 143 [] -class_Rings_Ocomm__semiring__0(A)|c_Polynomial_Osynthetic__div(A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.19/15.15  ** KEPT (pick-wt=20): 144 [] -class_Rings_Ocomm__semiring__0(A)|c_Polynomial_Osmult(A,B,c_Polynomial_OpCons(A,C,D))=c_Polynomial_OpCons(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Polynomial_Osmult(A,B,D)).
% 15.19/15.15  ** KEPT (pick-wt=19): 145 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(c_Polynomial_Ocoeff(A,c_Polynomial_Osmult(A,B,C)),D)=c_Groups_Otimes__class_Otimes(A,B,hAPP(c_Polynomial_Ocoeff(A,C),D)).
% 15.19/15.15  ** KEPT (pick-wt=19): 146 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(c_Polynomial_Opoly(A,c_Polynomial_Osmult(A,B,C)),D)=c_Groups_Otimes__class_Otimes(A,B,hAPP(c_Polynomial_Opoly(A,C),D)).
% 15.19/15.15  ** KEPT (pick-wt=17): 147 [] -class_Rings_Ocomm__semiring__0(A)|c_Polynomial_Osmult(A,B,c_Polynomial_Omonom(A,C,D))=c_Polynomial_Omonom(A,c_Groups_Otimes__class_Otimes(A,B,C),D).
% 15.19/15.15  ** KEPT (pick-wt=13): 148 [] -class_Groups_Ozero(A)|hAPP(c_Polynomial_Ocoeff(A,c_Polynomial_OpCons(A,B,C)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=B.
% 15.19/15.15  ** KEPT (pick-wt=22): 149 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(c_Polynomial_Opoly(A,c_Polynomial_OpCons(A,B,C)),D)=c_Groups_Oplus__class_Oplus(A,B,c_Groups_Otimes__class_Otimes(A,D,hAPP(c_Polynomial_Opoly(A,C),D))).
% 15.19/15.15  ** KEPT (pick-wt=13): 150 [] -class_Groups_Ozero(A)|c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(A,B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.19/15.15  ** KEPT (pick-wt=13): 151 [] -class_Groups_Ozero(A)|c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(A,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.19/15.15  ** KEPT (pick-wt=14): 153 [copy,152,flip.2] -class_Groups_Ozero(A)|c_Polynomial_OpCons(A,B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))=c_Polynomial_Omonom(A,B,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.19/15.15  ** KEPT (pick-wt=24): 154 [] -class_Groups_Ozero(A)|hAPP(hAPP(hAPP(B,c_Groups_Ozero__class_Ozero(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))),C)!=C|c_Polynomial_Opoly__rec(D,A,C,B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))=C.
% 15.19/15.15  ** KEPT (pick-wt=24): 155 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,B),c_Groups_Otimes__class_Otimes(A,C,C)))|B!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.15  ** KEPT (pick-wt=20): 156 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,B),c_Groups_Otimes__class_Otimes(A,C,C)))|B=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.15  ** KEPT (pick-wt=20): 157 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,B),c_Groups_Otimes__class_Otimes(A,C,C)))|C=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.15  ** KEPT (pick-wt=16): 158 [] -class_Rings_Olinordered__ring(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,B),c_Groups_Otimes__class_Otimes(A,C,C)),c_Groups_Ozero__class_Ozero(A)).
% 15.19/15.15  ** KEPT (pick-wt=19): 159 [] -class_Rings_Olinordered__ring__strict(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,B),c_Groups_Otimes__class_Otimes(A,C,C))!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.15  ** KEPT (pick-wt=19): 160 [] -class_Rings_Olinordered__ring__strict(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,B),c_Groups_Otimes__class_Otimes(A,C,C))!=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.15  ** KEPT (pick-wt=23): 161 [] -class_Rings_Olinordered__ring__strict(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,B),c_Groups_Otimes__class_Otimes(A,C,C))=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.15  ** KEPT (pick-wt=18): 162 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,C,c_Groups_Oplus__class_Oplus(A,B,D)).
% 15.19/15.15  ** KEPT (pick-wt=21): 163 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,D,C),c_Groups_Otimes__class_Otimes(A,D,B)).
% 15.19/15.15  ** KEPT (pick-wt=21): 164 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,C,D),c_Groups_Otimes__class_Otimes(A,B,D)).
% 15.19/15.15  ** KEPT (pick-wt=21): 165 [] -class_Rings_Olinordered__comm__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,D,B),c_Groups_Otimes__class_Otimes(A,D,C)).
% 15.19/15.15  ** KEPT (pick-wt=21): 166 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,D,B),c_Groups_Otimes__class_Otimes(A,D,C)).
% 15.19/15.15  ** KEPT (pick-wt=21): 167 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,D)).
% 15.19/15.15  ** KEPT (pick-wt=20): 168 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)).
% 15.19/15.15  ** KEPT (pick-wt=13): 169 [] -class_Rings_Olinordered__idom(A)|B=C|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B).
% 15.19/15.15  ** KEPT (pick-wt=17): 170 [] -class_Rings_Ono__zero__divisors(A)|c_Groups_Otimes__class_Otimes(A,B,C)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.15    Following clause subsumed by 170 during input processing: 0 [] -class_Rings_Ono__zero__divisors(A)|B=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A)|c_Groups_Otimes__class_Otimes(A,B,C)!=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.15  ** KEPT (pick-wt=17): 171 [] -class_Rings_Oring__no__zero__divisors(A)|c_Groups_Otimes__class_Otimes(A,B,C)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.15  ** KEPT (pick-wt=13): 172 [] -class_Rings_Oring__no__zero__divisors(A)|c_Groups_Otimes__class_Otimes(A,B,C)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.15  ** KEPT (pick-wt=13): 173 [] -class_Rings_Oring__no__zero__divisors(A)|c_Groups_Otimes__class_Otimes(A,B,C)=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.15  ** KEPT (pick-wt=10): 174 [] -class_Rings_Omult__zero(A)|c_Groups_Otimes__class_Otimes(A,B,c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.15  ** KEPT (pick-wt=10): 175 [] -class_Rings_Omult__zero(A)|c_Groups_Otimes__class_Otimes(A,c_Groups_Ozero__class_Ozero(A),B)=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.15  ** KEPT (pick-wt=20): 176 [] -class_Rings_Ocomm__semiring(A)|c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,C),D)=c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,D)).
% 15.19/15.15  ** KEPT (pick-wt=26): 178 [copy,177,flip.2] -class_Rings_Osemiring(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,C),D),E)=c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,C,D),E)).
% 15.19/15.15  ** KEPT (pick-wt=10): 179 [] -class_Rings_Olinordered__ring(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,B),c_Groups_Ozero__class_Ozero(A)).
% 15.19/15.15  ** KEPT (pick-wt=22): 180 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,C))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)).
% 15.19/15.15  ** KEPT (pick-wt=21): 181 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,C))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,D,B).
% 15.19/15.15  ** KEPT (pick-wt=21): 182 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,C))|c_Orderings_Oord__class_Oless(A,B,D)|c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A)).
% 15.19/15.15  ** KEPT (pick-wt=20): 183 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,C))|c_Orderings_Oord__class_Oless(A,B,D)|c_Orderings_Oord__class_Oless(A,D,B).
% 15.19/15.15  ** KEPT (pick-wt=21): 184 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,C))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)| -c_Orderings_Oord__class_Oless(A,B,D).
% 15.19/15.15    Following clause subsumed by 164 during input processing: 0 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,C))| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,D,B).
% 15.19/15.15  ** KEPT (pick-wt=22): 185 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 15.19/15.15  ** KEPT (pick-wt=21): 186 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D))|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,D,C).
% 15.19/15.15  ** KEPT (pick-wt=21): 187 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D))|c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A)).
% 15.19/15.15  ** KEPT (pick-wt=20): 188 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D))|c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,D,C).
% 15.19/15.15  ** KEPT (pick-wt=21): 189 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,C,D).
% 15.19/15.15    Following clause subsumed by 163 during input processing: 0 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D))| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,D,C).
% 15.19/15.15  ** KEPT (pick-wt=21): 190 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D))|c_Orderings_Oord__class_Oless(A,C,D).
% 15.19/15.15    Following clause subsumed by 189 during input processing: 0 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D))| -c_Orderings_Oord__class_Oless(A,C,D).
% 15.19/15.15  ** KEPT (pick-wt=20): 191 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)).
% 15.19/15.15  ** KEPT (pick-wt=20): 192 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Ozero__class_Ozero(A)).
% 15.19/15.15  ** KEPT (pick-wt=20): 193 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,C,B),c_Groups_Ozero__class_Ozero(A)).
% 15.19/15.15  ** KEPT (pick-wt=20): 194 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C).
% 15.19/15.15  ** KEPT (pick-wt=20): 195 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B).
% 15.19/15.15  ** KEPT (pick-wt=21): 196 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D))|c_Orderings_Oord__class_Oless(A,D,C).
% 15.19/15.15    Following clause subsumed by 163 during input processing: 0 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D))| -c_Orderings_Oord__class_Oless(A,D,C).
% 15.19/15.15    Following clause subsumed by 193 during input processing: 0 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Ozero__class_Ozero(A)).
% 15.19/15.15  ** KEPT (pick-wt=5): 197 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.19/15.15  ** KEPT (pick-wt=10): 198 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)!=A|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.15  ** KEPT (pick-wt=11): 199 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.15  ** KEPT (pick-wt=11): 200 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.15  ** KEPT (pick-wt=15): 201 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.15  ** KEPT (pick-wt=18): 202 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B).
% 15.19/15.15  ** KEPT (pick-wt=13): 203 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A).
% 15.19/15.15  ** KEPT (pick-wt=13): 204 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B).
% 15.19/15.15  ** KEPT (pick-wt=20): 205 [] -class_RealVector_Oreal__normed__algebra(A)|c_Groups_Otimes__class_Otimes(A,B,c_Groups_Oplus__class_Oplus(A,C,D))=c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)).
% 15.19/15.15    Following clause subsumed by 205 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|c_Groups_Otimes__class_Otimes(A,B,c_Groups_Oplus__class_Oplus(A,C,D))=c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)).
% 15.19/15.15  ** KEPT (pick-wt=20): 206 [] -class_RealVector_Oreal__normed__algebra(A)|c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,C),D)=c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,D)).
% 15.19/15.15  ** KEPT (pick-wt=7): 207 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A!=B.
% 15.19/15.15  ** KEPT (pick-wt=7): 208 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|B!=A.
% 15.19/15.15  ** KEPT (pick-wt=4): 209 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,A).
% 15.19/15.15    Following clause subsumed by 207 during input processing: 0 [] A!=B| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 15.19/15.15    Following clause subsumed by 208 during input processing: 0 [] A!=B| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A).
% 15.19/15.15    Following clause subsumed by 209 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,A).
% 15.19/15.15  ** KEPT (pick-wt=8): 210 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.15    Following clause subsumed by 197 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.19/15.15    Following clause subsumed by 210 during input processing: 0 [] A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A).
% 15.19/15.15    Following clause subsumed by 197 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.19/15.15  ** KEPT (pick-wt=19): 211 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,A),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,B)).
% 15.19/15.15  ** KEPT (pick-wt=19): 212 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,C)).
% 15.19/15.15  ** KEPT (pick-wt=16): 213 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)!=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,B)|A=C|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.15  ** KEPT (pick-wt=12): 214 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,B)|A!=C.
% 15.19/15.15  ** KEPT (pick-wt=13): 215 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,B)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.15  ** KEPT (pick-wt=16): 216 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)!=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C)|B=C|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.15  ** KEPT (pick-wt=12): 217 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C)|B!=C.
% 15.19/15.15  ** KEPT (pick-wt=13): 218 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.15  ** KEPT (pick-wt=15): 219 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B).
% 15.19/15.15  ** KEPT (pick-wt=14): 220 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,C).
% 15.19/15.15    Following clause subsumed by 212 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,C).
% 15.19/15.15  ** KEPT (pick-wt=15): 221 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A).
% 15.19/15.15  ** KEPT (pick-wt=14): 222 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 15.19/15.15    Following clause subsumed by 211 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 15.19/15.15  ** KEPT (pick-wt=15): 223 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.15  ** KEPT (pick-wt=11): 224 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.15  ** KEPT (pick-wt=11): 225 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.15  ** KEPT (pick-wt=13): 226 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A).
% 15.19/15.15  ** KEPT (pick-wt=13): 227 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B).
% 15.19/15.15  ** KEPT (pick-wt=18): 228 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B).
% 15.19/15.15  ** KEPT (pick-wt=12): 229 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)|A=C.
% 15.19/15.15  ** KEPT (pick-wt=12): 230 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)|A!=C.
% 15.19/15.15  ** KEPT (pick-wt=12): 231 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)|B=C.
% 15.19/15.15  ** KEPT (pick-wt=12): 232 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)|B!=C.
% 15.19/15.15  ** KEPT (pick-wt=7): 233 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),A).
% 15.19/15.15  ** KEPT (pick-wt=7): 234 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),B).
% 15.19/15.15  ** KEPT (pick-wt=14): 235 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 15.19/15.15  ** KEPT (pick-wt=14): 236 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 15.19/15.15  ** KEPT (pick-wt=11): 237 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)).
% 15.19/15.15  ** KEPT (pick-wt=11): 238 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)).
% 15.19/15.15  ** KEPT (pick-wt=14): 239 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)).
% 15.19/15.15  ** KEPT (pick-wt=18): 240 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,D)).
% 15.19/15.15  ** KEPT (pick-wt=17): 241 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,D)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,D).
% 15.19/15.15  ** KEPT (pick-wt=11): 242 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,C).
% 15.19/15.15  ** KEPT (pick-wt=10): 243 [] -class_RealVector_Oreal__normed__algebra(A)|c_Groups_Otimes__class_Otimes(A,c_Groups_Ozero__class_Ozero(A),B)=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.15    Following clause subsumed by 243 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|c_Groups_Otimes__class_Otimes(A,c_Groups_Ozero__class_Ozero(A),B)=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.15  ** KEPT (pick-wt=10): 244 [] -class_RealVector_Oreal__normed__algebra(A)|c_Groups_Otimes__class_Otimes(A,B,c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.15    Following clause subsumed by 244 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|c_Groups_Otimes__class_Otimes(A,B,c_Groups_Ozero__class_Ozero(A))=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.15    Following clause subsumed by 206 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,C),D)=c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,D)).
% 15.19/15.15    Following clause subsumed by 237 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)).
% 15.19/15.15    Following clause subsumed by 238 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)).
% 15.19/15.15    Following clause subsumed by 222 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 15.19/15.15    Following clause subsumed by 211 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 15.19/15.15  ** KEPT (pick-wt=17): 245 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)!=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C)|B=C.
% 15.19/15.15    Following clause subsumed by 217 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C)|B!=C.
% 15.19/15.15  ** KEPT (pick-wt=15): 246 [] -class_Groups_Ozero(A)|c_Polynomial_Ocoeff(A,c_Polynomial_OpCons(A,B,C))=c_Nat_Onat_Onat__case(A,B,c_Polynomial_Ocoeff(A,C)).
% 15.19/15.15  ** KEPT (pick-wt=16): 247 [] -class_Rings_Olinordered__idom(A)| -c_Polynomial_Opos__poly(A,B)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B))).
% 15.19/15.15  ** KEPT (pick-wt=16): 248 [] -class_Rings_Olinordered__idom(A)|c_Polynomial_Opos__poly(A,B)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B))).
% 15.19/15.15  ** KEPT (pick-wt=35): 249 [] -class_Rings_Ocomm__semiring__0(A)|hAPP(c_Polynomial_Ocoeff(A,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(A,B),c_Polynomial_Odegree(A,C)))=c_Groups_Otimes__class_Otimes(A,hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B)),hAPP(c_Polynomial_Ocoeff(A,C),c_Polynomial_Odegree(A,C))).
% 15.19/15.15  ** KEPT (pick-wt=11): 250 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),$f3(B,A)).
% 15.19/15.15  ** KEPT (pick-wt=12): 251 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,$f3(B,A))=B.
% 15.19/15.15  ** KEPT (pick-wt=12): 252 [] -class_Rings_Ocomm__semiring__0(A)|c_Polynomial_Odegree(A,c_Fundamental__Theorem__Algebra__Mirabelle_Ooffset__poly(A,B,C))=c_Polynomial_Odegree(A,B).
% 15.19/15.15  ** KEPT (pick-wt=10): 253 [] -class_Groups_Ozero(A)|c_Polynomial_Odegree(A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.15  ** KEPT (pick-wt=14): 254 [] -class_Groups_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A)|c_Polynomial_Odegree(A,c_Polynomial_Omonom(A,B,C))=C.
% 15.19/15.15  ** KEPT (pick-wt=21): 255 [] -class_Groups_Ocomm__monoid__add(A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(A,B),c_Polynomial_Odegree(A,C))|c_Polynomial_Odegree(A,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),C,B))=c_Polynomial_Odegree(A,C).
% 15.19/15.15  ** KEPT (pick-wt=21): 256 [] -class_Groups_Ocomm__monoid__add(A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(A,B),c_Polynomial_Odegree(A,C))|c_Polynomial_Odegree(A,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,C))=c_Polynomial_Odegree(A,C).
% 15.19/15.15  ** KEPT (pick-wt=24): 257 [] -class_Groups_Ocomm__monoid__add(A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(A,B),C)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(A,D),C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(A,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D)),C).
% 15.19/15.15  ** KEPT (pick-wt=15): 258 [] -class_Rings_Oidom(A)|B!=c_Groups_Ozero__class_Ozero(A)|c_Polynomial_Odegree(A,c_Polynomial_Osmult(A,B,C))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.15  ** KEPT (pick-wt=16): 259 [] -class_Rings_Oidom(A)|B=c_Groups_Ozero__class_Ozero(A)|c_Polynomial_Odegree(A,c_Polynomial_Osmult(A,B,C))=c_Polynomial_Odegree(A,C).
% 15.19/15.15  ** KEPT (pick-wt=16): 260 [] -class_Groups_Ozero(A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(A,B),C)|hAPP(c_Polynomial_Ocoeff(A,B),C)=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.15  ** KEPT (pick-wt=17): 261 [] -class_Groups_Ozero(A)|hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B))!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.19/15.15  ** KEPT (pick-wt=17): 262 [] -class_Groups_Ozero(A)|hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B))=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.19/15.15    Following clause subsumed by 261 during input processing: 0 [] -class_Groups_Ozero(A)|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|hAPP(c_Polynomial_Ocoeff(A,B),c_Polynomial_Odegree(A,B))!=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.15  ** KEPT (pick-wt=13): 263 [] -class_Groups_Ozero(A)|c_Polynomial_Odegree(A,c_Polynomial_OpCons(A,B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.15  ** KEPT (pick-wt=28): 264 [] -class_Rings_Oidom(A)|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|C=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|c_Polynomial_Odegree(A,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(A,B),c_Polynomial_Odegree(A,C)).
% 15.19/15.15  ** KEPT (pick-wt=16): 265 [] -class_Rings_Ocomm__semiring__0(A)|c_Polynomial_Osynthetic__div(A,B,C)!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|c_Polynomial_Odegree(A,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.15  ** KEPT (pick-wt=16): 266 [] -class_Rings_Ocomm__semiring__0(A)|c_Polynomial_Osynthetic__div(A,B,C)=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|c_Polynomial_Odegree(A,B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.15    Following clause subsumed by 216 during input processing: 0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)!=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B=C.
% 15.19/15.15    Following clause subsumed by 218 during input processing: 0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.15    Following clause subsumed by 217 during input processing: 0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C)|B!=C.
% 15.19/15.15  ** KEPT (pick-wt=19): 267 [] -class_Fields_Ofield(A)| -c_Polynomial_Opdivmod__rel(A,B,C,D,E)|B=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),D,C),E).
% 15.19/15.15  ** KEPT (pick-wt=18): 268 [] -class_Fields_Ofield(A)| -c_Polynomial_Opdivmod__rel(A,B,C,D,E)|C!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|D=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.19/15.15  ** KEPT (pick-wt=26): 269 [] -class_Fields_Ofield(A)| -c_Polynomial_Opdivmod__rel(A,B,C,D,E)|C=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|E=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(A,E),c_Polynomial_Odegree(A,C)).
% 15.19/15.15  ** KEPT (pick-wt=29): 270 [] -class_Fields_Ofield(A)|c_Polynomial_Opdivmod__rel(A,B,C,D,E)|B!=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),D,C),E)|C=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|E!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.19/15.15  ** KEPT (pick-wt=32): 271 [] -class_Fields_Ofield(A)|c_Polynomial_Opdivmod__rel(A,B,C,D,E)|B!=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),D,C),E)|C=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(A,E),c_Polynomial_Odegree(A,C)).
% 15.19/15.15  ** KEPT (pick-wt=29): 272 [] -class_Fields_Ofield(A)|c_Polynomial_Opdivmod__rel(A,B,C,D,E)|B!=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),D,C),E)|D!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|C!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.19/15.15  ** KEPT (pick-wt=29): 273 [] -class_Fields_Ofield(A)|c_Polynomial_Opdivmod__rel(A,B,C,D,E)|B!=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),D,C),E)|D!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|E!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.19/15.15  ** KEPT (pick-wt=32): 274 [] -class_Fields_Ofield(A)|c_Polynomial_Opdivmod__rel(A,B,C,D,E)|B!=c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),D,C),E)|D!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(A,E),c_Polynomial_Odegree(A,C)).
% 15.19/15.15  ** KEPT (pick-wt=27): 275 [] -class_Groups_Ozero(A)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(A,B),C)|hAPP(c_Polynomial_Ocoeff(A,B),C)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Polynomial_Odegree(A,B),C).
% 15.19/15.15  ** KEPT (pick-wt=15): 277 [copy,276,flip.2] -class_Groups_Ozero(A)|c_Polynomial_OAbs__poly(A,c_Nat_Onat_Onat__case(A,B,c_Polynomial_Ocoeff(A,C)))=c_Polynomial_OpCons(A,B,C).
% 15.19/15.15    Following clause subsumed by 151 during input processing: 0 [] -class_Groups_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(A,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.15  ** KEPT (pick-wt=15): 279 [copy,278,flip.3] -class_Groups_Ozero(A)|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|c_Nat_OSuc(c_Polynomial_Odegree(A,B))=c_Fundamental__Theorem__Algebra__Mirabelle_Opsize(A,B).
% 15.19/15.15  ** KEPT (pick-wt=15): 280 [] -class_Groups_Ozero(A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Polynomial_Odegree(A,C))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,$f4(C,B,A)).
% 15.19/15.15  ** KEPT (pick-wt=19): 281 [] -class_Groups_Ozero(A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Polynomial_Odegree(A,C))|hAPP(c_Polynomial_Ocoeff(A,C),$f4(C,B,A))!=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.15  ** KEPT (pick-wt=16): 282 [] -class_Groups_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|c_Polynomial_Odegree(A,c_Polynomial_OpCons(A,C,B))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.15  ** KEPT (pick-wt=18): 283 [] -class_Groups_Ozero(A)|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|c_Polynomial_Odegree(A,c_Polynomial_OpCons(A,C,B))=c_Nat_OSuc(c_Polynomial_Odegree(A,B)).
% 15.19/15.15  ** KEPT (pick-wt=18): 284 [] -class_Rings_Ocomm__semiring__0(A)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(A,c_Polynomial_Opcompose(A,B,C)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Polynomial_Odegree(A,B),c_Polynomial_Odegree(A,C))).
% 15.19/15.15  ** KEPT (pick-wt=10): 285 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(A),c_Nat_OSuc(B)).
% 15.19/15.15  ** KEPT (pick-wt=16): 286 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(A),B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(A),C))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C).
% 15.19/15.15  ** KEPT (pick-wt=16): 287 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(A),B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(A),C))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C).
% 15.19/15.15  ** KEPT (pick-wt=17): 288 [] -class_Fields_Ofield(A)| -c_Polynomial_Opdivmod__rel(A,B,C,D,E)| -c_Polynomial_Opdivmod__rel(A,B,C,F,G)|D=F.
% 15.19/15.15  ** KEPT (pick-wt=17): 289 [] -class_Fields_Ofield(A)| -c_Polynomial_Opdivmod__rel(A,B,C,D,E)| -c_Polynomial_Opdivmod__rel(A,B,C,F,G)|E=G.
% 15.19/15.15    Following clause subsumed by 289 during input processing: 0 [] -class_Fields_Ofield(A)| -c_Polynomial_Opdivmod__rel(A,B,C,D,E)| -c_Polynomial_Opdivmod__rel(A,B,C,F,G)|E=G.
% 15.19/15.15    Following clause subsumed by 288 during input processing: 0 [] -class_Fields_Ofield(A)| -c_Polynomial_Opdivmod__rel(A,B,C,D,E)| -c_Polynomial_Opdivmod__rel(A,B,C,F,G)|D=F.
% 15.19/15.15  ** KEPT (pick-wt=9): 290 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(A),B).
% 15.19/15.15  ** KEPT (pick-wt=9): 291 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(A),B).
% 15.19/15.15  ** KEPT (pick-wt=9): 292 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 15.19/15.15  ** KEPT (pick-wt=9): 293 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 15.19/15.15    Following clause subsumed by 291 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(A),B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 15.19/15.15    Following clause subsumed by 290 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(A),B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 15.19/15.15    Following clause subsumed by 293 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B)).
% 15.19/15.15    Following clause subsumed by 290 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(A),B).
% 15.19/15.15  ** KEPT (pick-wt=12): 294 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Nat_OSuc(A))|B=A.
% 15.19/15.15  ** KEPT (pick-wt=12): 295 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Nat_OSuc(A))|B!=A.
% 15.19/15.15    Following clause subsumed by 291 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(A),B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 15.19/15.15  ** KEPT (pick-wt=8): 296 [] c_Nat_OSuc(A)!=c_Nat_OSuc(B)|A=B.
% 15.19/15.15  ** KEPT (pick-wt=9): 297 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(A),B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 15.19/15.15  ** KEPT (pick-wt=13): 298 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Nat_OSuc(B))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|A=c_Nat_OSuc(B).
% 15.19/15.15  ** KEPT (pick-wt=11): 299 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,A)|A=B.
% 15.19/15.15  ** KEPT (pick-wt=12): 300 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C).
% 15.19/15.15  ** KEPT (pick-wt=9): 301 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Nat_OSuc(B)).
% 15.19/15.15  ** KEPT (pick-wt=7): 302 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 15.19/15.15  ** KEPT (pick-wt=10): 303 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(A),c_Nat_OSuc(B))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 15.19/15.15  ** KEPT (pick-wt=10): 304 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(A),c_Nat_OSuc(B))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 15.19/15.15    Following clause subsumed by 296 during input processing: 0 [] c_Nat_OSuc(A)!=c_Nat_OSuc(B)|A=B.
% 15.19/15.15  ** KEPT (pick-wt=8): 305 [] c_Nat_OSuc(A)=c_Nat_OSuc(B)|A!=B.
% 15.19/15.15    Following clause subsumed by 298 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Nat_OSuc(B))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|A=c_Nat_OSuc(B).
% 15.19/15.15    Following clause subsumed by 301 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Nat_OSuc(B))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 15.19/15.15    Following clause subsumed by 302 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Nat_OSuc(B))|A!=c_Nat_OSuc(B).
% 15.19/15.15  ** KEPT (pick-wt=9): 306 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(B),A).
% 15.19/15.15  ** KEPT (pick-wt=5): 307 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(A),A).
% 15.19/15.15  ** KEPT (pick-wt=4): 308 [] c_Nat_OSuc(A)!=A.
% 15.19/15.15    Following clause subsumed by 308 during input processing: 0 [flip.1] c_Nat_OSuc(A)!=A.
% 15.19/15.15  ** KEPT (pick-wt=15): 309 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A).
% 15.19/15.15  ** KEPT (pick-wt=15): 310 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B).
% 15.19/15.15  ** KEPT (pick-wt=21): 311 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B).
% 15.19/15.15  ** KEPT (pick-wt=14): 312 [] -class_Groups_Ozero(A)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(A,c_Polynomial_OpCons(A,B,C)),c_Nat_OSuc(c_Polynomial_Odegree(A,C))).
% 15.19/15.15  ** KEPT (pick-wt=16): 313 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D))|c_Orderings_Oord__class_Oless__e_q(A,C,D).
% 15.19/15.15  ** KEPT (pick-wt=16): 314 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C))|c_Orderings_Oord__class_Oless__e_q(A,B,D).
% 15.19/15.15  ** KEPT (pick-wt=20): 315 [] -class_Groups_Oordered__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,E)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)).
% 15.19/15.15  ** KEPT (pick-wt=16): 316 [] -class_Groups_Oordered__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,D,B),c_Groups_Oplus__class_Oplus(A,D,C)).
% 15.19/15.15  ** KEPT (pick-wt=16): 317 [] -class_Groups_Oordered__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,D)).
% 15.19/15.15    Following clause subsumed by 313 during input processing: 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D))|c_Orderings_Oord__class_Oless__e_q(A,C,D).
% 15.19/15.15  ** KEPT (pick-wt=16): 318 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,B,D))| -c_Orderings_Oord__class_Oless__e_q(A,C,D).
% 15.19/15.15    Following clause subsumed by 314 during input processing: 0 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C))|c_Orderings_Oord__class_Oless__e_q(A,B,D).
% 15.19/15.15  ** KEPT (pick-wt=16): 319 [] -class_Groups_Oordered__ab__semigroup__add__imp__le(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Oplus__class_Oplus(A,D,C))| -c_Orderings_Oord__class_Oless__e_q(A,B,D).
% 15.19/15.15  ** KEPT (pick-wt=5): 321 [copy,320,flip.1] c_Nat_OSuc(A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.15    Following clause subsumed by 321 during input processing: 0 [flip.1] c_Nat_OSuc(A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.15    Following clause subsumed by 321 during input processing: 0 [] c_Nat_OSuc(A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.15    Following clause subsumed by 321 during input processing: 0 [] c_Nat_OSuc(A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.15    Following clause subsumed by 321 during input processing: 0 [flip.1] c_Nat_OSuc(A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.15    Following clause subsumed by 321 during input processing: 0 [] c_Nat_OSuc(A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.15  ** KEPT (pick-wt=10): 322 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(A),c_Nat_OSuc(B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 15.19/15.15  ** KEPT (pick-wt=9): 323 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(A),B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 15.19/15.15  ** KEPT (pick-wt=12): 324 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A=B.
% 15.19/15.15  ** KEPT (pick-wt=13): 325 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(A),C).
% 15.19/15.15  ** KEPT (pick-wt=13): 326 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Nat_OSuc(A)=B|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(A),B).
% 15.19/15.15  ** KEPT (pick-wt=9): 327 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B)).
% 15.19/15.15  ** KEPT (pick-wt=12): 328 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B))|B=A.
% 15.19/15.15    Following clause subsumed by 324 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B))|A=B.
% 15.19/15.15  ** KEPT (pick-wt=12): 329 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B))|A!=B.
% 15.19/15.15    Following clause subsumed by 322 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(A),c_Nat_OSuc(B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 15.19/15.15    Following clause subsumed by 285 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(A),c_Nat_OSuc(B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 15.19/15.15    Following clause subsumed by 324 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A=B.
% 15.19/15.15    Following clause subsumed by 327 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 15.19/15.15  ** KEPT (pick-wt=8): 330 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B))|A!=B.
% 15.19/15.15  ** KEPT (pick-wt=9): 331 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,c_Nat_OSuc(A)).
% 15.19/15.15  ** KEPT (pick-wt=9): 332 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.15    Following clause subsumed by 302 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.15  ** KEPT (pick-wt=14): 333 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(A),B)!=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(A),C)|B=C.
% 15.19/15.15    Following clause subsumed by 217 during input processing: 0 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(A),B)=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(A),C)|B!=C.
% 15.19/15.15  ** KEPT (pick-wt=8): 334 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 15.19/15.15    Following clause subsumed by 302 during input processing: 0 [] A!=B|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 15.19/15.15  ** KEPT (pick-wt=11): 335 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|A=B|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 15.19/15.15    Following clause subsumed by 334 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 15.19/15.15    Following clause subsumed by 335 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A=B.
% 15.19/15.15    Following clause subsumed by 334 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B).
% 15.19/15.15    Following clause subsumed by 302 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|A!=B.
% 15.19/15.15    Following clause subsumed by 334 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 15.19/15.15    Following clause subsumed by 207 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|A!=B.
% 15.19/15.15    Following clause subsumed by 335 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|A=B.
% 15.19/15.15    Following clause subsumed by 334 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 15.19/15.15  ** KEPT (pick-wt=11): 336 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),C)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C).
% 15.19/15.15  ** KEPT (pick-wt=11): 337 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),C)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C).
% 15.19/15.15    Following clause subsumed by 336 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),C)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C).
% 15.19/15.15    Following clause subsumed by 337 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),C)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C).
% 15.19/15.15  ** KEPT (pick-wt=18): 338 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,D)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,D)).
% 15.19/15.15  ** KEPT (pick-wt=14): 339 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)).
% 15.19/15.15  ** KEPT (pick-wt=11): 340 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)).
% 15.19/15.15  ** KEPT (pick-wt=11): 341 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)).
% 15.19/15.15  ** KEPT (pick-wt=14): 342 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C).
% 15.19/15.15  ** KEPT (pick-wt=14): 343 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C).
% 15.19/15.15  ** KEPT (pick-wt=12): 345 [copy,344,flip.2] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,$f5(B,A))=B.
% 15.19/15.15  ** KEPT (pick-wt=10): 346 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|B!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C).
% 15.19/15.15    Following clause subsumed by 341 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C)).
% 15.19/15.15    Following clause subsumed by 340 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)).
% 15.19/15.15  ** KEPT (pick-wt=18): 347 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,D)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,D)).
% 15.19/15.15  ** KEPT (pick-wt=14): 348 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,A),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,B)).
% 15.19/15.15  ** KEPT (pick-wt=14): 349 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,C)).
% 15.19/15.15  ** KEPT (pick-wt=12): 350 [] -class_Fields_Ofield(A)|c_Polynomial_Opdivmod__rel(A,B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B).
% 15.19/15.15  ** KEPT (pick-wt=14): 351 [] -class_Fields_Ofield(A)|c_Polynomial_Opdivmod__rel(A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))).
% 15.19/15.15  ** KEPT (pick-wt=15): 352 [] -class_Fields_Ofield(A)| -c_Polynomial_Opdivmod__rel(A,B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,D)|C=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.19/15.15  ** KEPT (pick-wt=13): 353 [] -class_Fields_Ofield(A)| -c_Polynomial_Opdivmod__rel(A,B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,D)|D=B.
% 15.19/15.15  ** KEPT (pick-wt=18): 354 [] -class_Fields_Ofield(A)|c_Polynomial_Opdivmod__rel(A,B,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),C,D)|C!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|D!=B.
% 15.19/15.15  ** KEPT (pick-wt=15): 355 [] -class_Fields_Ofield(A)| -c_Polynomial_Opdivmod__rel(A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,C,D)|C=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.19/15.15  ** KEPT (pick-wt=15): 356 [] -class_Fields_Ofield(A)| -c_Polynomial_Opdivmod__rel(A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,C,D)|D=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.19/15.15  ** KEPT (pick-wt=20): 357 [] -class_Fields_Ofield(A)|c_Polynomial_Opdivmod__rel(A,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)),B,C,D)|C!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|D!=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)).
% 15.19/15.15  ** KEPT (pick-wt=23): 358 [] -class_Fields_Ofield(A)| -c_Polynomial_Opdivmod__rel(A,B,C,D,E)|c_Polynomial_Opdivmod__rel(A,c_Polynomial_Osmult(A,F,B),C,c_Polynomial_Osmult(A,F,D),c_Polynomial_Osmult(A,F,E)).
% 15.19/15.15  ** KEPT (pick-wt=9): 359 [] -class_Groups_Ozero(A)|c_Polynomial_OAbs__poly(A,c_Polynomial_Ocoeff(A,B))=B.
% 15.19/15.15  ** KEPT (pick-wt=20): 360 [] -class_Rings_Oordered__cancel__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Ozero__class_Ozero(A)).
% 15.19/15.15  ** KEPT (pick-wt=20): 361 [] -class_Rings_Oordered__cancel__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Ozero__class_Ozero(A)).
% 15.19/15.15  ** KEPT (pick-wt=20): 362 [] -class_Rings_Oordered__ring(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)).
% 15.19/15.15  ** KEPT (pick-wt=20): 363 [] -class_Rings_Oordered__ring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)).
% 15.19/15.15  ** KEPT (pick-wt=30): 364 [] -class_Rings_Oordered__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,E)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,E)).
% 15.19/15.15  ** KEPT (pick-wt=30): 365 [] -class_Rings_Oordered__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,E)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,E)).
% 15.19/15.15  ** KEPT (pick-wt=21): 366 [] -class_Rings_Oordered__ring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Otimes__class_Otimes(A,D,C),c_Groups_Otimes__class_Otimes(A,D,B)).
% 15.19/15.15  ** KEPT (pick-wt=21): 367 [] -class_Rings_Oordered__ring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Otimes__class_Otimes(A,C,D),c_Groups_Otimes__class_Otimes(A,B,D)).
% 15.19/15.15  ** KEPT (pick-wt=21): 368 [] -class_Rings_Oordered__comm__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Otimes__class_Otimes(A,D,B),c_Groups_Otimes__class_Otimes(A,D,C)).
% 15.19/15.15  ** KEPT (pick-wt=21): 369 [] -class_Rings_Oordered__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Otimes__class_Otimes(A,D,B),c_Groups_Otimes__class_Otimes(A,D,C)).
% 15.19/15.15  ** KEPT (pick-wt=21): 370 [] -class_Rings_Oordered__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,D)).
% 15.19/15.15    Following clause subsumed by 363 during input processing: 0 [] -class_Rings_Oordered__ring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)).
% 15.19/15.15    Following clause subsumed by 361 during input processing: 0 [] -class_Rings_Oordered__cancel__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Ozero__class_Ozero(A)).
% 15.19/15.15    Following clause subsumed by 361 during input processing: 0 [] -class_Rings_Oordered__cancel__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Otimes__class_Otimes(A,C,B),c_Groups_Ozero__class_Ozero(A)).
% 15.19/15.15    Following clause subsumed by 360 during input processing: 0 [] -class_Rings_Oordered__cancel__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Ozero__class_Ozero(A)).
% 15.19/15.15  ** KEPT (pick-wt=20): 371 [] -class_Rings_Oordered__cancel__semiring(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C)).
% 15.19/15.15  ** KEPT (pick-wt=20): 372 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 15.19/15.15  ** KEPT (pick-wt=20): 373 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C).
% 15.19/15.15  ** KEPT (pick-wt=20): 374 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 15.19/15.15  ** KEPT (pick-wt=20): 375 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C).
% 15.19/15.15  ** KEPT (pick-wt=20): 376 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A)).
% 15.19/15.15  ** KEPT (pick-wt=20): 377 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C).
% 15.19/15.15  ** KEPT (pick-wt=20): 378 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 15.19/15.15  ** KEPT (pick-wt=20): 379 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A)).
% 15.19/15.15  ** KEPT (pick-wt=20): 380 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 15.19/15.15  ** KEPT (pick-wt=20): 381 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A)).
% 15.19/15.15  ** KEPT (pick-wt=20): 382 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C).
% 15.19/15.15  ** KEPT (pick-wt=20): 383 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,C))| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A)).
% 15.19/15.15  ** KEPT (pick-wt=10): 384 [] -class_Rings_Olinordered__ring(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Otimes__class_Otimes(A,B,B)).
% 15.19/15.15  ** KEPT (pick-wt=15): 385 [] -class_Groups_Olinordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,B))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B).
% 15.19/15.16  ** KEPT (pick-wt=15): 386 [] -class_Groups_Olinordered__ab__group__add(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,B))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B).
% 15.19/15.16  ** KEPT (pick-wt=15): 387 [] -class_Groups_Olinordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 15.19/15.16  ** KEPT (pick-wt=15): 388 [] -class_Groups_Olinordered__ab__group__add(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,B),c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A)).
% 15.19/15.16  ** KEPT (pick-wt=20): 389 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,C)).
% 15.19/15.16  ** KEPT (pick-wt=23): 390 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Ozero__class_Ozero(A)|B=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.16  ** KEPT (pick-wt=23): 391 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Groups_Oplus__class_Oplus(A,B,C)!=c_Groups_Ozero__class_Ozero(A)|C=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.16  ** KEPT (pick-wt=27): 392 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Groups_Oplus__class_Oplus(A,B,C)=c_Groups_Ozero__class_Ozero(A)|B!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(A).
% 15.19/15.16  ** KEPT (pick-wt=18): 393 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Oplus__class_Oplus(A,B,D)).
% 15.19/15.16  ** KEPT (pick-wt=18): 394 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Oplus__class_Oplus(A,D,B)).
% 15.19/15.16  ** KEPT (pick-wt=20): 395 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Ozero__class_Ozero(A)).
% 15.19/15.16  ** KEPT (pick-wt=20): 396 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,E)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)).
% 15.19/15.16  ** KEPT (pick-wt=20): 397 [] -class_Groups_Oordered__cancel__ab__semigroup__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,E)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,D),c_Groups_Oplus__class_Oplus(A,C,E)).
% 15.19/15.16  ** KEPT (pick-wt=10): 399 [copy,398,flip.2] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|c_Nat_OSuc($f6(A))=A.
% 15.19/15.16  ** KEPT (pick-wt=9): 400 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|A!=c_Nat_OSuc(B).
% 15.19/15.16  ** KEPT (pick-wt=10): 401 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.16    Following clause subsumed by 330 during input processing: 0 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.16  ** KEPT (pick-wt=15): 403 [copy,402,flip.3] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Nat_OSuc($f7(B,A))=A.
% 15.19/15.16  ** KEPT (pick-wt=15): 404 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,$f7(B,A),B).
% 15.19/15.16  ** KEPT (pick-wt=9): 405 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B))|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.16  ** KEPT (pick-wt=13): 406 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(B))|A!=c_Nat_OSuc(C)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,C,B).
% 15.19/15.16  ** KEPT (pick-wt=17): 407 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)|A=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.16  ** KEPT (pick-wt=18): 408 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)|A=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.19/15.16  ** KEPT (pick-wt=16): 409 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.16  ** KEPT (pick-wt=17): 410 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.19/15.16  ** KEPT (pick-wt=17): 411 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)|A!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.16  ** KEPT (pick-wt=17): 412 [] c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.19/15.16  ** KEPT (pick-wt=17): 413 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.16  ** KEPT (pick-wt=18): 414 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.19/15.16  ** KEPT (pick-wt=16): 415 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.16  ** KEPT (pick-wt=17): 416 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.19/15.16  ** KEPT (pick-wt=17): 417 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.19/15.16  ** KEPT (pick-wt=17): 418 [] c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|B!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.19/15.16  ** KEPT (pick-wt=13): 419 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.19/15.16  ** KEPT (pick-wt=13): 420 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.19/15.16  ** KEPT (pick-wt=18): 421 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|A!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))|B!=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.19/15.16  ** KEPT (pick-wt=13): 423 [copy,422,flip.2] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,$f8(B,A)))=B.
% 15.19/15.16  ** KEPT (pick-wt=11): 424 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|B!=c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)).
% 15.19/15.16    Following clause subsumed by 222 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(A),B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(A),C))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 15.19/15.16  ** KEPT (pick-wt=16): 425 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(A),B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Nat_OSuc(A),C))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 15.19/15.16  ** KEPT (pick-wt=17): 426 [] -class_Groups_Ozero(A)|hAPP(c_Polynomial_Ocoeff(A,c_Polynomial_OpCons(A,B,C)),c_Nat_OSuc(D))=hAPP(c_Polynomial_Ocoeff(A,C),D).
% 15.19/15.16  ** KEPT (pick-wt=13): 427 [] -class_Rings_Ocomm__semiring__0(A)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(A,c_Polynomial_Osmult(A,B,C)),c_Polynomial_Odegree(A,C)).
% 15.19/15.16  ** KEPT (pick-wt=24): 428 [] -class_Groups_Ocomm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(A,B),C)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(A,D),C)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(A,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),B,D)),C).
% 15.19/15.16  ** KEPT (pick-wt=11): 429 [] -class_Groups_Ozero(A)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(A,c_Polynomial_Omonom(A,B,C)),C).
% 15.19/15.16  ** KEPT (pick-wt=21): 430 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless__e_q(A,C,D).
% 15.19/15.16  ** KEPT (pick-wt=21): 431 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,C))| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless__e_q(A,B,D).
% 15.19/15.16  ** KEPT (pick-wt=21): 432 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,C,D).
% 15.19/15.16  ** KEPT (pick-wt=21): 433 [] -class_Rings_Olinordered__semiring(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless(A,C,D).
% 15.19/15.16  ** KEPT (pick-wt=21): 434 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,C))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,B,D).
% 15.19/15.16  ** KEPT (pick-wt=21): 435 [] -class_Rings_Olinordered__semiring(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,D,C))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,B,D).
% 15.19/15.16  ** KEPT (pick-wt=30): 436 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,E)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,E)).
% 15.19/15.16  ** KEPT (pick-wt=30): 437 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,E)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,E)).
% 15.19/15.16  ** KEPT (pick-wt=30): 438 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,E)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,E)).
% 15.19/15.16  ** KEPT (pick-wt=30): 439 [] -class_Rings_Olinordered__semiring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,E)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),D)|c_Orderings_Oord__class_Oless(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,E)).
% 15.19/15.16  ** KEPT (pick-wt=21): 440 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D))|c_Orderings_Oord__class_Oless__e_q(A,D,C).
% 15.19/15.16  ** KEPT (pick-wt=21): 441 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D))| -c_Orderings_Oord__class_Oless__e_q(A,D,C).
% 15.19/15.16  ** KEPT (pick-wt=21): 442 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D))|c_Orderings_Oord__class_Oless__e_q(A,C,D).
% 15.19/15.16  ** KEPT (pick-wt=21): 443 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D))| -c_Orderings_Oord__class_Oless__e_q(A,C,D).
% 15.19/15.16  ** KEPT (pick-wt=20): 444 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Ozero__class_Ozero(A)).
% 15.19/15.16  ** KEPT (pick-wt=20): 445 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless(A,B,c_Groups_Ozero__class_Ozero(A))| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Ozero__class_Ozero(A))|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,B,C),c_Groups_Ozero__class_Ozero(A)).
% 15.19/15.16  ** KEPT (pick-wt=18): 446 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,C,c_Groups_Oplus__class_Oplus(A,B,D)).
% 15.19/15.16  ** KEPT (pick-wt=18): 447 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Orderings_Oord__class_Oless(A,C,c_Groups_Oplus__class_Oplus(A,B,D)).
% 15.19/15.16    Following clause subsumed by 446 during input processing: 0 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,C)).
% 15.19/15.16    Following clause subsumed by 447 during input processing: 0 [] -class_Groups_Oordered__comm__monoid__add(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,B,C)).
% 15.19/15.16  ** KEPT (pick-wt=20): 448 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,B),c_Groups_Otimes__class_Otimes(A,C,C)),c_Groups_Ozero__class_Ozero(A))|B=c_Groups_Ozero__class_Ozero(A).
% 15.24/15.16  ** KEPT (pick-wt=20): 449 [] -class_Rings_Olinordered__ring__strict(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,B),c_Groups_Otimes__class_Otimes(A,C,C)),c_Groups_Ozero__class_Ozero(A))|C=c_Groups_Ozero__class_Ozero(A).
% 15.24/15.16  ** KEPT (pick-wt=24): 450 [] -class_Rings_Olinordered__ring__strict(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,B),c_Groups_Otimes__class_Otimes(A,C,C)),c_Groups_Ozero__class_Ozero(A))|B!=c_Groups_Ozero__class_Ozero(A)|C!=c_Groups_Ozero__class_Ozero(A).
% 15.24/15.16  ** KEPT (pick-wt=16): 451 [] -class_Rings_Olinordered__ring(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,B),c_Groups_Otimes__class_Otimes(A,C,C))).
% 15.24/15.16  ** KEPT (pick-wt=21): 452 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,A)).
% 15.24/15.16  ** KEPT (pick-wt=19): 453 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)).
% 15.24/15.16  ** KEPT (pick-wt=19): 454 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,A)).
% 15.24/15.16  ** KEPT (pick-wt=19): 455 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C).
% 15.24/15.16    Following clause subsumed by 349 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,C,B))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C).
% 15.24/15.16  ** KEPT (pick-wt=19): 456 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C).
% 15.24/15.16    Following clause subsumed by 348 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C).
% 15.24/15.16    Following clause subsumed by 456 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C).
% 15.24/15.16    Following clause subsumed by 348 during input processing: 0 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B),c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C).
% 15.24/15.16  ** KEPT (pick-wt=32): 457 [] -class_Fields_Ofield(A)| -c_Polynomial_Opdivmod__rel(A,B,C,D,E)| -c_Polynomial_Opdivmod__rel(A,D,F,G,H)|c_Polynomial_Opdivmod__rel(A,B,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,F),G,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(A),c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),C,H),E)).
% 15.24/15.16  ** KEPT (pick-wt=16): 458 [] -class_Groups_Ozero(A)|hAPP(c_Polynomial_Ocoeff(A,B),C)=c_Groups_Ozero__class_Ozero(A)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,c_Polynomial_Odegree(A,B)).
% 15.24/15.16    Following clause subsumed by 283 during input processing: 0 [] -class_Groups_Ozero(A)|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|c_Polynomial_Odegree(A,c_Polynomial_OpCons(A,C,B))=c_Nat_OSuc(c_Polynomial_Odegree(A,B)).
% 15.24/15.16  ** KEPT (pick-wt=16): 459 [] -class_Groups_Ozero(A)|c_Polynomial_Omonom(A,B,c_Nat_OSuc(C))=c_Polynomial_OpCons(A,c_Groups_Ozero__class_Ozero(A),c_Polynomial_Omonom(A,B,C)).
% 15.24/15.16  ** KEPT (pick-wt=19): 460 [] -class_Rings_Ocomm__semiring__0(A)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(A,c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(A),B,C)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Polynomial_Odegree(A,B),c_Polynomial_Odegree(A,C))).
% 15.24/15.16  ** KEPT (pick-wt=16): 461 [] -class_Rings_Oidom(A)|B=c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Oorder(A,C,B),c_Polynomial_Odegree(A,B)).
% 15.24/15.16  ** KEPT (pick-wt=16): 462 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A=c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)).
% 15.24/15.16  ** KEPT (pick-wt=6): 463 [] -class_Orderings_Opreorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,B).
% 15.24/15.16  ** KEPT (pick-wt=12): 465 [copy,464,flip.2] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,$f9(B,A))=B.
% 15.24/15.16    Following clause subsumed by 346 during input processing: 0 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|B!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C).
% 15.24/15.16  ** KEPT (pick-wt=10): 466 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 15.24/15.16  ** KEPT (pick-wt=10): 467 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 15.24/15.16    Following clause subsumed by 466 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B).
% 15.24/15.16    Following clause subsumed by 467 during input processing: 0 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 15.24/15.16    Following clause subsumed by 466 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B).
% 15.24/15.16  ** KEPT (pick-wt=10): 468 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 15.24/15.16  ** KEPT (pick-wt=9): 469 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C.
% 15.24/15.16  ** KEPT (pick-wt=13): 470 [] -class_Orderings_Oorder(A)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|B=C.
% 15.24/15.16  ** KEPT (pick-wt=10): 471 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 15.24/15.16  ** KEPT (pick-wt=16): 472 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,E),hAPP(D,E)).
% 15.24/15.16  ** KEPT (pick-wt=14): 473 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,B)|c_Orderings_Oord__class_Oless__e_q(A,D,C).
% 15.24/15.16  ** KEPT (pick-wt=13): 474 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B)|C=B.
% 15.24/15.16  ** KEPT (pick-wt=14): 475 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Orderings_Oord__class_Oless__e_q(A,B,D).
% 15.24/15.16    Following clause subsumed by 474 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B)|B=C.
% 15.24/15.16  ** KEPT (pick-wt=13): 476 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|B!=D|c_Orderings_Oord__class_Oless__e_q(A,D,C).
% 15.24/15.16  ** KEPT (pick-wt=13): 477 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|C!=D|c_Orderings_Oord__class_Oless__e_q(A,B,D).
% 15.24/15.16  ** KEPT (pick-wt=13): 478 [] -class_Orderings_Oorder(A)|B!=C| -c_Orderings_Oord__class_Oless__e_q(A,D,C)|c_Orderings_Oord__class_Oless__e_q(A,D,B).
% 15.24/15.16  ** KEPT (pick-wt=13): 479 [] -class_Orderings_Oord(A)|B!=C| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Orderings_Oord__class_Oless__e_q(A,B,D).
% 15.24/15.16    Following clause subsumed by 474 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B)|C=B.
% 15.24/15.16  ** KEPT (pick-wt=13): 480 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B)|C!=B.
% 15.24/15.16    Following clause subsumed by 472 during input processing: 0 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,E),hAPP(D,E)).
% 15.24/15.16  ** KEPT (pick-wt=9): 481 [] -class_Orderings_Opreorder(A)|B!=C|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 15.24/15.16  ** KEPT (pick-wt=9): 482 [] -class_Orderings_Oorder(A)|B!=C|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 15.24/15.16  ** KEPT (pick-wt=9): 483 [] -class_Orderings_Oorder(A)|B!=C|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 15.24/15.16    Following clause subsumed by 474 during input processing: 0 [] -class_Orderings_Oorder(A)|B=C| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 15.24/15.16    Following clause subsumed by 471 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 15.24/15.16    Following clause subsumed by 472 during input processing: 0 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D)|c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,E),hAPP(D,E)).
% 15.24/15.16  ** KEPT (pick-wt=24): 484 [] -class_Orderings_Oord(A)|c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D)| -c_Orderings_Oord__class_Oless__e_q(A,hAPP(C,$f10(D,C,B,A)),hAPP(D,$f10(D,C,B,A))).
% 15.24/15.16  ** KEPT (pick-wt=13): 485 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|B=C|c_Orderings_Oord__class_Oless(A,C,B).
% 15.24/15.16  ** KEPT (pick-wt=10): 486 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 15.24/15.16  ** KEPT (pick-wt=14): 487 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,B)|c_Orderings_Oord__class_Oless(A,D,C).
% 15.24/15.16  ** KEPT (pick-wt=14): 488 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,B,D).
% 15.24/15.16  ** KEPT (pick-wt=13): 489 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=D|c_Orderings_Oord__class_Oless(A,D,C).
% 15.24/15.16  ** KEPT (pick-wt=13): 490 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless(A,B,C)|C!=D|c_Orderings_Oord__class_Oless(A,B,D).
% 15.24/15.16  ** KEPT (pick-wt=13): 491 [] -class_Orderings_Oorder(A)|B!=C| -c_Orderings_Oord__class_Oless(A,D,C)|c_Orderings_Oord__class_Oless(A,D,B).
% 15.24/15.16  ** KEPT (pick-wt=13): 492 [] -class_Orderings_Oord(A)|B!=C| -c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,B,D).
% 15.24/15.16  ** KEPT (pick-wt=10): 493 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 15.24/15.16    Following clause subsumed by 486 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 15.24/15.16  ** KEPT (pick-wt=9): 494 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|C!=B.
% 15.24/15.16    Following clause subsumed by 469 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C.
% 15.24/15.16    Following clause subsumed by 486 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 15.24/15.16    Following clause subsumed by 486 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 15.24/15.16    Following clause subsumed by 469 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C.
% 15.24/15.16    Following clause subsumed by 485 during input processing: 0 [] -class_Orderings_Olinorder(A)|B=C|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B).
% 15.24/15.16    Following clause subsumed by 485 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B)|C=B.
% 15.24/15.16  ** KEPT (pick-wt=13): 495 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B)|C!=B.
% 15.24/15.16    Following clause subsumed by 485 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|B=C|c_Orderings_Oord__class_Oless(A,C,B).
% 15.24/15.16    Following clause subsumed by 485 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B)|B=C.
% 15.24/15.16  ** KEPT (pick-wt=10): 496 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 15.24/15.16  ** KEPT (pick-wt=9): 497 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C.
% 15.24/15.16    Following clause subsumed by 485 during input processing: 0 [] -class_Orderings_Olinorder(A)|B=C|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B).
% 15.24/15.16    Following clause subsumed by 497 during input processing: 0 [] -class_Orderings_Olinorder(A)|B!=C| -c_Orderings_Oord__class_Oless(A,B,C).
% 15.24/15.16  ** KEPT (pick-wt=9): 498 [] -class_Orderings_Olinorder(A)|B!=C| -c_Orderings_Oord__class_Oless(A,C,B).
% 15.24/15.16  ** KEPT (pick-wt=6): 499 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,B).
% 15.24/15.16  ** KEPT (pick-wt=14): 500 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,B)|c_Orderings_Oord__class_Oless(A,D,C).
% 15.24/15.16  ** KEPT (pick-wt=14): 501 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,D)|c_Orderings_Oord__class_Oless(A,B,D).
% 15.24/15.16  ** KEPT (pick-wt=14): 502 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,B)|c_Orderings_Oord__class_Oless(A,D,C).
% 15.24/15.16  ** KEPT (pick-wt=14): 503 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,D)|c_Orderings_Oord__class_Oless(A,B,D).
% 15.24/15.16  ** KEPT (pick-wt=13): 504 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|C=B|c_Orderings_Oord__class_Oless(A,B,C).
% 15.24/15.16    Following clause subsumed by 470 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|B=C|c_Orderings_Oord__class_Oless(A,B,C).
% 15.24/15.16    Following clause subsumed by 470 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,B,C)|B=C.
% 15.24/15.16  ** KEPT (pick-wt=13): 505 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,B,C)|B=C.
% 15.24/15.16    Following clause subsumed by 497 during input processing: 0 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,B,C)|B!=C.
% 15.24/15.16  ** KEPT (pick-wt=10): 506 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 15.24/15.16    Following clause subsumed by 467 during input processing: 0 [] -class_Orderings_Olinorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,C,B).
% 15.24/15.16    Following clause subsumed by 504 during input processing: 0 [] -class_Orderings_Oorder(A)|B=C| -c_Orderings_Oord__class_Oless__e_q(A,C,B)|c_Orderings_Oord__class_Oless(A,C,B).
% 15.24/15.16    Following clause subsumed by 470 during input processing: 0 [] -class_Orderings_Oorder(A)|B=C| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,B,C).
% 15.24/15.16    Following clause subsumed by 505 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|B=C.
% 15.24/15.16  ** KEPT (pick-wt=13): 507 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|B!=C.
% 15.24/15.16    Following clause subsumed by 466 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,C,B).
% 15.24/15.16    Following clause subsumed by 466 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 15.24/15.16    Following clause subsumed by 470 during input processing: 0 [] -class_Orderings_Oorder(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless(A,B,C)|B=C.
% 15.24/15.16    Following clause subsumed by 468 during input processing: 0 [] -class_Orderings_Oorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless(A,B,C).
% 15.24/15.16    Following clause subsumed by 482 during input processing: 0 [] -class_Orderings_Oorder(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)|B!=C.
% 15.24/15.16    Following clause subsumed by 506 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,B,C).
% 15.24/15.16  ** KEPT (pick-wt=10): 508 [] -class_Orderings_Opreorder(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 15.24/15.16  ** KEPT (pick-wt=14): 509 [] -class_Orderings_Opreorder(A)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,C,B).
% 15.24/15.16  ** KEPT (pick-wt=15): 510 [] -class_Groups_Ozero(A)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,$f11(C,B,A))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(A,C),B).
% 15.24/15.16  ** KEPT (pick-wt=19): 511 [] -class_Groups_Ozero(A)|hAPP(c_Polynomial_Ocoeff(A,B),$f11(B,C,A))!=c_Groups_Ozero__class_Ozero(A)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Polynomial_Odegree(A,B),C).
% 15.24/15.16  ** KEPT (pick-wt=40): 512 [] -class_Rings_Olinordered__semiring__1__strict(A)| -c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),E)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),F)|c_Groups_Oplus__class_Oplus(A,E,F)!=c_Groups_Oone__class_Oone(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,E,B),c_Groups_Otimes__class_Otimes(A,F,D)),C).
% 15.24/15.16  ** KEPT (pick-wt=33): 513 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),D),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,C),E))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,D,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),C),E)).
% 15.24/15.16  ** KEPT (pick-wt=33): 514 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),D),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,C),E))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,D,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),C),E)).
% 15.24/15.16  ** KEPT (pick-wt=33): 515 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,C),D),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),E))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),C),D),E).
% 15.24/15.16  ** KEPT (pick-wt=33): 516 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,C),D),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),E))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),C),D),E).
% 15.24/15.16  ** KEPT (pick-wt=14): 517 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless(tc_fun(B,A),C,D)|c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D).
% 15.24/15.16  ** KEPT (pick-wt=14): 518 [] -class_Orderings_Oord(A)| -c_Orderings_Oord__class_Oless(tc_fun(B,A),C,D)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),D,C).
% 15.24/15.16  ** KEPT (pick-wt=20): 519 [] -class_Orderings_Oord(A)|c_Orderings_Oord__class_Oless(tc_fun(B,A),C,D)| -c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),C,D)|c_Orderings_Oord__class_Oless__e_q(tc_fun(B,A),D,C).
% 15.24/15.16  ** KEPT (pick-wt=9): 520 [] -class_Groups_Ogroup__add(A)|c_Groups_Ominus__class_Ominus(A,B,c_Groups_Ozero__class_Ozero(A))=B.
% 15.24/15.16  ** KEPT (pick-wt=9): 521 [] -class_Groups_Ogroup__add(A)|c_Groups_Ominus__class_Ominus(A,B,B)=c_Groups_Ozero__class_Ozero(A).
% 15.24/15.16  ** KEPT (pick-wt=12): 522 [] -class_Groups_Oab__group__add(A)|B!=C|c_Groups_Ominus__class_Ominus(A,B,C)=c_Groups_Ozero__class_Ozero(A).
% 15.24/15.16  ** KEPT (pick-wt=12): 523 [] -class_Groups_Oab__group__add(A)|B=C|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ozero__class_Ozero(A).
% 15.24/15.16  ** KEPT (pick-wt=12): 524 [] -class_Groups_Ogroup__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ozero__class_Ozero(A)|B=C.
% 15.24/15.16  ** KEPT (pick-wt=12): 525 [] -class_Groups_Ogroup__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)=c_Groups_Ozero__class_Ozero(A)|B!=C.
% 15.24/15.16  ** KEPT (pick-wt=19): 526 [] -class_Groups_Oordered__ab__group__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ominus__class_Ominus(A,D,E)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,D,E).
% 15.24/15.16  ** KEPT (pick-wt=19): 527 [] -class_Groups_Oordered__ab__group__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ominus__class_Ominus(A,D,E)|c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,E).
% 15.24/15.16  ** KEPT (pick-wt=19): 528 [] -class_Groups_Oordered__ab__group__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ominus__class_Ominus(A,D,E)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,D,E).
% 15.24/15.16  ** KEPT (pick-wt=19): 529 [] -class_Groups_Oordered__ab__group__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ominus__class_Ominus(A,D,E)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,D,E).
% 15.24/15.16  ** KEPT (pick-wt=13): 531 [copy,530,flip.2] -class_Rings_Ocomm__semiring__1(A)|c_Polynomial_OpCons(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(A)))=c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)).
% 15.24/15.16  ** KEPT (pick-wt=20): 532 [] -class_RealVector_Oreal__normed__algebra(A)|c_Groups_Otimes__class_Otimes(A,B,c_Groups_Ominus__class_Ominus(A,C,D))=c_Groups_Ominus__class_Ominus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)).
% 15.24/15.16    Following clause subsumed by 532 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|c_Groups_Otimes__class_Otimes(A,B,c_Groups_Ominus__class_Ominus(A,C,D))=c_Groups_Ominus__class_Ominus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,B,D)).
% 15.24/15.16  ** KEPT (pick-wt=20): 533 [] -class_RealVector_Oreal__normed__algebra(A)|c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,C),D)=c_Groups_Ominus__class_Ominus(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,D)).
% 15.24/15.16    Following clause subsumed by 533 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,C),D)=c_Groups_Ominus__class_Ominus(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,D)).
% 15.24/15.16  ** KEPT (pick-wt=11): 534 [] -class_Groups_Ogroup__add(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Ominus__class_Ominus(A,B,C),C)=B.
% 15.24/15.16  ** KEPT (pick-wt=11): 535 [] -class_Groups_Ogroup__add(A)|c_Groups_Ominus__class_Ominus(A,c_Groups_Oplus__class_Oplus(A,B,C),C)=B.
% 15.24/15.16  ** KEPT (pick-wt=7): 536 [] -class_Rings_Ozero__ne_q__one(A)|c_Groups_Ozero__class_Ozero(A)!=c_Groups_Oone__class_Oone(A).
% 15.24/15.16    Following clause subsumed by 536 during input processing: 0 [flip.2] -class_Rings_Ozero__ne_q__one(A)|c_Groups_Ozero__class_Ozero(A)!=c_Groups_Oone__class_Oone(A).
% 15.24/15.16  ** KEPT (pick-wt=17): 537 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|A=B.
% 15.24/15.16  ** KEPT (pick-wt=9): 538 [] -class_Groups_Omonoid__mult(A)|c_Groups_Otimes__class_Otimes(A,c_Groups_Oone__class_Oone(A),B)=B.
% 15.24/15.16  ** KEPT (pick-wt=9): 539 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Otimes__class_Otimes(A,c_Groups_Oone__class_Oone(A),B)=B.
% 15.24/15.16  ** KEPT (pick-wt=9): 540 [] -class_Groups_Ocomm__monoid__mult(A)|c_Groups_Otimes__class_Otimes(A,c_Groups_Oone__class_Oone(A),B)=B.
% 15.24/15.16  ** KEPT (pick-wt=9): 541 [] -class_Groups_Omonoid__mult(A)|c_Groups_Otimes__class_Otimes(A,B,c_Groups_Oone__class_Oone(A))=B.
% 15.24/15.16  ** KEPT (pick-wt=9): 542 [] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Otimes__class_Otimes(A,B,c_Groups_Oone__class_Oone(A))=B.
% 15.24/15.16  ** KEPT (pick-wt=9): 543 [] -class_Groups_Ocomm__monoid__mult(A)|c_Groups_Otimes__class_Otimes(A,B,c_Groups_Oone__class_Oone(A))=B.
% 15.24/15.16  ** KEPT (pick-wt=11): 544 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,C),B).
% 15.24/15.16  ** KEPT (pick-wt=18): 545 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,B),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A)).
% 15.24/15.16  ** KEPT (pick-wt=14): 546 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,B),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A)).
% 15.24/15.16  ** KEPT (pick-wt=14): 547 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,C),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)).
% 15.24/15.16  ** KEPT (pick-wt=13): 548 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))=A.
% 15.24/15.16  ** KEPT (pick-wt=20): 549 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)!=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A)|B=C.
% 15.24/15.16  ** KEPT (pick-wt=20): 550 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A)|B!=C.
% 15.24/15.16  ** KEPT (pick-wt=23): 551 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C).
% 15.24/15.16  ** KEPT (pick-wt=22): 552 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C).
% 15.24/15.16    Following clause subsumed by 547 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,B,C).
% 15.24/15.16  ** KEPT (pick-wt=25): 554 [copy,553,flip.2] -class_Groups_Oab__group__add(A)|c_Polynomial_OpCons(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),D,E))=c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),c_Polynomial_OpCons(A,B,D),c_Polynomial_OpCons(A,C,E)).
% 15.24/15.16  ** KEPT (pick-wt=24): 555 [] -class_Groups_Oab__group__add(A)|hAPP(c_Polynomial_Ocoeff(A,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C)),D)=c_Groups_Ominus__class_Ominus(A,hAPP(c_Polynomial_Ocoeff(A,B),D),hAPP(c_Polynomial_Ocoeff(A,C),D)).
% 15.24/15.16  ** KEPT (pick-wt=21): 556 [] -class_Rings_Ocomm__ring(A)|c_Polynomial_Osmult(A,c_Groups_Ominus__class_Ominus(A,B,C),D)=c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),c_Polynomial_Osmult(A,B,D),c_Polynomial_Osmult(A,C,D)).
% 15.24/15.16  ** KEPT (pick-wt=24): 557 [] -class_Rings_Ocomm__ring(A)|hAPP(c_Polynomial_Opoly(A,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),B,C)),D)=c_Groups_Ominus__class_Ominus(A,hAPP(c_Polynomial_Opoly(A,B),D),hAPP(c_Polynomial_Opoly(A,C),D)).
% 15.24/15.16  ** KEPT (pick-wt=21): 558 [] -class_Groups_Oab__group__add(A)|c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(A),c_Polynomial_Omonom(A,B,C),c_Polynomial_Omonom(A,D,C))=c_Polynomial_Omonom(A,c_Groups_Ominus__class_Ominus(A,B,D),C).
% 15.24/15.16  ** KEPT (pick-wt=12): 559 [] -class_Rings_Ocomm__semiring__1(A)|hAPP(c_Polynomial_Opoly(A,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),B)=c_Groups_Oone__class_Oone(A).
% 15.24/15.16  ** KEPT (pick-wt=17): 560 [] -class_Groups_Oab__group__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ominus__class_Ominus(A,D,E)|B!=C|D=E.
% 15.24/15.16  ** KEPT (pick-wt=17): 561 [] -class_Groups_Oab__group__add(A)|c_Groups_Ominus__class_Ominus(A,B,C)!=c_Groups_Ominus__class_Ominus(A,D,E)|B=C|D!=E.
% 15.24/15.16  ** KEPT (pick-wt=10): 562 [] -class_Groups_Oone(A)|c_Groups_Oone__class_Oone(A)!=B|B=c_Groups_Oone__class_Oone(A).
% 15.24/15.16  ** KEPT (pick-wt=10): 563 [] -class_Groups_Oone(A)|c_Groups_Oone__class_Oone(A)=B|B!=c_Groups_Oone__class_Oone(A).
% 15.24/15.16  ** KEPT (pick-wt=16): 564 [] -class_Rings_Ocomm__semiring__0(A)|c_Polynomial_Odegree(A,c_Polynomial_Osynthetic__div(A,B,C))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Polynomial_Odegree(A,B),c_Groups_Oone__class_Oone(tc_Nat_Onat)).
% 15.24/15.16  ** KEPT (pick-wt=11): 565 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|A=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.24/15.16  ** KEPT (pick-wt=11): 566 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|B=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.24/15.16  ** KEPT (pick-wt=15): 567 [] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)=c_Groups_Oone__class_Oone(tc_Nat_Onat)|A!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|B!=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.24/15.16  ** KEPT (pick-wt=11): 568 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)!=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)|A=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.24/15.16  ** KEPT (pick-wt=11): 569 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)!=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)|B=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.24/15.16  ** KEPT (pick-wt=15): 570 [] c_Groups_Oone__class_Oone(tc_Nat_Onat)=c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)|A!=c_Groups_Oone__class_Oone(tc_Nat_Onat)|B!=c_Groups_Oone__class_Oone(tc_Nat_Onat).
% 15.24/15.16  ** KEPT (pick-wt=9): 571 [] -class_Rings_Ocomm__semiring__1(A)|c_Polynomial_Osmult(A,c_Groups_Oone__class_Oone(A),B)=B.
% 15.24/15.16  ** KEPT (pick-wt=13): 572 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=A.
% 15.24/15.16    Following clause subsumed by 572 during input processing: 0 [flip.2] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,c_Groups_Oone__class_Oone(tc_Nat_Onat)))=A.
% 15.24/15.16  ** KEPT (pick-wt=10): 573 [] A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,B)=B.
% 15.24/15.16    Following clause subsumed by 224 during input processing: 0 [] A!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.24/15.16  ** KEPT (pick-wt=16): 574 [] -class_Rings_Ocomm__semiring__1(A)|B!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Polynomial_Ocoeff(A,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),B)=c_Groups_Oone__class_Oone(A).
% 15.24/15.16  ** KEPT (pick-wt=16): 575 [] -class_Rings_Ocomm__semiring__1(A)|B=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|hAPP(c_Polynomial_Ocoeff(A,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A))),B)=c_Groups_Ozero__class_Ozero(A).
% 15.24/15.16  ** KEPT (pick-wt=14): 576 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)).
% 15.24/15.16  ** KEPT (pick-wt=14): 577 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)).
% 15.24/15.16  ** KEPT (pick-wt=14): 578 [] -class_Groups_Oordered__ab__group__add(A)| -c_Orderings_Oord__class_Oless(A,B,C)|c_Orderings_Oord__class_Oless(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)).
% 15.24/15.16  ** KEPT (pick-wt=14): 579 [] -class_Groups_Oordered__ab__group__add(A)|c_Orderings_Oord__class_Oless(A,B,C)| -c_Orderings_Oord__class_Oless(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ozero__class_Ozero(A)).
% 15.24/15.16  ** KEPT (pick-wt=41): 581 [copy,580,flip.2] -class_RealVector_Oreal__normed__algebra(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,C),c_Groups_Ominus__class_Ominus(A,D,E)),c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,C),E)),c_Groups_Otimes__class_Otimes(A,C,c_Groups_Ominus__class_Ominus(A,D,E)))=c_Groups_Ominus__class_Ominus(A,c_Groups_Otimes__class_Otimes(A,B,D),c_Groups_Otimes__class_Otimes(A,C,E)).
% 15.24/15.16  ** KEPT (pick-wt=29): 582 [] -class_Rings_Oring(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),D)!=c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,E,C),F)|c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,E),C),D)=F.
% 15.24/15.16  ** KEPT (pick-wt=29): 583 [] -class_Rings_Oring(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),D)=c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,E,C),F)|c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,E),C),D)!=F.
% 15.24/15.16  ** KEPT (pick-wt=29): 584 [] -class_Rings_Oring(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),D)!=c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,E,C),F)|D=c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,E,B),C),F).
% 15.24/15.16  ** KEPT (pick-wt=29): 585 [] -class_Rings_Oring(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),D)=c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,E,C),F)|D!=c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,E,B),C),F).
% 15.24/15.16  ** KEPT (pick-wt=8): 586 [] -class_Rings_Olinordered__semidom(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oone__class_Oone(A)).
% 15.24/15.16  ** KEPT (pick-wt=8): 587 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(A)).
% 15.24/15.16  ** KEPT (pick-wt=8): 588 [] -class_Rings_Olinordered__semidom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oone__class_Oone(A)).
% 15.24/15.16  ** KEPT (pick-wt=8): 589 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Groups_Ozero__class_Ozero(A)).
% 15.24/15.16  ** KEPT (pick-wt=20): 590 [] -class_Rings_Olinordered__semidom(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),B)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),C)|c_Orderings_Oord__class_Oless(A,c_Groups_Oone__class_Oone(A),c_Groups_Otimes__class_Otimes(A,B,C)).
% 15.24/15.16  ** KEPT (pick-wt=10): 591 [] -class_Rings_Olinordered__semidom(A)|c_Orderings_Oord__class_Oless(A,B,c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oone__class_Oone(A))).
% 15.24/15.16  ** KEPT (pick-wt=16): 593 [copy,592,flip.2] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Oone__class_Oone(A),c_Groups_Oone__class_Oone(A)),B)=c_Groups_Oplus__class_Oplus(A,B,B).
% 15.24/15.17  ** KEPT (pick-wt=18): 595 [copy,594,flip.2] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oone__class_Oone(A)),C)=c_Groups_Oplus__class_Oplus(A,C,c_Groups_Otimes__class_Otimes(A,B,C)).
% 15.24/15.17  ** KEPT (pick-wt=18): 597 [copy,596,flip.2] -class_Rings_Ocomm__semiring__1(A)|c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oone__class_Oone(A)),C)=c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),C).
% 15.24/15.17  ** KEPT (pick-wt=12): 598 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A).
% 15.24/15.17  ** KEPT (pick-wt=12): 599 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,A).
% 15.24/15.17  ** KEPT (pick-wt=17): 600 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),B).
% 15.24/15.17  ** KEPT (pick-wt=11): 601 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.24/15.17  ** KEPT (pick-wt=11): 602 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B)!=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 15.24/15.17    Following clause subsumed by 601 during input processing: 0 [] c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B)=c_Groups_Ozero__class_Ozero(tc_Nat_Onat)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B).
% 15.24/15.17  ** KEPT (pick-wt=15): 604 [copy,603,flip.2] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(B),A).
% 15.24/15.17  ** KEPT (pick-wt=14): 605 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),B).
% 15.24/15.17  ** KEPT (pick-wt=14): 606 [] c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C),B).
% 15.24/15.17  ** KEPT (pick-wt=18): 607 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,A)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,C),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)).
% 15.24/15.17  ** KEPT (pick-wt=22): 608 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C)| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 15.24/15.17    Following clause subsumed by 607 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,C)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,A))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C).
% 15.24/15.17  ** KEPT (pick-wt=19): 610 [copy,609,flip.2] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),C)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C),A).
% 15.24/15.17    Following clause subsumed by 610 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),C)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C),A).
% 15.24/15.17  ** KEPT (pick-wt=19): 612 [copy,611,flip.2] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B),A).
% 15.24/15.17  ** KEPT (pick-wt=16): 613 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)!=C|B=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,A).
% 15.24/15.17  ** KEPT (pick-wt=16): 614 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)=C|B!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,A).
% 15.24/15.17  ** KEPT (pick-wt=13): 615 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),A)=B.
% 15.24/15.17  ** KEPT (pick-wt=18): 616 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,A),B).
% 15.24/15.17  ** KEPT (pick-wt=18): 617 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,A),B).
% 15.24/15.17    Following clause subsumed by 612 during input processing: 0 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B),A).
% 15.24/15.17  ** KEPT (pick-wt=13): 618 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))=B.
% 15.24/15.17  ** KEPT (pick-wt=14): 619 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,C,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B,C),A)).
% 15.24/15.17  ** KEPT (pick-wt=14): 620 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B),C)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)).
% 15.24/15.17  ** KEPT (pick-wt=14): 621 [] c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,B),C)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,B)).
% 15.24/15.17  ** KEPT (pick-wt=19): 622 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,A),B).
% 15.24/15.17  ** KEPT (pick-wt=14): 624 [copy,623,flip.1] c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B)!=A|B=c_Groups_Oone__class_Oone(tc_Nat_Onat)|A=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.24/15.17  ** KEPT (pick-wt=10): 625 [] -class_Rings_Ocomm__semiring__1(A)|c_Polynomial_Odegree(A,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(A)))=c_Groups_Ozero__class_Ozero(tc_Nat_Onat).
% 15.24/15.17  ** KEPT (pick-wt=31): 626 [] -class_Rings_Oordered__ring(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),D),c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,E,C),F))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,E),C),D),F).
% 15.24/15.17  ** KEPT (pick-wt=31): 627 [] -class_Rings_Oordered__ring(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),D),c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,E,C),F))| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,E),C),D),F).
% 15.24/15.17  ** KEPT (pick-wt=31): 628 [] -class_Rings_Oordered__ring(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),D),c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,E,C),F))|c_Orderings_Oord__class_Oless__e_q(A,D,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,E,B),C),F)).
% 15.24/15.17  ** KEPT (pick-wt=31): 629 [] -class_Rings_Oordered__ring(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),D),c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,E,C),F))| -c_Orderings_Oord__class_Oless__e_q(A,D,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,E,B),C),F)).
% 15.24/15.17  ** KEPT (pick-wt=31): 630 [] -class_Rings_Oordered__ring(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),D),c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,E,C),F))|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,E),C),D),F).
% 15.24/15.17  ** KEPT (pick-wt=31): 631 [] -class_Rings_Oordered__ring(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),D),c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,E,C),F))| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,E),C),D),F).
% 15.24/15.17  ** KEPT (pick-wt=31): 632 [] -class_Rings_Oordered__ring(A)| -c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),D),c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,E,C),F))|c_Orderings_Oord__class_Oless(A,D,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,E,B),C),F)).
% 15.24/15.17  ** KEPT (pick-wt=31): 633 [] -class_Rings_Oordered__ring(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,C),D),c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,E,C),F))| -c_Orderings_Oord__class_Oless(A,D,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,E,B),C),F)).
% 15.24/15.17  ** KEPT (pick-wt=24): 634 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Oone__class_Oone(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Otimes__class_Otimes(A,C,B),B).
% 15.24/15.17  ** KEPT (pick-wt=24): 635 [] -class_Rings_Olinordered__idom(A)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),B)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),C)| -c_Orderings_Oord__class_Oless__e_q(A,C,c_Groups_Oone__class_Oone(A))|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Otimes__class_Otimes(A,B,C),B).
% 15.24/15.17  ** KEPT (pick-wt=12): 636 [] -class_Rings_Olinordered__semidom(A)|c_Orderings_Oord__class_Oless(A,c_Groups_Ozero__class_Ozero(A),c_Groups_Oplus__class_Oplus(A,c_Groups_Oone__class_Oone(A),c_Groups_Oone__class_Oone(A))).
% 15.24/15.17  ** KEPT (pick-wt=14): 637 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))=A.
% 15.24/15.17  ** KEPT (pick-wt=13): 638 [] -c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),A)|c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,A,c_Nat_OSuc(B)),A).
% 15.24/15.17  ** KEPT (pick-wt=16): 639 [] -hBOOL(hAPP(A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C)|hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.24/15.17  ** KEPT (pick-wt=17): 640 [] -hBOOL(hAPP(A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)))|B!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,D)|hBOOL(hAPP(A,D)).
% 15.24/15.17  ** KEPT (pick-wt=18): 641 [] hBOOL(hAPP(A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C)| -hBOOL(hAPP(A,$f12(C,B,A))).
% 15.24/15.17  ** KEPT (pick-wt=21): 643 [copy,642,flip.3] hBOOL(hAPP(A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)))| -hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,$f12(C,B,A))=B.
% 15.24/15.17  ** KEPT (pick-wt=19): 644 [] hBOOL(hAPP(A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)))| -hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(A,$f12(C,B,A))).
% 15.24/15.17    Following clause subsumed by 639 during input processing: 0 [] -hBOOL(hAPP(A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)))| -c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C)|hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))).
% 15.24/15.17    Following clause subsumed by 640 during input processing: 0 [] -hBOOL(hAPP(A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)))|B!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,D)|hBOOL(hAPP(A,D)).
% 15.24/15.17  ** KEPT (pick-wt=18): 645 [] hBOOL(hAPP(A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)))|c_Orderings_Oord__class_Oless(tc_Nat_Onat,B,C)| -hBOOL(hAPP(A,$f13(C,B,A))).
% 15.24/15.17  ** KEPT (pick-wt=21): 647 [copy,646,flip.3] hBOOL(hAPP(A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)))| -hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,$f13(C,B,A))=B.
% 15.24/15.17  ** KEPT (pick-wt=19): 648 [] hBOOL(hAPP(A,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,C)))| -hBOOL(hAPP(A,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))| -hBOOL(hAPP(A,$f13(C,B,A))).
% 15.24/15.17  ** KEPT (pick-wt=21): 649 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)),C)=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(B),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,A,C)).
% 15.24/15.17  ** KEPT (pick-wt=21): 650 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,C,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A)))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,C,A),c_Nat_OSuc(B)).
% 15.24/15.17  ** KEPT (pick-wt=33): 651 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,C),D),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),E))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),C),D),E).
% 15.24/15.17  ** KEPT (pick-wt=33): 652 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,C),D),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),E))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),C),D),E).
% 15.24/15.17  ** KEPT (pick-wt=34): 653 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,C),D),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),E))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),C),D),E).
% 15.24/15.17  ** KEPT (pick-wt=31): 654 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,C),D)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),E)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),C),D)=E.
% 15.24/15.17  ** KEPT (pick-wt=31): 655 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,C),D)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),E)|c_Groups_Oplus__class_Oplus(tc_Na
% 15.24/15.17  Search stopped in tp_alloc by max_mem option.
% 15.24/15.17  t_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),C),D)!=E.
% 15.24/15.17  ** KEPT (pick-wt=33): 656 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),D),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,C),E))|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,D,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),C),E)).
% 15.24/15.17  ** KEPT (pick-wt=33): 657 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),D),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,C),E))| -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,D,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),C),E)).
% 15.24/15.17  ** KEPT (pick-wt=34): 658 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),D),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,C),E))=c_Groups_Ominus__class_Ominus(tc_Nat_Onat,D,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),C),E)).
% 15.24/15.17  ** KEPT (pick-wt=31): 659 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),D)!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,C),E)|D=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),C),E).
% 15.24/15.17  ** KEPT (pick-wt=31): 660 [] -c_Orderings_Oord__class_Oless__e_q(tc_Nat_Onat,A,B)|c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,C),D)=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,C),E)|D!=c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,B,A),C),E).
% 15.24/15.17  ** KEPT (pick-wt=40): 661 [] -class_Rings_Olinordered__semiring__1(A)| -c_Orderings_Oord__class_Oless__e_q(A,B,C)| -c_Orderings_Oord__class_Oless__e_q(A,D,C)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),E)| -c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Ozero__class_Ozero(A),F)|c_Groups_Oplus__class_Oplus(A,E,F)!=c_Groups_Oone__class_Oone(A)|c_Orderings_Oord__class_Oless__e_q(A,c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,E,B),c_Groups_Otimes__class_Otimes(A,F,D)),C).
% 15.24/15.17  ** KEPT (pick-wt=23): 663 [copy,662,flip.2] -class_Rings_Oring__1(A)|c_Groups_Otimes__class_Otimes(A,c_Groups_Oplus__class_Oplus(A,B,c_Groups_Oone__class_Oone(A)),c_Groups_Ominus__class_Ominus(A,B,c_Groups_Oone__class_Oone(A)))=c_Groups_Ominus__class_Ominus(A,c_Groups_Otimes__class_Otimes(A,B,B),c_Groups_Oone__class_Oone(A)).
% 15.24/15.17  ** KEPT (pick-wt=29): 665 [copy,664,flip.2] -class_Rings_Oring(A)|c_Groups_Oplus__class_Oplus(A,c_Groups_Otimes__class_Otimes(A,B,c_Groups_Ominus__class_Ominus(A,C,D)),c_Groups_Otimes__class_Otimes(A,c_Groups_Ominus__class_Ominus(A,B,E),D))=c_Groups_Ominus__class_Ominus(A,c_Groups_Otimes__class_Otimes(A,B,C),c_Groups_Otimes__class_Otimes(A,E,D)).
% 15.24/15.17  
% 15.24/15.17  Search stopped in tp_alloc by max_mem option.
% 15.24/15.17  
% 15.24/15.17  ============ end of search ============
% 15.24/15.17  
% 15.24/15.17  -------------- statistics -------------
% 15.24/15.17  clauses given                  0
% 15.24/15.17  clauses generated              0
% 15.24/15.17  clauses kept                 630
% 15.24/15.17  clauses forward subsumed     138
% 15.24/15.17  clauses back subsumed          0
% 15.24/15.17  Kbytes malloced            11718
% 15.24/15.17  
% 15.24/15.17  ----------- times (seconds) -----------
% 15.24/15.17  user CPU time          0.17          (0 hr, 0 min, 0 sec)
% 15.24/15.17  system CPU time        0.01          (0 hr, 0 min, 0 sec)
% 15.24/15.17  wall-clock time       14             (0 hr, 0 min, 14 sec)
% 15.24/15.17  
% 15.24/15.17  Process 29288 finished Wed Jul 27 02:49:00 2022
% 15.24/15.17  Otter interrupted
% 15.24/15.17  PROOF NOT FOUND
%------------------------------------------------------------------------------